{ "generated_at": "2026-04-29", "quality_note": "Generated source-text concordance. Counts are OCR/PDF text aids, not final conceptual claims. Verify exact passages against scans before quotation or interpretation.", "person": "Charles Proteus Steinmetz", "collection": "steinmetz", "source_count": 15, "section_count": 394, "total_concepts": 77, "concepts": [ { "id": "magnetism", "label": "Magnetism", "aliases": [ "flux", "magnetic", "magnetism", "magnetization", "magnetizing", "reluctance" ], "total_occurrences": 6872, "matching_section_count": 250, "matching_source_count": 14, "source_totals": [ { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 1015, "section_count": 16 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 901, "section_count": 72 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 896, "section_count": 20 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 821, "section_count": 25 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 696, "section_count": 22 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 587, "section_count": 26 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 578, "section_count": 20 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 402, "section_count": 9 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 394, "section_count": 9 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 337, "section_count": 8 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 110, "section_count": 11 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 71, "section_count": 6 }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 43, "section_count": 3 }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 21, "section_count": 3 } ], "section_hits": [ { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-18", "section_label": "Chapter 20: Single-Phase Commutator Motors", "section_title": "Single-Phase Commutator Motors", "kind": "chapter", "sequence": 18, "number": 20, "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 244, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "... uency. The direction of rotation of a direct-current motor, whether shunt or series motor, remains the same at a reversal of the im- pressed e.m.f., as in this case the current in the armature circuit and the current in the field circuit and so the field magnetism both reverse. Theoretically, a direct-current motor therefore could be operated on an alternating impressed e.m.f. provided that the magnetic circuit of the motor is laminated, so as to fol- low the alternations of magnetism without serious loss of power, ...", "... .m.f., as in this case the current in the armature circuit and the current in the field circuit and so the field magnetism both reverse. Theoretically, a direct-current motor therefore could be operated on an alternating impressed e.m.f. provided that the magnetic circuit of the motor is laminated, so as to fol- low the alternations of magnetism without serious loss of power, and that precautions are taken to have the field reverse simul- taneously with the armature. If the reversal of field magnetism should occur ...", "... field circuit and so the field magnetism both reverse. Theoretically, a direct-current motor therefore could be operated on an alternating impressed e.m.f. provided that the magnetic circuit of the motor is laminated, so as to fol- low the alternations of magnetism without serious loss of power, and that precautions are taken to have the field reverse simul- taneously with the armature. If the reversal of field magnetism should occur later than the reversal of armature current, during the time after the armature cur ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-08", "section_label": "Chapter 8: Shaping Of Waves By Magnetic Saturation", "section_title": "Shaping Of Waves By Magnetic Saturation", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 12962-16963", "status": "candidate", "occurrence_count": 176, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-08/", "snippets": [ "CHAPTER VIII SHAPING OF WAVES BY MAGNETIC SATURATION 66. The wave shapes of current or volt^e produced by a closed magnetic circuit at moderate magnetic densities, such as are com- monly used in transformers and other induction apparatus, have 10 / ^ ^ 8- in.4 /' / -' ...", "CHAPTER VIII SHAPING OF WAVES BY MAGNETIC SATURATION 66. The wave shapes of current or volt^e produced by a closed magnetic circuit at moderate magnetic densities, such as are com- monly used in transformers and other induction apparatus, have 10 / ^ ^ 8- in.4 /' / -' f / '■ 1 i- 10 / 1 / 1 B- n.» / 1 / / ...", "CHAPTER VIII SHAPING OF WAVES BY MAGNETIC SATURATION 66. The wave shapes of current or volt^e produced by a closed magnetic circuit at moderate magnetic densities, such as are com- monly used in transformers and other induction apparatus, have 10 / ^ ^ 8- in.4 /' / -' f / '■ 1 i- 10 / 1 / 1 B- n.» / 1 / / / / 1 ' / / ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-12", "section_label": "Chapter 12: Reactance Of Induction Apparatus", "section_title": "Reactance Of Induction Apparatus", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 22634-23465", "status": "candidate", "occurrence_count": 172, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-12/", "snippets": [ "CHAPTER XII REACTANCE OF INDUCTION APPARATUS 109. An electric current passing through a conductor is ac- companied by a magnetic field surrounding this conductor, and this magnetic field is as integral a part of the phenomenon, as is the energy dissipation by the resistance of the conductor. It is represented by the inductance, L, of the conductor, or the number of magnetic interli ...", "CHAPTER XII REACTANCE OF INDUCTION APPARATUS 109. An electric current passing through a conductor is ac- companied by a magnetic field surrounding this conductor, and this magnetic field is as integral a part of the phenomenon, as is the energy dissipation by the resistance of the conductor. It is represented by the inductance, L, of the conductor, or the number of magnetic interlinkages with unit current in the conductor. Every cir ...", "... ed by a magnetic field surrounding this conductor, and this magnetic field is as integral a part of the phenomenon, as is the energy dissipation by the resistance of the conductor. It is represented by the inductance, L, of the conductor, or the number of magnetic interlinkages with unit current in the conductor. Every circuit thus has a resistance, and an inductance, however small the latter may be in the so-called \"non-inductive\" circuit. With continuous current in stationary conditions, the inductance, L, has no ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-12", "section_label": "Chapter 12: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 10718-13483", "status": "candidate", "occurrence_count": 162, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-12/", "snippets": [ "... iculties met in dealing analytically with alternating-current circuits containing iron. 90. The foremost sources of energy loss in alternating-current circuits, outside of the true ohmic resistance loss, are as follows : 1. Molecular friction, as, (a) Magnetic hysteresis; (6) Dielectric hysteresis. 2. Primary electric currents, as, (a) Leakage or escape of current through the insulation, brush discharge, corona. (6) Eddy currents in the conductor or unequal current distribution. EFFECTIVE RESISTANCE AN ...", "... ent through the insulation, brush discharge, corona. (6) Eddy currents in the conductor or unequal current distribution. EFFECTIVE RESISTANCE AND REACTANCE 113 -» 3. Secondary or induced currents, as, (a) Eddy or Foucault currents in surrounding magnetic materials; (b) Eddy or Foucault currents in surrounding conducting materials ; (c) Secondary currents of mutual inductance in neighboring circuits. 4. Induced electric charges, electrostatic induction or influence. While all these losses can be ...", "... nding conducting materials ; (c) Secondary currents of mutual inductance in neighboring circuits. 4. Induced electric charges, electrostatic induction or influence. While all these losses can be included in the terms effective resistance, etc., the magnetic hysteresis and the eddy currents are the most frequent and important sources of energy loss. Magnetic Hysteresis 91. In an alternating-current circuit surrounded by iron or other magnetic material, energy is expended outside of the con- ductor in the i ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-34", "section_label": "Chapter 12: Magnetic Saturation And Hysteresis In Alternat Ing-Current Circuits", "section_title": "Magnetic Saturation And Hysteresis In Alternat Ing-Current Circuits", "kind": "chapter", "sequence": 34, "number": 12, "location": "lines 12885-13935", "status": "candidate", "occurrence_count": 134, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-34/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-34/", "snippets": [ "CHAPTER XII. MAGNETIC SATURATION AND HYSTERESIS IN ALTERNAT- ING-CURRENT CIRCUITS. 99. If an alternating e.m.f. is impressed upon a circuit con- taining resistance and inductance, the current and thereby the magnetic flux produced by the current immediately assume their fina ...", "CHAPTER XII. MAGNETIC SATURATION AND HYSTERESIS IN ALTERNAT- ING-CURRENT CIRCUITS. 99. If an alternating e.m.f. is impressed upon a circuit con- taining resistance and inductance, the current and thereby the magnetic flux produced by the current immediately assume their final or permanent values only in case the circuit is closed at that point of the e.m:f. wave at which the permanent current is zero. Closing the circuit at any other point of the e.m.f. wave produces ...", "CHAPTER XII. MAGNETIC SATURATION AND HYSTERESIS IN ALTERNAT- ING-CURRENT CIRCUITS. 99. If an alternating e.m.f. is impressed upon a circuit con- taining resistance and inductance, the current and thereby the magnetic flux produced by the current immediately assume their final or permanent values only in case the circuit is closed at that point of the e.m:f. wave at which the permanent current is zero. Closing the circuit at any other point of the e.m.f. wave produces a tra ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "section_label": "Chapter 10: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 128, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "... lties met in dealing analytically with alternating-current circuits containing iron. 73. The foremost sources of energy loss in alternating- current circuits, outside of the true ohmic resistance loss, are as follows : 1.) Molecular friction, as, a.) Magnetic hysteresis ; b.) Dielectric hysteresis. 106 .ALTERNATING-CURRENT PHENOMENA. 2.) Primary electric currents, as, a.} Leakage or escape of current through the insu- lation, brush discharge ; b.) Eddy currents in the conductor or unequal current distrib ...", "... surrounding conducting materials ; c.} Sec- ondary currents of mutual inductance in neigh- boring circuits. 4.) Induced electric charges, electrostatic influence. While all these losses can be included in the terms effec- tive resistance, etc., only the magnetic hysteresis and the eddy currents in the iron will form the subject of what fol- lows, since they are the most frequent and important sources of energy loss. Magnetic Hysteresis. 74. In an alternating-current circuit surrounded by iron or other magneti ...", "... le all these losses can be included in the terms effec- tive resistance, etc., only the magnetic hysteresis and the eddy currents in the iron will form the subject of what fol- lows, since they are the most frequent and important sources of energy loss. Magnetic Hysteresis. 74. In an alternating-current circuit surrounded by iron or other magnetic material, energy is expended outside of the conductor in the iron, by a kind of molecular friction, which, when the energy is supplied electrically, appears as magnet ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-10", "section_label": "Lecture 10: Light Flux And Distribution", "section_title": "Light Flux And Distribution", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 9389-12573", "status": "candidate", "occurrence_count": 124, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-10/", "snippets": [ "LECTURE X. LIGHT FLUX AND DISTRIBUTION. 86. The light flux of an illuminant is its total radiation power, in physiological measure. It therefore is the useful output of the illuminant, and the efficiency of an illuminant thus is the ratio of the total light flux divided by th ...", "LECTURE X. LIGHT FLUX AND DISTRIBUTION. 86. The light flux of an illuminant is its total radiation power, in physiological measure. It therefore is the useful output of the illuminant, and the efficiency of an illuminant thus is the ratio of the total light flux divided by the power input. In general, the distr ...", "... URE X. LIGHT FLUX AND DISTRIBUTION. 86. The light flux of an illuminant is its total radiation power, in physiological measure. It therefore is the useful output of the illuminant, and the efficiency of an illuminant thus is the ratio of the total light flux divided by the power input. In general, the distribution of the light flux throughout space is not uniform, but the light-flux density is different in different directions from an illuminant. Unit light-flux density is the light-flux density which give ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-03", "section_label": "Chapter 3: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 5445-6941", "status": "candidate", "occurrence_count": 124, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-03/", "snippets": [ "CHAPTER III MAGNETISM Reluctivity 29. Considering magnetism as the phenomena of a \"magnetic circuit,\" the foremost differences between the characteristics of the magnetic circuit and the electric circuit are: (a) The maintenance of an electric circuit requires the ex- pen ...", "CHAPTER III MAGNETISM Reluctivity 29. Considering magnetism as the phenomena of a \"magnetic circuit,\" the foremost differences between the characteristics of the magnetic circuit and the electric circuit are: (a) The maintenance of an electric circuit requires the ex- penditure of energy, while the maintenance of ...", "CHAPTER III MAGNETISM Reluctivity 29. Considering magnetism as the phenomena of a \"magnetic circuit,\" the foremost differences between the characteristics of the magnetic circuit and the electric circuit are: (a) The maintenance of an electric circuit requires the ex- penditure of energy, while the maintenance of a magnetic circuit does not re ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-46", "section_label": "Chapter 6: Alternating Magnetic Flux Distribution", "section_title": "Alternating Magnetic Flux Distribution", "kind": "chapter", "sequence": 46, "number": 6, "location": "lines 23948-24980", "status": "candidate", "occurrence_count": 123, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "snippets": [ "CHAPTER VI. ALTERNATING MAGNETIC FLUX DISTRIBUTION. 48. As carrier of magnetic flux iron is used, as far as possible, since it has the highest permeability or magnetic conductivity. If the magnetic flux is alternating or otherwise changing rapidly, an e.m.f. is generated by the change o ...", "CHAPTER VI. ALTERNATING MAGNETIC FLUX DISTRIBUTION. 48. As carrier of magnetic flux iron is used, as far as possible, since it has the highest permeability or magnetic conductivity. If the magnetic flux is alternating or otherwise changing rapidly, an e.m.f. is generated by the change of mag ...", "CHAPTER VI. ALTERNATING MAGNETIC FLUX DISTRIBUTION. 48. As carrier of magnetic flux iron is used, as far as possible, since it has the highest permeability or magnetic conductivity. If the magnetic flux is alternating or otherwise changing rapidly, an e.m.f. is generated by the change of magnetic flux in the iron, and to avoid energ ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-10", "section_label": "Chapter 10: F", "section_title": "F", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 8269-10499", "status": "candidate", "occurrence_count": 119, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "snippets": [ "... lties met in dealing analytically with alternating-current circuits containing iron. 73. The foremost sources of energy loss in alternating- current circuits, outside of the true ohmic resistance loss, are as follows : 1.) Molecular friction, as, a.) Magnetic hysteresis; b) Dielectric hysteresis. 106 ALTERNATING-CURRENT PHENOMENA. [§ 74 2.) Primary electric currents, as, a.) Leakage or escape of current through the in- sulation, brush discharge ; b.) Eddy currents in the conductor or unequal current dis ...", "... n surrounding con- ducting materials ; r.) Secondary currents of mutual inductance in neighboring circuits. 4.) Induced electric charges, electrostatic influence. While all these losses can be included in the terms effective resistance, etc., only the magnetic hysteresis and the eddy currents in the iron will form the subject of what follows. Magnetic Hysteresis, 74. In an alternating-current circuit surrounded by iron or other magnetic material, energy is expended outside of the conductor in the iron, by a ...", "... ing circuits. 4.) Induced electric charges, electrostatic influence. While all these losses can be included in the terms effective resistance, etc., only the magnetic hysteresis and the eddy currents in the iron will form the subject of what follows. Magnetic Hysteresis, 74. In an alternating-current circuit surrounded by iron or other magnetic material, energy is expended outside of the conductor in the iron, by a kind of molecular friction, which, when the energy is supplied electrically, appears as magnet ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-13", "section_label": "Chapter 13: Reactance Of Synchronous Machines", "section_title": "Reactance Of Synchronous Machines", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 23466-24022", "status": "candidate", "occurrence_count": 119, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-13/", "snippets": [ "... synchronous machine — ^alternating-current generator, synchronous motor or synchronous condenser — consists of an armature containing one or more electric circuits traversed by alternating currents and synchronously revolving relative to a unidirectional magnetic field, excited by direct current. The armature circuit, like every electric circuit, has a resistance, r, in which power is being dissipated by the current, /, and an in- ductance, L, or reactance, a; = 2 irfL^ which represents the mag- netic flux produce ...", "... nal magnetic field, excited by direct current. The armature circuit, like every electric circuit, has a resistance, r, in which power is being dissipated by the current, /, and an in- ductance, L, or reactance, a; = 2 irfL^ which represents the mag- netic flux produced by the current in the armature circuit, and interlinked with this circuit. Thus, if ^^ = voltage induced in the armature circuit by its rotation through the magnetic field — or, as now more usually the case, the rotation of the magnetic field thr ...", "... , and an in- ductance, L, or reactance, a; = 2 irfL^ which represents the mag- netic flux produced by the current in the armature circuit, and interlinked with this circuit. Thus, if ^^ = voltage induced in the armature circuit by its rotation through the magnetic field — or, as now more usually the case, the rotation of the magnetic field through the armature circuit — the terminal voltage of the armature circuit is ^ = ^o-(r+jx)/. In Fig. 110 is shown diagrammatically the path of the field flux, in two differ ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-04", "section_label": "Chapter 4: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 6942-9061", "status": "candidate", "occurrence_count": 112, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-04/", "snippets": [ "CHAPTER IV MAGNETISM Hysteresis 36. Unlike the electric current, which requires power for its maintenance, the maintenance of a magnetic flux does not require energy expenditure (the energy consumed by the magnetizing current in the ohmic resistance of the magnetizing wind ...", "CHAPTER IV MAGNETISM Hysteresis 36. Unlike the electric current, which requires power for its maintenance, the maintenance of a magnetic flux does not require energy expenditure (the energy consumed by the magnetizing current in the ohmic resistance of the magnetizing winding being an electrical and not a magnetic effect), but energy is required to produce a magnetic flux, is then stored a ...", "CHAPTER IV MAGNETISM Hysteresis 36. Unlike the electric current, which requires power for its maintenance, the maintenance of a magnetic flux does not require energy expenditure (the energy consumed by the magnetizing current in the ohmic resistance of the magnetizing winding being an electrical and not a magnetic effect), but energy is required to produce a magnetic flux, is then stored as pot ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-12", "section_label": "Lecture 12: Illumination And Illuminating Engineering", "section_title": "Illumination And Illuminating Engineering", "kind": "lecture", "sequence": 12, "number": 12, "location": "lines 16485-17445", "status": "candidate", "occurrence_count": 109, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-12/", "snippets": [ "... NEERING. 110. Artificial light is used for the purpose of seeing and distinguishing objects clearly and comfortably when the day- light fails. The problem of artificial lighting thus comprises con- sideration of the source of light or the illuminant; the flux of light issuing from it; the distribution of the light flux in space, that is, the light flux density in space and more particularly at the illuminated objects; the illumination, that is, the light flux density reflected from the illuminated objects, and ...", "... eing and distinguishing objects clearly and comfortably when the day- light fails. The problem of artificial lighting thus comprises con- sideration of the source of light or the illuminant; the flux of light issuing from it; the distribution of the light flux in space, that is, the light flux density in space and more particularly at the illuminated objects; the illumination, that is, the light flux density reflected from the illuminated objects, and the effect produced thereby on the human eye. In the latter, ...", "... early and comfortably when the day- light fails. The problem of artificial lighting thus comprises con- sideration of the source of light or the illuminant; the flux of light issuing from it; the distribution of the light flux in space, that is, the light flux density in space and more particularly at the illuminated objects; the illumination, that is, the light flux density reflected from the illuminated objects, and the effect produced thereby on the human eye. In the latter, we have left the field of physics ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-25", "section_label": "Chapter 25: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 29375-32539", "status": "candidate", "occurrence_count": 102, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-25/", "snippets": [ "... ffect will cause distortion of the current wave, while with a sine wave of current passing through the circuit, a dis- torting effect will cause higher harmonics of e.m.f. 233. In a conductor revolving with uniform velocity through a uniform and constant magnetic field, a sine wave of e.m.f. is generated. In a circuit with constant resistance and constant reactance, this sine wave of e.m.f. produces a sine wave of current. Thus distortion of the wave-shape or higher har- monics may be due to lack of uniformity of ...", "... and constant reactance, this sine wave of e.m.f. produces a sine wave of current. Thus distortion of the wave-shape or higher har- monics may be due to lack of uniformity of the velocity of the revolving conductor; lack of uniformity or pulsation of the magnetic field; pulsation of the resistance or pulsation of the reactance. 341 342 ALTERNATING-CURRENT PHENOMENA The first two cases, lack of uniformity of the rotation or of the magnetic field, cause higher harmonics of e.m.f. at open circuit. The last, pul ...", "... ty of the revolving conductor; lack of uniformity or pulsation of the magnetic field; pulsation of the resistance or pulsation of the reactance. 341 342 ALTERNATING-CURRENT PHENOMENA The first two cases, lack of uniformity of the rotation or of the magnetic field, cause higher harmonics of e.m.f. at open circuit. The last, pulsation of resistance and reactance, causes higher har- monics only when there is current in the circuit, that is, underload. Lack of uniformity of the rotation is hardly ever of practic ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 883-1530", "status": "candidate", "occurrence_count": 100, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "snippets": [ "... circuit L. While power flows through the conductors A, power is con- sumed in these conductors by conversion into heat, repre- sented by i?r. This, however, Fig. 7. is not all, but in the space surrounding the conductor cer- tain phenomena occur: magnetic and electrostatic forces appear. Fig. 8. — Electric Field of Conductor. The conductor is surrounded by a magnetic field, or a magnetic flux, which is measured by the number of lines of magnetic force . With a single conductor, the lines of magnetic ...", "... heat, repre- sented by i?r. This, however, Fig. 7. is not all, but in the space surrounding the conductor cer- tain phenomena occur: magnetic and electrostatic forces appear. Fig. 8. — Electric Field of Conductor. The conductor is surrounded by a magnetic field, or a magnetic flux, which is measured by the number of lines of magnetic force . With a single conductor, the lines of magnetic force are concentric circles, as shown in Fig. 8. By the return conductor, the circles 10 THE ELECTRIC FIELD. ...", "... d by i?r. This, however, Fig. 7. is not all, but in the space surrounding the conductor cer- tain phenomena occur: magnetic and electrostatic forces appear. Fig. 8. — Electric Field of Conductor. The conductor is surrounded by a magnetic field, or a magnetic flux, which is measured by the number of lines of magnetic force . With a single conductor, the lines of magnetic force are concentric circles, as shown in Fig. 8. By the return conductor, the circles 10 THE ELECTRIC FIELD. 11 are crowded tog ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1003-1658", "status": "candidate", "occurrence_count": 99, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-02/", "snippets": [ "... ircuit M. While power flows through the conductors A, power is con- sumed in these conductors by JV[ conversion into heat, repre- sented by ^2r. This, however, Fig. 7. is not all, but in the space surrounding the conductor cer- tain phenomena occur: magnetic and electrostatic forces appear. Fig. 8. — Electric Field of Conductor. The conductor is surrounded by a magnetic field, or a magnetic flux, which is measured by the number of lines of magnetic force $. With a single conductor, the lines of magnetic f ...", "... o heat, repre- sented by ^2r. This, however, Fig. 7. is not all, but in the space surrounding the conductor cer- tain phenomena occur: magnetic and electrostatic forces appear. Fig. 8. — Electric Field of Conductor. The conductor is surrounded by a magnetic field, or a magnetic flux, which is measured by the number of lines of magnetic force $. With a single conductor, the lines of magnetic force are concentric circles, as shown in Fig. 8. By the return conductor, the circles 10 THE ELECTRIC FIELD. 11 ...", "... d by ^2r. This, however, Fig. 7. is not all, but in the space surrounding the conductor cer- tain phenomena occur: magnetic and electrostatic forces appear. Fig. 8. — Electric Field of Conductor. The conductor is surrounded by a magnetic field, or a magnetic flux, which is measured by the number of lines of magnetic force $. With a single conductor, the lines of magnetic force are concentric circles, as shown in Fig. 8. By the return conductor, the circles 10 THE ELECTRIC FIELD. 11 are crowded toget ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "section_label": "Chapter 16: Induction Motor", "section_title": "Induction Motor", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 98, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "... d, but not the transfer of electrical energy, and thus the secondary circuits closed upon themselves. Transformer and induction motor thus are the two limiting cases of the general alternating- current transformer. Hence the induction motor consists of a magnetic circuit interlinked with two electric circuits or sets of circuits, the primary and the secondary circuit, which are movable with regard to each other. In general a num- ber of primary and a number of secondary circuits are used, angularly displaced aroun ...", "... ion, as secondary quantities, the values reduced to the primary system shall be exclusively used, so that, to derive the true secondary values, these quantities have to be reduced backwards again by the factor a = ?*£-. «iA 153. Let $ = total maximum flux of the magnetic field per motor pole, We then have E— V2 77-72 TV^ 10 ~8 = effective E.M.F. induced by the mag- netic field per primary circuit. Counting the time from the moment where the rising magnetic flux of mutual induction & (flux interlinked wi ...", "... ndary quantities, the values reduced to the primary system shall be exclusively used, so that, to derive the true secondary values, these quantities have to be reduced backwards again by the factor a = ?*£-. «iA 153. Let $ = total maximum flux of the magnetic field per motor pole, We then have E— V2 77-72 TV^ 10 ~8 = effective E.M.F. induced by the mag- netic field per primary circuit. Counting the time from the moment where the rising magnetic flux of mutual induction & (flux interlinked with both electri ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-01", "section_label": "Theory Section 1: Magnetism and Electric Current", "section_title": "Magnetism and Electric Current", "kind": "theory-section", "sequence": 1, "number": 1, "location": "lines 477-909", "status": "candidate", "occurrence_count": 97, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-01/", "snippets": [ "1. MAGNETISM AND ELECTRIC CURRENT 1. A magnet pole attracting (or repelling) another magnet pole of equal strength at unit distance with unit force1 is called a unit magnet pole. The space surrounding a magnet pole is called a magne ...", "... ETISM AND ELECTRIC CURRENT 1. A magnet pole attracting (or repelling) another magnet pole of equal strength at unit distance with unit force1 is called a unit magnet pole. The space surrounding a magnet pole is called a magnetic field of force, or magnetic field. The magnetic field at unit distance from a unit magnet pole is called a unit magnetic field, and is represented by one line of magnetic force (or shortly \"one line\") per square centime ...", "... . A magnet pole attracting (or repelling) another magnet pole of equal strength at unit distance with unit force1 is called a unit magnet pole. The space surrounding a magnet pole is called a magnetic field of force, or magnetic field. The magnetic field at unit distance from a unit magnet pole is called a unit magnetic field, and is represented by one line of magnetic force (or shortly \"one line\") per square centimeter, and from a unit magnet ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-15", "section_label": "Chapter 17: Inductor Machines", "section_title": "Inductor Machines", "kind": "chapter", "sequence": 15, "number": 17, "location": "lines 20294-20974", "status": "candidate", "occurrence_count": 93, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-15/", "snippets": [ "... , Etc. 156. Synchronous machines may be built with stationary field and revolving armature, as shown diagrammatically in Fig. 134, or with revolving field and stationary armature, Fig. 135, or with stationary field and stationary armature, but revolving magnetic circuit. The revolving-armature type was the most frequent in the early days, but has practically gone out of use except for special Fia. 134. — Revolving armature alternator Fig. 135.— Revolving field al ternator. purposes, and for synchronous ...", "... in this field, its use is rapidly increasing. A typical inductor alternator is shown in Fig. 136. as eight- polar quarter-phase machine. 274 INDUCTOR MACHINES 275 Its armature coils, A, are stationary. One stationary field coil, F, surrounds the magnetic circuit of the machine, which consists of two sections, the stationary external one, B, which contains the armature, A, and a movable one, C, which contains the inductor, N. The inductor contains as many polar projec- tions, N, as there are cycles or pair ...", "... machine, which consists of two sections, the stationary external one, B, which contains the armature, A, and a movable one, C, which contains the inductor, N. The inductor contains as many polar projec- tions, N, as there are cycles or pairs of poles. The magnetic flux in the air gap and inductor does not reverse or alternate, as in the revolving-field type of alternator, Fig. 135, but is constant in direction, that is, all the inductor teeth are of the same polarity, but the flux density varies or pulsates, betwee ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-19", "section_label": "Chapter 21: Regulating Pole Converters", "section_title": "Regulating Pole Converters", "kind": "chapter", "sequence": 19, "number": 21, "location": "lines 30088-31715", "status": "candidate", "occurrence_count": 93, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-19/", "snippets": [ "CHAPTER XXI REGULATING POLE CONVERTERS 230. With a sine wave of alternating voltage, and the com- mutator brushes set at the magnetic neutral, that is, at right angles to the resultant magnetic flux, the direct voltage of a syn- chronous converter is constant at constant impressed alternating voltage. It equals the maximum value of the alternating voltaga between two diametrically oppos ...", "CHAPTER XXI REGULATING POLE CONVERTERS 230. With a sine wave of alternating voltage, and the com- mutator brushes set at the magnetic neutral, that is, at right angles to the resultant magnetic flux, the direct voltage of a syn- chronous converter is constant at constant impressed alternating voltage. It equals the maximum value of the alternating voltaga between two diametrically opposite points of the commutator, or \"diametrical voltage,\" and ...", "CHAPTER XXI REGULATING POLE CONVERTERS 230. With a sine wave of alternating voltage, and the com- mutator brushes set at the magnetic neutral, that is, at right angles to the resultant magnetic flux, the direct voltage of a syn- chronous converter is constant at constant impressed alternating voltage. It equals the maximum value of the alternating voltaga between two diametrically opposite points of the commutator, or \"diametrical voltage,\" and the d ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-05", "section_label": "Chapter 5: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 9062-11050", "status": "candidate", "occurrence_count": 88, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-05/", "snippets": [ "CHAPTER V MAGNETISM Magnetic Constants 47. With the exception of a few ferromagnetic substances, the magnetic permeability of all materials, conductors and dielectrics, gases, liquids and solids, is practically unity for all industrial purposes. Even liquid oxygen, which ...", "CHAPTER V MAGNETISM Magnetic Constants 47. With the exception of a few ferromagnetic substances, the magnetic permeability of all materials, conductors and dielectrics, gases, liquids and solids, is practically unity for all industrial purposes. Even liquid oxygen, which has the hig ...", "CHAPTER V MAGNETISM Magnetic Constants 47. With the exception of a few ferromagnetic substances, the magnetic permeability of all materials, conductors and dielectrics, gases, liquids and solids, is practically unity for all industrial purposes. Even liquid oxygen, which has the highest permea- bility, differs only by a fraction of a per cent, from non-magnetic m ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-109", "section_label": "Apparatus Section 3: Induction Machines: Single -phase Induction Motor", "section_title": "Induction Machines: Single -phase Induction Motor", "kind": "apparatus-section", "sequence": 109, "number": 3, "location": "lines 20428-21157", "status": "candidate", "occurrence_count": 81, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-109/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-109/", "snippets": [ "... reaction machines. A single-phase induction motor will not start from rest, but when started in either direction will accelerate with increasing torque and approach synchronism. When running at or very near synchronism, the magnetic field of the single-phase induction motor is practically identical with that of a polyphase motor, that is, can be represented by the theory of the rotating field. Thus, in a turn wound under angle r to the primary windi ...", "... winding of the single-phase induction motor, at synchronism an e.m.f. is generated equal to that generated in a turn of the primary winding, but differing therefrom by angle 6 = T in time phase. In a polyphase motor the magnetic flux in any direction is due to the resultant m.m.f. of primary and of secondary currents, in the same way as in a transformer. The same is the case in the direction of the axis of the exciting coil of the single-phas ...", "... f the single-phase induction motor, at synchronism an e.m.f. is generated equal to that generated in a turn of the primary winding, but differing therefrom by angle 6 = T in time phase. In a polyphase motor the magnetic flux in any direction is due to the resultant m.m.f. of primary and of secondary currents, in the same way as in a transformer. The same is the case in the direction of the axis of the exciting coil of the single-phase ind ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-22", "section_label": "Chapter 22: Armature Reactions Of Alternators", "section_title": "Armature Reactions Of Alternators", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 23971-25134", "status": "candidate", "occurrence_count": 80, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-22/", "snippets": [ "... is due to the combined effect of armature reaction and armature self-induction. The counter m.m.f. of the armature current, or armature reaction, combines with the impressed m.m.f. or field excitation to the resultant m.m.f., which produces the resultant magnetic field in the field poles and generates in the armature an e.m.f. called the \"virtual generated e.m.f.,\" since it has no actual existence, but is merely a mathematical fiction. The counter e.m.f. of self-induction of the armature current, that is, e.m.f. g ...", "... he armature an e.m.f. called the \"virtual generated e.m.f.,\" since it has no actual existence, but is merely a mathematical fiction. The counter e.m.f. of self-induction of the armature current, that is, e.m.f. generated by the armature current by a local magnetic flux, combines with the virtual generated e.m.f. to the actual generated e.m.f. of the armature, which corresponds to the magnetic flux in the armature core. This combined with the e.m.f. consumed by the armature resist- ance gives the terminal voltage. ...", "... re an e.m.f. called the \"virtual generated e.m.f.,\" since it has no actual existence, but is merely a mathematical fiction. The counter e.m.f. of self-induction of the armature current, that is, e.m.f. generated by the armature current by a local magnetic flux, combines with the virtual generated e.m.f. to the actual generated e.m.f. of the armature, which corresponds to the magnetic flux in the armature core. This combined with the e.m.f. consumed by the armature resist- ance gives the terminal voltage. In m ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "section_label": "Lecture 10: Continual And Cumulative Oscillations", "section_title": "Continual And Cumulative Oscillations", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 78, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... is the phenomenon by which the stored energy readjusts itself to a change of circuit conditions. In an oscilla- tory transient, the difference of stored energy of the previous and the after condition of the circuit, at a circuit change, oscillates between magnetic and dielectric energy. As there always must be some energy dissipation in the circuit, the oscillating energy of the transient must steadily decline, that is, the transient must die out, at a rate depending on the energy dissipation in the cir- cuit. Th ...", "... erters. The mechanism, by which the hysteresis cycle supplies the energy of continual oscillations, has been investigated in the case of the hunting of synchronous machines,* but is still practically un- known in the case of continual oscillations between magnetic and dielectric energy in electric circuits. Recurrent oscillations, as in Fig. 59, must be or very soon be- come continual, that is, the successive wave trains are of approx- imately constant amplitude, since each starts with the same energy, the stored ...", "... nt thereto. 2. A continual oscillation involves an energy transformation from the power supply of the system to the oscillation frequency. The energy of the oscillation which gives its destructiveness thus is not limited to the small amount of the stored magnetic and dielectric energy of the system, but is supplied continuously from the engine or turbine power. 3. The continual oscillation is not a resonance phenomenon which depends on the frequency of the exciting disturbance just coinciding with one of the nat ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-06", "section_label": "Chapter 6: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 11051-12221", "status": "candidate", "occurrence_count": 78, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-06/", "snippets": [ "CHAPTER VI MAGNETISM MECHANICAL FORCES 1. General 61. Mechanical forces appear wherever magnetic fields act on electric currents. The work done by all electric motors is the result of these forces. In electric generators, they oppose the driving power and thereby consume ...", "CHAPTER VI MAGNETISM MECHANICAL FORCES 1. General 61. Mechanical forces appear wherever magnetic fields act on electric currents. The work done by all electric motors is the result of these forces. In electric generators, they oppose the driving power and thereby consume the power which finds its equivalent in the electric power output. The motions p ...", "... of the transformer, between conductor and return conductor of an electric circuit, etc., such mechanical forces appear. The electromagnet, and all electrodynamic machinery, are based on the use of these mechanical forces between electric conductors and magnetic fields. So also is that type of trans- former which transforms constant alternating voltage into con- stant alternating current. In most other cases, however, these mechanical forces are not used, and therefore are often neglected in the design of the app ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 75, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "CHAPTER XI. FOUCAULT OR EDDY CURRENTS. 86. While magnetic hysteresis or molecular friction is a magnetic phenomenon, eddy currents are rather an elec- trical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the ...", "CHAPTER XI. FOUCAULT OR EDDY CURRENTS. 86. While magnetic hysteresis or molecular friction is a magnetic phenomenon, eddy currents are rather an elec- trical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric conductor, the ...", "CHAPTER XI. FOUCAULT OR EDDY CURRENTS. 86. While magnetic hysteresis or molecular friction is a magnetic phenomenon, eddy currents are rather an elec- trical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric conductor, the magnetic field induces a current therein. The M.M.F. of this current reacts upon and affects the mag ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-10", "section_label": "Lecture 10: Inductance And Capacity Of Round Parallel Conductors", "section_title": "Inductance And Capacity Of Round Parallel Conductors", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6089-7274", "status": "candidate", "occurrence_count": 74, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "snippets": [ "... two circuit constants which represent the energy storage, and which therefore are of fundamental importance in the study of transients, their calcula- tion is discussed in the following. The inductance is the ratio of the interlinkages of the mag- netic flux to the current, £ = ?- (i) i/ where = magnetic flux or number of lines of magnetic force, and n the number of times which each line of magnetic force interlinks with the current i. The capacity is the ratio of the dielectric flux to the voltage, ...", "... rage, and which therefore are of fundamental importance in the study of transients, their calcula- tion is discussed in the following. The inductance is the ratio of the interlinkages of the mag- netic flux to the current, £ = ?- (i) i/ where = magnetic flux or number of lines of magnetic force, and n the number of times which each line of magnetic force interlinks with the current i. The capacity is the ratio of the dielectric flux to the voltage, where \\f/ is the dielectric flux, or number of lines ...", "... which therefore are of fundamental importance in the study of transients, their calcula- tion is discussed in the following. The inductance is the ratio of the interlinkages of the mag- netic flux to the current, £ = ?- (i) i/ where = magnetic flux or number of lines of magnetic force, and n the number of times which each line of magnetic force interlinks with the current i. The capacity is the ratio of the dielectric flux to the voltage, where \\f/ is the dielectric flux, or number of lines of di ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 74, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "CHAPTER XI. FOUOAULT OR EDDY 0UBBENT8. • 86. While magnetic hysteresis or molecular friction is a magnetic phenomenon, eddy currents are rather an elec- trical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the ...", "CHAPTER XI. FOUOAULT OR EDDY 0UBBENT8. • 86. While magnetic hysteresis or molecular friction is a magnetic phenomenon, eddy currents are rather an elec- trical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric conductor, the ...", "CHAPTER XI. FOUOAULT OR EDDY 0UBBENT8. • 86. While magnetic hysteresis or molecular friction is a magnetic phenomenon, eddy currents are rather an elec- trical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric conductor, the magnetic field induces a current therein. The M.M.F. of this current reacts upon and affects the mag ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-17", "section_label": "Chapter 17: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16521-17716", "status": "candidate", "occurrence_count": 72, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-17/", "snippets": [ "CHAPTER XVII THE ALTERNATING-CURRENT TRANSFORMER 141. The simplest alternating-current apparatus is the trans- former. It consists of a magnetic circuit interlinked with two electric circuits, a primary and a secondary. The primary circuit is excited by an impressed e.m.f., while in the secondary circuit an e.m.f. is generated. Thus, in the primary circuit power is consumed, and in the secondary a ...", "... d a secondary. The primary circuit is excited by an impressed e.m.f., while in the secondary circuit an e.m.f. is generated. Thus, in the primary circuit power is consumed, and in the secondary a corresponding amount of power is produced. Since the same magnetic circuit is interlinked with both electric circuits, the e.m.f. generated per turn must be the same in the secondary as in the primary circuit; hence, the primary generated e.m.f. being approximately equal to the impressed e.m.f., the e.m.fs. at primary an ...", "... approximately the ratio of their respective turns. Since the power produced in the secondary is approximately the same as that consumed in the primary, the primary and secondary currents are approximately in inverse ratio to the turns. 142. Besides the magnetic flux interlinked with both electric circuits — which flux, in a closed magnetic circuit transformer, has a circuit of low reluctance — a magnetic cross-flux passes between the primary and secondarj^ coils, surrounding one coil only, without being interlin ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 69, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... ell as conductance have a negative term added, which depends on the decrement a. Such a negative resistance repre- sents energy production, and its meaning in the present case is, that with the decrease of the oscillating current and voltage, their stored magnetic and dielectric energy become available. Circuits of Zero Impedance 190. In an oscillating-current circuit of decrement, a, of resistance, r, inductive reactance, x, and condensive reactance, Xc, the impedance was represented in symbolic expression by ...", "... e have _ r _ r 14 L hence, by substitution, / = — je -J J- dec a, ^, = — jer yjj- dec a, a = the final equations of the oscillating discharge, in symbolic ex- pression. 23 INDEX Admittance, with oscillating cur- rents, 348 Air gap in magnetic circuit reducing wave distortion, 145 Alloys, resistance, 2 Alternating component of power of general system, 317 current electromagnet, 95 magnetic characteristic, 51 Alternations by capacity inductance shunt to arc, 187 Aluminum cell as condenser ...", "... in symbolic ex- pression. 23 INDEX Admittance, with oscillating cur- rents, 348 Air gap in magnetic circuit reducing wave distortion, 145 Alloys, resistance, 2 Alternating component of power of general system, 317 current electromagnet, 95 magnetic characteristic, 51 Alternations by capacity inductance shunt to arc, 187 Aluminum cell as condenser, 10 Amorphous carbon resistance, 23 Annealing, magnetic effect, 78 Anode, 6 Anthracite, resistance, 23 Apparatus economy of constant po- tential, co ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1659-2484", "status": "candidate", "occurrence_count": 68, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-03/", "snippets": [ "... 0 volts, and 2200 volts. In them the capac- ity is small, due to the limited extent of the circuit, resulting from the low voltage, and at the low voltage the dielectric energy thus is negligible, that is, the circuit stores appreciable energy only by the magnetic field. A circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectric field. The usual high-voltage capacity circuit, as that of an electrostatic machine, while of ...", "... voltage capacity circuit, as that of an electrostatic machine, while of very small inductance, also is of very small resistance, and the momentary discharge currents may be very consider- able, so that in spite of the very small inductance, considerable magnetic-energy storage may oc- cur; that is, the system is one storing energy in two forms, and oscillations appear, as in the dis- charge of the Leyden jar. Let, as represented in Fig. 10, a continuous voltage eo be im- pressed upon a wire coil of resistance ...", "... ge of the Leyden jar. Let, as represented in Fig. 10, a continuous voltage eo be im- pressed upon a wire coil of resistance r and inductance L (but A current Iq = — flows through the coil and % t 1 % io A C c c ..1. 1 Fig. 10. — Magnetic Single-energy Transient. negligible capacity), a magnetic field $0 10' Lio interlinks with the coil. Assuming now that the voltage eo is suddenly withdrawn, without changing 19 20 ELECTRIC DISCHARGES, WAVES AND IMPULSES. the constants ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-13", "section_label": "Chapter 13: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 13484-14333", "status": "candidate", "occurrence_count": 68, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-13/", "snippets": [ "CHAPTER XIII FOUCAULT OR EDDY CURRENTS 105. While magnetic hysteresis due to molecular friction is a magnetic phenomenon, eddy currents are rather an electrical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon th ...", "CHAPTER XIII FOUCAULT OR EDDY CURRENTS 105. While magnetic hysteresis due to molecular friction is a magnetic phenomenon, eddy currents are rather an electrical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric conductor, the ma ...", "CHAPTER XIII FOUCAULT OR EDDY CURRENTS 105. While magnetic hysteresis due to molecular friction is a magnetic phenomenon, eddy currents are rather an electrical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric conductor, the magnetic field produces a current therein. The m.m.f. of this current reacts upon and affects the mag ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1531-2161", "status": "candidate", "occurrence_count": 67, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "snippets": [ "... 0 volts, and 2200 volts. In them the capac- ity is small, due to the limited extent of the circuit, resulting from the low voltage, and at the low voltage the dielectric energy thus is negligible, that is, the circuit stores appreciable energy only by the magnetic field. A circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectric field. The usual high-voltage capacity circuit, as that of an electrostatic machine, while of ...", "... ge capacity circuit, as that of an electrostatic machine, while of very small inductance, also is of very small resistance, and the momentary discharge currents may be very consider- able, so that in spite of the very small inductance, considerable __ magnetic-energy storage may oc- cur; that is, the system is one eo storing energy in two forms, and ^ oscillations appear, as in the dis- ' ~ charge of the Leyden jar. Fig 10._Magnetie Single.energy Let, as represented in Fig. 10, Transient, a continuous vol ...", "... eyden jar. Fig 10._Magnetie Single.energy Let, as represented in Fig. 10, Transient, a continuous voltage e0 be im- pressed upon a wire coil of resistance r and inductance L (but negligible capacity). A current iQ = — flows through the coil and a magnetic field $0 10~8 = - - interlinks with the coil. Assuming now that the voltage e0 is suddenly withdrawn, without changing 19 20 ELECTRIC DISCHARGES, WAVES AND IMPULSES. the constants of the coil circuit, as for instance by short- circuiting the termina ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-14", "section_label": "Chapter 16: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 14, "number": 16, "location": "lines 19374-20293", "status": "candidate", "occurrence_count": 64, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-14/", "snippets": [ "... ine is a constant. While this is more or less approximately the case in many alternators, in others, especially in machines of large armature reaction, the reactance, x, is variable, and is different in the different positions of the armature coils in the magnetic circuit. This variation of the reactance causes phenomena which do not find their explanation by the theoretical calculations made under the assumption of constant reactance. It is known that synchronous motors or converters of large and variable reacta ...", "... ear if the generator field circuit is broken, or even reversed to a small negative value, in which tatter case the current is against the e.m.f., Ea, of the generator. Furthermore, a shuttle armature without any winding (Fig. 120) will in an alternating magnetic field revolve when once brought up to synchronism, and do considerable work as a motor. These phenomena are not due to remanent magnetism nor to the magnetizing effect of eddy currents, because they exist also in machines with laminated fields, and exist ...", "... e.m.f., Ea, of the generator. Furthermore, a shuttle armature without any winding (Fig. 120) will in an alternating magnetic field revolve when once brought up to synchronism, and do considerable work as a motor. These phenomena are not due to remanent magnetism nor to the magnetizing effect of eddy currents, because they exist also in machines with laminated fields, and exist if the alternator is brought up to synchronism by external means and the rema- nent magnetism of the field poles destroyed beforehand by ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-25", "section_label": "Chapter 3: Inductance And Resistance In Continuous Current Circuits", "section_title": "Inductance And Resistance In Continuous Current Circuits", "kind": "chapter", "sequence": 25, "number": 3, "location": "lines 2659-3514", "status": "candidate", "occurrence_count": 63, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-25/", "snippets": [ "... in direct-current circuits to reduce the inductance than in alternating-current circuits, where the inductance usually causes a drop of voltage, and direct-current circuits as a rule have higher inductance, especially if the circuit is used for producing magnetic flux, as in solenoids, electro- magnets, machine-fields. Any change of the condition of a continuous-current circuit, as a change of e.m.f., of resistance, etc., which leads to a change of current from one value i0 to another value iv results in the app ...", "... t-current circuits to reduce the inductance than in alternating-current circuits, where the inductance usually causes a drop of voltage, and direct-current circuits as a rule have higher inductance, especially if the circuit is used for producing magnetic flux, as in solenoids, electro- magnets, machine-fields. Any change of the condition of a continuous-current circuit, as a change of e.m.f., of resistance, etc., which leads to a change of current from one value i0 to another value iv results in the appearan ...", "... ablished in the circuit in a practically inappre- ciable time, a fraction of a hundredth of a second. 22. Excitation of a motor field. Let, in a continuous-current shunt motor, e0 = 250 volts = impressed e.m.f., and the number of poles = 8. Assume the magnetic flux per pole, 0 = 12.5 megalines, and the ampere-turns per pole required to produce this magnetic flux as $ = 9000. Assume 1000 watts used for the excitation of the motor field gives an exciting current 1000 h =- = 4 amperes, and herefrom the r ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2485-3386", "status": "candidate", "occurrence_count": 62, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-04/", "snippets": [ "... ses in the manner as discussed in para- graph 13, that is, with a duration T = — - The permanent current 12 may be continuous, or alternating, or may be a changing current, as a transient of long duration, etc. The same reasoning applies to the voltage, magnetic flux, etc. Thus, let, in an alternating-current circuit traversed by current i'l, in Fig. 15 A, the conditions be changed, at the moment t = 0, so as to produce the current iV The instantaneous value of the current ii at the moment t = 0 can be considere ...", "... e manner as discussed in para- graph 13, that is, with a duration T = — - The permanent current 12 may be continuous, or alternating, or may be a changing current, as a transient of long duration, etc. The same reasoning applies to the voltage, magnetic flux, etc. Thus, let, in an alternating-current circuit traversed by current i'l, in Fig. 15 A, the conditions be changed, at the moment t = 0, so as to produce the current iV The instantaneous value of the current ii at the moment t = 0 can be considered as ...", "... e resultant currents (shown in drawn line) must be zero at any moment, not only during the permanent condition, but also dur- ing the transition period existing before the permanent condi- tion is reached. It is interesting to apply this to the resultant magnetic field produced by three equal three-phase magnetizing coils placed under equal angles, that is, to the starting of the three-phase rotating magnetic field, or in general any polyphase rotating magnetic field. Fig. 18. — Construction of Starting Transie ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-04", "section_label": "Chapter 5: Single-Phase Induction Motor", "section_title": "Single-Phase Induction Motor", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 8555-10582", "status": "candidate", "occurrence_count": 61, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-04/", "snippets": [ "... ulation of Alternating-current Phenomena,\" the single-phase induction motor has inherently, no torque at standstill, that is, when used without special device to produce such torque by converting the motor into an unsym- metrical ployphase motor, etc. The magnetic flux at standstill is a single-phase alternating flux of constant direction, and the line of polarization of the armature or secondary currents, that is, the resultant m.m.f. of the armature currents, coincides with the axis of magnetic flux impressed by ...", "... f Alternating-current Phenomena,\" the single-phase induction motor has inherently, no torque at standstill, that is, when used without special device to produce such torque by converting the motor into an unsym- metrical ployphase motor, etc. The magnetic flux at standstill is a single-phase alternating flux of constant direction, and the line of polarization of the armature or secondary currents, that is, the resultant m.m.f. of the armature currents, coincides with the axis of magnetic flux impressed by the p ...", "... e induction motor has inherently, no torque at standstill, that is, when used without special device to produce such torque by converting the motor into an unsym- metrical ployphase motor, etc. The magnetic flux at standstill is a single-phase alternating flux of constant direction, and the line of polarization of the armature or secondary currents, that is, the resultant m.m.f. of the armature currents, coincides with the axis of magnetic flux impressed by the primary circuit. When revolving, however, even at ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-19", "section_label": "Theory Section 19: Fields of Force", "section_title": "Fields of Force", "kind": "theory-section", "sequence": 19, "number": 19, "location": "lines 7737-7990", "status": "candidate", "occurrence_count": 60, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-19/", "snippets": [ "... a solid mass of metal rapidly through it, the motion is resisted, and heat produced in the metal by induced currents. Materials of high permeability, as iron filings, brought into this space arrange themselves in chains; a magnetic needle is moved and places itself in a definite direction. Due to the passage of the current in the conductor, there are therefore in the spaces outside of the con- ductor — where the current does not flow — forces exer ...", "... not neutral space, but has become a field of force, and the cause of the field, in this case the electric current in the conductor, is its \"motive force.\" As in this case the actions exerted in the field of force are magnetic, the space surrounding a conductor traversed by a current is a field of magnetic force, and the current in the conductor is the magneto- motive force. In the space surrounding a ponderable mass, as our earth, forces are ...", "... in this case the electric current in the conductor, is its \"motive force.\" As in this case the actions exerted in the field of force are magnetic, the space surrounding a conductor traversed by a current is a field of magnetic force, and the current in the conductor is the magneto- motive force. In the space surrounding a ponderable mass, as our earth, forces are exerted on other masses — which cause the stone to fall toward the earth, and wate ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2162-2971", "status": "candidate", "occurrence_count": 59, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "snippets": [ "... ses in the manner as discussed in para- graph 13, that is, with a duration T = — - The permanent current i2 may be continuous, or alternating, or may be a changing current, as a transient of long duration, etc. The same reasoning applies to the voltage, magnetic flux, etc. Thus, let, in an alternating-current circuit traversed by current t'i, in Fig. 15 A, the conditions be changed, at the moment t = 0, so as to produce the current i2. The instantaneous value of the current ii at the moment t = 0 can be consider ...", "... e manner as discussed in para- graph 13, that is, with a duration T = — - The permanent current i2 may be continuous, or alternating, or may be a changing current, as a transient of long duration, etc. The same reasoning applies to the voltage, magnetic flux, etc. Thus, let, in an alternating-current circuit traversed by current t'i, in Fig. 15 A, the conditions be changed, at the moment t = 0, so as to produce the current i2. The instantaneous value of the current ii at the moment t = 0 can be considered as ...", "... e resultant currents (shown in drawn line) must be zero at any moment, not only during the permanent condition, but also dur- ing the transition period existing before the permanent condi- tion is reached. It is interesting to apply this to the resultant magnetic field produced by three equal three-phase magnetizing coils placed under equal angles, that is, to the starting of the three-phase rotating magnetic field, or in general any polyphase rotating magnetic field. Fig. 18. — Construction of Starting Transie ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-14", "section_label": "Chapter 14: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 11605-12682", "status": "candidate", "occurrence_count": 57, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "snippets": [ "CHAPTER XIV. THE ALTERNATING-CURRENT TRANSFORMER. 126. The simplest alternating-current apparatus is the transformer. It consists of a magnetic circuit interlinked with two electric circuits, a primary and a secondary. The primary circuit is excited by an impressed E.M.F., while in the secondary circuit an E.M.F. is induced. Thus, in the primary circuit power is consumed, and in the secondary a ...", "... and a secondary. The primary circuit is excited by an impressed E.M.F., while in the secondary circuit an E.M.F. is induced. Thus, in the primary circuit power is consumed, and in the secondary a corresponding amount of power is produced. Since the same magnetic circuit is interlinked with both electric circuits, the E.M.F. induced per turn must be the same in the secondary as in the primary circuit ; hence, the primary induced E.M.F. being approximately equal to the impressed E.M.F., the E.M.Fs. at primary and a ...", "... roximately the ratio of their respective turns. Since the power produced in the second- ary is approximately the same as that consumed in the primary, the primary and secondary currents are approxi- mately in inverse ratio to the turns. 127. Besides the magnetic flux interlinked with both electric circuits — which flux, in a closed magnetic circuit transformer, has a circuit of low reluctance — a magnetic cross-flux passes between the primary and secondary coils, surrounding one coil only, without being interlink ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-13", "section_label": "Chapter 13: Ths Alternating^Cnrrent Traxsfobmer", "section_title": "Ths Alternating^Cnrrent Traxsfobmer", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 12673-14088", "status": "candidate", "occurrence_count": 56, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "snippets": [ "CHAPTER XIII. THS ALTERNATING^CnRRENT TRAXSFOBMER. 116. The simplest alternating-current apparatus is the transformer. It consists of a magnetic circuit interlinked with two electric circuits, a primary and a secondary. The primary circuit is excited by an impressed E.M.F., while in the secondary circuit an E.M.F. is induced. Thus, in the primary circuit power is consumed, and in the secondary a ...", "... and a secondary. The primary circuit is excited by an impressed E.M.F., while in the secondary circuit an E.M.F. is induced. Thus, in the primary circuit power is consumed, and in the secondary a corresponding amount of power is produced. Since the same magnetic circuit is interlinked with both electric circuits, the E.M.F. induced per turn must be the same in the secondary as in the primary circuit ; hence, the primary induced E.M.F. being approximately equal to the impressed E.M.F., the E.M.Fs. at primary and a ...", "... roximately the ratio of their respective turns. Since the power produced in the second- ary is approximately the same as that consumed in the primary, the primary and secondary currents are approxi- mately in inverse ratio to the turns. 117. Besides the magnetic flux interlinked with both electric circuits — which flux, in a closed magnetic circuit transformer, has a circuit of low reluctance — a magnetic cross-flux passes between the primary and secondary coils, surrounding one coil only, without being interlink ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-22", "section_label": "Chapter 22: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 21190-21982", "status": "candidate", "occurrence_count": 55, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "snippets": [ "... effect will cause distortion of the current wave, while with a sine wave of current passing through the circuit, a distorting effect will cause higher harmonics of E.M.F. 234. In a conductor revolving with uniform velocity through a uniform and constant magnetic field, a sine wave of E.M.F. is induced. In a circuit with constant resistance and constant reactance, this sine wave of E.M.F. produces 384 ALTERNATING-CURRENT PHENOMENA. a sine wave of current. Thus distortion of the wave-shape or higher harmonics m ...", "... of E.M.F. produces 384 ALTERNATING-CURRENT PHENOMENA. a sine wave of current. Thus distortion of the wave-shape or higher harmonics may be due to : lack of uniformity of the velocity of the revolving conductor ; lack of uniformity or pulsation of the magnetic field ; pulsation of the resis- tance ; or pulsation of the reactance. The first two cases, lack of uniformity of the rotation or of the magnetic field, cause higher harmonics of E.M.F. at open circuit. The last, pulsation of resistance and reac- tance, ...", "... to : lack of uniformity of the velocity of the revolving conductor ; lack of uniformity or pulsation of the magnetic field ; pulsation of the resis- tance ; or pulsation of the reactance. The first two cases, lack of uniformity of the rotation or of the magnetic field, cause higher harmonics of E.M.F. at open circuit. The last, pulsation of resistance and reac- tance, causes higher harmonics only with a current flowing in the circuit, that is, under load. Lack of uniformity of the rotation is of no practical in- ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-32", "section_label": "Chapter 10: Mutual Inductance", "section_title": "Mutual Inductance", "kind": "chapter", "sequence": 32, "number": 10, "location": "lines 10475-12216", "status": "candidate", "occurrence_count": 55, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "snippets": [ "... nd capacity, but no mutual inductance; that is, the phenomena which take place in the circuit have been assumed as depending upon the impressed e.m.f. and the constants of the circuit, but not upon the phenomena taking place in any other circuit. Of the magnetic flux produced by the current in a circuit and interlinked with this circuit, a part may be interlinked with a second circuit also, and so by its change generate an e.m.f. in the second circuit, and part of the magnetic flux produced by Fig. 38. Mutual i ...", "... ty, but no mutual inductance; that is, the phenomena which take place in the circuit have been assumed as depending upon the impressed e.m.f. and the constants of the circuit, but not upon the phenomena taking place in any other circuit. Of the magnetic flux produced by the current in a circuit and interlinked with this circuit, a part may be interlinked with a second circuit also, and so by its change generate an e.m.f. in the second circuit, and part of the magnetic flux produced by Fig. 38. Mutual induct ...", "... place in any other circuit. Of the magnetic flux produced by the current in a circuit and interlinked with this circuit, a part may be interlinked with a second circuit also, and so by its change generate an e.m.f. in the second circuit, and part of the magnetic flux produced by Fig. 38. Mutual inductance between circuits. the current in a second circuit and interlinked with the second circuit may be interlinked also with the first circuit, and a change of current in the second circuit, that is, a change of m ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-20", "section_label": "Chapter 20: Single-Phase Induction Motors", "section_title": "Single-Phase Induction Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 21538-22301", "status": "candidate", "occurrence_count": 52, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-20/", "snippets": [ "CHAPTER XX SINGLE-PHASE INDUCTION MOTORS 177. The magnetic circuit of the induction motor at or near synchronism consists of two magnetic fluxes superimposed upon each other in quadrature, in time, and in position. In the polyphase motor these fluxes are produced by e.m.fs. displaced in phase. In the monocyclic m ...", "CHAPTER XX SINGLE-PHASE INDUCTION MOTORS 177. The magnetic circuit of the induction motor at or near synchronism consists of two magnetic fluxes superimposed upon each other in quadrature, in time, and in position. In the polyphase motor these fluxes are produced by e.m.fs. displaced in phase. In the monocyclic motor one of the fluxes is due to the primary power circuit, the other to the pr ...", "... e, and in position. In the polyphase motor these fluxes are produced by e.m.fs. displaced in phase. In the monocyclic motor one of the fluxes is due to the primary power circuit, the other to the primary exciting circuit. In the single-phase motor the one flux is produced by the primary circuit, the other by the currents produced in the secondary or armature, which are carried into quadrature posi- tion by the rotation of the armature. In consequence thereof, while in all these motors the magnetic distribution ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-23", "section_label": "Chapter 1: The Constants Of The Electric Circuit", "section_title": "The Constants Of The Electric Circuit", "kind": "chapter", "sequence": 23, "number": 1, "location": "lines 1317-1992", "status": "candidate", "occurrence_count": 48, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "snippets": [ "... nergy.) In the space outside of the conductor, during the flow of energy through the circuit, a condition of stress exists which is called the electric field of the conductor. That is, the surrounding space is not uniform, but has different electric and magnetic properties in different directions. No power is required to maintain the electric field, but energy 3 4 TRANSIENT PHENOMENA is required to produce the electric field, and this energy is returned, more or less completely, when the electric field dis- ...", "... electric energy pulsates, as in an alternating- current circuit, continuously electric energy is stored in the field during a rise of the power, and returned to the circuit again during a decrease of the power. The electric field of the conductor exerts magnetic and elec- trostatic actions. The magnetic action is a maximum in the direction concen- tric, or approximately so, to the conductor. That is, a needle- shaped magnetizable body, as an iron needle, tends to set itself in a direction concentric to the cond ...", "... ng- current circuit, continuously electric energy is stored in the field during a rise of the power, and returned to the circuit again during a decrease of the power. The electric field of the conductor exerts magnetic and elec- trostatic actions. The magnetic action is a maximum in the direction concen- tric, or approximately so, to the conductor. That is, a needle- shaped magnetizable body, as an iron needle, tends to set itself in a direction concentric to the conductor. The electrostatic action has a maxim ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-05", "section_label": "Lecture 5: Single-Energy Tra.Nsient Of Ironclad Circuit", "section_title": "Single-Energy Tra.Nsient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3387-3720", "status": "candidate", "occurrence_count": 45, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-05/", "snippets": [ "LECTURE V. SINGLE-ENERGY TRA.NSIENT OF IRONCLAD CIRCUIT. 22. Usually in electric circuits; current, voltage, the magnetic field and the dielectric field are proportional to each other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic fiel ...", "... the magnetic field and the dielectric field are proportional to each other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnetic materials, or if the dielectric field reaches densities beyond the dielectric strength of the carrier of the field, etc.; and the proportionality between current or voltage and their respective fields, the magnetic an ...", "... field are proportional to each other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnetic materials, or if the dielectric field reaches densities beyond the dielectric strength of the carrier of the field, etc.; and the proportionality between current or voltage and their respective fields, the magnetic and the dielectric, thus ceases, or, as i ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-05", "section_label": "Lecture 5: Single-Energy Transient Of Ironclad Circuit", "section_title": "Single-Energy Transient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2972-3286", "status": "candidate", "occurrence_count": 45, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "snippets": [ "LECTURE V. SINGLE-ENERGY TRANSIENT OF IRONCLAD CIRCUIT. 22. Usually in electric circuits, current, voltage, the magnetic field and the dielectric field are proportional to each other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic fiel ...", "... the magnetic field and the dielectric field are proportional to each other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnetic materials, or if the dielectric field reaches densities beyond the dielectric strength of the carrier of the field, etc. ; and the proportionality between current or voltage and their respective fields, the magnetic a ...", "... field are proportional to each other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnetic materials, or if the dielectric field reaches densities beyond the dielectric strength of the carrier of the field, etc. ; and the proportionality between current or voltage and their respective fields, the magnetic and the dielectric, thus ceases, or, as ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-14", "section_label": "Lecture 14: Alternating Current Railway Motor", "section_title": "Alternating Current Railway Motor", "kind": "lecture", "sequence": 14, "number": 14, "location": "lines 8649-9342", "status": "candidate", "occurrence_count": 44, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-14/", "snippets": [ "... f. be reversed, as field and arma- ture both reverse. Since a reversal of voltage does not change the operation of the motor, such a direct current motor there- fore can operate also on alternating current. With an alter- nating voltage supply, the field magnetism of the motor also alternates ; the motor field must therefore be laminated, to avoid excessive energy losses and heating by eddy currents (cur- rents produced in the field iron by the alternation of the mag- netism) just as in the direct current motor the ...", "... irect current motor the armature must be laminated. In the shunt motor — in which the supply current divides between field and armature — when built for alternating voltage, arrangements must be made to have the current in the field (or rather the field magnetism) and the current in the armature, reverse simultaneously. In the series motor, in which the same current traverses field and armature, the field magnetism and the armature current are necessarily in phase with each other, or nearly so. Only the series or ...", "... alternating voltage, arrangements must be made to have the current in the field (or rather the field magnetism) and the current in the armature, reverse simultaneously. In the series motor, in which the same current traverses field and armature, the field magnetism and the armature current are necessarily in phase with each other, or nearly so. Only the series or varying speed type of alternating current commutator motor has so far become of industrial importance. In the alternating current motor in addition to th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-20", "section_label": "Chapter 20: Commutator Motors", "section_title": "Commutator Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 19458-20501", "status": "candidate", "occurrence_count": 44, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "snippets": [ "... former motor ; that is, a motor in which the main current enters the primary member or field only, while in the secondary member, or armature, a current is in- duced, arid thus the action is due to the repulsive thrust between induced current and inducing magnetism. As stated under the heading of induction motors, a multiple circuit armature is required for the purpose of having always secondary circuits in inductive relation to the primary circuit during the rotation. If with a single- coil field, these secondary ...", "... induced so as to give a rotary effort in the one direction, and in the other half the current is induced to COMMUTATOR MOTORS. 355 give a rotary effort in the opposite direction, as shown by the arrows in Fig. 157. In the induction motor a second magnetic field is used to act upon the currents induced by the first, or inducing magnetic field, and thereby cause a rotation. That means the motor consists of a primary electric circuit, inducing Fig. 157. in the armature the secondary currents, and a primar ...", "... he current is induced to COMMUTATOR MOTORS. 355 give a rotary effort in the opposite direction, as shown by the arrows in Fig. 157. In the induction motor a second magnetic field is used to act upon the currents induced by the first, or inducing magnetic field, and thereby cause a rotation. That means the motor consists of a primary electric circuit, inducing Fig. 157. in the armature the secondary currents, and a primary magnetizing circuit producing the magnetism to act upon the secondary currents. ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-10", "section_label": "Theory Section 10: Hysteresis and Effective Resistance", "section_title": "Hysteresis and Effective Resistance", "kind": "theory-section", "sequence": 10, "number": 10, "location": "lines 3234-3585", "status": "candidate", "occurrence_count": 43, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-10/", "snippets": [ "10. HYSTERESIS AND EFFECTIVE RESISTANCE 46. If an alternating current 01 = I, in Fig. 21, exists in a circuit of reactance x = 2 irfL and of negligible resistance, the HYSTERESIS AND EFFECTIVE RESISTANCE 49 magnetic flux produced by the current, 0$ = $, is in phase with the current, and the e.m.f. generated by this flux, or counter e.m.f. of self-inductance, OE'\" = E'\" = xl, lags 90 degrees be- hind the current. The e.m.f. consumed ...", "... . HYSTERESIS AND EFFECTIVE RESISTANCE 46. If an alternating current 01 = I, in Fig. 21, exists in a circuit of reactance x = 2 irfL and of negligible resistance, the HYSTERESIS AND EFFECTIVE RESISTANCE 49 magnetic flux produced by the current, 0$ = $, is in phase with the current, and the e.m.f. generated by this flux, or counter e.m.f. of self-inductance, OE'\" = E'\" = xl, lags 90 degrees be- hind the current. The e.m.f. consumed by ...", "... ircuit of reactance x = 2 irfL and of negligible resistance, the HYSTERESIS AND EFFECTIVE RESISTANCE 49 magnetic flux produced by the current, 0$ = $, is in phase with the current, and the e.m.f. generated by this flux, or counter e.m.f. of self-inductance, OE'\" = E'\" = xl, lags 90 degrees be- hind the current. The e.m.f. consumed by self-inductance or impressed e.m.f. OE\" = E\" = xl is thus 90 degrees ahead of the current. Inversely, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-19", "section_label": "Chapter 19: Commutatob Motobs", "section_title": "Commutatob Motobs", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 21339-22387", "status": "candidate", "occurrence_count": 41, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "snippets": [ "... sformer motor ; that is, a motor in which the main current enters the primary member or field only, while in the secondary member, or armature, a current is in- duced, and thus the action is due to the repulsive thrust between induced current and inducing magnetism. As stated under the heading of induction motors, a multiple circuit armature is required for the purpose of having always secondary circuits in inductive relation to the primary circuit during the rotation. If with a single- coil field, these secondary ...", "... ve a rotary effort in the one direction, and in the other half the current is induced to 292 ALTERNATING-CURRENT PHENOMENA, [§ 193 give a rotary effort in the opposite direction, as shown by the arrows in Fig. 141. In the induction motor a second magnetic field is used to act upon the currents induced by the first, or inducing magnetic field, and thereby cause a rotation. That means the motor consists of a primary electric circuit, inducing Fig. 14h in the armature the secondary currents, and a primar ...", "... ed to 292 ALTERNATING-CURRENT PHENOMENA, [§ 193 give a rotary effort in the opposite direction, as shown by the arrows in Fig. 141. In the induction motor a second magnetic field is used to act upon the currents induced by the first, or inducing magnetic field, and thereby cause a rotation. That means the motor consists of a primary electric circuit, inducing Fig. 14h in the armature the secondary currents, and a primary magnetizing circuit producing the magnetism to act upon the secondary currents. ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-21", "section_label": "Chapter 21: Dibtobtiox Of Wavs-Shafe And Its Causes", "section_title": "Dibtobtiox Of Wavs-Shafe And Its Causes", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 23274-24559", "status": "candidate", "occurrence_count": 41, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "snippets": [ "... effect will cause distortion of the current wave, while with a sine wave of current passing through the circuit, a distorting effect will cause higher harmonics of E.M.F. 213. In a conductor revolving with uniform velocity through a uniform and constant magnetic field, a sine wave of E.M.F. is induced. In a circuit with constant resistance and constant reactance, this sine wave of E.M.F. produces 1214] DISTORTION OF WAVE-SHAPE. 321 a sine wave of current. Thus distortion of the wave-shape or higher harmonics ...", "... of E.M.F. produces 1214] DISTORTION OF WAVE-SHAPE. 321 a sine wave of current. Thus distortion of the wave-shape or higher harmonics may be due to : lack of uniformity of the velocity of the revolving conductor ; lack of uniformity or pulsation of the magnetic field ; pulsation of the resis- tance ; or pulsation of the reactance. The first two cases, lack of uniformity of the rotation or of the magnetic field, cause higher harmonics of E.M.F. at open circuit. The last, pulsation of resistance and reac- tance, ...", "... to : lack of uniformity of the velocity of the revolving conductor ; lack of uniformity or pulsation of the magnetic field ; pulsation of the resis- tance ; or pulsation of the reactance. The first two cases, lack of uniformity of the rotation or of the magnetic field, cause higher harmonics of E.M.F. at open circuit. The last, pulsation of resistance and reac- tance, causes higher harmonics only with a current flowing in the circuit, that is, under load. Lack of uniformity of the rotation is of no practical in- ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-21", "section_label": "Chapter 21: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 20502-21189", "status": "candidate", "occurrence_count": 40, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-21/", "snippets": [ "... ine is a constant. While this is more or less approximately the case in many alternators, in others, especially in machines of large arma- ture reaction, the reactance x is variable, and is different in the different positions of the armature coils in the magnetic circuit. This variation of the reactance causes phenomena which do not find their explanation by the theoretical cal- culations made under the assumption of constant reactance. It is known that synchronous motors of large and variable reactance keep in ...", "... or do not disappear if the gene- rator field is broken, or even reversed to a small negative value, in which latter case the current flows against the E.M.F. EQ of the generator. Furthermore, a shuttle armature without any winding will in an alternating magnetic field revolve when once brought up to synchronism, and do considerable work as a motor. These phenomena are not due to remanent magnetism nor to the magnetizing effect of Foucault currents, because 372 AL TERNA TING-CURRENT PHENOMENA. they exist als ...", "... against the E.M.F. EQ of the generator. Furthermore, a shuttle armature without any winding will in an alternating magnetic field revolve when once brought up to synchronism, and do considerable work as a motor. These phenomena are not due to remanent magnetism nor to the magnetizing effect of Foucault currents, because 372 AL TERNA TING-CURRENT PHENOMENA. they exist also in machines with laminated fields, and exist if the alternator is brought up to synchronism by external means and the remanent magnetism o ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-02", "section_label": "Chapter 2: Multiple Squirrel-Cage Induction Motor", "section_title": "Multiple Squirrel-Cage Induction Motor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3543-5554", "status": "candidate", "occurrence_count": 40, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-02/", "snippets": [ "... cage, and thus of higher reactance, a \"double squirrel-cage induction motor\" in derived, which to some extent combines the characteristics of the high- resistance and the low-resistance secondary. That is, at start- ing and low speed, the frequency of the magnetic flux in the arma- ture, and therefore the voltage induced in the secondary winding is high, and the high-resistance squirrel cage thus carries con- siderable current, gives good torque and torque efficiency, while the low-resistance squirrel cage is ineff ...", "... thus of higher reactance, a \"double squirrel-cage induction motor\" in derived, which to some extent combines the characteristics of the high- resistance and the low-resistance secondary. That is, at start- ing and low speed, the frequency of the magnetic flux in the arma- ture, and therefore the voltage induced in the secondary winding is high, and the high-resistance squirrel cage thus carries con- siderable current, gives good torque and torque efficiency, while the low-resistance squirrel cage is ineffectiv ...", "... nd the innermost squirrel cage, of low resistance ami high reactance, gives its torque at full speed, near synchronism. Mechanically, the rotor iron may be slotted down to the inner- most squirrel cage, so as to avoid the excessive reactance of a closed magnetic circuit, that is, have the magnetic leakage flux or self-inductive flux pass an air gap. 19. In the calculation of the standard induction motor, it is usual to start with the mutual magnetic flux, *, or rather with the voltage induced by this flux, the m ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-20", "section_label": "Chapter 20: Beactiox Machines", "section_title": "Beactiox Machines", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 22388-23273", "status": "candidate", "occurrence_count": 39, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "snippets": [ "... ine is a constant. While this is more or less approximately thd case in many alternators, in others, especially in machines of large arma- ture reaction, the reactance x is variable, and is different in the different positions of the armature coils in the magnetic circuit. This variation of the reactance causes phenomena which do not find their explanation by the theoretical cal- culations made under the assumption of constant reactance. It is known that synchronous motors of large and variable reactance keep in ...", "... or do not disappear if the gene- rator field is broken, or even reversed to a small negative value, in which latter case the current flows against the E.M.F. E^ of the generator. Furthermore, a shuttle armature without any winding will in an alternating magnetic field revolve when once brought up to synchronism, and do considerable work as a motor. These phenomena are not due to remanant magnetism nor to the magnetizing effect of Foucault currents, because 206, 206] REACTION MACHINES, 809 they exist also in ...", "... against the E.M.F. E^ of the generator. Furthermore, a shuttle armature without any winding will in an alternating magnetic field revolve when once brought up to synchronism, and do considerable work as a motor. These phenomena are not due to remanant magnetism nor to the magnetizing effect of Foucault currents, because 206, 206] REACTION MACHINES, 809 they exist also in machines with laminated fields, and exist if the alternator is brought up to synchronism by external means and the remanant magnetism of th ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-09", "section_label": "Chapter 10: Hysteresis Motor", "section_title": "Hysteresis Motor", "kind": "chapter", "sequence": 9, "number": 10, "location": "lines 14551-14761", "status": "candidate", "occurrence_count": 38, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-09/", "snippets": [ "CHAPTER X HYSTERESIS MOTOR 98. In it revolving magnetic field, a circular iron disk, or iron cylinder of uniform magnetic reluctance in the direction of the revolving field, is set in rotation, even if subdivided so as to preclude the production of eddy currents. Thin rotation is due to the effect of hysteresi ...", "CHAPTER X HYSTERESIS MOTOR 98. In it revolving magnetic field, a circular iron disk, or iron cylinder of uniform magnetic reluctance in the direction of the revolving field, is set in rotation, even if subdivided so as to preclude the production of eddy currents. Thin rotation is due to the effect of hysteresis of the revolving disk or cylinder, and such a motor may thus be ...", "CHAPTER X HYSTERESIS MOTOR 98. In it revolving magnetic field, a circular iron disk, or iron cylinder of uniform magnetic reluctance in the direction of the revolving field, is set in rotation, even if subdivided so as to preclude the production of eddy currents. Thin rotation is due to the effect of hysteresis of the revolving disk or cylinder, and such a motor may thus be called a hy ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-11", "section_label": "Lecture 11: Light Intensity And Illumination", "section_title": "Light Intensity And Illumination", "kind": "lecture", "sequence": 11, "number": 11, "location": "lines 12574-16484", "status": "candidate", "occurrence_count": 37, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-11/", "snippets": [ "LECTURE XI. LIGHT INTENSITY AND ILLUMINATION. A. INTENSITY CURVES FOR UNIFORM ILLUMINATION. 102. The distribution of the light flux in space, and thus the illumination, depends on the location of the light sources, and on their distribution curves. The character of the required illumi- nation depends on the purpose for which it is used: a general illumination of low and approximately ...", "... , for instance, to read labels on bottles — con- stancy of the vertical illumination iv is desirable. By \"horizontal illumination\" ih is here understood the illumi- nation of a horizontal plane, which is due to the vertical compo- nent of the total light flux, while the \"vertical illumination \" iv is the illumination of a vertical plane, due to the horizontal component of the light flux. LIGHT INTENSITY AND ILLUMINATION. 229 In Fig. 96, the intensity curves of the light source required to give uniform ...", "... \" ih is here understood the illumi- nation of a horizontal plane, which is due to the vertical compo- nent of the total light flux, while the \"vertical illumination \" iv is the illumination of a vertical plane, due to the horizontal component of the light flux. LIGHT INTENSITY AND ILLUMINATION. 229 In Fig. 96, the intensity curves of the light source required to give uniform total illumination i0 (11) in a horizontal plane are plotted as curves I, II and III; the intensity distribution for uniform horiz ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 37, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "CHAPTER IV INDUCTION MOTOR WITH SECONDARY EXCITATION 38. While in the typical synchronous machine and eommu- tating machine the magnetic field is excited by a direct current, characteristic of the induction machine is, that the magnetic field is excited by an alternating current derived from the alter- nating supply voltage, just as in the alternating-current trans- former. As the alternat ...", "CHAPTER IV INDUCTION MOTOR WITH SECONDARY EXCITATION 38. While in the typical synchronous machine and eommu- tating machine the magnetic field is excited by a direct current, characteristic of the induction machine is, that the magnetic field is excited by an alternating current derived from the alter- nating supply voltage, just as in the alternating-current trans- former. As the alternating magnetizing current is a wattless reactive current, the result is, that the alternating-current ...", "... ld is excited by a direct current, characteristic of the induction machine is, that the magnetic field is excited by an alternating current derived from the alter- nating supply voltage, just as in the alternating-current trans- former. As the alternating magnetizing current is a wattless reactive current, the result is, that the alternating-current input into the induction motor is always lagging, the more so, the larger a part of the total current is given by the magnetizing current. To secure good power-factor in a ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-07", "section_label": "Chapter 7: Shaping Of Waves : General", "section_title": "Shaping Of Waves : General", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 12222-12961", "status": "candidate", "occurrence_count": 36, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-07/", "snippets": [ "... ge, such as Fig. 48, and such as the common saw-tooth wave of the uni tooth alternator, is superior in transformers and similar devices, as it transform s tho energy with less hysteresis loss. The peaked voltage wave. Fig. 4:8, gives a flat-topped wave of magnetism. Fig. 47, and therciby transforms the voltage with a lesser maximum magnetic flux, than ^ sine wave of the same effective value, that is, the same powc^r. the hysteresis loss depends on the maximum value of t\\u) mag- 5tic flux, the reduction of the maximu ...", "... ternator, is superior in transformers and similar devices, as it transform s tho energy with less hysteresis loss. The peaked voltage wave. Fig. 4:8, gives a flat-topped wave of magnetism. Fig. 47, and therciby transforms the voltage with a lesser maximum magnetic flux, than ^ sine wave of the same effective value, that is, the same powc^r. the hysteresis loss depends on the maximum value of t\\u) mag- 5tic flux, the reduction of the maximum value of tho magncitic; fl^Jx, due to a peaked voltage wave, results in a l ...", "... is superior in transformers and similar devices, as it transform s tho energy with less hysteresis loss. The peaked voltage wave. Fig. 4:8, gives a flat-topped wave of magnetism. Fig. 47, and therciby transforms the voltage with a lesser maximum magnetic flux, than ^ sine wave of the same effective value, that is, the same powc^r. the hysteresis loss depends on the maximum value of t\\u) mag- 5tic flux, the reduction of the maximum value of tho magncitic; fl^Jx, due to a peaked voltage wave, results in a lower ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1120-1683", "status": "candidate", "occurrence_count": 35, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-01/", "snippets": [ "... or z — \\/r\" + X\". The resistance, r, in circuits where energy is expended only in heating the conductor, is the same as the ohmic resistance of continuous-current circuits. In circuits, however, where energy is also expended outside of the conductor by magnetic hysteresis, mutual inductance, dielectric hysteresis, etc., r is larger than the true ohmic resistance of the conductor, since it refers to the total expenditure of energy. It may be called then the effective re- sistance. It may no longer be a constant o ...", "... actance, X, refers to the wattless or reactive component of e.m.f., or the e.m.f. in quadrature with the current. 3. The principal sources of reactance are electromagnetism and capacity. Electromagnetism An electric current, i, in a circuit produces a magnetic flux surrounding the conductor in lines of magnetic force (or more correctly, lines of magnetic induction), of closed, circular, or other form, which alternate with the alternations of the current, INTRODUCTION 3 and thereby generate an e.m.f. in the ...", "... X, refers to the wattless or reactive component of e.m.f., or the e.m.f. in quadrature with the current. 3. The principal sources of reactance are electromagnetism and capacity. Electromagnetism An electric current, i, in a circuit produces a magnetic flux surrounding the conductor in lines of magnetic force (or more correctly, lines of magnetic induction), of closed, circular, or other form, which alternate with the alternations of the current, INTRODUCTION 3 and thereby generate an e.m.f. in the condu ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "section_label": "Chapter 14: Dielectric Losses", "section_title": "Dielectric Losses", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 35, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "CHAPTER XIV DIELECTRIC LOSSES Dielectric Hysteresis 116. Just as magnetic hysteresis and eddy currents give a power component in the inductive reactance, as \"effective resistance,\" so the energy losses in the dielectric lead to a power component in the condensive reactance, which may be repre- sented by an \"effective resistance ...", "... resistance,\" so the energy losses in the dielectric lead to a power component in the condensive reactance, which may be repre- sented by an \"effective resistance of dielectric losses\" or an \"effective conductance of dielectric losses.\" In the alternating magnetic field, power is consumed by mag- netic hysteresis. This is proportional to the frequency, and to the 1.6*'' power of the magnetic density, and is considerable, amounting in a closed magnetic circuit to 40 to 60 per cent, of the total volt-amperes. In th ...", "... ted by an \"effective resistance of dielectric losses\" or an \"effective conductance of dielectric losses.\" In the alternating magnetic field, power is consumed by mag- netic hysteresis. This is proportional to the frequency, and to the 1.6*'' power of the magnetic density, and is considerable, amounting in a closed magnetic circuit to 40 to 60 per cent, of the total volt-amperes. In the dielectric field, the energy losses usually are very much smaller, rarely amounting to more than a few per cent., though they ma ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-17", "section_label": "Chapter 19: Alternating- Current Motors In General", "section_title": "Alternating- Current Motors In General", "kind": "chapter", "sequence": 17, "number": 19, "location": "lines 21713-23905", "status": "candidate", "occurrence_count": 35, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-17/", "snippets": [ "... be made to the rotating member either by ooIIesSsi rings— that is, to fixed points of the windings — or by commutator —that is, to fixed points in space. The alternating-current motors can he subdivided into two classes — those in which the electric and magnetic relation between stationary and moving members do not vary with their relative positions, ami those in which they vary with the relatifl positions of stator and rotor. In the latter a cycle of rotation exists, and therefrom the tendency of the motor resul ...", "... ent — polyphase or single-phase synchronous motors, 2. One member excited by alternating current, the other taining a single circuit closed upon itself — synchronous induction motors. 3. One member excited by alternating current, the other of different magnetic reluctance iii different direction! construction) — reaction motors. 4. One member excited by alternating current, the other by altcrnating current of different frequency or different direction of rotation- — general alternating-current transformer or fr ...", "... yphase or single-phase synchronous motors, 2. One member excited by alternating current, the other taining a single circuit closed upon itself — synchronous induction motors. 3. One member excited by alternating current, the other of different magnetic reluctance iii different direction! construction) — reaction motors. 4. One member excited by alternating current, the other by altcrnating current of different frequency or different direction of rotation- — general alternating-current transformer or fre- quency ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-21", "section_label": "Chapter 21: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 22302-23970", "status": "candidate", "occurrence_count": 34, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-21/", "snippets": [ "CHAPTER XXI ALTERNATING-CURRENT GENERATOR 185. In the alternating-current generator, e.m.f. is generated in the armature conductors by their relative motion through a constant or approximately constant magnetic field. When yielding current, two distinctly different m.m.fs. are acting upon the alternator armature — the m.m.f. of the field due to the field-exciting spools, and the m.m.f. of the armature current. The former is constant, or approximately so, while ...", "... FiG. 129. directional; but pulsating in a single-phase alternator. In the polyphase alternator, when evenly loaded or balanced, the result- ant m.m.f. of the armature current is more or less constant. The e.m.f. generated in the armature is due to the magnetic flux passing through and interhnked with the armature con- ductors. This flux is produced by the resultant of both m.m.fs., that of the field, and that of the armature. On open-circuit, the m.m.f. of the armature is zero, and the e.m.f. of the armature ...", "... . directional; but pulsating in a single-phase alternator. In the polyphase alternator, when evenly loaded or balanced, the result- ant m.m.f. of the armature current is more or less constant. The e.m.f. generated in the armature is due to the magnetic flux passing through and interhnked with the armature con- ductors. This flux is produced by the resultant of both m.m.fs., that of the field, and that of the armature. On open-circuit, the m.m.f. of the armature is zero, and the e.m.f. of the armature is due ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-47", "section_label": "Chapter 7: Distribution Of Alternating-Current Density In Conductor", "section_title": "Distribution Of Alternating-Current Density In Conductor", "kind": "chapter", "sequence": 47, "number": 7, "location": "lines 24981-26094", "status": "candidate", "occurrence_count": 34, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "snippets": [ "CHAPTER VII. DISTRIBUTION OF ALTERNATING-CURRENT DENSITY IN CONDUCTOR. 59. If the frequency of an alternating or oscillating current is high, or the section of the conductor which carries the current is very large, or its electric conductivity or its magnetic per- meability high, the current density is not uniform throughout the conductor section, but decreases towards the interior of the conductor, due to the higher e.m.f. of self-inductance in the interior of the conductor, caused by the magnetic flux inside ...", "... vity or its magnetic per- meability high, the current density is not uniform throughout the conductor section, but decreases towards the interior of the conductor, due to the higher e.m.f. of self-inductance in the interior of the conductor, caused by the magnetic flux inside of the conductor. The phase of the current inside of the conductor also differs from that on the surface and lags behind it. In consequence of this unequal current distribution in a large conductor traversed by ^alternating currents, the effe ...", "... ts magnetic per- meability high, the current density is not uniform throughout the conductor section, but decreases towards the interior of the conductor, due to the higher e.m.f. of self-inductance in the interior of the conductor, caused by the magnetic flux inside of the conductor. The phase of the current inside of the conductor also differs from that on the surface and lags behind it. In consequence of this unequal current distribution in a large conductor traversed by ^alternating currents, the effective ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-03", "section_label": "Chapter 3: Law Of Electromagnetic Induction", "section_title": "Law Of Electromagnetic Induction", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 2012-2148", "status": "candidate", "occurrence_count": 33, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-03/", "snippets": [ "CHAPTER III LAW OF ELECTROMAGNETIC INDUCTION 13. If an electric conductor moves relatively to a magnetic field, an e.m.f. is generated in the conductor which is propor- tional to the intensity of the magnetic field, to the length of the conductor, and to the speed of its motion perpendicular to the magnetic field and the direction of the conductor; or, in ot ...", "CHAPTER III LAW OF ELECTROMAGNETIC INDUCTION 13. If an electric conductor moves relatively to a magnetic field, an e.m.f. is generated in the conductor which is propor- tional to the intensity of the magnetic field, to the length of the conductor, and to the speed of its motion perpendicular to the magnetic field and the direction of the conductor; or, in other words, proportional to the number of lines of magnetic force cut per second by the conductor. As a ...", "... 13. If an electric conductor moves relatively to a magnetic field, an e.m.f. is generated in the conductor which is propor- tional to the intensity of the magnetic field, to the length of the conductor, and to the speed of its motion perpendicular to the magnetic field and the direction of the conductor; or, in other words, proportional to the number of lines of magnetic force cut per second by the conductor. As a practical unit of e.m.f., the volt is defined by the e.m.f. generated in a conductor, which cuts 10^ ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-15", "section_label": "Chapter 15: The General Alternating-Current Transformer Or Frequency Converter", "section_title": "The General Alternating-Current Transformer Or Frequency Converter", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 12683-13648", "status": "candidate", "occurrence_count": 33, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "snippets": [ "CHAPTER XV. THE GENERAL ALTERNATING-CURRENT TRANSFORMER OR FREQUENCY CONVERTER. 141. The simplest alternating-current apparatus is the alternating-current transformer. It consists of a magnetic- circuit, interlinked with two electric circuits or sets of electric circuits. The one, the primary circuit, is excited by an impressed E.M.F., while in the other, the secondary circuit, an E.M.F. is induced. Thus, in the primary circuit, power is consum ...", "... ed movably with re- gard to the primary in such a way that, while set in rota- tion, it still remains in the primary field of force. The condition that the secondary circuit, while revolving with regard to the primary, does not leave the primary field of magnetic force, requires that this field is not undirectional, but that an active field exists in every direction. One way of producing such a magnetic field is by exciting different primary circuits angularly displaced in space with each other by currents of diff ...", "... tion that the secondary circuit, while revolving with regard to the primary, does not leave the primary field of magnetic force, requires that this field is not undirectional, but that an active field exists in every direction. One way of producing such a magnetic field is by exciting different primary circuits angularly displaced in space with each other by currents of different phase. Another way is to excite the primary field in one direction only, and get the cross magnetization, or the angularly displaced magn ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-17", "section_label": "Chapter 17: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16362-17596", "status": "candidate", "occurrence_count": 33, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "snippets": [ "CHAPTER XVII. ALTERNATING-CURRENT GENERATOR. 182. In the alternating-current generator, E.M.F. is induced in the armature conductors by their relative motion through a constant or approximately constant magnetic field. When yielding current, two distinctly different M.M.Fs. are acting upon the alternator armature — the M.M.F. of the field due to the field-exciting 'spools, and the M.M.F. of the armature current. The former is constant, or approx- imately so, w ...", "... uni-directional, but pulsating in a single-phase alternator. In the polyphase alternator, when evenly loaded or balanced, the resultant M.M.F. of the armature current is more or less constant. The E.M.F. induced in the armature is due to the mag- netic flux passing through and interlinked with the arma- ture conductors. This flux is produced by the resultant of both M.M.Fs., that of the field, and that of the armature. On open circuit, the M.M.F. of the armature is zero, and the E.M.F. of the armature is du ...", "... hase alternator, when evenly loaded or balanced, the resultant M.M.F. of the armature current is more or less constant. The E.M.F. induced in the armature is due to the mag- netic flux passing through and interlinked with the arma- ture conductors. This flux is produced by the resultant of both M.M.Fs., that of the field, and that of the armature. On open circuit, the M.M.F. of the armature is zero, and the E.M.F. of the armature is due to the M.M.F. of the field coils only. In this case the E.M.F. is, in ge ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-13", "section_label": "Lecture 13: Physiological Problems Of Illuminating Engineering", "section_title": "Physiological Problems Of Illuminating Engineering", "kind": "lecture", "sequence": 13, "number": 13, "location": "lines 17446-17956", "status": "candidate", "occurrence_count": 32, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-13/", "snippets": [ "LECTURE XIII. PHYSIOLOGICAL PROBLEMS OF ILLUMINATING ENGINEERING. 123. The design of an illumination requires the solution of physiological as well as physical problems. Physical considera- tions, for instance, are the distribution of light-flux intensity throughout the illuminated space, as related to size, location and number of light sources, while the relation, to the satisfac- tory character of the illumination, of the direction of the light, its subdivision and diffusion, etc., are physiolo ...", "... cience, as is, for instance, apparatus design, but much further physiological investigation is needed to determine the requirements and conditions of satisfactory illumination. The physical side of illuminating engineering: — to produce a definite light flux density throughout the illuminated space, — is ah engineering problem, which can be solved with any desired degree of exactness, usually in a number of different ways. The solution of the physical problem of light distribution, however, does not yet comp ...", "... ly in a number of different ways. The solution of the physical problem of light distribution, however, does not yet complete the problem of illuminating engineering, does not yet assure a satisfactory illumination, but with the same distribution of light flux density throughout the illuminated surface, the illumination may be anything between entirely unsatisfactory and highly successful, depending on the ful- fillment or failure to fulfill numerous physiological requirements. Some of these are well understood ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-14", "section_label": "Chapter 14: The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "section_title": "The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14089-14918", "status": "candidate", "occurrence_count": 32, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "snippets": [ "CHAPTER XIV. THE OSNI!RAIj AIiTEBNATINa-CUBBENT TBAKBFOBMSB. 131. The simplest alternating-current apparatus is the alternating-current transformer. It consists of a magnetic circuit, interlinked with two electric circuits or sets of electric circuits. The one, the primary circuit, is excited by an impressed E.M.F., while in the other, the secondary circuit, an E.M.F. is induced. Thus, in the primary circuit, power is consume ...", "... nted movably with re- gard to the primary in such a way that, while set in rota- tion, it still remains in the primary field of force. The condition that the secondary circuit, while moving with regard to the primary, does not leave the primary field of magnetic force, requires that this field is not undirec- tional, but that an active field exists in every direction. One way of producing such a magnetic field is by exciting different primary circuits angularly displaced in space with each other by currents of di ...", "... ition that the secondary circuit, while moving with regard to the primary, does not leave the primary field of magnetic force, requires that this field is not undirec- tional, but that an active field exists in every direction. One way of producing such a magnetic field is by exciting different primary circuits angularly displaced in space with each other by currents of different phase. Another way is to excite the primary field in one direction only, and get the cross magnetization, or the angularly displaced mag- ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3721-4369", "status": "candidate", "occurrence_count": 31, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-06/", "snippets": [ "... presentation still is by a decrease of the transient. This transient then is the difference between the energy storage in the permanent condition and the energy storage during the transition period. If the law of proportionality between current, voltage, magnetic flux, etc., apphes, the single-energy transient is a simple exponential function : _ j_ y = 2/oe ^°, (1) where 2/0 = initial value of the transient, and To = duration of the transient, that is, the time which the transient voltage, current, etc. ...", "... on still is by a decrease of the transient. This transient then is the difference between the energy storage in the permanent condition and the energy storage during the transition period. If the law of proportionality between current, voltage, magnetic flux, etc., apphes, the single-energy transient is a simple exponential function : _ j_ y = 2/oe ^°, (1) where 2/0 = initial value of the transient, and To = duration of the transient, that is, the time which the transient voltage, current, etc., woul ...", "... at is, the time which the transient voltage, current, etc., would last if maintained at its initial value. The duration To is the ratio of the energy-storage coefficient to the power-dissipation coefficient. Thus, if energy is stored by the current i, as magnetic field. To = -, (2) r where L = inductance = coefficient of energy storage by the cur- rent, r = resistance = coefficient of power dissipation by the current. If the energy is stored by the voltage e, as dielectric field, the duration of the transient ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3287-3955", "status": "candidate", "occurrence_count": 31, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "snippets": [ "... presentation still is by a decrease of the transient. This transient then is the difference between the energy storage in the permanent condition and the energy storage during the transition period. If the law of proportionality between current, voltage, magnetic flux, etc., applies, the single-energy transient is a simple exponential function : j_ y = i/oe T°, (1) where ?/o = initial value of the transient, and TO = duration of the transient, that is, the time which the transient voltage, current, etc., ...", "... on still is by a decrease of the transient. This transient then is the difference between the energy storage in the permanent condition and the energy storage during the transition period. If the law of proportionality between current, voltage, magnetic flux, etc., applies, the single-energy transient is a simple exponential function : j_ y = i/oe T°, (1) where ?/o = initial value of the transient, and TO = duration of the transient, that is, the time which the transient voltage, current, etc., would ...", "... at is, the time which the transient voltage, current, etc., would last if maintained at its initial value. The duration T0 is the ratio of the energy-storage coefficient to the power-dissipation coefficient. Thus, if energy is stored by the current i, as magnetic field, T0 = £, (2) where L = inductance = coefficient of energy storage by the cur- rent, r = resistance = coefficient of power dissipation by the current. If the energy is stored by the voltage e, as dielectric field, the duration of the transient wou ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-16", "section_label": "Chapter 16: Aiitebnatingh-Current Osnebator", "section_title": "Aiitebnatingh-Current Osnebator", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 17025-18828", "status": "candidate", "occurrence_count": 31, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "snippets": [ "CHAPTER XVI. AIiTEBNATINGh-CURRENT OSNEBATOR. 159. In the alternating-current generator, E.M.F. is induced in the armature conductors by their relative motion through a constant or approximately constant magnetic field. When yielding current, two distinctly different M.M.Fs. are acting upon the alternator armature — the M.M.F. of the field due to the field-exciting spools, and the M.M.F. of the armature current. The former is constant, or approx- imately so, wh ...", "... uni-directional, but pulsating in a single-phase alternator. In the polyphase alternator, when evenly loaded or balanced, the resultant M.M.F. of the armature current is more or less constant. The E.M.F. induced in the armature is due to the mag- netic flux passing through and interlinked with the arma- ture conductors. This flux is produced by the resultant of both M.M.Fs., that of the field, and that of the armature. On open circuit, the M.M.F. of the armature is zero, and the E.M.F. of the armature is di ...", "... hase alternator, when evenly loaded or balanced, the resultant M.M.F. of the armature current is more or less constant. The E.M.F. induced in the armature is due to the mag- netic flux passing through and interlinked with the arma- ture conductors. This flux is produced by the resultant of both M.M.Fs., that of the field, and that of the armature. On open circuit, the M.M.F. of the armature is zero, and the E.M.F. of the armature is diie to the M.M.F. of the field coils only. In this case the E.M.F. is, in g ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-03", "section_label": "Chapter 3: Law Of Electro-Magnetic Induction", "section_title": "Law Of Electro-Magnetic Induction", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 1606-1742", "status": "candidate", "occurrence_count": 31, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-03/", "snippets": [ "CHAPTER III. LAW OF ELECTRO-MAGNETIC INDUCTION. 11. If an electric conductor moves relatively to a mag- netic field, an E.M.F. is induced in the conductor which is proportional to the intensity of the magnetic field, to the length of the conductor, and to the speed of its motion perpendicu ...", "CHAPTER III. LAW OF ELECTRO-MAGNETIC INDUCTION. 11. If an electric conductor moves relatively to a mag- netic field, an E.M.F. is induced in the conductor which is proportional to the intensity of the magnetic field, to the length of the conductor, and to the speed of its motion perpendicular to the magnetic field and the direction of the conductor ; or, in other words, proportional to the number of lines of magnetic force cut per second by the conductor. As ...", "... 11. If an electric conductor moves relatively to a mag- netic field, an E.M.F. is induced in the conductor which is proportional to the intensity of the magnetic field, to the length of the conductor, and to the speed of its motion perpendicular to the magnetic field and the direction of the conductor ; or, in other words, proportional to the number of lines of magnetic force cut per second by the conductor. As a practical unit of E.M.F., the volt is defined as the E.M.F. induced in a conductor, which cuts 108 ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-11", "section_label": "Chapter 12: Frequency Converter Or General Alternating Current Transformer", "section_title": "Frequency Converter Or General Alternating Current Transformer", "kind": "chapter", "sequence": 11, "number": 12, "location": "lines 14897-17124", "status": "candidate", "occurrence_count": 31, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-11/", "snippets": [ "CHAPTER XII FREQUENCY CONVERTER OR GENERAL ALTERNATING- CURRENT TRANSFORMER 103. In general, an alternating-current transformer conafete of a magnetic circuit, interlinked with two electric circuits or sets of electric circuits, the primary circuit, in which power, sup- plied by the impressed voltage, is consumed, and the secondary circuit, in which a corresponding amount of electric power is produced; ...", "... f electric circuits, the primary circuit, in which power, sup- plied by the impressed voltage, is consumed, and the secondary circuit, in which a corresponding amount of electric power is produced; or in other words, power is transferred through space, by magnetic energy, from primary to secondary circuit. This power finds its mechanical equivalent in a repulsive llirusi acting between primary and secondary conductors. Thus, if the secondary is not held rigidly, with regards to the primary, it will be repelled and ...", "... in which the secondary is mounted niovably with regards to the primary, in such a manner that, while set in motion, it still remains in the primary field of force. This requires, i hat the induction motor field is not constant in one direction, but that a magnetic field exists in every direction, in other words that the magnetic field successively assumes all directions, as a so- called rotating field. The induction motor and the stationary transformer thus are merely two applications of the same structure, the fo ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-03", "section_label": "Chapter 3: Iiaw Of Eucctbo-Maonimc Induction", "section_title": "Iiaw Of Eucctbo-Maonimc Induction", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 1973-2121", "status": "candidate", "occurrence_count": 30, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-03/", "snippets": [ "CHAPTER III. IiAW OF EUCCTBO-MAONimC INDUCTION. 11. If an electric conductor moves relatively to a mag- netic field, an E.M.F. is induced in the conductor which is proportional to the intensity of the magnetic field, to the length of the conductor, and to the speed of its motion perpendicular to the magnetic field and the direction of the conductor ; or, in other words, proportional to the number of lines of magnetic force cut per second by the conductor. As ...", "... 11. If an electric conductor moves relatively to a mag- netic field, an E.M.F. is induced in the conductor which is proportional to the intensity of the magnetic field, to the length of the conductor, and to the speed of its motion perpendicular to the magnetic field and the direction of the conductor ; or, in other words, proportional to the number of lines of magnetic force cut per second by the conductor. As a practical unit of E.M.F., the volt is defined as the E.M.F. induced in a conductor, which cuts 10« ...", "... ich is proportional to the intensity of the magnetic field, to the length of the conductor, and to the speed of its motion perpendicular to the magnetic field and the direction of the conductor ; or, in other words, proportional to the number of lines of magnetic force cut per second by the conductor. As a practical unit of E.M.F., the volt is defined as the E.M.F. induced in a conductor, which cuts 10« = 100,000,000 lines of magnetic force per second. If the conductor is closed upon itself, the induced E.M.F. ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-01", "section_label": "Chapter 1: Speed Control Of Induction Motors", "section_title": "Speed Control Of Induction Motors", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1368-3542", "status": "candidate", "occurrence_count": 30, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-01/", "snippets": [ "... s- ing slip, to get high torque at low speeds, the same result can be produced by the use of an effective resistance, such as the effect- ive or equivalent resistance of hysteresis, or of eddy currents. As the frequency of the secondary current varies, a magnetic circuit energized by the secondary current operates at the varying frequency of the slip, s. At a given current, i\\, the voltage required to send the current through the magnetic circuit is proportional to the frequency, that is, to 8. Hence, the suacep ...", "... or of eddy currents. As the frequency of the secondary current varies, a magnetic circuit energized by the secondary current operates at the varying frequency of the slip, s. At a given current, i\\, the voltage required to send the current through the magnetic circuit is proportional to the frequency, that is, to 8. Hence, the suaceptance is inverse proportional to «: V = 6- (5) 8 The angle of hysteretic advance of phase, a, and the power- factor, in a closed magnetic circuit, are independent of the frequ ...", "... uired to send the current through the magnetic circuit is proportional to the frequency, that is, to 8. Hence, the suaceptance is inverse proportional to «: V = 6- (5) 8 The angle of hysteretic advance of phase, a, and the power- factor, in a closed magnetic circuit, are independent of the frequency, and vary relatively little with the magnetic density and thus the current, over a wide range,1 thus may approxi- mately be assumed as constant. That is, the hysteretic con- ductance is proportional to the suscept ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-05", "section_label": "Theory Section 5: Self-inductance and Mutual Inductance", "section_title": "Self-inductance and Mutual Inductance", "kind": "theory-section", "sequence": 5, "number": 5, "location": "lines 1573-1784", "status": "candidate", "occurrence_count": 29, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-05/", "snippets": [ "5. SELF-INDUCTANCE AND MUTUAL INDUCTANCE 26. The number of inter-linkages of an electric circuit with the lines of magnetic force of the flux produced by unit current in the circuit is called the inductance of the circuit. The number of interlinkages of an electric circuit with the lines of magnetic force of the flux produced by unit current ...", "5. SELF-INDUCTANCE AND MUTUAL INDUCTANCE 26. The number of inter-linkages of an electric circuit with the lines of magnetic force of the flux produced by unit current in the circuit is called the inductance of the circuit. The number of interlinkages of an electric circuit with the lines of magnetic force of the flux produced by unit current in a second elect ...", "... of an electric circuit with the lines of magnetic force of the flux produced by unit current in the circuit is called the inductance of the circuit. The number of interlinkages of an electric circuit with the lines of magnetic force of the flux produced by unit current in a second electric circuit is called the mutual inductance of the second upon the first circuit. It is equal to the mutual induc- tance of the first upon the second circuit, ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-101", "section_label": "Apparatus Section 4: Alternating-current Transformer: Regulation", "section_title": "Alternating-current Transformer: Regulation", "kind": "apparatus-section", "sequence": 101, "number": 4, "location": "lines 17538-18397", "status": "candidate", "occurrence_count": 29, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-101/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-101/", "snippets": [ "... can- not occupy the same space, and in addition some insulation — more or less depending on the voltage — must be between them, there is thus a space between primary and secondary through which the primary current can send magnetic flux which does not interlink with the secondary winding, but is a self-induc- tive or leakage flux and in the same manner the secondary current sends self-inductive or leakage flux through the space between primary and sec ...", "... occupy the same space, and in addition some insulation — more or less depending on the voltage — must be between them, there is thus a space between primary and secondary through which the primary current can send magnetic flux which does not interlink with the secondary winding, but is a self-induc- tive or leakage flux and in the same manner the secondary current sends self-inductive or leakage flux through the space between primary and secondary ...", "... — must be between them, there is thus a space between primary and secondary through which the primary current can send magnetic flux which does not interlink with the secondary winding, but is a self-induc- tive or leakage flux and in the same manner the secondary current sends self-inductive or leakage flux through the space between primary and secondary winding. These fluxes give rise to the self -inductive or leakage reactances x\\ and Xz of the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1224-1727", "status": "candidate", "occurrence_count": 29, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "snippets": [ "... nce, x, or — , The resistance, r, in circuits where energy is expended only in heating the conductor, is the same as the ohmic resistance of continuous-current circuits. In circuits, how- ever, where energy is also expended outside of the con- ductor by magnetic hysteresis, mutual inductance, dielectric hysteresis, etc., r is larger than the true ohmic resistance of the conductor, since it refers to the total expenditure of energy. It may be called then the effective resistance. It is no longer a constant of the ...", "... ponent of E.M.F., or the E.M.F. in phase with the current, the reactance, ;r, refers to the wattless component of E.M.F., or the E.M.F. in quadrature with the current. 3. The principal sources of reactance are electro-mag- netism and capacity. ELECTRO-MAGNETISM, An electric current, /, flowing through a circuit, produces a magnetic flux surrounding the conductor in lines of magnetic force (or more correctly, lines of magnetic induc- tion), of closed, circular, or other form, which alternate with the alternatio ...", "... r, refers to the wattless component of E.M.F., or the E.M.F. in quadrature with the current. 3. The principal sources of reactance are electro-mag- netism and capacity. ELECTRO-MAGNETISM, An electric current, /, flowing through a circuit, produces a magnetic flux surrounding the conductor in lines of magnetic force (or more correctly, lines of magnetic induc- tion), of closed, circular, or other form, which alternate with the alternations of the current, and thereby induce an E.M.F. in the conductor. Since th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 963-1366", "status": "candidate", "occurrence_count": 29, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "snippets": [ "... 0= Vr2 + Ar2. The resistance, r, in circuits where energy is expended only in heating the conductor, is the same as the ohmic resistance of continuous-current circuits. In circuits, how- ever, where energy is also expended outside of the con- ductor by magnetic hysteresis, mutual inductance, dielectric hysteresis, etc., r is larger than the true ohmic resistance of the conductor, since it refers to the total expenditure of energy. It may be called then the effective resistance. It is no longer a constant of the ...", "... ponent of E.M.F., or the E.M.F. in phase with the current, the reactance, x, refers to the wattless component of E.M.F., or the E.M.F. in quadrature with the current. 3. The principal sources of reactance are electro-mag- netism and capacity. ELECTRO— MAGNETISM. An electric current, i, flowing through a circuit, produces a magnetic flux surrounding the conductor in lines of magnetic force (or more correctly, lines of magnetic induc- tion), of closed, circular, or other form, which alternate with the alternatio ...", "... , refers to the wattless component of E.M.F., or the E.M.F. in quadrature with the current. 3. The principal sources of reactance are electro-mag- netism and capacity. ELECTRO— MAGNETISM. An electric current, i, flowing through a circuit, produces a magnetic flux surrounding the conductor in lines of magnetic force (or more correctly, lines of magnetic induc- tion), of closed, circular, or other form, which alternate with the alternations of the current, and thereby induce an E.M.F. in the conductor. Since th ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-06", "section_label": "Chapter 7: Higher Harmonics In Induction Motors", "section_title": "Higher Harmonics In Induction Motors", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 12398-13955", "status": "candidate", "occurrence_count": 29, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-06/", "snippets": [ "... * Theoretical Elements of Electrical Enginccr- ing\" and in \"Theory and Calculation of Alternating-current Phenomena,\" is based on the assumption of the sine wave. That U, it is assumed that the voltage impressed upon the motor per phase, and therefore the magnetic flux and the current, KM sine waves, and it is further assumed, that the distribution of the winding on the circumference of the armature or primary, is sinusoidal in space. While in most eases this is sufficicntly the ease, it is not always so, and espec ...", "... ical Elements of Electrical Enginccr- ing\" and in \"Theory and Calculation of Alternating-current Phenomena,\" is based on the assumption of the sine wave. That U, it is assumed that the voltage impressed upon the motor per phase, and therefore the magnetic flux and the current, KM sine waves, and it is further assumed, that the distribution of the winding on the circumference of the armature or primary, is sinusoidal in space. While in most eases this is sufficicntly the ease, it is not always so, and especially ...", "... further assumed, that the distribution of the winding on the circumference of the armature or primary, is sinusoidal in space. While in most eases this is sufficicntly the ease, it is not always so, and especially the space or air-gap distribution of the magnetic flux may sufficiently differ from sine shape, to exert an appreciable effect on the torque at lower speeds, and require consideration where motor action and braking action with considerable power is required throughout the entire range of speed. Let the ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-20", "section_label": "Chapter 22: Unipolar Machines", "section_title": "Unipolar Machines", "kind": "chapter", "sequence": 20, "number": 22, "location": "lines 31716-32137", "status": "candidate", "occurrence_count": 29, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-20/", "snippets": [ "CHAPTER XXII UNIPOLAR MACHINES Homopolar or Acyclic Machines 247.. If a conductor, C, revolves around, one pole of a stationary magnet shown as NS in Fig. 215, a continuous voltage is induced in the conductor by its cutting of the lines of magnetic force of the pole, N, and this voltage can be supplied to an external cir- cuit, D, by stationary brushes, Bi and B2) bearing on the ends of the revolving conductor, C. The voltage is: e = /$ 10-8, where / is the number of revolutions per second, $ t ...", "... rce of the pole, N, and this voltage can be supplied to an external cir- cuit, D, by stationary brushes, Bi and B2) bearing on the ends of the revolving conductor, C. The voltage is: e = /$ 10-8, where / is the number of revolutions per second, $ the magnetic flux of the magnet, cut by the conductor, C. N Fig. 215. — Diagrammatic illustration of unipolar machine with two high- speed collectors. Such a machine is called a unipolar machine, as the conductor during its rotation traverses the same polarity, ...", "... e pole, N, and this voltage can be supplied to an external cir- cuit, D, by stationary brushes, Bi and B2) bearing on the ends of the revolving conductor, C. The voltage is: e = /$ 10-8, where / is the number of revolutions per second, $ the magnetic flux of the magnet, cut by the conductor, C. N Fig. 215. — Diagrammatic illustration of unipolar machine with two high- speed collectors. Such a machine is called a unipolar machine, as the conductor during its rotation traverses the same polarity, in di ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-107", "section_label": "Apparatus Section 1: Induction Machines: General", "section_title": "Induction Machines: General", "kind": "apparatus-section", "sequence": 107, "number": 1, "location": "lines 18949-19165", "status": "candidate", "occurrence_count": 27, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-107/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-107/", "snippets": [ "... nt in a direct-current motor the direction of rotation remains the same. Thus theoretically any continuous-current motor should operate also with alternating currents. Obviously in this case not only the armature but also the magnetic field of the motor must be thoroughly laminated to exclude eddy currents, and care taken that the currents in the field and armature circuits reverse simultaneously. Obviously the simplest way of fulfilling the latter condit ...", "... tor on an alternating-current circuit has the objection that in the armature winding the current should be power current, thus in phas£ with the e.m.f., while in the field winding the current is lagging nearly 90 deg., as magnetizing current. Thus field and armature would be out of phase with each other. To overcome this objection either there is inserted in series with the field circuit a condenser of such capacity as to bring the current back into ...", "... In the latter arrangement the armature winding of the motor is fed by one, the field winding by the other phase of a quarter-phase sys- tem, and thus the current in the armature brought approximately into phase with the magnetic flux of the field. Such an arrangement obviously loads the two phases of the system unsymmetrically, the one with the armature power current, the other with the lagging field current. To balance the system two such motors ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-21", "section_label": "Chapter 23: Review", "section_title": "Review", "kind": "chapter", "sequence": 21, "number": 23, "location": "lines 32138-32819", "status": "candidate", "occurrence_count": 27, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-21/", "snippets": [ "... er Inductively Compensated Single-phase Series Motor. — 193. Single-phase commutating machine with series field and inductive compensating winding. Eickemeyer Inductor Alternator. — 160. Inductor alternator with field coils parallel to shaft, so that the magnetic flux disposi- tion is that of a bipolar or multipolar machine, in which the multitooth inductor takes the place of the armature of the stand- ard machine. Voltage induction then takes place in armature coils in the pole faces, and the magnetic flux in the ...", "... ively Compensated Single-phase Series Motor. — 193. Single-phase commutating machine with series field and inductive compensating winding. Eickemeyer Inductor Alternator. — 160. Inductor alternator with field coils parallel to shaft, so that the magnetic flux disposi- tion is that of a bipolar or multipolar machine, in which the multitooth inductor takes the place of the armature of the stand- ard machine. Voltage induction then takes place in armature coils in the pole faces, and the magnetic flux in the indu ...", "... so that the magnetic flux disposi- tion is that of a bipolar or multipolar machine, in which the multitooth inductor takes the place of the armature of the stand- ard machine. Voltage induction then takes place in armature coils in the pole faces, and the magnetic flux in the inductor re- verses, with a frequency much lower than that of the induced voltage. This type of inductor machine is specially adopted for moderately high frequencies, 300 to 2000 cycles, and used in in- ductor alternators and inductor converte ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 27, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... ties 249 rectification 249 rectifiers 222 resistivities 9 starting 249 Arcing ground on lines and cables, as periodic transient phenomenon . . 23 Armature reactance, reaction and short-circuit current of alternator 199 Attenuation of alternating magnetic flux in iron 361 constants 434 of traveling wave, and loading 462 Booster, response to change of load 158 Brush arc machine 221, 230, 242, 248 Building up of direct-current generator 32 of overcompounded direct-current machine 49 Cable, high-pot ...", "... rectification 249 rectifiers 222 resistivities 9 starting 249 Arcing ground on lines and cables, as periodic transient phenomenon . . 23 Armature reactance, reaction and short-circuit current of alternator 199 Attenuation of alternating magnetic flux in iron 361 constants 434 of traveling wave, and loading 462 Booster, response to change of load 158 Brush arc machine 221, 230, 242, 248 Building up of direct-current generator 32 of overcompounded direct-current machine 49 Cable, high-potentia ...", "... of electric field 5 shunting direct-current circuit 133 specific, numerical values 11 suppressing pulsations in direct-current circuit 134 Cast iron, effective penetration of alternating current 378 Cathode of arcs 249 Charge of condenser 51 of magnetic field 27 Circuit, complex, see Complex circuit. control by periodic transient phenomena 220, 223 electric, speed of propagation in 422 Closed circuit transmission line 306 Col al 392, 394 Commutation and rectification 222 as transient phenomenon ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-36", "section_label": "Chapter 14: Short-Circuit Currents Of Alternators", "section_title": "Short-Circuit Currents Of Alternators", "kind": "chapter", "sequence": 36, "number": 14, "location": "lines 14549-15353", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "snippets": [ "... self-inductance; that is, the current in the armature represents a m.m.f. which with lagging current, as at short circuit, is demagnetizing or opposing the impressed m.m.f. of field excitation, and by combining therewith to a resultant m.m.f. reduces the magnetic flux from that corre- sponding to the field excitation to that corresponding to the resultant of field excitation and armature reaction, and thus reduces the generated e.m.f. from the nominal generated e.m.f., eOJ to the virtual generated e.m.f., er The a ...", "... uctance; that is, the current in the armature represents a m.m.f. which with lagging current, as at short circuit, is demagnetizing or opposing the impressed m.m.f. of field excitation, and by combining therewith to a resultant m.m.f. reduces the magnetic flux from that corre- sponding to the field excitation to that corresponding to the resultant of field excitation and armature reaction, and thus reduces the generated e.m.f. from the nominal generated e.m.f., eOJ to the virtual generated e.m.f., er The armatu ...", "... field excitation to that corresponding to the resultant of field excitation and armature reaction, and thus reduces the generated e.m.f. from the nominal generated e.m.f., eOJ to the virtual generated e.m.f., er The armature current also produces a local magnetic flux in the armature iron and pole- faces which does not interlink with the field coils, but is a true self-inductive flux, and therefore is represented by a reactance xr Combined with the effective resistance, rv of the armature winding, this gives the s ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-06", "section_label": "Lecture 6: Higher Harmonics Of The Generator Wave", "section_title": "Higher Harmonics Of The Generator Wave", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3133-3507", "status": "candidate", "occurrence_count": 25, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-06/", "snippets": [ "... it currents, due to the constant potential character, and is therefore dangerous. HIGHER HARMONICS OF SYNCHRONOUS MACHINES In synchronous machines, as alternating current genera- tors, the higher harmonics are : At No Load I St. The distribution of magnetism in the air gap depends on the shape of the field poles; it is not a sine wave; neither is the e. m. f . induced by it in an armature a sine wave. Since there are a number of conductors in series on the armature, the voltage wave is more evened out than t ...", "... e. Since there are a number of conductors in series on the armature, the voltage wave is more evened out than that of a single conductor ; but still it is not a sine wave, that is, contains harmonics of which the third is the lowest. 2nd. The change of magnetic flux by the passage of open armature slots over the field pole produces harmonics of e. m. f . ; that is, when a large open armature slot stands in front of the field pole, the magnetic reluctance is high ; the magnetism is lower than when no slot is in f ...", "... e there are a number of conductors in series on the armature, the voltage wave is more evened out than that of a single conductor ; but still it is not a sine wave, that is, contains harmonics of which the third is the lowest. 2nd. The change of magnetic flux by the passage of open armature slots over the field pole produces harmonics of e. m. f . ; that is, when a large open armature slot stands in front of the field pole, the magnetic reluctance is high ; the magnetism is lower than when no slot is in front ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-04", "section_label": "Chapter 4: Vector Representation", "section_title": "Vector Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2149-2759", "status": "candidate", "occurrence_count": 25, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-04/", "snippets": [ "... ynchronous motor circuit under the circumstances stated above. 23. As a further example, we may consider the diagram of an alternating-current transformer, feeding through its secondary circuit an inductive load. For simplicity, we may neglect here the magnetic hysteresis, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the magnetic flux is zero and rising. The magnetic flux then passes its maxi- mum at the time ?? = 90°, and the pha ...", "... mer, feeding through its secondary circuit an inductive load. For simplicity, we may neglect here the magnetic hysteresis, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the magnetic flux is zero and rising. The magnetic flux then passes its maxi- mum at the time ?? = 90°, and the phase of the magnetic flux thus is ?? = 90°, the flux thus represented by the vector 0* in Fig. 18, vertically downward. The e.m.f. generated by this mag- ...", "... ng through its secondary circuit an inductive load. For simplicity, we may neglect here the magnetic hysteresis, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the magnetic flux is zero and rising. The magnetic flux then passes its maxi- mum at the time ?? = 90°, and the phase of the magnetic flux thus is ?? = 90°, the flux thus represented by the vector 0* in Fig. 18, vertically downward. The e.m.f. generated by this mag- netic ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-63", "section_label": "Apparatus Subsection 63: Direct-current Commutating Machines: C. Commutating Machines 197", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 197", "kind": "apparatus-subsection", "sequence": 63, "number": null, "location": "lines 11795-11863", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-63/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-63/", "snippets": [ "... e-turns armature reaction of the angle of shift of brushes TI requires an increase of field excitation by riFa. (Section VII.) 3. The distorting effect of armature reaction does not change the total m.m.f. producing the magnetic flux. If, however, mag- netic saturation is reached or approached in a part of the mag- netic circuit adjoining the air gap, the increase of magnetic density at the strengthened pole corner is less than the decrease at ...", "... rmature reaction of the angle of shift of brushes TI requires an increase of field excitation by riFa. (Section VII.) 3. The distorting effect of armature reaction does not change the total m.m.f. producing the magnetic flux. If, however, mag- netic saturation is reached or approached in a part of the mag- netic circuit adjoining the air gap, the increase of magnetic density at the strengthened pole corner is less than the decrease at the w ...", "... ct of armature reaction does not change the total m.m.f. producing the magnetic flux. If, however, mag- netic saturation is reached or approached in a part of the mag- netic circuit adjoining the air gap, the increase of magnetic density at the strengthened pole corner is less than the decrease at the weakened pole corner, and thus the total magnetic flux with the same total m.m.f. is reduced, and to produce the same total magnetic flux an increa ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-18", "section_label": "Chapter 18: Polyphase Induction Motors", "section_title": "Polyphase Induction Motors", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17717-20445", "status": "candidate", "occurrence_count": 23, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-18/", "snippets": [ "CHAPTER XVIII POLYPHASE INDUCTION MOTORS 155. The induction motor consists of a magnetic circuit inter- linked with two electric circuits or sets of circuits, the primary and the secondary. It therefore is electromagnetically the same structure as the transformer. The difference is, that in the transformer secondary and primary are stationary ...", "... e two limiting cases. In the induction motor, only the mechanical force be- tween primary and secondary is used, but not the transfer of electrical energy, and thus the secondary circuits are closed upon themselves. Hence the induction motor consists of a magnetic circuit interlinked with two electric circuits or sets of circuits, the primary and the secondary circuit, which are movable with regard to each other. In general a number of primary and a number of secondary circuits are used, angularly displaced around ...", "... , as secondary quantities, the values reduced to the primary system shall be exclusively used, so that, to derive the true secondary values, these quan- tities have to be reduced backward again by the factor a^b ni^pi 157. Let \"J> = total maximum flux of the magnetic field per motor pole. We then have E = \\/2 TT/io/ ^ 10~^ = effective e.m.f. generated by the magnetic field per primary circuit. Counting the time from the moment where the rising mag- netic flux of mutual induction, (flux interlink ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-03", "section_label": "Theory Section 3: Generation of E.m.f.", "section_title": "Generation of E.m.f.", "kind": "theory-section", "sequence": 3, "number": 3, "location": "lines 1033-1243", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-03/", "snippets": [ "i 3. GENERATION OF E.M.F. 15. A closed conductor, convolution or turn, revolving in a magnetic field, passes during each revolution through two positions of maximum inclosure of lines of magnetic force A in Fig. 5, and two positions of zero inclosure of lines of mag- netic force B in Fig. 5. 1 cm.3 refers to a ...", "i 3. GENERATION OF E.M.F. 15. A closed conductor, convolution or turn, revolving in a magnetic field, passes during each revolution through two positions of maximum inclosure of lines of magnetic force A in Fig. 5, and two positions of zero inclosure of lines of mag- netic force B in Fig. 5. 1 cm.3 refers to a cube whose side is 1 cm., and should not be confused with cu. cm. 12 ELEMENTS OF ELECTRICAL ...", "... . is, E = 4 fn$ absolute units, = 4fn3> ID\"8 volts. FIG. 5. — Generation of e.m.f. If / is given in hundreds of cycles, <£ in megalines, E = 4n$ volts. If a coil revolves with uniform velocity through a uniform magnetic field, the magnetism inclosed by the coil at any instant is, $ COS T where $ = the maximum magnetism inclosed by the coil arid T = angle between coil and its position of maximum inclosure of magnetism. The e.m.f. ge ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-26", "section_label": "Chapter 26: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 32540-33010", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-26/", "snippets": [ "... e current are increased. In consequence hereof alterna- tors and synchronous motors of iron-clad unitooth construction — that is, machines giving waves with pronounced higher harmonics — may give with the same number of turns on the armature, and the same magnetic flux per field-pole at the same frequency, a higher output than machines built to produce sine waves. 255. This explains an apparent paradox: If in the three-phase star-connected generator with the mag- netic field constructed as shown diagrammatically ...", "... are increased. In consequence hereof alterna- tors and synchronous motors of iron-clad unitooth construction — that is, machines giving waves with pronounced higher harmonics — may give with the same number of turns on the armature, and the same magnetic flux per field-pole at the same frequency, a higher output than machines built to produce sine waves. 255. This explains an apparent paradox: If in the three-phase star-connected generator with the mag- netic field constructed as shown diagrammatically in F ...", "... le at the same frequency, a higher output than machines built to produce sine waves. 255. This explains an apparent paradox: If in the three-phase star-connected generator with the mag- netic field constructed as shown diagrammatically in Fig. 188 the magnetic flux per pole = 4>, the number of turns in series per circuit = n, the frequency = /, the e.m.f. between any two collector rings is E = \\/2Trf2n^ 10-^ . since 2 n armature turns simultaneously interlink with the magnetic flux, . The e.m.f. per arm ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-22", "section_label": "Chapter 20: Ri", "section_title": "Ri", "kind": "chapter", "sequence": 22, "number": 20, "location": "lines 24560-25119", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "snippets": [ "... ent, are increased. In consequence hereof alternators and synchronous motors of ironclad unitooth construction — that is, machines giving waves with pronounced higher harmonics — give with the same number of turns on the armature, and the same mag- netic flux per field pole at the same frequency, a higher output than machines built to produce sine waves. 227. This explains an apparent paradox : If in the three-phase star-connected generator with the magnetic field constructed as shown diagrammatically in Fi ...", "... ber of turns on the armature, and the same mag- netic flux per field pole at the same frequency, a higher output than machines built to produce sine waves. 227. This explains an apparent paradox : If in the three-phase star-connected generator with the magnetic field constructed as shown diagrammatically in Fig. 162, the magnetic flux per pole = J/, the number of turns in series per circuit = ;/, the frequency = N^ the E.M.F. between any two collector rings is: since 2;/ armature turns simultaneously interlink ...", "... ole at the same frequency, a higher output than machines built to produce sine waves. 227. This explains an apparent paradox : If in the three-phase star-connected generator with the magnetic field constructed as shown diagrammatically in Fig. 162, the magnetic flux per pole = J/, the number of turns in series per circuit = ;/, the frequency = N^ the E.M.F. between any two collector rings is: since 2;/ armature turns simultaneously interlink with the magnetic flux O. The E.M.F. per armature circuit is : e = ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-23", "section_label": "Chapter 23: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 21983-22448", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "snippets": [ "... ent, are increased. In consequence hereof alternators and synchronous motors of ironclad unitooth construction — that is, machines giving waves with pronounced higher harmonics — give with the same number of turns on the armature, and the same mag- netic flux per field pole at the same frequency, a higher output than machines built to produce sine waves. 248. This explains an apparent paradox : If in the three-phase star-connected generator with the magnetic field constructed as shown diagrammatically in Fi ...", "... ber of turns on the armature, and the same mag- netic flux per field pole at the same frequency, a higher output than machines built to produce sine waves. 248. This explains an apparent paradox : If in the three-phase star-connected generator with the magnetic field constructed as shown diagrammatically in Fig. 162, the magnetic flux per pole = $, the number of turns in series per circuit = n, the frequency = N, the E.M.F. between any two collector rings is: E= V2~7T^2;z10-8. since 2« armature turns simul ...", "... ole at the same frequency, a higher output than machines built to produce sine waves. 248. This explains an apparent paradox : If in the three-phase star-connected generator with the magnetic field constructed as shown diagrammatically in Fig. 162, the magnetic flux per pole = $, the number of turns in series per circuit = n, the frequency = N, the E.M.F. between any two collector rings is: E= V2~7T^2;z10-8. since 2« armature turns simultaneously interlink with the magnetic flux 3>. The E.M.F. per armatu ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... ctric circuit, as a change of load; or, disturbances entering the circuit from the outside or originating in it, etc. Periodic phenomena are the alternating currents and voltages, pulsating currents as those produced by rectifiers, the distribution of the magnetic flux in the air-gap of a machine, or the distribution of voltage around the commutator of the direct-current machine, the motion of the piston in the steam-engine cylinder, the variation of the. mean daily temperature with the seasons of the year, etc. ...", "... cuit, as a change of load; or, disturbances entering the circuit from the outside or originating in it, etc. Periodic phenomena are the alternating currents and voltages, pulsating currents as those produced by rectifiers, the distribution of the magnetic flux in the air-gap of a machine, or the distribution of voltage around the commutator of the direct-current machine, the motion of the piston in the steam-engine cylinder, the variation of the. mean daily temperature with the seasons of the year, etc. The c ...", "... It therefore is of importance in engineering to translate thejicite or the table \"^ of numerical values of a periodic function into a mathematical expression thereof. • ' , (B) If one of the engineering quantities, as the e.m.f. of an alternator or the magnetic flux in the air-gap of an electric machine, is given as a general periodic function in the form of a trigonometric series, to determine therefrom other engineer- ing quantities, as the current, the generated e.m.f., etc. A. Evaluation of the Constants of ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-09", "section_label": "Lecture 9: Measurement Of Light And Radiation", "section_title": "Measurement Of Light And Radiation", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 8511-9388", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-09/", "snippets": [ "... nometer, can be secured by using gray print on white back- ground, and lights of different colors thereby compared over a wide range of illuminations. With a luminometer chart of gray letters, of albedo a, on white background, the illumination or light flux density, at which the luminometer readings are made as described above, is: where i0 is the illumination or light flux density when using black print on white background. 81. Since light is a physiological effect, the measurement of this effect requi ...", "... a wide range of illuminations. With a luminometer chart of gray letters, of albedo a, on white background, the illumination or light flux density, at which the luminometer readings are made as described above, is: where i0 is the illumination or light flux density when using black print on white background. 81. Since light is a physiological effect, the measurement of this effect requires a physiological unit, which is more or less arbi- trarily chosen. Such a unit may be a unit of light, that is, of ligh ...", "... black print on white background. 81. Since light is a physiological effect, the measurement of this effect requires a physiological unit, which is more or less arbi- trarily chosen. Such a unit may be a unit of light, that is, of light intensity or light flux, as a flame, or it may be a unit of light-flux density or illumination, that is, of light flux per unit area. Thus, a fairly rational unit of light-flux density or illumination would be the illumination required at the limits of distinguish- ability of ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-15", "section_label": "Chapter 15: Induction Motob", "section_title": "Induction Motob", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 14919-17024", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "snippets": [ "... ussion, as secondary quantities ex- clusively, the values reduced to the primary system shall be used, so that, to derive the true secondary values, these quantities have* to be reduced backwards again by the factor np «iA 142. Let * = total maximum flux of the magnetic field per motor pole. It is then E = V2ir«iV*10\"® = effective E.M.F. induced by the mag- netic field per primary circuit. Counting the time from the moment where the rising magnetic flux of mutual induction * (flux interlinked with bo ...", "... econdary quantities ex- clusively, the values reduced to the primary system shall be used, so that, to derive the true secondary values, these quantities have* to be reduced backwards again by the factor np «iA 142. Let * = total maximum flux of the magnetic field per motor pole. It is then E = V2ir«iV*10\"® = effective E.M.F. induced by the mag- netic field per primary circuit. Counting the time from the moment where the rising magnetic flux of mutual induction * (flux interlinked with both electric circ ...", "... in by the factor np «iA 142. Let * = total maximum flux of the magnetic field per motor pole. It is then E = V2ir«iV*10\"® = effective E.M.F. induced by the mag- netic field per primary circuit. Counting the time from the moment where the rising magnetic flux of mutual induction * (flux interlinked with both electric circuits, primary and secondary) passes through zero, in complex quantities, the magnetic flux is denoted by and the primary induced E.M.F., j5 = — ^; where e = V2 TTfiN^ 10~* may be co ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-05", "section_label": "Chapter 6: Empirical Curves", "section_title": "Empirical Curves", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 16483-21988", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-05/", "snippets": [ "... ues can be taken from the plotted curve, no general conclusions can be derived from it, no general investigations based on it regarding the conditions of efficiency, output, etc. An illustration hereof is afforded by the comparison of the electric and the magnetic circuit. In the electric circuit, the relation between e.m.f. and e current is given by Ohm's law, i = -, and calculations are uni- versally and easily made. In the magnetic circuit, however, the term corresponding to the resistance, the reluctance, is ...", "... c. An illustration hereof is afforded by the comparison of the electric and the magnetic circuit. In the electric circuit, the relation between e.m.f. and e current is given by Ohm's law, i = -, and calculations are uni- versally and easily made. In the magnetic circuit, however, the term corresponding to the resistance, the reluctance, is not a constant, and the relation between m.m.f. and magnetic flux cannot be expressed by a general law, but only by an empirical curve, the magnetic characteristic, and as the ...", "... nd the magnetic circuit. In the electric circuit, the relation between e.m.f. and e current is given by Ohm's law, i = -, and calculations are uni- versally and easily made. In the magnetic circuit, however, the term corresponding to the resistance, the reluctance, is not a constant, and the relation between m.m.f. and magnetic flux cannot be expressed by a general law, but only by an empirical curve, the magnetic characteristic, and as the result, calcula- tions of magnetic circuits cannot be made as conveniently ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-02", "section_label": "Lecture 2: Conclusions From The Relativity Theory", "section_title": "Conclusions From The Relativity Theory", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 736-2388", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... pose we have a permanent bar magnet M (Fig. 2) and bring a piece of iron / near it. It is attracted, or moved; that is, a force is exerted on it. We bring a piece of copper near the magnet, and nothing happens. We say the space surrounding the magnet is a magnetic field. A field, or field of force, we define as \"a condition in space exerting a force on a body susceptible to this field.\" Thus, a piece of iron being magnetizable — that is, susceptible to a magnetic field^ — ^will be acted upon; a piece of copper, not ...", "... appens. We say the space surrounding the magnet is a magnetic field. A field, or field of force, we define as \"a condition in space exerting a force on a body susceptible to this field.\" Thus, a piece of iron being magnetizable — that is, susceptible to a magnetic field^ — ^will be acted upon; a piece of copper, not being magnetizable, shows no action. A field is completely defined and characterized at any point by its intensity and its direction, and in Faraday's pictorial representation of the field by the lines ...", "... quires energy, and this energy is stored in the space we call the field. Thus we can go further and define the field as ''a condition of energy storage in space exerting a force on a body susceptible to this energy.'' The space surrounding a magnet is a magnetic field. If we electrify a piece of sealing wax by rubbing it, it surrounds itself by a dielectric or electrostatic field, and bodies susceptible to electrostatic forces- — such as light pieces of paper — are attracted. The earth is surrounded by a gravita ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-108", "section_label": "Apparatus Section 2: Induction Machines: Polyphase Induction Motor", "section_title": "Induction Machines: Polyphase Induction Motor", "kind": "apparatus-section", "sequence": 108, "number": 2, "location": "lines 19166-20427", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-108/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-108/", "snippets": [ "II. Polyphase Induction Motor 1. INTRODUCTION 135. The typical induction motor is the polyphase motor. By gradual development from the direct-current shunt motor we arrive at the polyphase induction motor. The magnetic field of any induction motor, whether supplied by polyphase, monocyclic, or single-phase e.m.f., is at normal condition of operation, that is, near synchronism, a polyphase field. Thus to a certain extent all induction motors ...", "... fs. the internal reactions of the induction motor are simplest and only those of a transformer with moving second- ary, while in the single-phase induction motor at the same time a phase transformation occurs, the second or magnetizing phase being produced from the impressed phase of e.m.f. by the rota- tion of the motor, which carries the secondary currents into quadrature position with the primary current. INDUCTION MACHINES 311 The polyphase induction ...", "... from the typical polyphase machine. 2. CALCULATION 136. In the polyphase induction motor, Let Y = g — jb = primary exciting admittance, or admit- tance of the primary circuit with open secondary circuit; that is, ge = magnetic power current, be = wattless magnetizing current, where e = counter-generated e.m.f. of the motor; ZQ = r0 + jxQ = primary self -inductive impedance, and Zi = 7*1 + jxi = secondary self-inductive impedance, reduced t ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-79", "section_label": "Apparatus Subsection 79: Direct-current Commutating Machines: C. Commutating Machines 219", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 219", "kind": "apparatus-subsection", "sequence": 79, "number": null, "location": "lines 13019-13119", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-79/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-79/", "snippets": [ "D. C. COMMUTATING MACHINES 219 In the alternating-current commutator motor, the field struc- ture as well as the armature must be laminated, since the mag- netic flux is alternating. The alternation of the field flux induces an e.m.f. of self induction in the field winding. In the shunt motor, this causes the field exciting current and with it the magnetic field flux to lag and there ...", "D. C. COMMUTATING MACHINES 219 In the alternating-current commutator motor, the field struc- ture as well as the armature must be laminated, since the mag- netic flux is alternating. The alternation of the field flux induces an e.m.f. of self induction in the field winding. In the shunt motor, this causes the field exciting current and with it the magnetic field flux to lag and thereby to be out of phase with the armature current w ...", "... laminated, since the mag- netic flux is alternating. The alternation of the field flux induces an e.m.f. of self induction in the field winding. In the shunt motor, this causes the field exciting current and with it the magnetic field flux to lag and thereby to be out of phase with the armature current which, to represent work, must essentially be an energy current, and thereby reduces output and efficiency and hence requires some method of compe ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-46", "section_label": "Apparatus Section 3: Direct-current Commutating Machines: Generated E.m.fs.", "section_title": "Direct-current Commutating Machines: Generated E.m.fs.", "kind": "apparatus-section", "sequence": 46, "number": 3, "location": "lines 10778-10835", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-46/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-46/", "snippets": [ "... rect- current machine, as discussed in the preceding, is e = where e = generated e.m.f., / = frequency = number of pairs of poles X hundreds of rev. per sec., n = number of turns in series between brushes, and <£ = magnetic flux passing through the armature per pole, in megalines. In ring-wound machines, is one-half the flux per field pole, since the flux divides in the armature into two circuits, and each 178 ELEMENTS OF ELECTRICAL ...", "... rent machine, as discussed in the preceding, is e = where e = generated e.m.f., / = frequency = number of pairs of poles X hundreds of rev. per sec., n = number of turns in series between brushes, and <£ = magnetic flux passing through the armature per pole, in megalines. In ring-wound machines, is one-half the flux per field pole, since the flux divides in the armature into two circuits, and each 178 ELEMENTS OF ELECTRICAL ENGIN ...", "... mber of pairs of poles X hundreds of rev. per sec., n = number of turns in series between brushes, and <£ = magnetic flux passing through the armature per pole, in megalines. In ring-wound machines, is one-half the flux per field pole, since the flux divides in the armature into two circuits, and each 178 ELEMENTS OF ELECTRICAL ENGINEERING armature turn incloses only half the flux per field pole. In ring- wound armatures, however, ea ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-02", "section_label": "Theory Section 2: Magnetism and E.m.f.", "section_title": "Magnetism and E.m.f.", "kind": "theory-section", "sequence": 2, "number": 2, "location": "lines 910-1032", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-02/", "snippets": [ "2. MAGNETISM AND E.M.F. 11. In an electric conductor moving relatively to a magnetic field, an e.m.f. is generated proportional to the rate of cutting of the lines of magnetic force by the conductor. Unit e.m.f. is the e.m.f. genera ...", "2. MAGNETISM AND E.M.F. 11. In an electric conductor moving relatively to a magnetic field, an e.m.f. is generated proportional to the rate of cutting of the lines of magnetic force by the conductor. Unit e.m.f. is the e.m.f. generated in a conductor cutting one line of magnetic force per second. 108 t ...", "2. MAGNETISM AND E.M.F. 11. In an electric conductor moving relatively to a magnetic field, an e.m.f. is generated proportional to the rate of cutting of the lines of magnetic force by the conductor. Unit e.m.f. is the e.m.f. generated in a conductor cutting one line of magnetic force per second. 108 times unit e.m.f. is the practical unit, called the volt. Coiling the conductor n fold increa ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-13", "section_label": "Theory Section 13: Alternating-current Transformer", "section_title": "Alternating-current Transformer", "kind": "theory-section", "sequence": 13, "number": 13, "location": "lines 4465-5263", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-13/", "snippets": [ "... . Let TI = resistance, x\\ = 2TrfSz = self-inductive or leakage reactance of secondary circuit, r0 = resistance, XQ = 2irfSi = self -inductive or leakage reactance of primary circuit, where S2 and Si refer to that magnetic flux which is interlinked with the one but not with the other circuit. Let a ratio of — — • — - turns (ratio of transformation), primary An alternating e.m.f. E0 impressed upon the primary electric circuit causes a ...", "... I = resistance, x\\ = 2TrfSz = self-inductive or leakage reactance of secondary circuit, r0 = resistance, XQ = 2irfSi = self -inductive or leakage reactance of primary circuit, where S2 and Si refer to that magnetic flux which is interlinked with the one but not with the other circuit. Let a ratio of — — • — - turns (ratio of transformation), primary An alternating e.m.f. E0 impressed upon the primary electric circuit causes a curre ...", "... with the one but not with the other circuit. Let a ratio of — — • — - turns (ratio of transformation), primary An alternating e.m.f. E0 impressed upon the primary electric circuit causes a current, which produces a magnetic flux $ inter- linked with primary and secondary circuits. This flux gener- ates e.m.fs. EI and E{ in secondary and in primary circuit, which Tjl are to each other as the ratio of turns, thus Ei = — - Let E = sec ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-38", "section_label": "Apparatus Section 17: Synchronous Machines: Short-circuit Currents of Alternators", "section_title": "Synchronous Machines: Short-circuit Currents of Alternators", "kind": "apparatus-section", "sequence": 38, "number": 17, "location": "lines 10190-10429", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-38/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-38/", "snippets": [ "... nt is limited only by the arma- ture self-inductance, and not by the armature reaction, and some appreciable time — occasionally several seconds — elapses before the armature reaction becomes effective. At short circuit, the magnetic field flux is greatly reduced by the demagnetizing action of the armature current, and the gen- SYNCHRONOUS MACHINES 161 erated e.m.f. thereby reduced from the nominal value EQ to the virtual value Ez; the latter is con ...", "... only by the arma- ture self-inductance, and not by the armature reaction, and some appreciable time — occasionally several seconds — elapses before the armature reaction becomes effective. At short circuit, the magnetic field flux is greatly reduced by the demagnetizing action of the armature current, and the gen- SYNCHRONOUS MACHINES 161 erated e.m.f. thereby reduced from the nominal value EQ to the virtual value Ez; the latter is consumed by th ...", "... to the virtual value Ez; the latter is consumed by the armature self- inductive impedance z, or self-inductive reactance, which is practically the same in most cases. The armature self-inductance is instantaneous, since the magnetic field rises simultaneously with the armature current which produces it; armature reaction, however, requires an appre- ciable time to reduce the magnetic flux from the open-circuit value to the much lower short-circuit value, ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-57", "section_label": "Apparatus Subsection 57: Direct-current Commutating Machines: C. Commutating Machines", "section_title": "Direct-current Commutating Machines: C. Commutating Machines", "kind": "apparatus-subsection", "sequence": 57, "number": null, "location": "lines 11401-11540", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-57/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-57/", "snippets": [ "... ine, n — number of armature slots per pair of poles, /i = nf. For instance,/ = 33.3, n = 51, thus/i = 1700. Under the assumption, width of slots equals width of teeth = 2 X width of air gap, the dis- tribution of magnetic flux at the pole face is plotted in Fig. 103. The drop of density opposite each slot consists of two curved branches equal to those in Fig. 92, that is, calculated by •B' -3 n FIG. 103.— I < « i slots on ...", "... number of armature slots per pair of poles, /i = nf. For instance,/ = 33.3, n = 51, thus/i = 1700. Under the assumption, width of slots equals width of teeth = 2 X width of air gap, the dis- tribution of magnetic flux at the pole face is plotted in Fig. 103. The drop of density opposite each slot consists of two curved branches equal to those in Fig. 92, that is, calculated by •B' -3 n FIG. 103.— I < « i slots on flu ...", "... op of density opposite each slot consists of two curved branches equal to those in Fig. 92, that is, calculated by •B' -3 n FIG. 103.— I < « i slots on flu Iffect of B distribution. V + 1*2 The average flux is 7525; that is, by cutting half the armature surface away by slots of a width equal to twice the length of air gap, the total flux under the field pole is reduced only in the proportion 8000 to 7525, or about 6 pe ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-appendix-01-synchronous-operation", "section_label": "Mathematical Appendix 5: Appendix: Synchronous Operation", "section_title": "Appendix: Synchronous Operation", "kind": "mathematical-appendix", "sequence": 5, "number": 5, "location": "PDF pages 27-68, lines 2165-5013", "status": "pdf-text-extracted-candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "snippets": [ "... That is, the one alternator has the voltage phase ( to), the other the voltage phase (0+w). We may assume the alternators as of equal voltage, since a voltage difference superposes on the synchronizing energy current due to the phase difference, a reactive magnetizing current due to the voltage difference without materially changing the energy relations. The EMFs of the two alternators then may be represented by: ei = E cos (0 co) 1 e2 = Ecos (0+co) / (1) and the resultant voltage in the circuit between the alternators the ...", "... other in frequency by 2s, that is, one alternator has the frequency (1 s) f, the other the frequency (1+s) f. We may again assume the alternators as of equal voltage, since a voltage difference merely superposes on the synchronizing energy current a reactive'magnetizing current, without materially changing the energy relations. The EMFs of the two alternators then may be represented by: CI=E cos (i s)j< \\ e 2 = E cos (1+s) J (9) The resultant voltage in'the circuit between the two alternators then is : e = ei e 2 = E'9 ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-53", "section_label": "Apparatus Subsection 53: Direct-current Commutating Machines: C. Commutating Machines 185", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 185", "kind": "apparatus-subsection", "sequence": 53, "number": null, "location": "lines 11132-11213", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-53/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-53/", "snippets": [ "D. C. COMMUTATING MACHINES 185 tion produces a magnetic field at the brushes. The e.m.f. gener- ated by the rotation of the armature through this field opposes the reversal of the current in the short-circuited armature coil under the brush, and thus impairs commutation. If ther ...", "... machine does not commutate satisfactorily under load, with the brushes midway between the field poles, and the brushes have to be shifted to the edge of the next field poles, as shown in Fig. 95, until the fringe of the magnetic flux of the field poles reverses the armature reac- tion and so generates an e.m.f. in the armature coil, which re- verses the current and thus acts as commutating flux. The commutating e.m.f. and therefore the commutating ...", "... oes not commutate satisfactorily under load, with the brushes midway between the field poles, and the brushes have to be shifted to the edge of the next field poles, as shown in Fig. 95, until the fringe of the magnetic flux of the field poles reverses the armature reac- tion and so generates an e.m.f. in the armature coil, which re- verses the current and thus acts as commutating flux. The commutating e.m.f. and therefore the commutating flux ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-35", "section_label": "Chapter 35: Balanced Symmetrical Polyphase Systems", "section_title": "Balanced Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 35, "number": 35, "location": "lines 37453-37957", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-35/", "snippets": [ "... f the polyphase system, in the resolution of the polyphase system into its constituent single-phase systems the effective value of the constant has to be used, which corresponds to the resultant effect. This, for instance, is the case in calcu- lating the magnetic field of the induction machine — which is energized by the combination of all phases — or the armature reaction of synchronous machines, etc. For instance, in the induction machine, from the generated e.m.f., e — in Chapter XVIII — the magnetic flux of t ...", "... ating the magnetic field of the induction machine — which is energized by the combination of all phases — or the armature reaction of synchronous machines, etc. For instance, in the induction machine, from the generated e.m.f., e — in Chapter XVIII — the magnetic flux of the machine is calculated, and from the magnetic flux and the dimensions of the magnetic circuit: length and section of air-gap, and length and section of the iron part, follows the ampere-turns excitation, that is, the ampere turns, Fo, required ...", "... magnetic field of the induction machine — which is energized by the combination of all phases — or the armature reaction of synchronous machines, etc. For instance, in the induction machine, from the generated e.m.f., e — in Chapter XVIII — the magnetic flux of the machine is calculated, and from the magnetic flux and the dimensions of the magnetic circuit: length and section of air-gap, and length and section of the iron part, follows the ampere-turns excitation, that is, the ampere turns, Fo, required to pr ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-12", "section_label": "Chapter 14: Phase Conversion And Single-Phase Generation", "section_title": "Phase Conversion And Single-Phase Generation", "kind": "chapter", "sequence": 12, "number": 14, "location": "lines 17125-18412", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-12/", "snippets": [ "... , or inductance, or momentum or a combination thereof: Energy storage by capacity, that is, in the dielectric fu Id, required per kilovolt-ampere at 60 cycles about 200O <-.•■. ol space, at a cost of about $10. Inductance, that is. energy storage by the magnetic field, requires about 1000 c.e. per kilo- volt-ampere at 60 cycles, at a cost of $1, while energy storage by momentum, as kinetic mechanical energy, assuming iron moving at 30 meter-seconds, stores 1 kva. at 60 cycles by about 3 c.c., at a cost of 0.2c, t ...", "... the mass of the mechanical structure (motor, etc.) is revolving, and that the energy storage takes place by a pulsation of speed of per cent., then 1 kva. at 60 cycles would require 600 c.e. of terial, at 40c, Obviously, at the limits of dielectric or magnetic field strength, or at the limits of mechanical speeds, very much larger amounts of energy per bulk could be stored. Thus for instance, at the limits of steam-turbine rotor speeds, about 400 meter-seconds, in a very heavy material as tungsten, 1 e.c. of ma ...", "... the voltage, eo, becomes a constant-current circuit, and this case is more fully discussed in Chapter XIV of \"Theory and Calculation of Electric Circuits \" as a constant-potential constant-current transforming device. Induction Phase Converter 130. The magnetic field of a single-phase induction motor at or near synchronism is a uniform rotating field, or nearly so, deviating from uniform intensity and uniform rotation only by the impedance drop of the primary winding. Thus, in any coil displaced in position from ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-09", "section_label": "Chapter 9: Wave Screens. Even Harmonics", "section_title": "Wave Screens. Even Harmonics", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 16964-17631", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-09/", "snippets": [ "... s to an appreciable extent. Such resonant wave screen, however, has the serious disadvan- tage to require very high constancy of /, since the resonance condi- tion between C» and Ln depends on the square of /, 79. Even harmonics are produced in a closed magnetic circuit by the superposition of a continuous current upon the alternating wave. With an alternating sine wave impressed upon an iron magnetic circuit, saturation, or in general the lack of proportional- 158 ELECTRIC CIRCUITS ity between magnetic f ...", "... resonance condi- tion between C» and Ln depends on the square of /, 79. Even harmonics are produced in a closed magnetic circuit by the superposition of a continuous current upon the alternating wave. With an alternating sine wave impressed upon an iron magnetic circuit, saturation, or in general the lack of proportional- 158 ELECTRIC CIRCUITS ity between magnetic flux and m.m.f., produces a, wave-shape dis- tortion, that is, higher harmonics, of voltage with a sine wave of current, of current with a sine ...", "... d magnetic circuit by the superposition of a continuous current upon the alternating wave. With an alternating sine wave impressed upon an iron magnetic circuit, saturation, or in general the lack of proportional- 158 ELECTRIC CIRCUITS ity between magnetic flux and m.m.f., produces a, wave-shape dis- tortion, that is, higher harmonics, of voltage with a sine wave of current, of current with a sine wave of impressed voltage. The constant term of a wave, however, is the first even harmonic, and thus, if the i ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-48", "section_label": "Chapter 8: Velocity Of Propagation Of Electric Field", "section_title": "Velocity Of Propagation Of Electric Field", "kind": "chapter", "sequence": 48, "number": 8, "location": "lines 26095-27002", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "snippets": [ "... turn conductor, that is, a conductor without return conductor, equation (6) gives L = oo ; that is, a finite length of an infinitely long conductor without return conductor has an infinite inductance L and inversely, zero capacity C. In equation (6) the magnetic field is assumed as instantaneous, that is, the velocity of propagation of the magnetic field is neglected. With alternating currents traversing the conductor this is permissible when the distance to the return conductor is a negligible fraction of the wa ...", "... ; that is, a finite length of an infinitely long conductor without return conductor has an infinite inductance L and inversely, zero capacity C. In equation (6) the magnetic field is assumed as instantaneous, that is, the velocity of propagation of the magnetic field is neglected. With alternating currents traversing the conductor this is permissible when the distance to the return conductor is a negligible fraction of the wave length; that is, if Z' is § negligible compared with -, where S = the speed of lig ...", "... in the space, as trees, mountains, etc., which may act as inductive returns. Since a vertical conductor is limited in length, very high fre- quencies are required, and therefore the wave is of moderate length, that is, the velocity of propagation of the magnetic (and electrostatic) field must be considered when investigating the self-induction and the mutual induction of such a conductor. The magnetic field at a distance I from the conductor and at time t corresponds to the current in the conductor at the time ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-104", "section_label": "Apparatus Section 7: Alternating-current Transformer: Types of Transformers", "section_title": "Alternating-current Transformer: Types of Transformers", "kind": "apparatus-section", "sequence": 104, "number": 7, "location": "lines 18521-18665", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-104/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-104/", "snippets": [ "VH. Types of Transformers 123. As the transformer consists of a magnetic circuit inter- linked with two electric circuits, two constructive arrangements are possible : The electric circuits may be inside, and surrounded by the magnetic circuit as shell, shell-type transformer; or the magnetic circuit ...", "... H. Types of Transformers 123. As the transformer consists of a magnetic circuit inter- linked with two electric circuits, two constructive arrangements are possible : The electric circuits may be inside, and surrounded by the magnetic circuit as shell, shell-type transformer; or the magnetic circuit may be arranged inside, as core, and sur- rounded by the electric circuits, core-type transformer. In their simplest form, Fig. 163 shows diagrammatically the ...", "... of a magnetic circuit inter- linked with two electric circuits, two constructive arrangements are possible : The electric circuits may be inside, and surrounded by the magnetic circuit as shell, shell-type transformer; or the magnetic circuit may be arranged inside, as core, and sur- rounded by the electric circuits, core-type transformer. In their simplest form, Fig. 163 shows diagrammatically the core-type transformer, with the iron Fe as inside circular ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-18", "section_label": "Theory Section 18: Equivalent Sine Waves", "section_title": "Equivalent Sine Waves", "kind": "theory-section", "sequence": 18, "number": 18, "location": "lines 7381-7736", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-18/", "snippets": [ "... c co\" co\"co\"co'Nco>i-r ^^^ooooooo 1— «O ..» 00 00^2 ^ ^ ^ se ^ oo oo . < r-l CO ?CI> i-H QJ CO EQUIVALENT SINE WAVES 109 Fig. 41 and Table I, the number of primary turns is 500, the length of the magnetic circuit 50 cm., and its section shall be chosen so as to give a maximum density B = 15,000. At this density the hysteretic cycle is as shown in Fig. 42 and Table II. FIG. 41. — Wave-shape of e.m.f. in example 88. ...", "... B = 15,000. At this density the hysteretic cycle is as shown in Fig. 42 and Table II. FIG. 41. — Wave-shape of e.m.f. in example 88. What is the shape of current wave, and what the equivalent sine waves of e.m.f., magnetism, and current? The calculation is carried out in attached table. TABLE II / B 0 ±8 ,000 2 + 10,400 - 2,500 4 + 11,700 + 5,800 6 + 12,400 + 9,300 8 + 13,000 + 11,200 10 + 13 ...", "... ENTS OF ELECTRICAL ENGINEERING Since the effective value of impressed e.m.f. is = 1000, the 1 000 instantaneous values are eQ = e^-^ as given in column (4). Since the e.m.f. e0 is proportional to the rate of change of magnetic flux, that is, to the differential coefficient of B} B is proportional to the integral of the e.m.f., that is, to Se0 plus an integration constant. 2e0 is given in column (5), and the integration constant follows from th ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-23", "section_label": "Apparatus Section 2: Synchronous Machines: Electromotive Forces", "section_title": "Synchronous Machines: Electromotive Forces", "kind": "apparatus-section", "sequence": 23, "number": 2, "location": "lines 8658-8740", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-23/", "snippets": [ "... sh between terminal voltage E, real generated e.m.f. #1, virtual generated e.m.f. EZ, and nominal generated e.m.f. EQ. The real generated e.m.f. EI is the e.m.f. generated in the alter- nator armature turns by the resultant magnetic flux, or mag- netic flux interlinked with them, that is, by the magnetic flux passing through the armature core. It is equal to the terminal voltage plus the e.m.f. consumed by the resistance of the arma- ture, these two ...", "... n terminal voltage E, real generated e.m.f. #1, virtual generated e.m.f. EZ, and nominal generated e.m.f. EQ. The real generated e.m.f. EI is the e.m.f. generated in the alter- nator armature turns by the resultant magnetic flux, or mag- netic flux interlinked with them, that is, by the magnetic flux passing through the armature core. It is equal to the terminal voltage plus the e.m.f. consumed by the resistance of the arma- ture, these two e.m.fs ...", "... , real generated e.m.f. #1, virtual generated e.m.f. EZ, and nominal generated e.m.f. EQ. The real generated e.m.f. EI is the e.m.f. generated in the alter- nator armature turns by the resultant magnetic flux, or mag- netic flux interlinked with them, that is, by the magnetic flux passing through the armature core. It is equal to the terminal voltage plus the e.m.f. consumed by the resistance of the arma- ture, these two e.m.fs. being taken in th ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-54", "section_label": "Apparatus Subsection 54: Direct-current Commutating Machines: C. Commutating Machines 187", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 187", "kind": "apparatus-subsection", "sequence": 54, "number": null, "location": "lines 11214-11300", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-54/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-54/", "snippets": [ "... e-turns as resultant com- mutating m.m.f . at full load, half as much at half load, etc. The resultant m.m.f. of the main field FQ, the armature Fa, and the commutating pole Ff is represented in Fig. 100 by Fz, and the flux produced by it is shown in Fig. 101. As seen, with the com- mutator brushes midway between the field poles, that is, in the center of the commutating pole, a commutating flux proportional to the armature current enters th ...", "... f is represented in Fig. 100 by Fz, and the flux produced by it is shown in Fig. 101. As seen, with the com- mutator brushes midway between the field poles, that is, in the center of the commutating pole, a commutating flux proportional to the armature current enters the armature at the brush B and 5', and is cut by the revolving armature during commutation. The use of the commutating pole or interpole thus permits controlling the commutation, ...", "... ing armature during commutation. The use of the commutating pole or interpole thus permits controlling the commutation, with fixed brush position midway between the field poles, and commutating poles therefore are FIG. 101. — Magnetic flux distribution with commutating pole. extensively used in larger machines, especially of the high-speed type. The commutating pole makes the commutation independent of the main field strength, and therefore permits the mac ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-04", "section_label": "Chapter 4: Graphic Befrisxintation", "section_title": "Graphic Befrisxintation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2122-2743", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "snippets": [ "... o- nous motor circuit under the circumstances stated above. 21. As a further example, we may consider the dia- gram of an alternating-current transformer, feeding through its secondary circuit an inductive load. For simplicity, we may neglect here the magnetic hysteresis, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the magnetic flux is zero. The phase of the flux, that is, the amplitude of its maximum value, is 90° in this case, ...", "... er, feeding through its secondary circuit an inductive load. For simplicity, we may neglect here the magnetic hysteresis, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the magnetic flux is zero. The phase of the flux, that is, the amplitude of its maximum value, is 90° in this case, and, consequently, the phase of the induced E.M.F., is 180% §21] GRAPHIC REPRESENTATION. 29 since the induced E.M.F. lags 90° behind the induc ...", "... ng through its secondary circuit an inductive load. For simplicity, we may neglect here the magnetic hysteresis, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the magnetic flux is zero. The phase of the flux, that is, the amplitude of its maximum value, is 90° in this case, and, consequently, the phase of the induced E.M.F., is 180% §21] GRAPHIC REPRESENTATION. 29 since the induced E.M.F. lags 90° behind the inducing ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-04", "section_label": "Chapter 4: Graphic Representation", "section_title": "Graphic Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 1743-2321", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "snippets": [ "... ro- nous motor circuit under the circumstances stated above. 21. As a further example, we may consider the dia- gram of an alternating-current transformer, feeding through its secondary circuit an inductive load. For simplicity, we may neglect here the magnetic hysteresis, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the magnetic flux is zero. The phase of the flux, that is, the amplitude of its maximum value, is 90° in this case, ...", "... er, feeding through its secondary circuit an inductive load. For simplicity, we may neglect here the magnetic hysteresis, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the magnetic flux is zero. The phase of the flux, that is, the amplitude of its maximum value, is 90° in this case, and, consequently, the phase of the induced E.M.F., is 180°, GRAPHIC REPRESEiVTA TIOiV. 29 since the induced E.M.F. lags 90° behind the inducing ...", "... ng through its secondary circuit an inductive load. For simplicity, we may neglect here the magnetic hysteresis, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the magnetic flux is zero. The phase of the flux, that is, the amplitude of its maximum value, is 90° in this case, and, consequently, the phase of the induced E.M.F., is 180°, GRAPHIC REPRESEiVTA TIOiV. 29 since the induced E.M.F. lags 90° behind the inducing flux ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-16", "section_label": "Chapter 18: Surging Of Synchronous Motors", "section_title": "Surging Of Synchronous Motors", "kind": "chapter", "sequence": 16, "number": 18, "location": "lines 20975-21712", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-16/", "snippets": [ "... p, in solid field poles, etc., a torque is produced more or less proportional to the deviation of speed from synchronism. This power assumes the form, Pi = c2s, where c is a function of the conductivity of the eddy-current circuit and the intensity of the magnetic field of the machine, c2 is the power which would be required to drive the magnetic field of the motor through the circuits of the anti-surging device at full frequency, if the same relative proportions could be retained at full fre- quency as at the freq ...", "... deviation of speed from synchronism. This power assumes the form, Pi = c2s, where c is a function of the conductivity of the eddy-current circuit and the intensity of the magnetic field of the machine, c2 is the power which would be required to drive the magnetic field of the motor through the circuits of the anti-surging device at full frequency, if the same relative proportions could be retained at full fre- quency as at the frequency of slip, s. That is, Pi is the power produced by the motor as induction machin ...", "... tive term represents a power: P2 = -h2s; (30) that is, a retarding torque during slow speed, or increasing £, and accelerating torque during high speed, or decreasing 0. The source of this torque may be found external to the motor, or internal, in its magnetic circuit. SURGING OF SYNCHRONOUS MOTORS 297 External sources of negative, Pi, may be, for instance, the magnetic field of a self-exciting, direct -current generator, driven r the synchronous motor. With decrease of Speed, this field 's, due to t ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-09", "section_label": "Lecture 9: Hunting Of Synchronous Machines", "section_title": "Hunting Of Synchronous Machines", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 4218-4594", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-09/", "snippets": [ "... flow between alternators due to dif- ferences in voltage, that is, differences in excitation; ■—^ and due to differences in phase, that is, differences in position of their rotors. Cross currents due to differences in excitation are watt- less currents, magnetizing the under-excited and demagnetiz- ing the over-excited machine. Cross currents due to differences in position are energy currents, accelerating the lagging and retarding the leading machine. Their magnetic action is a distortion or a shift of the field, ...", "... ences in excitation are watt- less currents, magnetizing the under-excited and demagnetiz- ing the over-excited machine. Cross currents due to differences in position are energy currents, accelerating the lagging and retarding the leading machine. Their magnetic action is a distortion or a shift of the field, ithat is, they increase the magnetic density at the one and decrease it at the other pole corner. If two machines are thrown together out of phase, or brought out of the phase by some cause (as the beat of ...", "... etiz- ing the over-excited machine. Cross currents due to differences in position are energy currents, accelerating the lagging and retarding the leading machine. Their magnetic action is a distortion or a shift of the field, ithat is, they increase the magnetic density at the one and decrease it at the other pole corner. If two machines are thrown together out of phase, or brought out of the phase by some cause (as the beat of an en- gine, or the change of load of a synchronous motor) then the two machines pul ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-04", "section_label": "Theory Section 4: Power and Effective Values", "section_title": "Power and Effective Values", "kind": "theory-section", "sequence": 4, "number": 4, "location": "lines 1244-1572", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-04/", "snippets": [ "... = EQ sin 6. Since E0 = 2 irfn$, it follows that J' ; = 4.44 fn& ; is the effective alternating e.m.f. generated in a coil of turns n rotating at a frequency of / (in hundreds of cycles per second) through a magnetic field of megalines of force. This is the formula of the alternating-current generator. 21. The formula of the direct-current generator, E = holds even if the e.m.fs. generated in the individual turns are not sine ...", "... The formula of the alternating-current generator, E = V2 *fn$, does not hold if the waves are not sine waves, since the ratios of average to maximum and of maximum to effective e.m.f. are changed. If the variation of magnetic flux is not sinusoidal, the effective generated alternating e.m.f. is, E = 7 \\/2 7 is called the form factor of the wave, and depends upon its shape, that is, the distribution of the magnetic flux in the magnetic fie ...", "... ula of the alternating-current generator, E = V2 *fn$, does not hold if the waves are not sine waves, since the ratios of average to maximum and of maximum to effective e.m.f. are changed. If the variation of magnetic flux is not sinusoidal, the effective generated alternating e.m.f. is, E = 7 \\/2 7 is called the form factor of the wave, and depends upon its shape, that is, the distribution of the magnetic flux in the magnetic field. ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-30", "section_label": "Apparatus Section 9: Synchronous Machines: Magnetic Characteristic or Saturation Curve", "section_title": "Synchronous Machines: Magnetic Characteristic or Saturation Curve", "kind": "apparatus-section", "sequence": 30, "number": 9, "location": "lines 9554-9650", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-30/", "snippets": [ "IX. Magnetic Characteristic or Saturation Curve 20. The dependence of the generated e.m.f., or terminal voltage at open circuit, upon the field excitation is called the magnetic characteristic, or saturation curve, of the synchronous 10 ...", "IX. Magnetic Characteristic or Saturation Curve 20. The dependence of the generated e.m.f., or terminal voltage at open circuit, upon the field excitation is called the magnetic characteristic, or saturation curve, of the synchronous 1000 2000 3000 4000 5000 FIG. 69. — Synchronous generator magnetic 7000 characteristics. machine. It has the same general shape as the curve of mag- n ...", "... ted e.m.f., or terminal voltage at open circuit, upon the field excitation is called the magnetic characteristic, or saturation curve, of the synchronous 1000 2000 3000 4000 5000 FIG. 69. — Synchronous generator magnetic 7000 characteristics. machine. It has the same general shape as the curve of mag- netic flux density, consisting of a straight part below saturation, a bend or knee, and a saturated part beyond the knee. Gener- ally th ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-24", "section_label": "Chapter 2: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 24, "number": 2, "location": "lines 1993-2658", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "snippets": [ "... tained only resistance but no inductance, this would take place instantly, that is, there would be no transition period. Every circuit, however, contains some inductance. The induc- tance L of the circuit means L interlinkages of the circuit with lines of magnetic force produced by unit current in the circuit, or iL interlinkages by current i. That is, in establishing current i0 in the circuit, the magnetic flux iQL must be produced. A change of the magnetic flux iL surrounding a circuit generates in the circuit an ...", "... ontains some inductance. The induc- tance L of the circuit means L interlinkages of the circuit with lines of magnetic force produced by unit current in the circuit, or iL interlinkages by current i. That is, in establishing current i0 in the circuit, the magnetic flux iQL must be produced. A change of the magnetic flux iL surrounding a circuit generates in the circuit an e.m.f., d e - * 16 INTRODUCTION 17 This opposes the impressed e.m.f. e0, and therefore lowers the e.m.f. available to produce the c ...", "... ome inductance. The induc- tance L of the circuit means L interlinkages of the circuit with lines of magnetic force produced by unit current in the circuit, or iL interlinkages by current i. That is, in establishing current i0 in the circuit, the magnetic flux iQL must be produced. A change of the magnetic flux iL surrounding a circuit generates in the circuit an e.m.f., d e - * 16 INTRODUCTION 17 This opposes the impressed e.m.f. e0, and therefore lowers the e.m.f. available to produce the curren ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 557-1002", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-01/", "snippets": [ "... smitted into the load L, where the power is used. The consideration of the electric power NATURE AND ORIGIN OF TRANSIENTS. 3 in generator, line, and load does not represent the entire phenome- non. While electric power flows over the line A, there is a magnetic field surrounding the line conductors, and an electrostatic field issuing from the line conductors. The magnetic field and the electrostatic or \" dielectric \" field represent stored energy. Thus, during the permanent conditions of the flow of power throug ...", "... TRANSIENTS. 3 in generator, line, and load does not represent the entire phenome- non. While electric power flows over the line A, there is a magnetic field surrounding the line conductors, and an electrostatic field issuing from the line conductors. The magnetic field and the electrostatic or \" dielectric \" field represent stored energy. Thus, during the permanent conditions of the flow of power through the circuit Fig. 3, there is electric energy stored in the space surround- ing the line conductors. There is en ...", "... ineers have therefore been driven by necessity to their careful and extensive study. 4. The simplest form of transient occurs where the effect is directly proportional to the cause. This is generally the case in electric circuits, since voltage, current, magnetic flux, etc., are proportional to each other, and the electrical transients therefore are usually of the simplest nature. In those cases, however, where this direct proportionality does not exist, as for instance in inductive circuits containing iron, or in ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 460-882", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "snippets": [ "... mitted into the load L, where the power is used. The consideration of the electric power NATURE AND ORIGIN OF TRANSIENTS. 3 in generator, line, and load does not represent the entire phenome- non. While electric power flows over the line A , there is a magnetic field surrounding the line conductors, and an electrostatic field issuing from the line conductors. The magnetic field and the electrostatic or \"dielectric \" field represent stored energy. Thus, during the permanent conditions of the flow of power through ...", "... RANSIENTS. 3 in generator, line, and load does not represent the entire phenome- non. While electric power flows over the line A , there is a magnetic field surrounding the line conductors, and an electrostatic field issuing from the line conductors. The magnetic field and the electrostatic or \"dielectric \" field represent stored energy. Thus, during the permanent conditions of the flow of power through the circuit Fig. 3, there is electric energy stored in the space surround- ing the line conductors. There is ene ...", "... ineers have therefore been driven by necessity to their careful and extensive study. 4. The simplest form of transient occurs where the effect is directly proportional to the cause. This is generally the case in electric circuits, since voltage, current, magnetic flux, etc., are proportional to each other, and the electrical transients therefore are usually of the simplest nature. In those cases, however, where this direct proportionality does not exist, as for instance in inductive circuits containing iron, or in ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-106", "section_label": "Apparatus Section 9: Alternating-current Transformer: Reactors", "section_title": "Alternating-current Transformer: Reactors", "kind": "apparatus-section", "sequence": 106, "number": 9, "location": "lines 18813-18948", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-106/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-106/", "snippets": [ "IX. Reactors (Reactive Coils, Reactances) 129. The reactor consists of one electric circuit interlinked with a magnetic circuit, and its purpose is, not to transform power, but to produce wattless or reactive power, that is, lagging current, or what amounts to the same, leading voltage. While therefore theoretically we cannot speak of an '' ...", "... s high, that is, the efficiency low. In the transformer, the exciting ampere-turns are the (vector) difference between primary and secondary ampere-turns, are wasted, and therefore made as low as possible, by using a closed magnetic circuit. In the reactor, no secondary circuit exists, but the exciting ampere-turns are the purpose of the device, thus should be as large as possible. That is, to convert a trans- former into a reactor, the reluctance of ...", "... losed magnetic circuit. In the reactor, no secondary circuit exists, but the exciting ampere-turns are the purpose of the device, thus should be as large as possible. That is, to convert a trans- former into a reactor, the reluctance of the magnetic circuit must be increased so as to make the exciting ampere-turns equal to the total full-load ampere-turns of the structure as transformer. This is done by inserting an air gap into the magnetic circuit. ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-22", "section_label": "Apparatus Section 1: Synchronous Machines: General", "section_title": "Synchronous Machines: General", "kind": "apparatus-section", "sequence": 22, "number": 1, "location": "lines 8518-8657", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-22/", "snippets": [ "... inal voltage and the generated e.m.f. are in synchronism with, that is, of the same frequency as, the speed of rotation. These machines consist of an armature, in which e.m.f. is generated by the rotation relatively to a magnetic field, and a continuous magnetic field, excited either by direct current, or by the reaction of displaced phase armature currents, or by per- manent magnetism. The formula for the e.m.f. generated in synchronous machines, co ...", "... m.f. are in synchronism with, that is, of the same frequency as, the speed of rotation. These machines consist of an armature, in which e.m.f. is generated by the rotation relatively to a magnetic field, and a continuous magnetic field, excited either by direct current, or by the reaction of displaced phase armature currents, or by per- manent magnetism. The formula for the e.m.f. generated in synchronous machines, commonly called alternators, is E ...", "... ure, in which e.m.f. is generated by the rotation relatively to a magnetic field, and a continuous magnetic field, excited either by direct current, or by the reaction of displaced phase armature currents, or by per- manent magnetism. The formula for the e.m.f. generated in synchronous machines, commonly called alternators, is E = S2irn3> = 4. where n is the number of armature turns in series interlinked with the magnetic flux <1> (in megalines ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-48", "section_label": "Apparatus Subsection 48: Direct-current Commutating Machines: C. Commutating Machines", "section_title": "Direct-current Commutating Machines: C. Commutating Machines", "kind": "apparatus-subsection", "sequence": 48, "number": null, "location": "lines 10845-10940", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-48/", "snippets": [ "... int having the distance lx from the end of the field pole on the armature surface, the distance from the next field pole is ld = Vk2 + lx2, and the density thus, approximately, B C FIG. 92. — Distribution of mganetic flux under a single pole. Herefrom the distribution of magnetic flux is calculated and plotted in Fig. 92, for a single pole BC, along the armature sur- face A, for the length of air gap la = 1, and such a m.m.f. as to ...", "... le on the armature surface, the distance from the next field pole is ld = Vk2 + lx2, and the density thus, approximately, B C FIG. 92. — Distribution of mganetic flux under a single pole. Herefrom the distribution of magnetic flux is calculated and plotted in Fig. 92, for a single pole BC, along the armature sur- face A, for the length of air gap la = 1, and such a m.m.f. as to L FIG. 93. — Distribution of magnetic force and flux at n ...", "... e armature surface, the distance from the next field pole is ld = Vk2 + lx2, and the density thus, approximately, B C FIG. 92. — Distribution of mganetic flux under a single pole. Herefrom the distribution of magnetic flux is calculated and plotted in Fig. 92, for a single pole BC, along the armature sur- face A, for the length of air gap la = 1, and such a m.m.f. as to L FIG. 93. — Distribution of magnetic force and flux at no loa ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-86", "section_label": "Apparatus Section 7: Synchronous Converters: Variable Ratio Converters (\"split Pole\" Converters)", "section_title": "Synchronous Converters: Variable Ratio Converters (\"split Pole\" Converters)", "kind": "apparatus-section", "sequence": 86, "number": 7, "location": "lines 15586-15734", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-86/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-86/", "snippets": [ "VII. Variable Ratio Converters (\"Split Pole\" Converters) 98. With a sine wave of alternating voltage, and the com- mutator brushes set at the magnetic neutral, that is, at right angles to the resultant magnetic flux, the direct voltage of a SYNCHRONOUS CONVERTERS 253 converter is constant at constant impressed alternating voltage. It equals the maximum value of the ...", "VII. Variable Ratio Converters (\"Split Pole\" Converters) 98. With a sine wave of alternating voltage, and the com- mutator brushes set at the magnetic neutral, that is, at right angles to the resultant magnetic flux, the direct voltage of a SYNCHRONOUS CONVERTERS 253 converter is constant at constant impressed alternating voltage. It equals the maximum value of the alternating voltage between two diametrically opposite points ...", "VII. Variable Ratio Converters (\"Split Pole\" Converters) 98. With a sine wave of alternating voltage, and the com- mutator brushes set at the magnetic neutral, that is, at right angles to the resultant magnetic flux, the direct voltage of a SYNCHRONOUS CONVERTERS 253 converter is constant at constant impressed alternating voltage. It equals the maximum value of the alternating voltage between two diametrically opposite points of t ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-08", "section_label": "Lecture 8: Arc Lamps And Arc Lighting", "section_title": "Arc Lamps And Arc Lighting", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 7141-8510", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-08/", "snippets": [ "... onstant-current transformer to direct current without requiring moving machinery. The Brush machine in its principle essentially is a quarter- phase constant-current alternator with rectifying commutator. An alternator of low armature reaction and strong magnetic field regulates for constant potential: the change of armature reaction, resulting from a change of load, has little effect on the field and thereby on the terminal voltage, if the armature reaction is low. An alternator of very high armature reaction an ...", "... and thereby on the terminal voltage, if the armature reaction is low. An alternator of very high armature reaction and weak field, however, regulates for constant current: if the m.m.f., that is, the ampere-turns required in the field coil to produce the magnetic flux, are small compared with the field ampere-turns required to take care of the armature reaction, and the resultant or magnetism-producing field ampere-turns thus the small difference between total field excitation and armature reaction, a moderate inc ...", "... eby on the terminal voltage, if the armature reaction is low. An alternator of very high armature reaction and weak field, however, regulates for constant current: if the m.m.f., that is, the ampere-turns required in the field coil to produce the magnetic flux, are small compared with the field ampere-turns required to take care of the armature reaction, and the resultant or magnetism-producing field ampere-turns thus the small difference between total field excitation and armature reaction, a moderate increase ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-49", "section_label": "Apparatus Subsection 49: Direct-current Commutating Machines: C. Commutating Machines 181", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 181", "kind": "apparatus-subsection", "sequence": 49, "number": null, "location": "lines 10941-11024", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-49/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-49/", "snippets": [ "D. C. COMMUTATING MACHINES 181 With the brushes set midway between adjacent field poles, the armature m.m.f. is additive on one side and subtractive on the other side of the center of the field pole. Thus the magnetic intensity is increased on one side and decreased on the other. The total m.m.f., however, and thus, neglecting saturation, the total flux entering the armature, are not changed. Thus, arma- ture reaction, with the brushes mi ...", "... ide and subtractive on the other side of the center of the field pole. Thus the magnetic intensity is increased on one side and decreased on the other. The total m.m.f., however, and thus, neglecting saturation, the total flux entering the armature, are not changed. Thus, arma- ture reaction, with the brushes midway between adjacent field poles, acts distorting upon the field, but neither magnetizes nor demagnetizes, if the field is below saturation ...", "... e not changed. Thus, arma- ture reaction, with the brushes midway between adjacent field poles, acts distorting upon the field, but neither magnetizes nor demagnetizes, if the field is below saturation. The distortion of the magnetic field takes place by the arma- ture ampere-turns beneath the pole, or from B to C. Thus, if T = pole arc, that is, the angle covered by pole face (two poles or one complete period being denoted by 360 degrees), the di ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-14", "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "section_title": "Constant-Potential Constant-Current Trans Formation", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "... aratus, as trans- formers from constant potential to constant ciurent, or regula- tors, this variation of series inductive reactance with the load is usually accomplished automatically by the mechanical motion caused by the mechanical force exerted by the magnetic field of the current, upon the conductor in which the ciurent exists. For instance, in the constant-current transformer, as shown diagrammatically in Fig. 114, the secondary coils, S, are arranged so that they can move away from the primary coils, P, or ...", "... nt transformer, as shown diagrammatically in Fig. 114, the secondary coils, S, are arranged so that they can move away from the primary coils, P, or in- versely. Primary and secondary currents are proportional to each other, as in any transformer, and the magnetic field between primary and secondary coils, or the magnetic stray field, in which the secondary coils float, is proportional to either current. The magnetic repulsion between primary coils and secondary coils is proportional to the current (or rather its a ...", "... secondary coils, S, are arranged so that they can move away from the primary coils, P, or in- versely. Primary and secondary currents are proportional to each other, as in any transformer, and the magnetic field between primary and secondary coils, or the magnetic stray field, in which the secondary coils float, is proportional to either current. The magnetic repulsion between primary coils and secondary coils is proportional to the current (or rather its ampere-turns), and to the magnetic stray field, hence is pro ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-51", "section_label": "Apparatus Subsection 51: Direct-current Commutating Machines: C. Commutating Machines 183", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 183", "kind": "apparatus-subsection", "sequence": 51, "number": null, "location": "lines 11047-11125", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-51/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-51/", "snippets": [ "D. C. COMMUTATING MACHINES 183 In Figs. 96, 97, 98, 99, curves are plotted corresponding to those in Figs. 92, 93, 94, and 95. As seen, the spread of mag- netic flux at the pole corners is greatly increased, but farther away from the field poles the magnetic distribution is not changed. 47. The magnetizing, or rather demagnetizing, effect of the load with shifted brushes is not changed ...", "... In Figs. 96, 97, 98, 99, curves are plotted corresponding to those in Figs. 92, 93, 94, and 95. As seen, the spread of mag- netic flux at the pole corners is greatly increased, but farther away from the field poles the magnetic distribution is not changed. 47. The magnetizing, or rather demagnetizing, effect of the load with shifted brushes is not changed. The distorting effect FIG. 96. — Flux distribution under a single pole. of the load is, h ...", "... orresponding to those in Figs. 92, 93, 94, and 95. As seen, the spread of mag- netic flux at the pole corners is greatly increased, but farther away from the field poles the magnetic distribution is not changed. 47. The magnetizing, or rather demagnetizing, effect of the load with shifted brushes is not changed. The distorting effect FIG. 96. — Flux distribution under a single pole. of the load is, however, very greatly decreased, to a small per- c ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-07", "section_label": "Theory Section 7: Inductance in Alternating-current Circuits", "section_title": "Inductance in Alternating-current Circuits", "kind": "theory-section", "sequence": 7, "number": 7, "location": "lines 2250-2717", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-07/", "snippets": [ "... nding angle at which the current reaches its zero value in the ascendant. If such a sine wave of alternating current i = IQ sin 2 irft or i = IQ sin 6 passes through a circuit of resistance r and induc- tance L, the magnetic flux produced by the current and thus its interlinkages with the current, iL = IoL sin 0, vary in a wave 32 ELEMENTS OF ELECTRICAL ENGINEERING line similar also to that of the current, as shown in Fig. 11 as $. ...", "... le at which the current reaches its zero value in the ascendant. If such a sine wave of alternating current i = IQ sin 2 irft or i = IQ sin 6 passes through a circuit of resistance r and induc- tance L, the magnetic flux produced by the current and thus its interlinkages with the current, iL = IoL sin 0, vary in a wave 32 ELEMENTS OF ELECTRICAL ENGINEERING line similar also to that of the current, as shown in Fig. 11 as $. The ...", "... ce, x, times the effective value of the current, /, and lags 90 time degrees, or a quarter period, behind the current. 35. By the counter e.m.f. of inductance, e'z = — xIQ cos 0, which is generated by the change in flux due to the passage of the current i — IQ sin 0 through the circuit of reactance x, an equal but opposite e.m.f. ez = xIQ cos 0 is consumed, and thus has to be impressed upon the circuit. This e.m.f. is called the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-21", "section_label": "Apparatus Introduction 21: Introduction", "section_title": "Introduction", "kind": "apparatus-introduction", "sequence": 21, "number": null, "location": "lines 8292-8517", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-21/", "snippets": [ "... . Standard- izing Committee, is used in the following discussion. It refers only to the apparatus transforming between electric and electric and between electric and mechanical power. 1st. Commutating machines, consisting of a magnetic field and a closed-coil armature, connected with a multi-segmental commutator. 121 122 ELEMENTS OF ELECTRICAL ENGINEERING 2d. Synchronous machines, consisting of a undirectional mag- netic field and an armature revolving r ...", "... Induction machines, consisting of an alternating mag- netic circuit or circuits interlinked with two electric circuits or sets of circuits moving with regard to each other. 5th. Stationary induction apparatus, consisting of a magnetic circuit interlinked with one or more electric circuits. 6th. Electrostatic and electrolytic apparatus as condensers and polarization cells. Apparatus changing from one to a different form of electric energy have been defined ...", "... more electric circuits. 6th. Electrostatic and electrolytic apparatus as condensers and polarization cells. Apparatus changing from one to a different form of electric energy have been defined as: A. Transformers, when using magnetism, and as B. Converters, when using mechanical momentum as inter- mediary form of energy. The transformers as a rule are stationary, the converters rotary apparatus. Motor-generators transforming from elec- trical over mechanic ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-33", "section_label": "Apparatus Section 12: Synchronous Machines: Starting of Synchronous Motors", "section_title": "Synchronous Machines: Starting of Synchronous Motors", "kind": "apparatus-section", "sequence": 33, "number": 12, "location": "lines 9749-9820", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-33/", "snippets": [ "... synchronous motor starts from rest and runs up to synchronism with more or less torque. In starting, the field excitation of the polyphase synchronous motor should be zero or very low. The starting torque is due to the magnetic attraction of the armature currents upon the remanent magnetism left in the field poles by the currents of the preceding phase, and to the eddy currents produced therein. Let Fig. 72 represent the magnetic circuit of a p ...", "... with more or less torque. In starting, the field excitation of the polyphase synchronous motor should be zero or very low. The starting torque is due to the magnetic attraction of the armature currents upon the remanent magnetism left in the field poles by the currents of the preceding phase, and to the eddy currents produced therein. Let Fig. 72 represent the magnetic circuit of a polyphase synchronous motor. The m.m.f. of the polyphase armature ...", "... is due to the magnetic attraction of the armature currents upon the remanent magnetism left in the field poles by the currents of the preceding phase, and to the eddy currents produced therein. Let Fig. 72 represent the magnetic circuit of a polyphase synchronous motor. The m.m.f. of the polyphase armature currents acting upon the successive projections or teeth of the armature, 1, 2, 3, etc., reaches a maximum in them successively; that is, the a ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-24", "section_label": "Chapter 24: Symmetbicaii Polyphase Ststems", "section_title": "Symmetbicaii Polyphase Ststems", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 25271-25604", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-24/", "snippets": [ "... uarter-phase or four-phase sys- tem, have not been used, and are of little practical interest. 237. A characteristic feature of the symmetrical n- phase system is that under certain conditions it can pro- duce a M.M.F. of constant intensity. If n equal magnetizing coils act upon a point under equal angular displacements in space, and are excited by the n E.M.Fs. of a symmetrical //-phase system, a M.M.F. of constant intensity is produced at this point, whose direction revolves synchronously with uniform velocity. ...", "... angular displacements in space, and are excited by the n E.M.Fs. of a symmetrical //-phase system, a M.M.F. of constant intensity is produced at this point, whose direction revolves synchronously with uniform velocity. Let, «' = number of turns of each magnetizing coil. E=^ effective value of impressed E.M.F. / = effective value of current. Hence, (F =///= effective M.M.F. of one of the magnetizing coils- $237] SYMMETRICAL POLYPHASE SYSTEMS, 853 Then the instantaneous value of the M.M.F. of the coil acting ...", "... at this point, whose direction revolves synchronously with uniform velocity. Let, «' = number of turns of each magnetizing coil. E=^ effective value of impressed E.M.F. / = effective value of current. Hence, (F =///= effective M.M.F. of one of the magnetizing coils- $237] SYMMETRICAL POLYPHASE SYSTEMS, 853 Then the instantaneous value of the M.M.F. of the coil acting in the direction 2 tt//;/ is : //= $FV2 sin /'i8-?^'\\ = ///V2sin/'i8-?^\\ The two rectangular components of this M.M.F. are: and fi' ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-26", "section_label": "Chapter 26: Symmetrical Polyphase Systems", "section_title": "Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 23781-24053", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-26/", "snippets": [ "... tput from these machines, and a symmetrical eight- phase system proposed for the same purpose. 265. A characteristic feature of the symmetrical »- phase system is that under certain conditions it can pro- duce a M.M.F. of constant intensity. If « equal magnetizing coils act upon a point under equal angular displacements in space, and are excited by the n E.M.Fs. of a symmetrical w-phase system, a M.M.F. of constant intensity is produced at this point, whose direction revolves synchronously with uniform velocity. ...", "... angular displacements in space, and are excited by the n E.M.Fs. of a symmetrical w-phase system, a M.M.F. of constant intensity is produced at this point, whose direction revolves synchronously with uniform velocity. Let, n' =• number of turns of each magnetizing coil. SYMMETRICAL POLYPHASE SYSTEMS. 437 E= effective value of impressed E.M.F. / = effective value of current. Hence, & =n'f= effective M.M.F. of one of the magnetizing coils. Then the instantaneous value of the M.M.F. of the coil acting in the d ...", "... olves synchronously with uniform velocity. Let, n' =• number of turns of each magnetizing coil. SYMMETRICAL POLYPHASE SYSTEMS. 437 E= effective value of impressed E.M.F. / = effective value of current. Hence, & =n'f= effective M.M.F. of one of the magnetizing coils. Then the instantaneous value of the M.M.F. of the coil acting in the direction 2 «•*'/» is : The two rectangular space components of this M.M.F. are ; and Hence the M.M.F. of this coil can be expressed by the symbolic formula : fi n \\ ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-24", "section_label": "Apparatus Section 3: Synchronous Machines: Armature Reaction", "section_title": "Synchronous Machines: Armature Reaction", "kind": "apparatus-section", "sequence": 24, "number": 3, "location": "lines 8741-8906", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-24/", "snippets": [ "III. Armature Reaction 8. The magnetic flux in the field of an alternator under load is produced by the resultant m.m.f. of the field exciting current and of the armature current. It depends upon the phase rela- tion of the armature current. The e.m.f. generat ...", "III. Armature Reaction 8. The magnetic flux in the field of an alternator under load is produced by the resultant m.m.f. of the field exciting current and of the armature current. It depends upon the phase rela- tion of the armature current. The e.m.f. generated by ...", "... rotation) in an. alternating-current generator A] magnetizes the following and demagnetizes the preceding mag- net pole in a synchronous motor A' (since in a generator the rotation is against, in a synchronous motor with the magnetic attractions and repulsions between field and armature). In this case the armature current neither magnetizes nor demag- netizes the field as a whole, but magnetizes the one side, demag- SYNCHRONOUS MACHINES 131 netizes t ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-55", "section_label": "Apparatus Subsection 55: Direct-current Commutating Machines: C. Commutating Machines 189", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 189", "kind": "apparatus-subsection", "sequence": 55, "number": null, "location": "lines 11301-11386", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-55/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-55/", "snippets": [ "D. C. COMMUTATING MACHINES 189 netic flux at the armature circumference therefore always has the same shape, and its intensity is proportional to the current, except as far as saturation limits it. As the result thereof, shifting the brushes to the edge of the fi ...", "... ction of the shift of brushes has to be reversed with the re- versal of rotation. In railway motors this cannot be done with- out objectionable complication, therefore the brushes have to be set midway, and the use of the magnetic flux at the edge of the next pole, as commutating flux, is not feasible. In this case a commutating pole is used, to give, without mechanical shifting of the brushes, the same effect which a brush shift would give. Ther ...", "... the shift of brushes has to be reversed with the re- versal of rotation. In railway motors this cannot be done with- out objectionable complication, therefore the brushes have to be set midway, and the use of the magnetic flux at the edge of the next pole, as commutating flux, is not feasible. In this case a commutating pole is used, to give, without mechanical shifting of the brushes, the same effect which a brush shift would give. Therefore ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-66", "section_label": "Apparatus Subsection 66: Direct-current Commutating Machines: C. Commutating Machines 201", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 201", "kind": "apparatus-subsection", "sequence": 66, "number": null, "location": "lines 11981-12083", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-66/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-66/", "snippets": [ "D. C. COMMUTATING MACHINES 201 is, in the armature during commutation an e.m.f. is generated by its rotation through a magnetic field. This magnetic field may be the magnetic field of armature reaction, or the reverse magnetic field of a commutating pole, or the fringe of the main field of the machine, into which the brushes are shifted. In this ...", "D. C. COMMUTATING MACHINES 201 is, in the armature during commutation an e.m.f. is generated by its rotation through a magnetic field. This magnetic field may be the magnetic field of armature reaction, or the reverse magnetic field of a commutating pole, or the fringe of the main field of the machine, into which the brushes are shifted. In this case the commutation ...", "D. C. COMMUTATING MACHINES 201 is, in the armature during commutation an e.m.f. is generated by its rotation through a magnetic field. This magnetic field may be the magnetic field of armature reaction, or the reverse magnetic field of a commutating pole, or the fringe of the main field of the machine, into which the brushes are shifted. In this case the commutation depends upon the inductance ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-84", "section_label": "Apparatus Section 5: Synchronous Converters: Armature Reaction", "section_title": "Synchronous Converters: Armature Reaction", "kind": "apparatus-section", "sequence": 84, "number": 5, "location": "lines 15161-15475", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-84/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-84/", "snippets": [ "... he com- mutator brushes are set at right angles to the field poles or without lead or lag, as is usually done in converters, the direct- current armature reaction consists in a polarization in quadra- ture behind the field magnetism. The armature reaction due to the power component of the alternating current in a synchro- nous motor consists of a polarization in quadrature ahead of the field magnetism, which is opposite to the armature reaction as dire ...", "... in a polarization in quadra- ture behind the field magnetism. The armature reaction due to the power component of the alternating current in a synchro- nous motor consists of a polarization in quadrature ahead of the field magnetism, which is opposite to the armature reaction as direct-current generator. Let m = total number of turns on the bipolar armature or per pair of poles of an n-phase converter, / = direct current, then the number of turns ...", "... e direct- current reaction. Hence, the armature reaction oscillates with twice the fre- quency of the alternating current, and with full intensity, and since it is in quadrature with the field excitation, tends to shift the magnetic flux rapidly across the field poles, and thereby tends to cause sparking and power losses. This oscillating reaction is, however, reduced by the damping effect of the mag- netic field structure. It is somewhat less in the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-96", "section_label": "Apparatus Section 2: Alternating-current Transformer: Excitation", "section_title": "Alternating-current Transformer: Excitation", "kind": "apparatus-section", "sequence": 96, "number": 2, "location": "lines 16912-17026", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-96/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-96/", "snippets": [ "... 30 FIG. 153. — Excitation and core loss of transformer. and does not become zero at no load or open circuit, but a small and lagging current ^o remains at no load, which is called the exciting current. It produces the magnetic flux and supplies the losses in the iron, so-called \"core loss.\" Its reactive com- ponent, imj is called the magnetizing current, and is usually greatly distorted in wave shape, while the energy component, 280 ELEMENTS ...", "... 153. — Excitation and core loss of transformer. and does not become zero at no load or open circuit, but a small and lagging current ^o remains at no load, which is called the exciting current. It produces the magnetic flux and supplies the losses in the iron, so-called \"core loss.\" Its reactive com- ponent, imj is called the magnetizing current, and is usually greatly distorted in wave shape, while the energy component, 280 ELEMENTS OF EL ...", "... small and lagging current ^o remains at no load, which is called the exciting current. It produces the magnetic flux and supplies the losses in the iron, so-called \"core loss.\" Its reactive com- ponent, imj is called the magnetizing current, and is usually greatly distorted in wave shape, while the energy component, 280 ELEMENTS OF ELECTRICAL ENGINEERING ih, does not much differ from a sine wave, and is the hysteresis energy current: /o = ih - ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-29", "section_label": "Chapter 29: Symmetrical Polyphase Systems", "section_title": "Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 29, "number": 29, "location": "lines 34929-35255", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-29/", "snippets": [ "... m these machines, and a symmetrical eight-phase system proposed for the same purpose. 271. A characteristic feature of the symmetrical n-phase sys- tem is that under certain conditions it can produce a rotating m.m.f. of constant intensity. If n equal magnetizing coils act upon a point under equal angular displacements in space, and are excited by the 7i e.m.fs. of a symmetrical n-phase system, a m.m.f. of constant intensity is produced at this point, whose direction revolves synchronously with uniform velocity. ...", "... angular displacements in space, and are excited by the 7i e.m.fs. of a symmetrical n-phase system, a m.m.f. of constant intensity is produced at this point, whose direction revolves synchronously with uniform velocity. Let n' = number of turns of each magnetizing coil. E — effective value of impressed e.m.f. 7 = effective value of current. Hence, F = n'l = effective m.m.f. of one of the magnetizing coils. Then the instantaneous value of the m.m.f. of the coil acting in the direction, , is n f. = FV2sin (^ ...", "... d at this point, whose direction revolves synchronously with uniform velocity. Let n' = number of turns of each magnetizing coil. E — effective value of impressed e.m.f. 7 = effective value of current. Hence, F = n'l = effective m.m.f. of one of the magnetizing coils. Then the instantaneous value of the m.m.f. of the coil acting in the direction, , is n f. = FV2sin (^-^■) = n'l \\/2 sin (& ^) * 26 402 ALTERNATING-CURRENT PHENOMENA The two rectangular space components of this m.m.f. are /T r- Zirl . ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-49", "section_label": "Chapter 9: High-Frequency Conductors", "section_title": "High-Frequency Conductors", "kind": "chapter", "sequence": 49, "number": 9, "location": "lines 27003-27760", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "snippets": [ "... ear the path of a lightning stroke, as \"side discharge.\" The inductance is reduced by the unequal current distribution in the conductor, which, by deflecting most of the current into the outer layer of the conductor, reduces or practically eliminates the magnetic field inside of the conductor. The lag of the mag- netic field in space, behind the current in the conductor, due to the finite velocity of radiation, also reduces the inductance to less than that from the conductor surface to a distance of one- half wave ...", "... the finite velocity of radiation, also reduces the inductance to less than that from the conductor surface to a distance of one- half wave. An exact determination of the inductance is, how- ever, not possible; the inductance is represented by the electro- magnetic field of the conductor, and this depends upon the presence and location of other conductors, etc., in space, on the length of the conductor, and the distance from the return con- ductor. Since very high frequency currents, as lightning dis- charges, frequ ...", "... return con- ductor. Since very high frequency currents, as lightning dis- charges, frequently have no return conductor, but the capacity at the end of the discharge path returns the current as \" dis- placement current,\" the extent and distribution of the magnetic field is indeterminate. If, however, the conductor under con- sideration is a small part of the total discharge — as the ground connection of a lightning arrester, a small part of the discharge path from cloud to ground — and the frequency very high, so ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... cent, while theoretically possible, thus would be practically useless, The calculation of the ampere-turns required for the shunt field excitation, or for the series field of a direct-current generator needs only moderate exactness, as variations in the magnetic material, in the speed regulation of the driving power, etc., produce differences amounting to several per cent. (c) Exact engineering calculations, as, for instance, the calculations of the efficiency of apparatus, the regulation of transformers, the c ...", "... ign Data. wrong impression that the variation of voltage is far greater than it really is. When curves are used to record numerical values and derive them from the curve, as, for instance, is connnonly the NUMERICAL CALCULATIONS. 259 case with magnetization curves, it is unnecessary to have the zero of the function coincide with the zero of the cross-sectioning, but rather preferable not to have it so, if thereby a better scale of the curve can be secured. It is desirable, however, to use suffi- ciently smal ...", "... hereby a better scale of the curve can be secured. It is desirable, however, to use suffi- ciently small cross-sectioning to make it possible to take numerical values from the curve with good accuracy. This is illustrated by Figs. 89 and 90. Both show the magnetic charac- teristic of soft steel, for the range above (B = 8000, in which it is usually employed. Fig. 89 shows the proper way of plotting for showing the shape of the function, Fig. 90 the proper way of plotting for use of the curve to derive numerical val ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-13", "section_label": "Lecture 13: Electric Railway: Motor Characteristics", "section_title": "Electric Railway: Motor Characteristics", "kind": "lecture", "sequence": 13, "number": 13, "location": "lines 7124-8648", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-13/", "snippets": [ "... ; the series motor thus gives a more economical utilization of apparatus and lines than the shunt or induction motor, and is therefore almost ex- clusively used. The torque, and so the pull produced by a motor, is approximately proportional to the field magnetism and the armature current; that is, neglecting the losses in the motor, or assuming ioo% efficiency, the torque is proportional to the product of magnetic field strength and armature current 1 66 GENERAL LECTURES In a shunt motor, at constant suppl ...", "... used. The torque, and so the pull produced by a motor, is approximately proportional to the field magnetism and the armature current; that is, neglecting the losses in the motor, or assuming ioo% efficiency, the torque is proportional to the product of magnetic field strength and armature current 1 66 GENERAL LECTURES In a shunt motor, at constant supply voltage e, the field exciting current, and thus the field strength, is constant ; and the torque, when neglecting losses, is thus proportional to the ar ...", "... as shown by the curve e at constant field strength, the speed decreases in the same proportion, as shown by the curve Si. The field strength, however, does not remain perfectly constant, but with MOTOR CHARACTERISTICS 167 increasing load the field magnetism slightly changes: it de- creases by field distortion and demagnetization, and the speed therefore increases in the same proportion, to the curve S. The current used as abscissae in Fig. 38 is the armature current. The total current consumed by the motor i ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-110", "section_label": "Apparatus Section 4: Induction Machines: Induction Generator", "section_title": "Induction Machines: Induction Generator", "kind": "apparatus-section", "sequence": 110, "number": 4, "location": "lines 21158-21588", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-110/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-110/", "snippets": [ "... d curves. 3. POWER-FACTOR OF INDUCTION GENERATOR 155. The induction generator differs 'essentially from a syn- chronous alternator (that is, a machine in which an armature revolves relatively through a constant or continuous magnetic field) by having a power-factor requiring leading current ; that is, in the synchronous alternator the phase relation between current and terminal voltage depends entirely upon the external circuit, and according to the nature ...", "... ent less, the induction generator fails to excite and generate. If the power-factor of the external circuit is lower than that of the induction generator, the latter excites and its voltage rises until by saturation of its magnetic circuit and the consequent increase of exciting admittance, that is, decrease of internal power-factor, its power-factor has fallen to equality with that of the external circuit. INDUCTION MACHINES 345 In this respect th ...", "... ant, or even increased with the load. When running from an induction generator, a synchronous motor gives a load curve very similar to the load curve of an induction motor running from a synchronous generator; that is, a magnetizing current at no load and a speed gradually decreas- ing with the increase of load up to a maximum output point, at which the speed curve bends sharply down, the current curve upward, and the motor drops out of step. The ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-112", "section_label": "Apparatus Section 6: Induction Machines: Phase Converter", "section_title": "Induction Machines: Phase Converter", "kind": "apparatus-section", "sequence": 112, "number": 6, "location": "lines 21647-21812", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-112/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-112/", "snippets": [ "... ronism, and as generator, above synchronism. In the single-phase induction machine the motor or generator action occurs in one primary circuit only, but in the direction in quadrature to the primary circuit there is a mere magnetizing current either in the secondary, in the single-phase motor proper, or in an auxiliary field-circuit, in the monocyclic motor. The motor and generator action can occur, however, simul- taneously in the same machine, some of ...", "... admittance, ZQ = TQ -f- JXQ = self -inductive impedance per primary or ter- tiary circuit, Zi = ri + jxi = resultant single-phase self-inductive impe- dance of secondary circuits. Let e = e.m.f. generated by the mutual flux and Z = r + jx = impedance of the external circuit supplied by the phase converter as generator of second phase. We then have /> I = 71? — current of second phase produced by phase Zr T Z»o converter, E — IZ ...", "... 1 L o ~~z tor circuit of phase converter. The current in the secondary of the phase converter is then /! = / + /'+ I\", where ^ I = load current = ~ „ I' = eY = exciting current of quadrature magnetic flux, €S I' = - ; — : — = current required to revolve the machi ri+jsxi and the primary current is ?•'-&> !', where /' = eY = exciting current of main magnetic flux. INDUCTION MACHINES 353 From these current ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-65", "section_label": "Apparatus Section 13: Direct-current Commutating Machines: Commutation", "section_title": "Direct-current Commutating Machines: Commutation", "kind": "apparatus-section", "sequence": 65, "number": 13, "location": "lines 11905-11980", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-65/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-65/", "snippets": [ "... ited by the brush, and the current iQ in the coil begins to die out, or rather to change at a rate depending upon the internal resistance and the inductance of the coil A and the e.m.f. gener- ated in the coil by the magnetic flux of armature reaction and by the field magnetic flux. The higher the internal resistance the faster is the change of current, and the higher the inductance the slower the current changes. Thus two cases have to ...", "... the brush, and the current iQ in the coil begins to die out, or rather to change at a rate depending upon the internal resistance and the inductance of the coil A and the e.m.f. gener- ated in the coil by the magnetic flux of armature reaction and by the field magnetic flux. The higher the internal resistance the faster is the change of current, and the higher the inductance the slower the current changes. Thus two cases have to be di ...", "... begins to die out, or rather to change at a rate depending upon the internal resistance and the inductance of the coil A and the e.m.f. gener- ated in the coil by the magnetic flux of armature reaction and by the field magnetic flux. The higher the internal resistance the faster is the change of current, and the higher the inductance the slower the current changes. Thus two cases have to be dis- tinguished. 1. No magnetic flux enters the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-11", "section_label": "Chapter 11: Phase Control", "section_title": "Phase Control", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 9767-10717", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-11/", "snippets": [ "... rs or converters: in a synchronous motor a lagging current can be produced by decreasing, a leading current by increasing, the field excitation. 81. If in a direct-current motor, at constant impressed voltage, the field excitation and therefore the field magnetism is decreased, the motor speed increases, as the armature has to revolve faster to consume the impressed e.m.f., and if the field excitation is increased, the motor slows down. A synchronous motor, however, cannot vary in speed, since it must keep in step ...", "... increased, the motor slows down. A synchronous motor, however, cannot vary in speed, since it must keep in step with the impressed frequency, and if, therefore, at constant impressed voltage the field excitation is decreased below that which gives a field magnetism, that at the synchronous speed consumes the impressed voltage, the field magnetism still must remain the same, and the armature current thus changes in phase in such a manner as to magnetize the field and make up for the deficiency in the field excitation ...", "... , since it must keep in step with the impressed frequency, and if, therefore, at constant impressed voltage the field excitation is decreased below that which gives a field magnetism, that at the synchronous speed consumes the impressed voltage, the field magnetism still must remain the same, and the armature current thus changes in phase in such a manner as to magnetize the field and make up for the deficiency in the field excitation. That is, the armature current becomes lagging. Inversely, if the field excitation ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-16", "section_label": "Chapter 16: Power, And Double-Frequency Quantities In", "section_title": "Power, And Double-Frequency Quantities In", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 16077-16520", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-16/", "snippets": [ "... ring the com- pensator as near as possible to the circuit to be compensated. + . . . . +Pn, 2+ . . . . +Pn\\ . +PJ. DOUBLE-FREQUENCY QUANTITIES 185 140. Like power, torque in alternating apparatus is a double- frequency vector product also, of magnetism and m.m.f. or current, and thus can be treated in the same way. In an induction motor, for instance, the torque is the product of the magnetic flux in one direction into the component of secondary current in phase with the magnetic flux in time, but in ...", "... ANTITIES 185 140. Like power, torque in alternating apparatus is a double- frequency vector product also, of magnetism and m.m.f. or current, and thus can be treated in the same way. In an induction motor, for instance, the torque is the product of the magnetic flux in one direction into the component of secondary current in phase with the magnetic flux in time, but in quadrature position therewith in space, times the number of turns of this current, or since the generated e.m.f. is in quad- rature and proportio ...", "... 185 140. Like power, torque in alternating apparatus is a double- frequency vector product also, of magnetism and m.m.f. or current, and thus can be treated in the same way. In an induction motor, for instance, the torque is the product of the magnetic flux in one direction into the component of secondary current in phase with the magnetic flux in time, but in quadrature position therewith in space, times the number of turns of this current, or since the generated e.m.f. is in quad- rature and proportional t ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-12", "section_label": "Chapter 12: Power, And Double Frequency Quantities In General", "section_title": "Power, And Double Frequency Quantities In General", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 9381-9740", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "snippets": [ "... sated for, wattless currents will flow, and for this reason it may be advisable to bring the compensator as near as possible to the circuit to be compensated. 106. Like power, torque in alternating apparatus is a double frequency vector product also, of magnetism and M.M.F. or current, and thus can be treated in the same way. In an induction motor, for instance, the torque is the product of the magnetic flux in one direction into the com- ponent of secondary induced current in phase with the magnetic flux in ti ...", "... compensated. 106. Like power, torque in alternating apparatus is a double frequency vector product also, of magnetism and M.M.F. or current, and thus can be treated in the same way. In an induction motor, for instance, the torque is the product of the magnetic flux in one direction into the com- ponent of secondary induced current in phase with the magnetic flux in time, but in quadrature position therewith in space, times the number of turns of this current, or since the induced E.M.F. is in quadrature and pro ...", "... ed. 106. Like power, torque in alternating apparatus is a double frequency vector product also, of magnetism and M.M.F. or current, and thus can be treated in the same way. In an induction motor, for instance, the torque is the product of the magnetic flux in one direction into the com- ponent of secondary induced current in phase with the magnetic flux in time, but in quadrature position therewith in space, times the number of turns of this current, or since the induced E.M.F. is in quadrature and proporti ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-10", "section_label": "Chapter 6: Alternating Magnetic Flux Distribution. 355", "section_title": "Alternating Magnetic Flux Distribution. 355", "kind": "chapter", "sequence": 10, "number": 6, "location": "lines 904-937", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-10/", "snippets": [ "CHAPTER VI. ALTERNATING MAGNETIC FLUX DISTRIBUTION. 355 48. Magnetic screening by secondary currents in alternating fields. 355 49. The differential equations of alternating magnetic flux in a lamina. 356 50. Their integral equations. 357 51. Terminal conditions, and the final eq ...", "CHAPTER VI. ALTERNATING MAGNETIC FLUX DISTRIBUTION. 355 48. Magnetic screening by secondary currents in alternating fields. 355 49. The differential equations of alternating magnetic flux in a lamina. 356 50. Their integral equations. 357 51. Terminal conditions, and the final equatio ...", "CHAPTER VI. ALTERNATING MAGNETIC FLUX DISTRIBUTION. 355 48. Magnetic screening by secondary currents in alternating fields. 355 49. The differential equations of alternating magnetic flux in a lamina. 356 50. Their integral equations. 357 51. Terminal conditions, and the final equations. 358 52. Equations for very ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-35", "section_label": "Chapter 13: Transient Term Of The Rotating Field", "section_title": "Transient Term Of The Rotating Field", "kind": "chapter", "sequence": 35, "number": 13, "location": "lines 13936-14548", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-35/", "snippets": [ "CHAPTER XIII. TRANSIENT TERM OF THE ROTATING FIELD. 106. The resultant of np equal m.m.fs. equally displaced from each other in space angle and in time-phase is constant in intensity, and revolves at constant synchronous velocity. When acting upon a magnetic circuit of constant reluctance in all directions, such a polyphase system of m.m.fs. produces a revolving magnetic flux, or a rotating field. (\" Theory and Calculation of Alternating Current Phenomena,\" 4th edition, Chapter XXXIII, paragraph 368.) That is ...", "... TERM OF THE ROTATING FIELD. 106. The resultant of np equal m.m.fs. equally displaced from each other in space angle and in time-phase is constant in intensity, and revolves at constant synchronous velocity. When acting upon a magnetic circuit of constant reluctance in all directions, such a polyphase system of m.m.fs. produces a revolving magnetic flux, or a rotating field. (\" Theory and Calculation of Alternating Current Phenomena,\" 4th edition, Chapter XXXIII, paragraph 368.) That is, if np equal mag- netizing co ...", "... from each other in space angle and in time-phase is constant in intensity, and revolves at constant synchronous velocity. When acting upon a magnetic circuit of constant reluctance in all directions, such a polyphase system of m.m.fs. produces a revolving magnetic flux, or a rotating field. (\" Theory and Calculation of Alternating Current Phenomena,\" 4th edition, Chapter XXXIII, paragraph 368.) That is, if np equal mag- netizing coils are arranged under equal space angles of - np electrical degrees, and connecte ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-04", "section_label": "Lecture 4: The Characteristics Of Space A. The Geometry Of The Gravitational Field", "section_title": "The Characteristics Of Space A. The Geometry Of The Gravitational Field", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3595-6820", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-04/", "snippets": [ "... 6 illogical, 18 unnecessary, 17 waves, 18 Euclid, 71 Euclidean geometry, 64, 72, 74 F Fallacy of ether conception, 16 Faraday, 12, 17 Field, centrifugal, 47 dielectric, 18 electromagnetic, 21 electrostatic, 18 gravitational, 18, 46, 47 magnetic, 18 of energy, 22 of force, 12, 18 Finite volume of universe, 63 Force, magnetic, 46 Four-dimensional space with sphere as element, 99 Fraction, meaning of, 38 Frequencies of electromagnetic waves, 22 Friction of ether, 14 G Gauss, 71 Gene ...", "... , 74 F Fallacy of ether conception, 16 Faraday, 12, 17 Field, centrifugal, 47 dielectric, 18 electromagnetic, 21 electrostatic, 18 gravitational, 18, 46, 47 magnetic, 18 of energy, 22 of force, 12, 18 Finite volume of universe, 63 Force, magnetic, 46 Four-dimensional space with sphere as element, 99 Fraction, meaning of, 38 Frequencies of electromagnetic waves, 22 Friction of ether, 14 G Gauss, 71 General differential space, 115 geometry, 64 or projective geometry space, 115 Geometry ...", "... 6 Imaginary number, meaning, 38 rotation, meaning, 39 representing relativity, 35 Inductance and wave velocity, 23 Inertial mass, 47 Infinitely distant elements in geom- etry, 96 Intensity of dielectric field, 47 of gravitational field, 47 of magnetic field, 47 Interference of light, 13 K Kinetic energy, 44, 47 Kinks, in space, 90 Law of gravitation, 50 Length, relativity, 6 of straight line, 87 shortening by motion, 5, 28 transformation by motion, 26 INDEX 125 Light, constancy of sp ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-08", "section_label": "Lecture 8: Generation", "section_title": "Generation", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 3781-4217", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-08/", "snippets": [ "... r therefore, in machines of very large armature reaction, as turbo-alternators, pulsations of the magnet field, and thereby loss in efficiency, and heating may result. An alternator has armature reaction and self-induction. The armature reaction is the magnetic action of the arma- ture current on the field, that is, the armature current demag- netizes or magnetizes the field according to its phase, and so lowers or raises the voltage. Armature reaction therefore is expressed in ampere turns. Self-induction is ...", "... that is, the armature current demag- netizes or magnetizes the field according to its phase, and so lowers or raises the voltage. Armature reaction therefore is expressed in ampere turns. Self-induction is the action of the armature current in producing magnetism in the armature, which magnetism does not go through the field. This magnetism induces an e. m. f. in the armature, which opposes or assists the e. m. f . produced by the field magnetism, according to the phase of the armature current, and so lowers or ra ...", "... ag- netizes or magnetizes the field according to its phase, and so lowers or raises the voltage. Armature reaction therefore is expressed in ampere turns. Self-induction is the action of the armature current in producing magnetism in the armature, which magnetism does not go through the field. This magnetism induces an e. m. f. in the armature, which opposes or assists the e. m. f . produced by the field magnetism, according to the phase of the armature current, and so lowers or raises the voltage. Self-induction, ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... y high armature reaction and relatively weak field excitation; that is, the armature ampere turns are nearly equal and opposite to the field ampere turns, and thus both very large compared with the difference, the resultant ampere turns, which produce the magnetic field. A moderate increase of current and consequent increase of armature ampere turns therefore greatly reduces the resultant ampere turns and ARC LIGHTING 221 so the field magnetism and the voltage, (that is, the machine tends to regulate for consta ...", "... d with the difference, the resultant ampere turns, which produce the magnetic field. A moderate increase of current and consequent increase of armature ampere turns therefore greatly reduces the resultant ampere turns and ARC LIGHTING 221 so the field magnetism and the voltage, (that is, the machine tends to regulate for constant current. Perfect constant current regulation then is secured by some governing device, as an auto- matic regulator varying a resistance shunted across the series field. It must, however ...", "... e, is immaterial, or rather, is determined by consideration of design). Fig. 48 shows the coil S suspended and its weight partially balanced by counter-weight W. With the secondary coil S close to the coil P, that is, in the lowest position, most of the magnetism produced by the primary coil P passes through the secondary coil S, and the secondary voltage therefore is a maximum. The further the secondary coil moves away from the primary coil, the more of the magnetism passes between the coils, the less through the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-85", "section_label": "Apparatus Section 6: Synchronous Converters: Reactive Currents and Compounding", "section_title": "Synchronous Converters: Reactive Currents and Compounding", "kind": "apparatus-section", "sequence": 85, "number": 6, "location": "lines 15476-15585", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-85/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-85/", "snippets": [ "VI. Reactive Currents and Compounding 96. Since the polarization due to the power component of the alternating current as synchronous motor is in quadrature ahead of the field magnetization, the polarization or magnetizing effect of the lagging component of alternating current is in phase, that of the leading component of alternating current in oppositon to the field magnetization; that is, in the converter no ...", "VI. Reactive Currents and Compounding 96. Since the polarization due to the power component of the alternating current as synchronous motor is in quadrature ahead of the field magnetization, the polarization or magnetizing effect of the lagging component of alternating current is in phase, that of the leading component of alternating current in oppositon to the field magnetization; that is, in the converter no magnetic distortion exists, and ...", "... quadrature ahead of the field magnetization, the polarization or magnetizing effect of the lagging component of alternating current is in phase, that of the leading component of alternating current in oppositon to the field magnetization; that is, in the converter no magnetic distortion exists, and no armature reaction at all if the current is in phase with the impressed e.m.f., while the- armature reaction is demagnetizing with a leading and mag- netizing ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-24", "section_label": "Chapter 24: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 25682-29374", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-24/", "snippets": [ "... (equivalent) resistance, r, and (equivalent) reactance, x = 2 irfL, containing the impressed e.m.f., eo and the counter e.m.f., d, of the syn- chronous motor ^; that is, the e.m.f. generated in the motor arma- ture by its rotation through the (resultant) magnetic field. Let i = current in the circuit (effective values). The mechanical power delivered by the synchronous motor (including friction and core loss) is the electric power consumed by the counter e.m.f., ei; hence ■p = iei cos {i, 6]); (1) thus, c ...", "... Co = e.m.f. at motor terminals, z = internal impedance of the motor; if So = terminal voltage of the generator, z = total impedance of line and motor; if eo = e.m.f. of generator, that is, e.m.f. generated in generator armature by its rotation through the magnetic field, z includes the generator impedance also. 316 ALTERNATING-CURRENT PHENOMENA form a triangle, that is, ei and e are components of eo, it is (Figs. 159 and 160), eo' e-^ + 6^ + 2 ee\\ cos (ei, e), hence, cos (ei, e) = eo 2-ei2 ...", "... proximations only, since a number of assumptions are made which are not, or only partly, fulfilled in practice. The fore- most of these are: 1. It is assumed that ei can be varied unrestrictedly, while in reality the possible increase of ei is limited by magnetic saturation. Thus in Fig. 162, at an impressed e.m.f., eo = 2500 volts, ei rises up to 5590 volts, which may or may not be beyond that which can be produced by the motor, but certainly is beyond that which can be constantly given by the motor. 2. The rea ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-18", "section_label": "Chapter 16: Il", "section_title": "Il", "kind": "chapter", "sequence": 18, "number": 16, "location": "lines 19346-21338", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-18/", "snippets": [ "... cuit of (equivalent) resistance r and (equivalent) reactance x = 2irJVZ, containing the impressed E.M.F. e^* and the counter E.M.F. tTi of the syn- chronous motor; that is, the E.M F. induced in the motor arma- ture by its rotation through the (resultant) magnetic field. Let / = current in the circuit (effective values). The mechanical power delivered by the synchronous motor (including friction and core loss) is the electric power consumed by the C. E.M.F. e^; hence — / = />i cos (/'i ^,), (1) thus, — cos ...", "... i\\y = E.M.F. at motor terminals, z = internal impedances of the motor; if eo= terminal voltage of the generator, s = total impedance of line and motor; if ^f^ = E.M.F. of generator, that is, E.M.F. induced in generator armature by its rotation through the magnetic field, z includes the generator impedance also. f6 ALTERNATJNG-CURRENT PHENOMENA. [S 184 The displacement of phase between current i and E.M.F. = si consumed by the impedance s is : cos (*>) = sin (»>) = Since the three E.M.Fs. acting in the clos ...", "... f assump- sioi] SYNCHRONOUS MOTOR. tions are made which are not, or only partly, fulfilled in practice. The foremost of these are ; 1. It is assumed that fj can be varied unrestrictedly, while in reality the possible increase of f, is limited by magnetic saturation. Thus in Fig. 139, at an impressed E.M.F., e^ = 2,500 volts, <■, rises up to 5,590 volts, which may or may not be beyond that which can be produced by the motor, but certainly is beyond that which can be constantly given by the motor. IM ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-19", "section_label": "Chapter 19: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 18053-19457", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "snippets": [ "... cuit of (equivalent) resistance r and (equivalent) reactance x = 2 TT NL, containing the impressed E.M.F. e0* and the counter E.M.F. et of the syn- chronous motor; that is, the E.M.F. induced in the motor arma- ture by its rotation through the (resultant) magnetic field. Let i = current in the circuit (effective values). The mechanical power delivered by the synchronous motor (including friction and core loss) is the electric power consumed by the C. E.M.F. e1; hence — p = *>! cos ft,^), (1) thus, — * If f ...", "... * If f0 = E.M.F. at motor terminals, z = internal impedance of the motor; if eo= terminal voltage of the generator, z = total impedance of line and motor; if t0= E.M.F. of generator, that is, E.M.F. induced in generator armature by its rotation through the magnetic field, z includes the generator impedance also. SYNCHRONOUS MOTOR. 339 The displacement of phase between current i and E.M.F. = z i consumed by the impedance z is : cos (ie) = - sin (/ and $, of different phases, as magnetic circuits of the two transformers, which generate the e m.fs., e and e, per turn, by the law of parallelogram the e.m.fs., El, E2, .... can be resolved into two components, Ei and El, E2 and E2, .... of th ...", "... nce-factor by two transformers only. 290. Let El, E^, E3 .... he the e.m.fs. of the primary sys- tem which shall be transformed into E\\, E'2, E'i .... the e.m.fs. of the secondary system. Choosing two magnetic fluxes, 4> and $, of different phases, as magnetic circuits of the two transformers, which generate the e m.fs., e and e, per turn, by the law of parallelogram the e.m.fs., El, E2, .... can be resolved into two components, Ei and El, E2 and E2, .... of the phases, e and e. Theri_ El, Ei, .... are the co ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-27", "section_label": "Chapter 27: Tbansfobmation Of Polyphase Systems", "section_title": "Tbansfobmation Of Polyphase Systems", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 26428-26583", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-27/", "snippets": [ "... ormed again in a balanced system, and an unbalanced system into an unbalanced sys- tem of the same balance factor, since the transformer is an apparatus not able to store energy, and thereby to change the nature of the flow of power. The energy stored as magnetism, amounts in a well-designed transformer only to a very small percentage of the total energy. This shows the futility of producing symmetrical balanced polyphase systems by transformation from the unbalanced single-phase system without additional apparatus ...", "... nto any other polyphase system of the same balance factor by two transformers only. 266. Let £*,, ^2, ^3 .... be the E.M.Fs. of the primary system which shall be transformed into — E(, E^, E^ , , , , the E.M.Fs. of the secondary system. Choosing two magnetic fluxes, T CO — 7), ^ . . e = eoe~\"' sin ((^ =F co — 7), where T co — 7), ) where 0 is the time angle, co the distance angle, u the exponential decrement, or the \"power-dissipation constant,\" and i0 and eQ th ...", "... ay be caused if by a lightning stroke, etc., a quantity of dielectric energy is impressed A • Fig. 39. — Starting of Impulse, or Traveling Wave. upon a part of the circuit, as shown by curve A in Fig. 39, or if by a local short circuit a quantity of magnetic energy is impressed upon a part of the circuit. This energy then gradually distributes over the circuit, as indicated by the curves B, C, etc., of Fig. 39, that is, moves along the circuit, and the dissipation of the stored energy thus occurs by a flow of ...", "... miles of line and 2500-kw. 100-kv. step-up and step-down transformers, and is produced by discon- necting this circuit by low-tension switches. In the transformer, the duration of the transient would be very great, possibly several seconds, as the stored magnetic energy (L) is very large, the dis- sipation of power (r and g) relatively small; in the line, the tran- sient is of fairly short duration, as r (and g) are considerable. Left to themselves, the line oscillations thus would die out much more rapidly, by th ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-04", "section_label": "Chapter 5: Methods Of Approximation", "section_title": "Methods Of Approximation", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 15156-16482", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-04/", "snippets": [ "... d ri — jxi the impedance of the secondary circuit of the motor at full frequency, and the exciting current of the motor is neglected; assuming s to be a small quantity; that is, the motor running at full speed? Let E be the e.m.f. generated by the mutual magnetic flux, that is, the magnetic flux which interlinks with primary and with secondary circuit, in the primary circuit. Since the fre- quency of the secondary circuit is the fraction 8 of the frequency 192 ENGINEERING MATHEMATICS. of the primary circuit, t ...", "... i the impedance of the secondary circuit of the motor at full frequency, and the exciting current of the motor is neglected; assuming s to be a small quantity; that is, the motor running at full speed? Let E be the e.m.f. generated by the mutual magnetic flux, that is, the magnetic flux which interlinks with primary and with secondary circuit, in the primary circuit. Since the fre- quency of the secondary circuit is the fraction 8 of the frequency 192 ENGINEERING MATHEMATICS. of the primary circuit, the ge ...", "... he secondary circuit of the motor at full frequency, and the exciting current of the motor is neglected; assuming s to be a small quantity; that is, the motor running at full speed? Let E be the e.m.f. generated by the mutual magnetic flux, that is, the magnetic flux which interlinks with primary and with secondary circuit, in the primary circuit. Since the fre- quency of the secondary circuit is the fraction 8 of the frequency 192 ENGINEERING MATHEMATICS. of the primary circuit, the generated e.m.f. of the se ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-06", "section_label": "Theory Section 6: Self-inductance of Continuous-current Circuits", "section_title": "Self-inductance of Continuous-current Circuits", "kind": "theory-section", "sequence": 6, "number": 6, "location": "lines 1785-2249", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-06/", "snippets": [ "... resistance, L = inductance of circuit, E = continuous e.m.-f. impressed upon circuit, i = current in circuit at time t after impressing e.m.f. E, and di the increase of current during time moment dt, then the increase of magnetic interlinkages during time dt is IM, and the e.m.f. generated thereby is r di ei = -L~di By Lentz's law it is negative, since it is opposite to the im- pressed e.m.f., its cause. Thus the e.m.f. acting in this mome ...", "... sed through a resistance r\\. Let the current be i at the time t after withdrawal of the e.m.f. E and the change of current during time moment dt be di. di is negative, that is, the current decreases. The decrease of magnetic interlinkages during moment dt is Ldi. Thus the e.m.f. generated thereby is Tdi ei== ~Ldi It is negative since di is negative, and e\\ must be positive, that is, in the same direction as E, to maintain the current o ...", "... time t of the e.m.f. of inductance in stop- ping the current is _ 2r + rif iei = io2 (r + n) c L ; thus the total energy of the generated e.m.f. >*» W = | z' Jo that is, the energy stored as magnetism in a circuit of current iQ and inductance L is 2 ' which is independent both of the resistance r of the circuit and the resistance n inserted in breaking the circuit. This energy has to be expended in stopping the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-47", "section_label": "Apparatus Section 4: Direct-current Commutating Machines: Distribution of Magnetic Flux", "section_title": "Direct-current Commutating Machines: Distribution of Magnetic Flux", "kind": "apparatus-section", "sequence": 47, "number": 4, "location": "lines 10836-10844", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-47/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-47/", "snippets": [ "IV. Distribution of Magnetic Flux 43. The distribution of magnetic flux in the air gap or at the armature surface can be calculated approximately by assuming the density at any point of the armature surface as proportional to the m.m.f. acting there ...", "IV. Distribution of Magnetic Flux 43. The distribution of magnetic flux in the air gap or at the armature surface can be calculated approximately by assuming the density at any point of the armature surface as proportional to the m.m.f. acting thereon, a ...", "IV. Distribution of Magnetic Flux 43. The distribution of magnetic flux in the air gap or at the armature surface can be calculated approximately by assuming the density at any point of the armature surface as proportional to the m.m.f. acting thereon, and inversely proportional to the n ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-56", "section_label": "Apparatus Section 7: Direct-current Commutating Machines: Effect of Slots on Magnetic Flux", "section_title": "Direct-current Commutating Machines: Effect of Slots on Magnetic Flux", "kind": "apparatus-section", "sequence": 56, "number": 7, "location": "lines 11387-11400", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-56/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-56/", "snippets": [ "VII. Effect of Slots on Magnetic Flux 53. With slotted armatures the pole face density opposite the armature slots is less than that opposite the armature teeth, due to the greater distance of the air path in the former case. Thus, with the passage of ...", "VII. Effect of Slots on Magnetic Flux 53. With slotted armatures the pole face density opposite the armature slots is less than that opposite the armature teeth, due to the greater distance of the air path in the former case. Thus, with the passage of the ...", "... armature slots is less than that opposite the armature teeth, due to the greater distance of the air path in the former case. Thus, with the passage of the armature slots across the field pole a local pulsation of the magnetic flux in the pole face is produced, which, while harmless with laminated field pole faces, generates eddy currents in solid pole pieces. The frequency of this pul- sation is extremely high, and thus the energy loss due to ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-94", "section_label": "Apparatus Subsection 94: Synchronous Converters: Thbee-wire Converter", "section_title": "Synchronous Converters: Thbee-wire Converter", "kind": "apparatus-subsection", "sequence": 94, "number": null, "location": "lines 16727-16803", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-94/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-94/", "snippets": [ "... se such a connection that the trans- former can operate as autotransformer, that is, that the direct current in each transformer divides into two branches of equal m.m.f., otherwise the direct-current produces a unidirectional magnetization in the transformer, which superimposed upon the magnetic cycle raises the magnetic induction beyond satura- tion, and thus causes excessive exciting current and heating, except when very small. SYNCHRONOUS CONVERTERS 275 k ...", "... utotransformer, that is, that the direct current in each transformer divides into two branches of equal m.m.f., otherwise the direct-current produces a unidirectional magnetization in the transformer, which superimposed upon the magnetic cycle raises the magnetic induction beyond satura- tion, and thus causes excessive exciting current and heating, except when very small. SYNCHRONOUS CONVERTERS 275 k *T. \\ FIG. 149. — Neutral of Y-connected transf ...", "... at the direct current in each transformer divides into two branches of equal m.m.f., otherwise the direct-current produces a unidirectional magnetization in the transformer, which superimposed upon the magnetic cycle raises the magnetic induction beyond satura- tion, and thus causes excessive exciting current and heating, except when very small. SYNCHRONOUS CONVERTERS 275 k *T. \\ FIG. 149. — Neutral of Y-connected transformers connected to neutral ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-13", "section_label": "Chapter 15: Synchronous Rectifier", "section_title": "Synchronous Rectifier", "kind": "chapter", "sequence": 13, "number": 15, "location": "lines 18413-19373", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-13/", "snippets": [ "... of separate impulses of cur- rent and voltage as shown in Fig. 100 as i\\. However, in this case the current in the alternating supply circuit is unidirectional also, is the same current, i\\. This current produces in the trans- former, T, a unidirectional magnetization, and, if of appreciable 246 ELECTRICAL APPARATUS magnitude, that is, larger than the exciting current of the trans- former, it .saturates the transformer iron. Running at or beyond magnetic saturation, the primary exciting current of the trans- fo ...", "... t produces in the trans- former, T, a unidirectional magnetization, and, if of appreciable 246 ELECTRICAL APPARATUS magnitude, that is, larger than the exciting current of the trans- former, it .saturates the transformer iron. Running at or beyond magnetic saturation, the primary exciting current of the trans- former then becomes excessive, the hysteresis heating due to the unsymmetrical magnetic cycle is greatly increased, and the transformer endangered or destroyed. Half-wave rectifiers thus are impract ...", "... larger than the exciting current of the trans- former, it .saturates the transformer iron. Running at or beyond magnetic saturation, the primary exciting current of the trans- former then becomes excessive, the hysteresis heating due to the unsymmetrical magnetic cycle is greatly increased, and the transformer endangered or destroyed. Half-wave rectifiers thus are impracticable except for extremely small power. The full-wave contact-making rectifier, Fig. 97 or 98, does not have this objection. In this type of ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-39", "section_label": "Chapter 3: Mechanical Rectification", "section_title": "Mechanical Rectification", "kind": "chapter", "sequence": 39, "number": 3, "location": "lines 15963-17754", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-39/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-39/", "snippets": [ "... however, very greatly from those of Fig. 59. In the arc machine, inherent regu- lation for constant current is produced by opposing a very high armature reaction to the field excitation, so that the resultant m.m.f., or m.m.f. which produces the effective magnetic flux, is .40 5D 90 100 110 120 16 y '^ 12 ''/' 10 t2 r ' — •— — — . --*^ 'x/' \\\\ 8 2000 £ ^ X <^ — -I — - •~~^ t*-\"- —- h^ f ^> — - — 4 1000 ^ .- •\"J **** ^ S. X * d2-2«50n ^ ...", "... very greatly from those of Fig. 59. In the arc machine, inherent regu- lation for constant current is produced by opposing a very high armature reaction to the field excitation, so that the resultant m.m.f., or m.m.f. which produces the effective magnetic flux, is .40 5D 90 100 110 120 16 y '^ 12 ''/' 10 t2 r ' — •— — — . --*^ 'x/' \\\\ 8 2000 £ ^ X <^ — -I — - •~~^ t*-\"- —- h^ f ^> — - — 4 1000 ^ .- •\"J **** ^ S. X * d2-2«50n ^, _ ...", "... UO Degrees > Fig. 59. Quarter-phase rectification. small compared with the total field m.m.f. and the armature reaction, and so greatly varies with a small variation of armature current. As result, a very great distortion of the field occurs, and the magnetic flux is concentrated at the pole corner. This gives an e.m.f. wave which has a very sharp and high peak, with very long flat zero, and so cannot be approximated by an equiva- lent sine wave, but the actual e.m.f. curves have to be used in a more exact inv ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "LECTURE VII. LINE OSCILLATIONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy surges between magnetic — and dielectric — , and a transient component, by which the total stored energy decreases. Considering only the periodic component, the maximum value of magnetic energy must equal the maximum value of dielectric '^'^e^gy- Li„^ Ce, 0 \"^^0 (1) ...", "... tran- sient consists of a periodic component, by which the stored energy surges between magnetic — and dielectric — , and a transient component, by which the total stored energy decreases. Considering only the periodic component, the maximum value of magnetic energy must equal the maximum value of dielectric '^'^e^gy- Li„^ Ce, 0 \"^^0 (1) where Iq = maximum value of transient current, 60 = maximum value of transient voltage. This gives the relation between Bq and Iq, ^^ = Jl ,^ = 1, (2) where Zq ...", "... the inductance is easily de- rived, equation (35) is useful in calculating the capacity by means of the inductance. This equation (35) also allows the calculation of the mutual capacity, and thereby the static induction between circuits, from the mutual magnetic inductance. The reverse equation, Lo = ^^. (36) is useful in calculating the inductance of cables from their meas- ured capacity, and the velocity of propagation equation (13). 31. If Zi is the length of a line, and its two ends are of different ele ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-07", "section_label": "Lecture 7: High Frequency Oscillations And Surges", "section_title": "High Frequency Oscillations And Surges", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3508-3780", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-07/", "snippets": [ "... 1\"^ N an electric circuit, in addition to the power consump- tion by the resistance of the lines, an energy storage ■^ occurs as electrostatic energy, or electrostatic charge due to the voltage on the line (capacity) ; and as electromag- netic energy, or magnetic field of the current in the line (inductance). In the long distance transmission line, both amounts of stored energy are very considerable, and of about equal magnitude; the former varying with the voltage, the latter with the current in the line. Any cha ...", "... e, or the current in the line, or the relation between volt- age and current, therefore requires a corresponding change of the stored energy; that is, a readjustment of the stored energy e^C in the system, the electrostatic energy and the electro- i'L magnetic energy — — , from the previous to the changed cir- cuit conditions. This readjustment occurs by an oscillation, that is, a series of waves of voltage and of current, which gradually decreases in intensity, that is, dies out. ' These oscillating voltages ...", "... mately conies from the generators, it is not the generator wave nor one of its harmonics which builds up, as discussed in the previous lectures; but the generator merely supplies the energy, which is stored as electrostatic charge of the capacity and as magnetic field of the inductance, and the readjustment of this stored energy to the change of circuit conditions then gives the oscillation. These oscillating voltages and currents, adding to the generator voltage and current, thus increase the voltage and the c ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-60", "section_label": "Apparatus Section 9: Direct-current Commutating Machines: Saturation Curves", "section_title": "Direct-current Commutating Machines: Saturation Curves", "kind": "apparatus-section", "sequence": 60, "number": 9, "location": "lines 11695-11710", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-60/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-60/", "snippets": [ "IX. Saturation Curves 57. As saturation curve or magnetic characteristic of the com- mutating machine is understood the curve giving the generated voltage, or terminal voltage at open circuit and normal speed, as function of the ampere-turns per pole field excitation. Such curves a ...", "... e giving the generated voltage, or terminal voltage at open circuit and normal speed, as function of the ampere-turns per pole field excitation. Such curves are of the shape shown in Fig. 105 as A. Owing to the remanent magnetism or hysteresis of the iron part of the magnetic circuit, the saturation curve taken with decreasing field excitation usually does not coincide with that taken with increasing field excitation, but is higher, and by gradually ...", "... e at open circuit and normal speed, as function of the ampere-turns per pole field excitation. Such curves are of the shape shown in Fig. 105 as A. Owing to the remanent magnetism or hysteresis of the iron part of the magnetic circuit, the saturation curve taken with decreasing field excitation usually does not coincide with that taken with increasing field excitation, but is higher, and by gradually first increasing the field excitation from zero ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-95", "section_label": "Apparatus Section 1: Alternating-current Transformer: General", "section_title": "Alternating-current Transformer: General", "kind": "apparatus-section", "sequence": 95, "number": 1, "location": "lines 16804-16911", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-95/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-95/", "snippets": [ "I. General 110. The alternating-current transformer consists of a magnetic circuit interlinked with two electric circuits, the primary, which receives power, and the secondary, which gives out power. Since the same magnetic flux interlinks primary and second- ary turns, the same voltage is induced ...", "I. General 110. The alternating-current transformer consists of a magnetic circuit interlinked with two electric circuits, the primary, which receives power, and the secondary, which gives out power. Since the same magnetic flux interlinks primary and second- ary turns, the same voltage is induced in every turn of the electric circuits, and the e.m.fs. induced in the primary and in the secondary winding therefore have the ratio of turns: «'i ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-02", "section_label": "Chapter 2: Instantaneous Values And Integral Values", "section_title": "Instantaneous Values And Integral Values", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 1684-2011", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-02/", "snippets": [ "... mutating and unipolar machines (or by the super- position of alternating upon direct currents, etc.). All inductive apparatus without commutation give exclusively alternating waves, because, no matter what conditions may exist in the circuit, any line of magnetic force which during a complete period is cut by the circuit, and thereby generates an e.m.f., must during the same period be cut again in the opposite direc- tion, and thereby generate the same total amount of e.m.f. (Ob- viously, this does not apply to ci ...", "... as the av- erage variation of the arc to that of the sine , that is, 1 -^ -, and since the variations of a sine function are sinusoidal also, we have Mean value of sine wave -r- maximum value = — ^ 1 = 0.63663. TT The quantities, \"current,\" \"e.m.f.,\" \"magnetism,\" etc., are in reality mathematical fictions only, as the components of the entities, \"energy,\" \"power,\" etc.; that is, they have no inde- pendent existence, but appear only as squares or products. Consequently, the only integral value of an alternating ...", "... eous values, as determined by wave-meter or oscillograph. Measurement of the alternating wave after rectification by a unidirectional conductor, as an arc, gives the inean value with direct-current instruments, that is, instruments employing a permanent magnetic field, and the effective value with alternating- current instruments. Voltage determination by spark-gap, that is, by the striking distance, gives a value approaching the maximum, especially with spheres as electrodes of a diameter larger than the spark- ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "section_label": "Chapter 30: Quartbr-Fhase System", "section_title": "Quartbr-Fhase System", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... jr = 2 IT N L = inductive reactance, Xc = l/2vN'C = capacity reactance of the total primary circuit, including the primary coil of the transformer. If ^/ = El dec o denotes the electromotive force induced in the secondary of the transformer by the mutual magnetic flux ; that is, by the oscillating magnetism interlinked with the primary and secondary coil, we have /j = £i Vi dec a = secondary current. Hence, // = / /i dec a = pE' Fj dec a = primary load current, or component of primary current corresponding to ...", "... N L = inductive reactance, Xc = l/2vN'C = capacity reactance of the total primary circuit, including the primary coil of the transformer. If ^/ = El dec o denotes the electromotive force induced in the secondary of the transformer by the mutual magnetic flux ; that is, by the oscillating magnetism interlinked with the primary and secondary coil, we have /j = £i Vi dec a = secondary current. Hence, // = / /i dec a = pE' Fj dec a = primary load current, or component of primary current corresponding to second ...", "... /2vN'C = capacity reactance of the total primary circuit, including the primary coil of the transformer. If ^/ = El dec o denotes the electromotive force induced in the secondary of the transformer by the mutual magnetic flux ; that is, by the oscillating magnetism interlinked with the primary and secondary coil, we have /j = £i Vi dec a = secondary current. Hence, // = / /i dec a = pE' Fj dec a = primary load current, or component of primary current corresponding to secondary current. Also, /^ = — E^ Y^ dec a = ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-32", "section_label": "Chapter 32: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 25904-27405", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "snippets": [ "... 2 TT NL = inductive reactance, xc = 1 / 2 TT N C = capacity reactance of the total primary circuit, including the primary coil of the transformer. If EI = EI dec a denotes the electromotive force induced in the secondary of the transformer by the mutual magnetic flux ; that is, by the oscillating magnetism interlinked with the primary and secondary coil, we have Iv = E^ Yl dec a = secondary current. Hence, // = / 7X dec a = pEJ Yl dec a = primary load current, or component of primary current corresponding to ...", "... inductive reactance, xc = 1 / 2 TT N C = capacity reactance of the total primary circuit, including the primary coil of the transformer. If EI = EI dec a denotes the electromotive force induced in the secondary of the transformer by the mutual magnetic flux ; that is, by the oscillating magnetism interlinked with the primary and secondary coil, we have Iv = E^ Yl dec a = secondary current. Hence, // = / 7X dec a = pEJ Yl dec a = primary load current, or component of primary current corresponding to second ...", "... TT N C = capacity reactance of the total primary circuit, including the primary coil of the transformer. If EI = EI dec a denotes the electromotive force induced in the secondary of the transformer by the mutual magnetic flux ; that is, by the oscillating magnetism interlinked with the primary and secondary coil, we have Iv = E^ Yl dec a = secondary current. Hence, // = / 7X dec a = pEJ Yl dec a = primary load current, or component of primary current corresponding to secondary current. Also, 70 = - 2j/ F0 dec a = ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-05", "section_label": "Chapter 6: Induction-Motor Regulation And Stability", "section_title": "Induction-Motor Regulation And Stability", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 10583-12397", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-05/", "snippets": [ "... ncrease of voltage, and thereby of motor torque, is required to bring the machine beyond the dead point, or rather \"dead range,\" of speed and make it run up to synchronism. In this case, however, the phenomenon is complicated by the effects due to varying magnetic reluctance (magnetic locking), inductor machine effect, etc. Instability of such character as here described occurs in elec- tric circuits in many instances, of which the most typical is the electric arc in a constant-potential supply. It occurs whenever ...", "... f voltage, and thereby of motor torque, is required to bring the machine beyond the dead point, or rather \"dead range,\" of speed and make it run up to synchronism. In this case, however, the phenomenon is complicated by the effects due to varying magnetic reluctance (magnetic locking), inductor machine effect, etc. Instability of such character as here described occurs in elec- tric circuits in many instances, of which the most typical is the electric arc in a constant-potential supply. It occurs whenever the effec ...", "... d thereby of motor torque, is required to bring the machine beyond the dead point, or rather \"dead range,\" of speed and make it run up to synchronism. In this case, however, the phenomenon is complicated by the effects due to varying magnetic reluctance (magnetic locking), inductor machine effect, etc. Instability of such character as here described occurs in elec- tric circuits in many instances, of which the most typical is the electric arc in a constant-potential supply. It occurs whenever the effect produced ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-15", "section_label": "Chapter 15: Constant-Voltage Series Operation", "section_title": "Constant-Voltage Series Operation", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 27996-29301", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-15/", "snippets": [ "... ent as at load, and thus have five times as high a voltage at its terminals. The latter, however, is not feasible, except by making the reactance abnormally large and therefore uneconomical. In general, long before five times normal voltage is reached, magnetic saturation will have occurred, and the reactance thereby decreased, that is, the susceptance, 6, increased, as more fully dis- cussed in Chapter VIII. This actual condition would correspond to a value, 6i, of the shunted susceptance when shunted by the l ...", "... a different, higher value, 62, of the shunted susceptance when the lamp is burned out. The question then arises, whether such values of 61 and 62 can be found, as to give voltage regulation. The increase of 62 over 61 naturally depends on the degree of magnetic saturation in the re- actance, that is, on the value of magnetic density chosen, and thus can be made anything, depending on the design. 167. Let then, as heretofore. ^0 — 60 = constant-supply voltage. / = current in series circuit. n = number of c ...", "... he lamp is burned out. The question then arises, whether such values of 61 and 62 can be found, as to give voltage regulation. The increase of 62 over 61 naturally depends on the degree of magnetic saturation in the re- actance, that is, on the value of magnetic density chosen, and thus can be made anything, depending on the design. 167. Let then, as heretofore. ^0 — 60 = constant-supply voltage. / = current in series circuit. n = number of consuming devices (lamps) in series. p = fraction of burned-out l ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-37", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 37, "number": 1, "location": "lines 15354-15625", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "snippets": [ "CHAPTER I. INTRODUCTION. 1. Whenever in an electric circuit a sudden change of the circuit conditions is produced, a transient term appears in the circuit, that is, at the moment when the change begins, the circuit quantities, as current, voltage, magnetic flux, etc., cor- respond to the circuit conditions existing before the change, but do not, in general, correspond to the circuit conditions brought about by the change, and therefore must pass from the values corresponding to the previous condition to the ...", "... TER I. INTRODUCTION. 1. Whenever in an electric circuit a sudden change of the circuit conditions is produced, a transient term appears in the circuit, that is, at the moment when the change begins, the circuit quantities, as current, voltage, magnetic flux, etc., cor- respond to the circuit conditions existing before the change, but do not, in general, correspond to the circuit conditions brought about by the change, and therefore must pass from the values corresponding to the previous condition to the valu ...", "... n, or an approach by a series of oscillations of gradual decreasing intensities. Gradually — after indefinite time theoretically, after relatively short time practically — the transient term disappears, and permanent conditions of current, of voltage, of magnetism, etc., are established. The numerical values of current, of voltage, etc., in the permanent state reached after the change of circuit con- ditions, in general, are different from the values of current, voltage, etc., existing in the permanent state before ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-41", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 41, "number": 1, "location": "lines 19260-19338", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "snippets": [ "... f the line, or current density at the surface of a solid conductor carrying alternating current, as the rail return of a single-phase railway, with the current density at the center or in general inside of the conductor, or the distribution of alternating magnetism inside of a solid iron, as a lamina of an alternating-current transformer, etc. In such transient phenom- ena in space, the electric quantities, which appear as functions of space or distance, are not the instantaneous values, as in the preceding chapters ...", "... tential lightning arresters (multi-gap arrester), etc. (b) The distribution of alternating current in solid conductors and the increase of effective resistance and decrease of effective inductance resulting therefrom. (c) The distribution of alternating magnetic flux in solid iron, or the screening effect of eddy currents produced in the iron, and the apparent decrease of permeability and increase of power consumption resulting therefrom. (d) The distribution of the electric field of a conductor through space, ...", "... ightning arresters (multi-gap arrester), etc. (b) The distribution of alternating current in solid conductors and the increase of effective resistance and decrease of effective inductance resulting therefrom. (c) The distribution of alternating magnetic flux in solid iron, or the screening effect of eddy currents produced in the iron, and the apparent decrease of permeability and increase of power consumption resulting therefrom. (d) The distribution of the electric field of a conductor through space, resul ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-56", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit", "section_title": "Power And Energy Of The Complex Circuit", "kind": "chapter", "sequence": 56, "number": 7, "location": "lines 33528-34202", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "snippets": [ "... rom the rest of the circuit, is proportional to the length of the section, A', to its trans- fer constant, s, and to the sum of the power of main wave and reflected wave. 51. The energy stored by the inductance L of a circuit element dXj that is, in the magnetic field of the circuit, is 'LV dwl =-^~A where U = inductance per unit length of circuit expressed by the distance coordinate A. Since L = the inductance per unit length of circuit, of distance coordinate Z, and X = 2 surges between magnetic -^- and dielectric — , and a transient £i A component, by which the total stored energy decreases. Considering only the periodic component, the maximum mag- netic energy must equal the maximum dielectric energy, Lio2 _ Ceo2 \"2\" ~2~' where i0 = max ...", "... the inductance is easily de- rived, equation (35) is useful in calculating the capacity by means of the inductance. This equation (35) also allows the calculation of the mutual capacity, and thereby the static induction between circuits, from the mutual magnetic inductance. The reverse equation, - (36) is useful in calculating the inductance of cables from their meas- ured capacity, and the velocity of propagation equation (13). 31. If li is the length of a line, and its two ends are of different electrica ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-01", "section_label": "Chapter 1: The General Number", "section_title": "The General Number", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 915-3491", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-01/", "snippets": [ "... olutions of differential equations frequently appear in this form, and then are reduced to the polar or the rectangular form. 37. For instance, the differential equation of the distribu- tion of alternating current in a flat conductor, or of alternating magnetic flux in a flat sheet of iron, has the form : and is integrated by y = A£~^'^, where. V=\\/-2jc^=±{l-j)c; hence, 2/=^£+(i-^*)\"^+A2£-^^~^*K This expression, reduced to the polar form, is y = Aie'^''^(cos ex -j sin ex) +A2£~''''(cos ex+j sin ex). T ...", "... of differential equations frequently appear in this form, and then are reduced to the polar or the rectangular form. 37. For instance, the differential equation of the distribu- tion of alternating current in a flat conductor, or of alternating magnetic flux in a flat sheet of iron, has the form : and is integrated by y = A£~^'^, where. V=\\/-2jc^=±{l-j)c; hence, 2/=^£+(i-^*)\"^+A2£-^^~^*K This expression, reduced to the polar form, is y = Aie'^''^(cos ex -j sin ex) +A2£~''''(cos ex+j sin ex). THE GE ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-11", "section_label": "Lecture 11: Lightning Protection", "section_title": "Lightning Protection", "kind": "lecture", "sequence": 11, "number": 11, "location": "lines 4931-5294", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-11/", "snippets": [ "... to ground became insufficient, and this addi- tional problem arose : to open the short circuit of the machine current, which resulted from and followed the lightning dis- charge. This problem of opening the circuit after the discharge was solved by the magnetic blow-out, which is still used to a large extent on 500 volt railway circuits; by the horn gap arrester — a gap between two horn-shaped terminals, between which the arc rises, and so lengthens itself until it blows out ; and later on, for alternating curre ...", "... at the bus bars of the station, and in cable systems, usually in addition to other protection on lines and feeders; it requires, however, occasional attention, and continuously consumes a small amount of power. Of other forms of lightning arresters, the magnetic blow- out 500 volt railway arrester is still in use to a large extent, but is beginning to be superseded by the aluminum cell. The multi-gap, being based on the non-arcing or rectifying prop- erty of the metal cylinders which exists only with alternating ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... mparing equation (8) with (4) it follows : Vl = d*-, (9) that is, the square of the refractive index d equals the product of permeability JJL and dielectric constant K. Since for most media the permeability /JL = 1, for all except e maneti mri the magnetic materials RELATION OF BODIES TO RADIATION. 25 This relation between the constant of the electric circuit K and the constant of optics d was one of the first evidences of the identity of the meclium in which the electric field exists with the mediu ...", "... f the part which is not transmitted is irregularly reflected inside of the body. The most perfectly transparent bodies, for visible light, are glass, water, quartz, etc. ; the most opaque are the metals, and perfectly, or almost perfectly opaque are the magnetic metals, perhaps due to the very low speed of propagation in these metals, which would result from the high value of the permeability /* by equation (8) paragraph 11. As example of colorless bodies I show you here a glass tube filled with water, transpar ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-105", "section_label": "Apparatus Section 8: Alternating-current Transformer: Autotransformer", "section_title": "Alternating-current Transformer: Autotransformer", "kind": "apparatus-section", "sequence": 105, "number": 8, "location": "lines 18666-18812", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-105/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-105/", "snippets": [ "... ons, that is, by e\\ X ii + £2 X iz FIG. 172. — Diagram of trans- former. FIG. 173. — Diagram of auto- transformer. (the turns being proportional to the voltage, the turn section to the current, the same magnetic flux assumed). But since 61 = aez and i\\ = — , e\\i\\ = e2i2, and the size of the transformer Fig. 172 thus is proportional to 2 e-#2, that is, to 2 P, or twice the output. In the autotransformer Fig. 173, ...", "... is, by e\\ X ii + £2 X iz FIG. 172. — Diagram of trans- former. FIG. 173. — Diagram of auto- transformer. (the turns being proportional to the voltage, the turn section to the current, the same magnetic flux assumed). But since 61 = aez and i\\ = — , e\\i\\ = e2i2, and the size of the transformer Fig. 172 thus is proportional to 2 e-#2, that is, to 2 P, or twice the output. In the autotransformer Fig. 173, the nz ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-113", "section_label": "Apparatus Section 7: Induction Machines: Frequency Converter or General Alternating-current Transformer", "section_title": "Induction Machines: Frequency Converter or General Alternating-current Transformer", "kind": "apparatus-section", "sequence": 113, "number": 7, "location": "lines 21813-21922", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-113/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-113/", "snippets": [ "... e synchronous alternator further discussed in the \"Theory and Calculation of Electrical Apparatus.\" As far as its transformer action is concerned, the frequency 356 ELEMENTS OF ELECTRICAL ENGINEERING converter is an open magnetic circuit transformer, that is, a trans- former of relatively high magnetizing current. It combines therewith, however, the action of an induction motor or generator. Excluding the case of over-synchronous rotation, it is approxi ...", "... of Electrical Apparatus.\" As far as its transformer action is concerned, the frequency 356 ELEMENTS OF ELECTRICAL ENGINEERING converter is an open magnetic circuit transformer, that is, a trans- former of relatively high magnetizing current. It combines therewith, however, the action of an induction motor or generator. Excluding the case of over-synchronous rotation, it is approxi- mately (that is, neglecting internal losses) electrical input -r- electrical ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-25", "section_label": "Apparatus Section 4: Synchronous Machines: Self-inductance", "section_title": "Synchronous Machines: Self-inductance", "kind": "apparatus-section", "sequence": 25, "number": 4, "location": "lines 8907-9034", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-25/", "snippets": [ "... f armature reaction, FlQ 50._Diagram of e m fs> and depends upon the phase relation in loaded generator, in the same manner. If EI = real generated voltage, 0i = lag of current behind generated voltage EI, the magnetic flux produced by the arma- ture current I is in phase with the current, and thus the counter e.m.f. of self-inductance is in quadrature behind the current, and therefore the e.m.f. consumed by self-inductance is in quadratu ...", "... e reaction, FlQ 50._Diagram of e m fs> and depends upon the phase relation in loaded generator, in the same manner. If EI = real generated voltage, 0i = lag of current behind generated voltage EI, the magnetic flux produced by the arma- ture current I is in phase with the current, and thus the counter e.m.f. of self-inductance is in quadrature behind the current, and therefore the e.m.f. consumed by self-inductance is in quadrature ah ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-26", "section_label": "Apparatus Section 5: Synchronous Machines: Synchronous Reactance", "section_title": "Synchronous Machines: Synchronous Reactance", "kind": "apparatus-section", "sequence": 26, "number": 5, "location": "lines 9035-9169", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-26/", "snippets": [ "... hase synchronous reactance.\" The resultant armature reac- tion of all phases of the polyphase machine is higher than that with the same current in one phase only, and so also the self- SYNCHRONOUS MACHINES 137 inductive flux, as resultant flux of several phases, and thus rep- resents a higher synchronous reactance. Let r = effective resistance, XQ = synchronous reactance of armature, as discussed in Section II. Let E = terminal voltage, / = ...", "... tance.\" The resultant armature reac- tion of all phases of the polyphase machine is higher than that with the same current in one phase only, and so also the self- SYNCHRONOUS MACHINES 137 inductive flux, as resultant flux of several phases, and thus rep- resents a higher synchronous reactance. Let r = effective resistance, XQ = synchronous reactance of armature, as discussed in Section II. Let E = terminal voltage, / = current, 0 = angl ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-36", "section_label": "Apparatus Section 15: Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "section_title": "Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "kind": "apparatus-section", "sequence": 36, "number": 15, "location": "lines 9918-10123", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-36/", "snippets": [ "... he crosscurrents thus in quadrature with the machine voltages OEi and OE%, and hence do not transfer energy, but are wattless. In one machine the cross current is a lagging or demagnetizing, and in the other a leading or magnetizing, current. Hence two kinds of cross currents may exist in parallel opera- tion of alternators — currents transferring power between the machines, due to phase displacement between their e.m.fs., and wattless currents transferring ...", "... current. Hence two kinds of cross currents may exist in parallel opera- tion of alternators — currents transferring power between the machines, due to phase displacement between their e.m.fs., and wattless currents transferring magnetization between the ma- chines, due to a difference of their induced e.m.fs. In compound-wound alternators, that is, alternators in which the field excitation is increased with the load by means of a series field excited by the r ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-40", "section_label": "Apparatus Subsection 40: Direct-current Commutating Machines: C. Commutating Machines", "section_title": "Direct-current Commutating Machines: C. Commutating Machines", "kind": "apparatus-subsection", "sequence": 40, "number": null, "location": "lines 10475-10519", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-40/", "snippets": [ "... - vantage of greater mechanical strength, but the disadvantage of higher self-inductance in commutation, and thus requires high- resistance, carbon or graphite, commutator brushes. The iron- clad type has the advantage of lesser magnetic stray field, due FIG. 78. — Series machine. FIG. 79. — Compound machine. to the shorter gap between field pole and armature iron, and of lesser magnet distortion under load, and thus can with carbon brushes be operated ...", "... armature is best adapted; the smooth-core type is hardly ever used nowadays. Either of these types can be drum wound or ring wound. The drum winding has the advantage of lesser self-inductance and lesser distortion of the magnetic field, and is generally less difficult to construct and thus mostly preferred. By the arma- ture winding, commutating machines are divided into multiple- wound and series-wound machines. The difference between multiple and seri ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-44", "section_label": "Apparatus Subsection 44: Direct-current Commutating Machines: C. Commutating Machines 175", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 175", "kind": "apparatus-subsection", "sequence": 44, "number": null, "location": "lines 10685-10736", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-44/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-44/", "snippets": [ "... windings have the advantage of shorter end connections and less self-inductance in commutation, since commutation of corresponding coils under different poles does not take place in the same, but in different, slots, and the flux of self-inductance in commutation is thus more subdivided. Fig. 91 shows the multiple drum winding of Fig. 81 as a frac- FIG. 91. — Multiple drum five-sixth fractional pitch winding. tional-pitch winding with five teeth sp ...", "... ead, or five-sixths pitch. During commutation the coils a b c d e f commutate simultane- ously. In Fig. 81 these coils lie by twos in the same slots, in Fig. 91 they lie in separate slots. Thus, in the former case the flux of self-inductance interlinked with the commutated coil is due to two coils; that is, twice that in the latter case. Frac- tional-pitch windings, however, have the disadvantage of reduc- ing the width of the neutral zone, or ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-64", "section_label": "Apparatus Section 12: Direct-current Commutating Machines: Efficiency and Losses", "section_title": "Direct-current Commutating Machines: Efficiency and Losses", "kind": "apparatus-section", "sequence": 64, "number": 12, "location": "lines 11864-11904", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-64/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-64/", "snippets": [ "... when solid and the air gap is small. 4. Friction of bearings, of brushes on the commutator, and windage. 5. Load losses, due to the increase of hysteresis and of eddy currents under load, caused by the change of the magnetic dis- tribution, as local increase of magnetic density and of stray field. The friction of the brushes and the loss in the contact resist- ance of the brushes are frequently quite considerable, especially with low-voltage mac ...", "... Friction of bearings, of brushes on the commutator, and windage. 5. Load losses, due to the increase of hysteresis and of eddy currents under load, caused by the change of the magnetic dis- tribution, as local increase of magnetic density and of stray field. The friction of the brushes and the loss in the contact resist- ance of the brushes are frequently quite considerable, especially with low-voltage machines. Constant or approximately constant loss ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-72", "section_label": "Apparatus Subsection 72: Direct-current Commutating Machines: Generators", "section_title": "Direct-current Commutating Machines: Generators", "kind": "apparatus-subsection", "sequence": 72, "number": null, "location": "lines 12400-12491", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-72/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-72/", "snippets": [ "... t of brushes. 10 20 30 40 50 60 70 80 90 100 110 120 130 FIG. 112. — Separately excited or magneto-generator demagnetization curve and load characteristic with variable shift of brushes. curve can be plotted from the magnetization or saturation curve A in Fig. 109. At current i, the resultant m.m.f . of the machine is FQ — iq, and the generated voltage corresponds thereto by the saturation curve A in Fig. 110. Thus, in Fig. Ill a de- magnetizati ...", "... gnetization or saturation curve A in Fig. 109. At current i, the resultant m.m.f . of the machine is FQ — iq, and the generated voltage corresponds thereto by the saturation curve A in Fig. 110. Thus, in Fig. Ill a de- magnetization curve A is plotted with the current ob = i as 210 ELEMENTS OF ELECTRICAL ENGINEERING abscissas and the generated e.m.f. ab as ordinates, under the assumption of constant coefficient of armature reaction q, that is, co ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-77", "section_label": "Apparatus Subsection 77: Direct-current Commutating Machines: C. Commutating Machines", "section_title": "Direct-current Commutating Machines: C. Commutating Machines", "kind": "apparatus-subsection", "sequence": 77, "number": null, "location": "lines 12929-13007", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-77/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-77/", "snippets": [ "... of arma- ture reaction. 10 60 FIG. 121 100 120 _110 160 ISO -Series motor speed curve. The torque of the series motor is shown also in Fig. 121, derived as proportional to A X i, that is, current X magnetic flux. Compound Motors 76. Compound motors can be built with cumulative com- pounding and with differential compounding. Cumulative compounding is used to a considerable extent, as in elevator motors, etc., to secure economy ...", "... ture reaction. 10 60 FIG. 121 100 120 _110 160 ISO -Series motor speed curve. The torque of the series motor is shown also in Fig. 121, derived as proportional to A X i, that is, current X magnetic flux. Compound Motors 76. Compound motors can be built with cumulative com- pounding and with differential compounding. Cumulative compounding is used to a considerable extent, as in elevator motors, etc., to secure economy of c ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-80", "section_label": "Apparatus Subsection 80: Direct-current Commutating Machines: C. Commutating Machines 221", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 221", "kind": "apparatus-subsection", "sequence": 80, "number": null, "location": "lines 13120-13188", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-80/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-80/", "snippets": [ "... ng a leading current, as from condenser or overexcited synchronous motor, or by in- troducing a lagging voltage. In the commutating machines, the voltage induced in the armature by its rotation is in phase with the field magnetism, and by lagging the field exciting current, 222 ELEMENTS OF ELECTRICAL ENGINEERING the commutating machines thus can be made to give a lagging voltage, that is, to compensate for low power-factor due to lagging current ...", "... ing- current commutator motors to get good power-factor. Thus in the series motor, by shunting the field by a non-inductive re- sistance, and thereby lagging the field exciting component of the current and with it the field flux and the voltage induced in the armature by its rotation, behind the main current, the series motor can at higher speeds be made to give unity power- factor. At low speeds, such complete compensation is not possible, as t ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-91", "section_label": "Apparatus Section 13: Synchronous Converters: Direct-current Converter", "section_title": "Synchronous Converters: Direct-current Converter", "kind": "apparatus-section", "sequence": 91, "number": 13, "location": "lines 16065-16540", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-91/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-91/", "snippets": [ "... t-current Converter 105. If n equidistant pairs of diametrically opposite points of a commutating machine armature are connected to the ends of n compensators or autotransformers, that is, electric circuits interlinked with a magnetic circuit, and the centers of these auto- transformers connected with each other to a neutral point as shown diagrammatically in Fig. 140 for n = 3, this neutral is equidis- tant in potential from the two sets of commutator ...", "... brushes. 264 ELEMENTS OF ELECTRICAL ENGINEERING In reality the current in each autotransformer section is *7* / irJf \\ -- h io \\/2 cos ( e — 60 ---- h «) t Ti \\ Ti I where iQ is the exciting current of the magnetic circuit of the auto- transformer, and a the angle of hysteretic advance of phase. At the commutator the current on the motor side is larger than the current on the generator side, by the amount required to cover the los ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-27", "section_label": "Chapter 27: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 33011-34776", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-27/", "snippets": [ "... ls in other cases, especially in circuits con- taining capacity, or in circuits containing periodically (and in synchronism with the wave) varying resistance or reactance (as alternating arcs, reaction machines, synchronous induction motors, oversaturated magnetic circuits, etc.). Since, however, the individual harmonics of the general alter- nating wave are independent of each other, that is, all products of different harmonics vanish, each term can be represented by a complex symbol, and the equations of the gen ...", "... wer-factor exists without corresponding phase displacement, the circuit-factor being less than one-half. Such circuits, for instance, are those including alternating arcs, reaction machines, synchronous induction motors, react- ances with over-saturated magnetic circuit, high potential lines in which the maximum difference of potential exceeds the corona voltage, polarization cells and in general electrolytic conductors above the dissociation voltage of the electrolyte, etc. Such cir- cuits cannot correctly, and ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-02", "section_label": "Chapter 2: Chapter II", "section_title": "Chapter II", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 1728-1972", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-02/", "snippets": [ "... by the superposi- tion of alternating waves upon continuous currents, etc.). All inductive apparatus without commutation give ex- clusively alternating waves, because, no matter what con- S. PmmUog WwK. ditions may exist in the circuit, any line of magnetic force, which during a complete period is cut by the circuit, and thereby induces an H.M.F., must during the same period be cut again in the opposite direction, and thereby induce the same total amount of E.M.F. (Obviously, this does not apply to cii-cuit ...", "... erage variation of the arc to that of the sine ; that is, 1 -=- 2 / a-, and since the variations of a sine-function are sinusoidal also, we have. Mean value of sine wave -5- maximum value = — -j- 1 IF = .63663. The quantities, \"current,\" \"E.M.F.,\" \"magnetism,\" etc., are in reality mathematical fictions only, as the components 14 ALTERNATING-CURRENT PHENOMENA. [§9 of the entities, \" energy,\" \" power,\" etc. ; that is, they have no independent existence, but appear only as squares or products. Conse ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-05", "section_label": "Chapter 5: Symbouc Mbthod", "section_title": "Symbouc Mbthod", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2744-3229", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "snippets": [ "... impressed upon the terminals of the condenser is -£\" = ~ , 90° behind the current ; and may be represented by —-^ — — - , or jx^ /, where x^^ = — • is the capacity reaciatice or condensance of the condenser. Capacity reactance is of opposite sign to magnetic re- actance ; both may be combined in the name reactance. We therefore have the conclusion that If r = resistance and L = inductance, then X = 2, icNL = magnetic reactance. If C = capacity, Xx = , = capacity reactance, or conden- sance ; Z = r — j ...", "... reaciatice or condensance of the condenser. Capacity reactance is of opposite sign to magnetic re- actance ; both may be combined in the name reactance. We therefore have the conclusion that If r = resistance and L = inductance, then X = 2, icNL = magnetic reactance. If C = capacity, Xx = , = capacity reactance, or conden- sance ; Z = r — j {x — jTi), is the impedance of the circuit. Ohm*s law is then reestablished as follows : ^ = Z/, 7=^, Z = ^. The more general form gives not only the intensity of ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-02", "section_label": "Chapter 2: Instantaneous Values And Integral Values", "section_title": "Instantaneous Values And Integral Values", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 1367-1605", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-02/", "snippets": [ "... (or by the superposition of alternating upon direct currents, etc.). All inductive apparatus without commutation give ex- clusively alternating waves, because, no matter what con- Fig. 5. Pulsating Wave. ditions may exist in the circuit, any line of magnetic force, which during a complete period is cut by the circuit, and thereby induces an E.M.F., must during the same period be cut again in the opposite direction, and thereby induce the same total amount of E.M.F. (Obviously, this does not apply to circuits ...", "... iation of the arc to that of the sine ; that is, 1 -f- 2 / 77-, and since the variations of a sine-function are sinusoidal also, we have, o Mean value of sine wave -r- maximum value = • — • -f- 1 7T = .63663. The quantities, \"current,\" \"E.M.F.,\" \"magnetism,\" etc., are in reality mathematical fictions only, as the components 14 AL TERNA TING-CURRENT PHENOMENA. of the entities, \"energy,\" \"power,\" etc. ; that is, they have no independent existence, but appear only as squares or products. Consequently, th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-05", "section_label": "Chapter 5: Symbolic Method", "section_title": "Symbolic Method", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2322-2773", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-05/", "snippets": [ "... mpressed upon the terminals of the condenser is E = - - , 90° behind the current ; and may be represented by — - - , or jx^ /, where x^ = - is the capacity reactance or condensatice 2 TT NC of the condenser. Capacity reactance is of opposite sign to magnetic re- actance ; both may be combined in the name reactance. We therefore have the conclusion that If r = resistance and L = inductance, then x = 2 IT NL = magnetic reactance. If C = capacity, x^ = - = capacity reactance, or conden- sance ; Z = r — j ...", "... e or condensatice 2 TT NC of the condenser. Capacity reactance is of opposite sign to magnetic re- actance ; both may be combined in the name reactance. We therefore have the conclusion that If r = resistance and L = inductance, then x = 2 IT NL = magnetic reactance. If C = capacity, x^ = - = capacity reactance, or conden- sance ; Z = r — j (x — JCi), is the impedance of the circuit Ohm's law is then reestablished as follows : , -, . The more general form gives not only the intensity of the wave, bu ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-01", "section_label": "Chapter 1: Electric Conduction. Soled And Liquid", "section_title": "Electric Conduction. Soled And Liquid", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 959-3894", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-01/", "snippets": [ "... t, about 30 per cent, higher than other pure metals, and at red heat, when approaching the temperature where the iron ceases to be magnetizable, the temperature coefficient becomes still higher, until the temperature is reached where the iron ceases to be magnetic. At this point its temperature coefficient becomes that of other pure metals. Iron wire — usually mounted in hydrogen to keep it from oxidizing — ^thus finds a use as series resistance for current limitation in vacuum arc circuits, etc. Electrolytic Con ...", "... \\ ^\\ a ' \\ S S 1(10 \\ \" \\ k\\ 200 ^T\"E \\ \\ kN , \\ \\ 1 , u a K.SO0. x)^c » I >i>flSQ_9O0J_ WoltOO-KOOJ. ffiU M acteristic derived therefrom, with log r as ordinates, of a magnetic rod 6 in. long and % in. in diameter, consisting of 90 per cent, magnetite (FejOO, 9 per cent, chromite (FeCr204) and 1 per cent, sodium silicate, sintered together. 10. As result of these volf^ampere characteristics. Figs. 4 to 10, pyroelectric conduct ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-16", "section_label": "Chapter 16: Load Balance Of Polyphase Systems", "section_title": "Load Balance Of Polyphase Systems", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 29302-30428", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-16/", "snippets": [ "... a — 1), where cos a is the power-factor of the single-phase load. Especially in alternators of very high armature reaction, as modern steam-turbine alternators, a pulsation of the armatiu^ reaction is very objectionable. It causes a pulsation of the field flux, leading to excessive eddy-current losses and consequent re- duction of the output. The use of a squirrel-cage winding in the 314 LOAD BALANCE OF POLYPHASE SYSTEMS 315 field pole faces of the single-phase alternator reduces the pulsation of the field ...", "... leading to excessive eddy-current losses and consequent re- duction of the output. The use of a squirrel-cage winding in the 314 LOAD BALANCE OF POLYPHASE SYSTEMS 315 field pole faces of the single-phase alternator reduces the pulsation of the field flux, but also increases the momentary short-circuit stresses. Thus, it is of interest to study the question of balancing unbal- anced polyphase circuits by stationary energy-storing devices, as reactor or condenser. 164. Let a voltage, e = E cos (1) ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-12", "section_label": "Chapter 8: Velocity Of Propagation Op Electric Field. 387", "section_title": "Velocity Of Propagation Op Electric Field. 387", "kind": "chapter", "sequence": 12, "number": 8, "location": "lines 972-1013", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-12/", "snippets": [ "... 387 68. Equations of decrease of electric field with the dis- tance. 388 69. Effect of return conductor on distance decrement of field. 389 70. Inductance of length I of infinitely long conductor with- out return conductor. 390 71. Equations of magnetic flux, effective resistance of radia- tion, inductance and impedance. 391 72. Evaluation of functions sil al and col al. 394 73. Self-inductive impedance, and numerical example. 395 74. Discussion of effective resistance and radiated power, as functi ...", "... . Equations of decrease of electric field with the dis- tance. 388 69. Effect of return conductor on distance decrement of field. 389 70. Inductance of length I of infinitely long conductor with- out return conductor. 390 71. Equations of magnetic flux, effective resistance of radia- tion, inductance and impedance. 391 72. Evaluation of functions sil al and col al. 394 73. Self-inductive impedance, and numerical example. 395 74. Discussion of effective resistance and radiated power, as function of ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... coil for generating oscillating currents. A 100-kv-amp. react- ive coil has approximately the same size as a 50-kw. trans- former and can indeed be made from such a transformer, of ratio 1 : 1, by connecting the two coils in series and inserting into the magnetic circuit an air gap of such length as to give the rated magnetic density at the rated current. A very large oscillating-current generator, therefore, would consist of 100-kv-amp. condenser and 100-kv-amp. reactor. 46. Assuming the condenser to be designe ...", "... ive coil has approximately the same size as a 50-kw. trans- former and can indeed be made from such a transformer, of ratio 1 : 1, by connecting the two coils in series and inserting into the magnetic circuit an air gap of such length as to give the rated magnetic density at the rated current. A very large oscillating-current generator, therefore, would consist of 100-kv-amp. condenser and 100-kv-amp. reactor. 46. Assuming the condenser to be designed for 10,000 volts alternating impressed e.m.f. at 60 cycles, th ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-29", "section_label": "Chapter 7: Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "section_title": "Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "kind": "chapter", "sequence": 29, "number": 7, "location": "lines 6798-7825", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "snippets": [ "... the condenser in - of the time of a half wave. That is, the period of the starting current is - and the amplitude n times that of the final current. How- n l ever, as soon as the condenser is charged, in - of a period of Ti the impressed e.m.f., the magnetic field of the charging current produces a return current, discharging the condenser again at the same rate. Thus the normal condition of start is an oscillation of such a frequency as to give the full condenser charge at a rate which when continued up to ...", "... cy would give an amplitude equal to the impressed e.m.f. divided by the line reactance. The effect of the line resistance is to consume e.m.f. and thus dampen the oscillation, until the resistance consumes during the condenser charge as much energy as the magnetic field would store up, and then the oscillation disappears and the start becomes exponential. Analytically the double transient term appears as the result of the two roots of a quadratic equation, as seen above." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... The alternating electromagnetic field of force set up by the line current produces in some materials a loss of power by mag- netic hysteresis, or an expenditure of e.m.f. in phase with the cur- rent, which acts as an increase of resistance. This electro- magnetic hysteresis loss may take place in the conductor proper if iron wires are used, and may then be very serious at high fre- quencies such as those of telephone currents. The effect of eddy currents has already been referred to under \" mutual inductance,\" of ...", "... r second, and the quarter-wave frequency of a line of 10 = 700 miles would be S / = — =67 cycles per sec. ; 4 LQ hence, fairly close to the standard frequency of 60 cycles. The loss of power in the line, and thus the increase of induc- tance by the magnetic field inside of the conductor (which would not exist in a conductor of perfect conductivity or zero resistance loss), the increase of capacity by insulators, poles, etc., lowers the frequency below that corresponding to the velocity of light and brings it ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-05", "section_label": "Lecture 5: Long Distance Transmission", "section_title": "Long Distance Transmission", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2562-3132", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-05/", "snippets": [ "... d or symmetrical, that is, have the same potential differences from all the conductors to the ground. Any electric circuit, and so also the transmission line, contains inductance and capacity, and therefore stores energy as electromagnetic energy in the magnetic field due to the cur- rent, and as electrostatic energy, or electrostatic charge, due to the voltage. LONG DISTANCE TRANSMISSION 69 If: e = voltage, C = capacity. i = current, L = inductance. the electrostatic energy is : e*C 2 and the electro ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-10", "section_label": "Lecture 10: Regulation And Control", "section_title": "Regulation And Control", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 4595-4930", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-10/", "snippets": [ "... secondary coil is in series and at right angles to the primary ; an iron shuttle moves inside of the coils and so turns the mag- netism of the primary coil into the secondary coil either one way or the other. On the dotted position the primary sends the magnetism through the secondary in opposite direction as in the drawn position, in Fig. 26. 134 GENERAL LECTURES Fife. 26 Advantage — Uniform variation. Disadvantage — More expensive than compensator regulator." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-16", "section_label": "Lecture 16: The Incandescent Lamp", "section_title": "The Incandescent Lamp", "kind": "lecture", "sequence": 16, "number": 16, "location": "lines 9687-9919", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-16/", "snippets": [ "... ve a meaning only when based on the same length of useful life, as 500 hours. Obviously, for other types of lamps, the economic life may be greater (as for more expensive lamps) or less than 500 hours. Illuminants are measured and compared by the total flux of light which they give. Usually, however, this is expressed in \"mean spherical candle power\"; that is, the candle power which would be given by the illuminant if this light were dis- tributed uniformly throughout. Since the object of a lamp is to give ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... UMINATION. The electric waves used in wireless telegraphy range in wave lengths from 100 feet or less to 10,000 feet or more, corresponding to 107 to 105 cycles per sec. Still very much longer waves are the fields of alternating cur- rent circuits: the magnetic and electrostatic field of an alterna- ting current progresses as a wave of radiation from the conductor. But as the wave length is very great, due to the low frequency, — 3 X 1010 a 60-cycle alternating current gives a wave length of ^ = 500 X 10\" cm. ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-14", "section_label": "Theory Section 14: Rectangular Coordinates", "section_title": "Rectangular Coordinates", "kind": "theory-section", "sequence": 14, "number": 14, "location": "lines 5264-5831", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-14/", "snippets": [ "... (6) and the primary load current corresponding thereto is I' = - aii = aii - jaiz. (7) The primary exciting current, Joo = h - jg, (8) where h = J0o sin a is the hysteresis current, g = I0o cos a the reactive magnetizing current. Thus the total primary current is J0 = I' + J00 = (aii + h) -j (aiz + g). (9) The e.m.f. consumed by primary resistance rQ is r0Jo = TQ (aii + h) - jr0 (aiz + 0). (10) The horizontal component of prim ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-16", "section_label": "Theory Section 16: Phase Control of Transmission Lines", "section_title": "Phase Control of Transmission Lines", "kind": "theory-section", "sequence": 16, "number": 16, "location": "lines 6222-6813", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-16/", "snippets": [ "... and i = io, e > eo, and the current is lagging. Above i = io, e < eQ, and the current is leading. By the reaction of the variation of e from eo upon the receiving apparatus producing reactive current z'i, and by magnetic satura- tion in the receiving apparatus, the deviation of e from eo is reduced, that is, the regulation improved. 2. Over-compounding of Transmission Lines 78. The impressed voltage at the generator end of the line was fo ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-17", "section_label": "Theory Section 17: Impedance and Admittance", "section_title": "Impedance and Admittance", "kind": "theory-section", "sequence": 17, "number": 17, "location": "lines 6814-7380", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-17/", "snippets": [ "... current i in the circuit. Such counter e.m.fs. may be due to inductance, as self-induc- tance, or mutual inductance, to capacity, chemical polarization, etc. The counter e.m.f. of self-induction, or e.m.f. generated by the magnetic field produced by the alternating current i, is repre- sented by a quantity of the same dimensions as resistance, and measured in ohms: reactance x. The e.m.f. consumed by reactance x is in quadrature with the current, tha ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-28", "section_label": "Apparatus Section 7: Synchronous Machines: Synchronous Motor", "section_title": "Synchronous Machines: Synchronous Motor", "kind": "apparatus-section", "sequence": 28, "number": 7, "location": "lines 9292-9398", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-28/", "snippets": [ "... armature is Po = i(Ep-ir); that is, the current times the power component of the nominal counter-generated e.m.f. Obviously to get the available mechan- ical power, the power consumed by mechanical friction and by molecular magnetic friction or hysteresis, and the power of field excitation, have to be subtracted from this value P0." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-31", "section_label": "Apparatus Section 10: Synchronous Machines: Efficiency and Losses", "section_title": "Synchronous Machines: Efficiency and Losses", "kind": "apparatus-section", "sequence": 31, "number": 10, "location": "lines 9651-9718", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-31/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-31/", "snippets": [ "... ng the losses, and the latter is therefore com- monly used. The losses consist of the following: the resistance loss in the armature; the resistance loss in the field circuit; the hysteresis and eddy current losses in the magnetic circuit; the friction and windage losses, and eventually load losses, that is, losses due to eddy currents and hysteresis produced by the load current in the armature. The resistance loss in the armature is proportional to ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-34", "section_label": "Apparatus Section 13: Synchronous Machines: Parallel Operation", "section_title": "Synchronous Machines: Parallel Operation", "kind": "apparatus-section", "sequence": 34, "number": 13, "location": "lines 9821-9878", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-34/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-34/", "snippets": [ "... two alternators are identically the same, but the field excitation not such as would give equal terminal voltage when operated in parallel, there is a local current between the two machines which is wattless and leading or magnetizing in the machine of lower field excitation, lagging or demagnetiz- ing in the machine of higher field excitation. At load this watt- less current is superimposed upon the currents from the machines into the external circuit. I ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-67", "section_label": "Apparatus Subsection 67: Direct-current Commutating Machines: C. Commutating Machines", "section_title": "Direct-current Commutating Machines: C. Commutating Machines", "kind": "apparatus-subsection", "sequence": 67, "number": null, "location": "lines 12084-12199", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-67/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-67/", "snippets": [ "... herefore, with low-resistance brushes, resistance commutation is not permissible except with machines of extremely low arma- FIG. 108. — Brush commutating coil A. ture inductance, that is, armature inductance so low that the magnetic energy -7^—, which appears as \"spark\" in this case, is & harmless. Voltage commutation is feasible with low-resistance brushes, but requires a commutating e.m.f. e proportional to current z'o; that is, requires shifting of ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-74", "section_label": "Apparatus Subsection 74: Direct-current Commutating Machines: C. Commutating Machines", "section_title": "Direct-current Commutating Machines: C. Commutating Machines", "kind": "apparatus-subsection", "sequence": 74, "number": null, "location": "lines 12660-12763", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-74/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-74/", "snippets": [ "... in Fig. 116. Above a certain external resistance the series generator loses its excitation, while the shunt generator loses its excitation below a certain external resistance. Compound Generator 73. The saturation curve or magnetic characteristic A, and the load saturation curves D and G of the compound generator, are shown in Fig. 118 with the ampere-turns of the shunt field 214 ELEMENTS OF ELECTRICAL ENGINEERING as abscissas. A is the sam ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "... tional to the e.m.f. and consisting of a power component, in phase with the e.m.f., and a reactive component, in quadrature thereto. The alternating electromagnetic field of force set up by the line current produces in some materials a loss of energy by magnetic hysteresis, or an expenditure of e.m.f. in phase with the current, which acts as an increase of resistance. This electromagnetic hysteretic loss may take place in the con- ductor proper if iron wires are used, and will then be very serious at high frequen ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-33", "section_label": "Chapter 33: Efficiency Of Systems", "section_title": "Efficiency Of Systems", "kind": "chapter", "sequence": 33, "number": 33, "location": "lines 36515-37127", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-33/", "snippets": [ "... em with grounded neutral, but has a greater self-induction, due to the greater distance between conductor and return conductor or ground, and has the objection of establishing current through the ground and so disturbing neighboring circuits, by electro- magnetic and electrostatic induction. The apparent saving in copper, in the single-phase system, by replacing one of the conductors by the ground as return, there- fore is a fallacy. By doing so, the potential difference of the other conductors against ground bec ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "section_title": "Dibtbisnted Capacity, Inductance, Besistance, And", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "... al to the E.M.F., and consisting of an energy component, in phase with the E.M.F., and a wattless component, in quadrature thereto. The alternating electromagnetic field of force set up by the line current produces in some materials a loss of energy by magnetic hysteresis, or an expenditure of E.M.F. in phase with the current, which acts as an increase of re- sistance. This electromagnetic hysteretic loss may take place in the conductor proper if iron wires are used, and will then be very serious at high frequen ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "... al to the E.M.F., and consisting of an energy component, in phase with the E.M.F., and a wattless component, in quadrature thereto. The alternating electromagnetic field of force set up by the line current produces in some materials a loss of energy by magnetic hysteresis, or an expenditure of E.M'.F. in phase with the current, which acts as an increase of re- sistance. This electromagnetic hysteretic loss may take place in the conductor proper if iron wires are used, and will then be very serious at high freque ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "... er factor exists without corresponding phase displace- ment, the circuit factor being less than one-half. Such circuits, for instance, are those including alternat- ing arcs, reaction machines, synchronous induction motors, reactances with over-saturated magnetic circuit, high poten- tial lines in which the maximum difference of potential ex- ceeds the voltage at which brush discharges begin, polariza- tion cells, and in general electrolytic conductors above the dissociation voltage of the electrolyte, etc. Such c ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-08", "section_label": "Chapter 9: Synchronous Induction Motor", "section_title": "Synchronous Induction Motor", "kind": "chapter", "sequence": 8, "number": 9, "location": "lines 14466-14550", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-08/", "snippets": [ "... electric circuit of an admittance varying with twice the periodicity of the primary frequency, since twice per period the axis of the armature coil and that of the primary coil coincide. A varying admittance is obviously identical in effeel with a varying reluctance, which will be discussed in the chapter on reaction machines. That is, the induction motor with one closed armature circuit is, at synchronism, nothing but a reaction machine, and consequently gives zero torque at synchronism if the maxima and minima of ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-10", "section_label": "Chapter 10: Instability Of Circuits : The Arc", "section_title": "Instability Of Circuits : The Arc", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 17632-21381", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-10/", "snippets": [ "... u 161 162 ELECTRIC CIRCUITS stance, if a switch is closed, and thereby a load put on the circuit, the ciurent can not instantly increase to the value corresponding to the increased load, but some time elapses, diu-ing which the increase of the stored magnetic energy corresponding to the in- creased current, is brought about. Or, if a motor switch is closed, a period of acceleration intervenes before the flow of current be- comes stationary, etc. The characteristic of transients therefore is, as implied in the ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-06", "section_label": "Chapter 2: Long Distance Transmission Line. 279", "section_title": "Long Distance Transmission Line. 279", "kind": "chapter", "sequence": 6, "number": 2, "location": "lines 755-835", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-06/", "snippets": [ "CHAPTER II. LONG DISTANCE TRANSMISSION LINE. 279 3. Relation of wave length of impressed frequency to natural frequency of line, and limits of approximate line cal- culations. 279 4. Electrical and magnetic phenomena in transmission line. 281 5. The four constants of the transmission line : r, L, g, C. 282 6. The problem of the transmission line. 283 7. The differential equations of the transmission line, and their integral equations. 8. Different form ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-20", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit. 513", "section_title": "Power And Energy Of The Complex Circuit. 513", "kind": "chapter", "sequence": 20, "number": 7, "location": "lines 1228-1261", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-20/", "snippets": [ "CHAPTER VII. POWER AND ENERGY OF THE COMPLEX CIRCUIT. 513 50. Instantaneous power. Effective or mean power. Power transferred. 513 51. Instantaneous and effective value of energy stored in the magnetic field ; its motion along the circuit, and varia- tion with distance and with time. 513 52. The energy stored in the electrostatic field and its compo- nents. Transfer of energy between electrostatic and electromagnetic field. 517 53. Energy stored in ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-26", "section_label": "Chapter 4: Inductance And Resistance In Alternating Current Circuits", "section_title": "Inductance And Resistance In Alternating Current Circuits", "kind": "chapter", "sequence": 26, "number": 4, "location": "lines 3515-4071", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-26/", "snippets": [ "... cos (0 — 00) is the circle, -r-e h x cos 00 the exponential or loxodromic spiral. As a rule, the transient term in alternating-current circuits containing resistance and inductance is of importance only in circuits containing iron, where hysteresis and magnetic saturation complicate the phenomenon, or in circuits where unidirectional or periodically recurring changes take place, as in rectifiers, and some such cases are considered in the following chapters." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-33", "section_label": "Chapter 40: General System Of Circuits", "section_title": "General System Of Circuits", "kind": "chapter", "sequence": 33, "number": 40, "location": "lines 12217-12884", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-33/", "snippets": [ "... erms of impressed or counter e.m.fs. are given as linear functions of the currents or of their differential coefficients, that is, the rate of change of the currents. (3) That resistance, inductance, and capacity are constant quantities, and for instance magnetic saturation does not appear. The determination of the transient terms requires the solution of an equation of 2 nth degree, which is lowered by one degree for every independent circuit which contains no capacity. Thus, for instance, a divided circuit hav ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-50", "section_label": "Chapter 1: General Equations", "section_title": "General Equations", "kind": "chapter", "sequence": 50, "number": 1, "location": "lines 27761-28694", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "snippets": [ "... on or alternation moves along the circuit with the speed — *., or, in other words, (15) is the speed of propagation of the electric phenomenon in the cir- cuit. (If no energy losses occur, r = 0, g = 0, in a straight con- ductor in a medium of unit magnetic and dielectric constant, that is, unit permeability and unit inductive capacity, S is the velocity of light.) 4. Since (11) is a quadratic equation, several pairs or corre- sponding values of a and b exist, which, in the most general case, are complex i ..." ] } ] }, { "id": "inductance", "label": "Inductance", "aliases": [ "inductance", "inductive", "mutual inductance", "self-inductance" ], "total_occurrences": 2809, "matching_section_count": 234, "matching_source_count": 14, "source_totals": [ { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 529, "section_count": 40 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 356, "section_count": 16 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 343, "section_count": 30 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 322, "section_count": 13 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 309, "section_count": 24 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 281, "section_count": 46 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 233, "section_count": 22 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 159, "section_count": 10 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 153, "section_count": 10 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 56, "section_count": 12 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 44, "section_count": 5 }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 13, "section_count": 1 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 7, "section_count": 3 }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 4, "section_count": 2 } ], "section_hits": [ { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-14", "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "section_title": "Constant-Potential Constant-Current Trans Formation", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 171, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "... escent lamps, the constant direct current is usually derived by rectification of constant alternating-current supply circuits. Such constant alternating currents are usually produced from constant- voltage supply circuits by means of constant or variable inductive reactances, and may be produced by the combination of inductive and condensive reactances; and the investigation of different methods of producing constant alternating current from constant alternating voltage, or inversely, constitutes a good application ...", "... rectification of constant alternating-current supply circuits. Such constant alternating currents are usually produced from constant- voltage supply circuits by means of constant or variable inductive reactances, and may be produced by the combination of inductive and condensive reactances; and the investigation of different methods of producing constant alternating current from constant alternating voltage, or inversely, constitutes a good application of the terms \"impedance,\" admittance,\" etc., and offers a large ...", "... rsely, constitutes a good application of the terms \"impedance,\" admittance,\" etc., and offers a large number of problems or examples for the symbolic method of dealing with alternating-current phenomena. Even outside of arc lighting, such combinations of inductance and capacity which t«nd toward constant-voltage constant-cur- rent transformation are of considerable importance as a poffsiblo source of danger to the system. In a constant-current circuit, the load is taken off by short-circuiting, while opc;n-circuitin ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-18", "section_label": "Chapter 20: Single-Phase Commutator Motors", "section_title": "Single-Phase Commutator Motors", "kind": "chapter", "sequence": 18, "number": 20, "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 83, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "... current motor, voltage is consumed by the counter e.m.f. of rotation, which represents the power output of the motor, and by the resistance, which represents the power loss. In addition thereto, in the alternating-cur rent motor voltage is consumed by the inductance, which is wattless or reactive and therefore causes a lag of current behind the vol- tage, that is, a lowering of the power-factor. While in the direct- current motor good design requires the combination of a strong field and a relatively weak armature, s ...", "... quires the combination of a strong field and a relatively weak armature, so as to reduce the armature reaction on the field to a minimum, in the design of the alter- iiatiiig-current motor considerations of power-factor predominate; that is, to secure low self-inductance and therewith a high power- factor, the combination of a strong armature and a weak field is required, and necessitates the use of methods to eliminate the harmful effects of high armature reaction. As the varying-speed single-phase commutator motor has ...", "... the magnetic field flux generates in the armature conductors by their rotation the e.m.f. which does the work of the motor, but, as the field flux is alternating, it also generates SINGLE-PHASE COMMUTATOR MOTORS 333 in the field conductors an e.m.f. of self-inductance, which is not useful but wattless, and therefore harmful in lowering the power- factor, hence must be kept as low as possible. This e.m.f. of self-inductance of the field, e0, is proportional to the field strength, $, to the number of field turns, n0, an ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-32", "section_label": "Chapter 10: Mutual Inductance", "section_title": "Mutual Inductance", "kind": "chapter", "sequence": 32, "number": 10, "location": "lines 10475-12216", "status": "candidate", "occurrence_count": 68, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "snippets": [ "CHAPTER X. MUTUAL INDUCTANCE. 82. In the preceding chapters, circuits have been considered containing resistance, self-inductance, and capacity, but no mutual inductance; that is, the phenomena which take place in the circuit have been assumed as depending upon the impressed e.m.f. ...", "CHAPTER X. MUTUAL INDUCTANCE. 82. In the preceding chapters, circuits have been considered containing resistance, self-inductance, and capacity, but no mutual inductance; that is, the phenomena which take place in the circuit have been assumed as depending upon the impressed e.m.f. and the constants of the circuit, but not upon the phenomena taking place in any other circuit. Of t ...", "CHAPTER X. MUTUAL INDUCTANCE. 82. In the preceding chapters, circuits have been considered containing resistance, self-inductance, and capacity, but no mutual inductance; that is, the phenomena which take place in the circuit have been assumed as depending upon the impressed e.m.f. and the constants of the circuit, but not upon the phenomena taking place in any other circuit. Of the magnetic flux produced by the current ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "section_label": "Lecture 10: Continual And Cumulative Oscillations", "section_title": "Continual And Cumulative Oscillations", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 65, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... grams, Figs. 62 to 65, were taken on an artificial transmission line.* Oscillations of the type 64 and 65 are industrially used, as ''sing- ing arc, \" in wireless telegraphy, and are produced by shunting a suitable arc by a circuit containing capacity and inductance in series with each other. Fig. 62. — Semi -continuous Recurrent Oscillation of Arcing Ground in Transmission Line. Fig. 63. — Semi-continuous Hecurrent Oscillation of Arcing Ground in Transmission Lino. * \"Design, Construction and Test of an Arti ...", "... in Figs. 59 and 60, while in high-potential trans- former windings, due to their much lesser damping, continuous oscillations seem to be more common, as in Fig. 46. Our knowl- edge of these phenomena is however still extremely incomplete. LECTUEE XI, INDUCTANCE AND CAPACITY OF ROUND PARALLEL CONDUCTORS. A. Inductance and capacity. 46. As inductance and capacity are the two circuit constants which represent the energy storage, and which therefore are of fundamental importance in the study of transients, their ...", "... windings, due to their much lesser damping, continuous oscillations seem to be more common, as in Fig. 46. Our knowl- edge of these phenomena is however still extremely incomplete. LECTUEE XI, INDUCTANCE AND CAPACITY OF ROUND PARALLEL CONDUCTORS. A. Inductance and capacity. 46. As inductance and capacity are the two circuit constants which represent the energy storage, and which therefore are of fundamental importance in the study of transients, their calcula- tion is discussed in the following. The inductan ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-10", "section_label": "Lecture 10: Inductance And Capacity Of Round Parallel Conductors", "section_title": "Inductance And Capacity Of Round Parallel Conductors", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6089-7274", "status": "candidate", "occurrence_count": 64, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "snippets": [ "LECTURE X. INDUCTANCE AND CAPACITY OF ROUND PARALLEL CONDUCTORS. A. Inductance and capacity. 43. As inductance and capacity are the two circuit constants which represent the energy storage, and which therefore are of fundamental importance in the study of transients, their ...", "LECTURE X. INDUCTANCE AND CAPACITY OF ROUND PARALLEL CONDUCTORS. A. Inductance and capacity. 43. As inductance and capacity are the two circuit constants which represent the energy storage, and which therefore are of fundamental importance in the study of transients, their calcula- tion is discussed in the following. The inductan ...", "LECTURE X. INDUCTANCE AND CAPACITY OF ROUND PARALLEL CONDUCTORS. A. Inductance and capacity. 43. As inductance and capacity are the two circuit constants which represent the energy storage, and which therefore are of fundamental importance in the study of transients, their calcula- tion is discussed in the following. The inductance is the ratio of the interlinkag ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 51, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "CHAPTER IX. INDUCTIVE DISCHARGES. 64. The discharge of an inductance into a transmission line may be considered as an illustration of the phenomena in a complex circuit comprising sections of very different constants; that is, a combination of a circuit section of high induct ...", "CHAPTER IX. INDUCTIVE DISCHARGES. 64. The discharge of an inductance into a transmission line may be considered as an illustration of the phenomena in a complex circuit comprising sections of very different constants; that is, a combination of a circuit section of high inductance and small resistance and negligible capacit ...", "... UCTIVE DISCHARGES. 64. The discharge of an inductance into a transmission line may be considered as an illustration of the phenomena in a complex circuit comprising sections of very different constants; that is, a combination of a circuit section of high inductance and small resistance and negligible capacity and conductance, as a generating station, with a circuit of distributed capacity and inductance, as a transmission line. The extreme case of such a discharge would occur if a short circuit at the busbars of a g ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-11", "section_label": "Chapter 12: Frequency Converter Or General Alternating Current Transformer", "section_title": "Frequency Converter Or General Alternating Current Transformer", "kind": "chapter", "sequence": 11, "number": 12, "location": "lines 14897-17124", "status": "candidate", "occurrence_count": 50, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-11/", "snippets": [ "... contain an air gap in the magnetic circuit, to permit movability between primary and secondary, and thus they require a higher magnetizing current than the closed magnetic circuit stationary transformer, and this again results in general in a higher self- inductive impedance. Thus, the frequency converter and in- duction motor magnetically represent transformers of high ex- citing admittance and high self-inductive impedance. 104. The mutual magnetic flux of the transformer is pro- duced by the resultant m.m.f. of ...", "... he closed magnetic circuit stationary transformer, and this again results in general in a higher self- inductive impedance. Thus, the frequency converter and in- duction motor magnetically represent transformers of high ex- citing admittance and high self-inductive impedance. 104. The mutual magnetic flux of the transformer is pro- duced by the resultant m.m.f. of both electric circuits. It is determined by the counter e.m.f., the number of turns, and the frequency of the electric circuit, by the equation : E = V ...", "... in series per circuit; nx = number of secondary turns in series per circuit; a = = ratio of turns; Til Y = g — jb = primary exciting admittance per circuit; where: g = effective conductance; b = susceptance; Zq = r0 + jxo = internal primary self-inductive impedance per circuit, where: r0 = effective resistance of primary circuit; Xq = self-inductive reactance of primary circuit; Zn = n + jx\\ = internal secondary self-inductive im- pedance per circuit at standstill, or for « = 1, where: rx = effecti ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-17", "section_label": "Chapter 19: Alternating- Current Motors In General", "section_title": "Alternating- Current Motors In General", "kind": "chapter", "sequence": 17, "number": 19, "location": "lines 21713-23905", "status": "candidate", "occurrence_count": 50, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-17/", "snippets": [ "... plied. The appearance of such \"dead points\" in the speed curve is due to a mechanical defect — as eccentricity of the rotor — or faulty electrical design: an improper distribution of primary and secondary windings causes a periodic variation of the mutual inductive reactance and so of the effective primary inductive reactance, (2) or the use of sharply defined and im- properly arranged teeth in both elements causes a periodic magnetic lock (opening and closing of the magnetic circuit, (3) and so a tendency to synchr ...", "... eed curve is due to a mechanical defect — as eccentricity of the rotor — or faulty electrical design: an improper distribution of primary and secondary windings causes a periodic variation of the mutual inductive reactance and so of the effective primary inductive reactance, (2) or the use of sharply defined and im- properly arranged teeth in both elements causes a periodic magnetic lock (opening and closing of the magnetic circuit, (3) and so a tendency to synchronize at the speed corresponding to this cycle. Sy ...", "... umed by self-induction, and power component: E\" = 2r/n* sin a = 2irfHI = r\"I = e.m.f. consumed by hysteresis (eddj currents, etc.), and is, therefore, in vector representation denoted by: E' = jxf and E\" = f>% where: x = 2 irfL — reactance, and L = inductance, r\" = effective hysteretic resistance. The ohmic resistance of the circuit, r', consumes an e.n r'(, in phase with the current, and the total or effective resistance of the circuit is, therefore, r = r' + r\", and the total e.m.f. consumed by the circuit ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-08", "section_label": "Chapter 8: Circuits Containing Resistance, Inductance, And Capacity", "section_title": "Circuits Containing Resistance, Inductance, And Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3577-5333", "status": "candidate", "occurrence_count": 42, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "snippets": [ "CHAPTER VIII. CIRCUITS CONTAINING RESISTANCE, INDUCTANCE, AND CAPACITY. 42. Having, in the foregoing, reestablished Ohm's law and Kirchhoff's laws as being also the fundamental laws of alternating-current circuits, when expressed in their com- plex form, E = ZS, or, / = YE, and *%E = 0 in a closed circuit ...", "... , and capacity in any combination, without meeting with greater difficulties than when dealing with continuous- current circuits. It is obviously not possible to discuss with any com- pleteness all the infinite varieties of combinations of resis- tance, inductance, and capacity which can be imagined, and which may exist, in a system or network of circuits ; there- fore only some of the more common or more . interesting combinations will here be considered. 1.) Resistance in series with a circuit. 43. In a consta ...", "... ork of circuits ; there- fore only some of the more common or more . interesting combinations will here be considered. 1.) Resistance in series with a circuit. 43. In a constant-potential system with impressed E.M.F., o = e. +/V, E. = RESISTANCE, INDUCTANCE, CAPACITY. 59 let the receiving circuit of impedance Z = r —jx, z = Vr2 + x'2, be connected in series with a resistance, r0 . The total impedance of the circuit is then Z + r0 = r + r0—jx\\ hence the current is ____ •\" Z + r0 r+r0 -jx (r + r0)2 - ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-10", "section_label": "Chapter 10: Resistance And Reactance Of Transmission", "section_title": "Resistance And Reactance Of Transmission", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6993-9766", "status": "candidate", "occurrence_count": 41, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-10/", "snippets": [ "... upon the consumption of power — that is, upon the load on the circuit — and thus cannot be varied for the purpose of regu- lation. Its susceptance, b, however, can be changed bj' shunt- ing the circuit with a reactance, and will be increased by a shunted inductive reactance, and decreased by a shunted con- densive reactance. Hence, for the purpose of investigation, the receiver circuit can be assumed to consist of two branches, a conductance, g, — the non-inductive part of the circuit — shunted by a susceptance, h, ...", "... th a reactance, and will be increased by a shunted inductive reactance, and decreased by a shunted con- densive reactance. Hence, for the purpose of investigation, the receiver circuit can be assumed to consist of two branches, a conductance, g, — the non-inductive part of the circuit — shunted by a susceptance, h, which can be varied without expenditure of energy. The two components of current can thus be considered separately, the energy component as deter- 78 TRANSMISSION LINES 79 mined by the load on the c ...", "... eceiver circuit may be considered as consisting of two components, the power component, in phase with the current, and the wattless com- ponent, in quadrature with the current. This will correspond to the case of a reactance connected in series to the non-inductive part of the circuit. Since the effect of either resolution into components is the same so far as the line is concerned, we need not make any assumption as to whether the wattless part of the . receiver circuit is in shunt, or in series, to the power part. ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-13", "section_label": "Chapter 13: Reactance Of Synchronous Machines", "section_title": "Reactance Of Synchronous Machines", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 23466-24022", "status": "candidate", "occurrence_count": 41, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-13/", "snippets": [ "... n Fig. 112A, all the lines of magnetic forces are inter- linked with the field circuit, but there is no line of magnetic flux interlinked with the armature circuit only, that is, there is ap- 232 REACTANCE OF SYNCHRONOUS MACHINES 233 parently no self-inductive armature flux, and no true self-inducts ive reactance, x, and the self-inductive armature flux of Fig. Ill thus merely is a mathematical fiction, a theoretical component of the resultant flux, Fig. 112. The effect of the armature current, Fra. 110. i ...", "... rcuit, but there is no line of magnetic flux interlinked with the armature circuit only, that is, there is ap- 232 REACTANCE OF SYNCHRONOUS MACHINES 233 parently no self-inductive armature flux, and no true self-inducts ive reactance, x, and the self-inductive armature flux of Fig. Ill thus merely is a mathematical fiction, a theoretical component of the resultant flux, Fig. 112. The effect of the armature current, Fra. 110. in changing flux distribution. Fig. IIOA to Fig. 112^, consists in reducing the fi ...", "... o field pole, without interlinking the armature circuit, and 234 ELECTRIC CIRCUITS still further decreasiDg the armature flux, that is, the flux issiuDg from the field and interlinking with the armature circuit. In position 1 12B, there is no self-inductive armature flux either, but every line of force, which interlinks with the armature circuit, Fig. in. is produced by and interlinked with the field circuit. The effect of the armature current in this case is to increase the field flux and the flux enter ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-09", "section_label": "Chapter 9: Resistance And Reactance Of Transmission Lines", "section_title": "Resistance And Reactance Of Transmission Lines", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 5334-6956", "status": "candidate", "occurrence_count": 39, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "snippets": [ "... ance is small if the current is in phase with the E.M.F., while a drop of potential is produced with a lagging, and a rise of potential with a leading, current in the receiver circuit. Thus the change of potential due to a line of given re- sistance and inductance depends upon the phase difference in the receiver circuit, and can be varied and controlled by varying this phase difference ; that is, by varying the admittance, Y = g -f jb, of the receiver circuit. The conductance, gy of the receiver circuit depends u ...", "... upon the consumption of power, — that is, upon the load on the circuit, — and thus cannot be varied for the purpose of reg- ulation. Its susceptance, b, however, can be changed by shunting the circuit with a reactance, and will be increased by a shunted inductance, and decreased by a shunted con- densance. Hence, for the purpose of investigation, the 84 ALTERNATING-CURRENT PHENOMENA. receiver circuit can be assumed to consist of two branches, a conductance, g, — the non-inductive part of the circuit, — shunted ...", "... will be increased by a shunted inductance, and decreased by a shunted con- densance. Hence, for the purpose of investigation, the 84 ALTERNATING-CURRENT PHENOMENA. receiver circuit can be assumed to consist of two branches, a conductance, g, — the non-inductive part of the circuit, — shunted by a susceptance, b, which can be varied without expenditure of energy. The two components of current can thus be considered separately, the energy component as determined by the load on the circuit, and the wattless compon ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-08", "section_label": "Chapter 8: Capacity", "section_title": "Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3872-6370", "status": "candidate", "occurrence_count": 38, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "snippets": [ "... , and capacity in any combination, without meeting with greater difficulties than when dealing with continuous- current circuits. It is obviously not possible to discuss with any com- pleteness all the infinite varieties of combinations of resis- tance, inductance, and capacity which can be imagined, and which may exist, in a system or network of circuits ; there- fore only some of the more common combinations will here be considered. 1.) R I sis fa nee in scries with a circuit, 43. In a constant-potential syste ...", "... may exist, in a system or network of circuits ; there- fore only some of the more common combinations will here be considered. 1.) R I sis fa nee in scries with a circuit, 43. In a constant-potential system with impressed E.M.F., ^ §43] KESISTANCEy INDUCTANCE, CAPACITY, 69 let the receiving circuit of impedance if = /• —jx^ z = V/\"*\"^ + xS be connected in series with a resistance, r^ . The total impedance of the circuit is then hence the current is /= ^o = ^o = ^oia+j'o+Jx) , Z + r^ r+ f\\, —jx (/- + r ...", "... x^y so that / and E assume the same value when x is negative, as when x is positive ; or, in other words, series resistance acts upon a circuit with leading current, or in a condenser circuit, in the same way as upon a circuit with lagging current, or an inductive circuit. For a given impedance, s^ of the receiver circuit, the cur- rent /, and E.M.F., E^ are smaller, as r is larger; that is, the less the difference of phase in the receiver circuit. As an instance, in Fig. 37 are shown in dotted lines the current ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-13", "section_label": "Chapter 15: Synchronous Rectifier", "section_title": "Synchronous Rectifier", "kind": "chapter", "sequence": 13, "number": 15, "location": "lines 18413-19373", "status": "candidate", "occurrence_count": 35, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-13/", "snippets": [ "... voltage wave, by a reversing commutator driven by a small synchronous motor, shown in Fig. 73. In the receiver circuit the voltage wave then is unidirectional but pul- sating, as shown by e0 in Fig. 74. If receiver circuit and supply circuit both are non-inductive, the current in the receiver circuit is a pulsating unidirectional current, shown as i0 in dotted lines in Fig. 74, and derived from the alternating current, i, Fig. 72, in the supply circuit. If, however, the receiver circuit is inductive, as a machine ...", "... t both are non-inductive, the current in the receiver circuit is a pulsating unidirectional current, shown as i0 in dotted lines in Fig. 74, and derived from the alternating current, i, Fig. 72, in the supply circuit. If, however, the receiver circuit is inductive, as a machine field, then the current, i«, in Fig. 75, pulsates less than the voltage, ee, which produces it, and the current thus does not go down in wo, but is continuous, and its pulsation the less, the higher the in- ductance. The current, i, in the a ...", "... ion the less, the higher the in- ductance. The current, i, in the alternating supply circuit, how- 234 SYNCHRONOUS RECTIFIER 235 Fia. 72. — Alternating sine wave. AC or DC Fig. 73. — Rectifying commutator. Fig. 74. — Rectified wave on non inductive load. Fig. 75. — Rectified wave on-inductive load. Fig. 76. — Alternating supply wave to rectifier on inductive load. 236 ELECTRICAL A I'I'A if A TU8 ever, from which the direct current, in, is derived by reversal, must go through zero twice durin ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-04", "section_label": "Chapter 5: Single-Phase Induction Motor", "section_title": "Single-Phase Induction Motor", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 8555-10582", "status": "candidate", "occurrence_count": 34, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-04/", "snippets": [ "... rimary circuit corres ponds. 61. Hereby the single-phase motor constants are derived from the constants of the same motor structure as polyphase motor. Let, in a polyphase motor: Y = g — jb = primary exciting admittance; 2o = To + Jin = primary self-inductive im- pedance; Z\\ = fi + jxi = secondary self-inductive im- pedance (reduced to the pri- mary by the ratio of turns, in the usual manner}; the characteristic constant of the motor then is: & - y (z„ + zx). (i) The total, or resultant admittance resp ...", "... se motor constants are derived from the constants of the same motor structure as polyphase motor. Let, in a polyphase motor: Y = g — jb = primary exciting admittance; 2o = To + Jin = primary self-inductive im- pedance; Z\\ = fi + jxi = secondary self-inductive im- pedance (reduced to the pri- mary by the ratio of turns, in the usual manner}; the characteristic constant of the motor then is: & - y (z„ + zx). (i) The total, or resultant admittance respectively impedance of SINGLE-PHASE INDUCTION MOTOR ...", "... en them. The motor circuits may be connected in series, and shunted by the impedance, or they may be connected in shunt with each other, but in series with their respective impedance, or they may be connected with each other by transformation, etc. B. Inductive Devices. — The motor is excited by two or more circuits which are in inductive relation with each other so as to produce a phase displacement. 98 ELECTRICAL APPARATUS This inductive relation may be established outside of the motor by an external phase ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-29", "section_label": "Chapter 7: Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "section_title": "Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "kind": "chapter", "sequence": 29, "number": 7, "location": "lines 6798-7825", "status": "candidate", "occurrence_count": 34, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "snippets": [ "CHAPTER VII. RESISTANCE, INDUCTANCE, AND CAPACITY IN SERIES IN ALTERNATING-CURRENT CIRCUIT. 65. Let, at time t = 0 or 0 = 0, the e.m.f., e = E cos (0 - 00), (1) be impressed upon a circuit containing in series the resistance, r, the inductance, L, and the capacity, C. The inductive re ...", "CHAPTER VII. RESISTANCE, INDUCTANCE, AND CAPACITY IN SERIES IN ALTERNATING-CURRENT CIRCUIT. 65. Let, at time t = 0 or 0 = 0, the e.m.f., e = E cos (0 - 00), (1) be impressed upon a circuit containing in series the resistance, r, the inductance, L, and the capacity, C. The inductive reactance is x = 2 TT/L 1 and the condensive reactance is xc = > 2 7T/C J where/ = frequency and 6 = 2 nft. (3) Then the e.m.f. consumed by resistance is ri\\ the e.m.f. consumed by inductance, is di di Ldt ...", "... , INDUCTANCE, AND CAPACITY IN SERIES IN ALTERNATING-CURRENT CIRCUIT. 65. Let, at time t = 0 or 0 = 0, the e.m.f., e = E cos (0 - 00), (1) be impressed upon a circuit containing in series the resistance, r, the inductance, L, and the capacity, C. The inductive reactance is x = 2 TT/L 1 and the condensive reactance is xc = > 2 7T/C J where/ = frequency and 6 = 2 nft. (3) Then the e.m.f. consumed by resistance is ri\\ the e.m.f. consumed by inductance, is di di Ldt = xJe' and the e.m.f. consumed by capac ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-05", "section_label": "Theory Section 5: Self-inductance and Mutual Inductance", "section_title": "Self-inductance and Mutual Inductance", "kind": "theory-section", "sequence": 5, "number": 5, "location": "lines 1573-1784", "status": "candidate", "occurrence_count": 30, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-05/", "snippets": [ "5. SELF-INDUCTANCE AND MUTUAL INDUCTANCE 26. The number of inter-linkages of an electric circuit with the lines of magnetic force of the flux produced by unit current in the circuit is called the inductance of the circuit. The number of ...", "5. SELF-INDUCTANCE AND MUTUAL INDUCTANCE 26. The number of inter-linkages of an electric circuit with the lines of magnetic force of the flux produced by unit current in the circuit is called the inductance of the circuit. The number of interlinkages of an el ...", "5. SELF-INDUCTANCE AND MUTUAL INDUCTANCE 26. The number of inter-linkages of an electric circuit with the lines of magnetic force of the flux produced by unit current in the circuit is called the inductance of the circuit. The number of interlinkages of an electric circuit with the lines of magnetic force of the flux produced by unit current in a second electric circuit is called the mutual inductance of the second upon th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-09", "section_label": "Chapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "section_title": "Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 4674-6992", "status": "candidate", "occurrence_count": 30, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-09/", "snippets": [ "CHAPTER IX CIRCUITS CONTAINING RESISTANCE, INDUCTIVE REACTANCE, AND CONDENSIVE REACTANCE 53. Having, in the foregoing, re-established Ohm's law and Kirchhoff 's laws as being also the fundamental laws of alternating- current circuits, when expressed in their complex form, E = ZI, or, 7 = YE, and \"EE ...", "... can now — by application of these laws, and in the same manner as with continuous-current circuits, keeping in mind, however, that E, I, Z, Y, are complex quanti- ties— calculate alternating-current circuits and networks of circuits containing resistance, inductive reactance, and conden- sive reactance in any combination, without meeting with greater difficulties than when dealing with continuous-current circuits. It is obviously not possible to discuss with any completeness all the infinite varieties of combination ...", "... onden- sive reactance in any combination, without meeting with greater difficulties than when dealing with continuous-current circuits. It is obviously not possible to discuss with any completeness all the infinite varieties of combinations of resistance, inductive reactance, and condensive reactance which can be imagined, and which may exist, in a system of network of circuits; there- fore only some of the more common or more interesting combina- tions will here be considered. 1. Resistance in Series with a Circu ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 30, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "... ry low. As illustration is shown in Fig. 20 the load curve of a typical 100-hp. 60-cycle 80-polar induction motor (90 revolutions per minute) of the constants: Impressed voltage: ea = 500. Primary exciting admittance: Ya = 0.02 — 0.6 j. Primary self-inductive impedance: Zu = 0.1 + 0.3j. Secondary self-inductive impedance: Zi = 0.1 + 0.3 j. INDUCTION MOTOR 53 As seen, at full-load of 75 kw. output, the efficiency is 80 per cent., which is fair for a slow-speed motor. But the power-factor is 55 per cen ...", "... curve of a typical 100-hp. 60-cycle 80-polar induction motor (90 revolutions per minute) of the constants: Impressed voltage: ea = 500. Primary exciting admittance: Ya = 0.02 — 0.6 j. Primary self-inductive impedance: Zu = 0.1 + 0.3j. Secondary self-inductive impedance: Zi = 0.1 + 0.3 j. INDUCTION MOTOR 53 As seen, at full-load of 75 kw. output, the efficiency is 80 per cent., which is fair for a slow-speed motor. But the power-factor is 55 per cent., the apparent efficiency only 44 per cent., and the ...", "... nction of giv- ing the field excitation. Thus in a slow-speed induction motor, of very high exciting current and correspondingly poor constants, by passing an exciting current of suitable value through the rotor or secondary, the primary can be made non-inductive, or even leading current produced, or — with a lesaer exciting current in the rotor — at least the power-factor increased. Various such methods of secondary excitation have been pro- posed, and to some extent used. 1. Passing a direct current through t ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-12", "section_label": "Chapter 12: Reactance Of Induction Apparatus", "section_title": "Reactance Of Induction Apparatus", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 22634-23465", "status": "candidate", "occurrence_count": 30, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-12/", "snippets": [ "... current passing through a conductor is ac- companied by a magnetic field surrounding this conductor, and this magnetic field is as integral a part of the phenomenon, as is the energy dissipation by the resistance of the conductor. It is represented by the inductance, L, of the conductor, or the number of magnetic interlinkages with unit current in the conductor. Every circuit thus has a resistance, and an inductance, however small the latter may be in the so-called \"non-inductive\" circuit. With continuous current in ...", "... phenomenon, as is the energy dissipation by the resistance of the conductor. It is represented by the inductance, L, of the conductor, or the number of magnetic interlinkages with unit current in the conductor. Every circuit thus has a resistance, and an inductance, however small the latter may be in the so-called \"non-inductive\" circuit. With continuous current in stationary conditions, the inductance, L, has no effect on the energy flow; with alternating current of frequency, /, the inductance, L, consumes a volta ...", "... conductor. It is represented by the inductance, L, of the conductor, or the number of magnetic interlinkages with unit current in the conductor. Every circuit thus has a resistance, and an inductance, however small the latter may be in the so-called \"non-inductive\" circuit. With continuous current in stationary conditions, the inductance, L, has no effect on the energy flow; with alternating current of frequency, /, the inductance, L, consumes a voltage 2 x/Li, and is, therefore, represented by the reactance, x = 2 ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-24", "section_label": "Chapter 2: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 24, "number": 2, "location": "lines 1993-2658", "status": "candidate", "occurrence_count": 30, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "snippets": [ "... current, In the moment of closing the circuit of e.m.f. e0 on resistance r, the current in the circuit is zero. Hence, after closing the circuit the current i has to rise from zero to its final value i0. If the circuit contained only resistance but no inductance, this would take place instantly, that is, there would be no transition period. Every circuit, however, contains some inductance. The induc- tance L of the circuit means L interlinkages of the circuit with lines of magnetic force produced by unit current ...", "... closing the circuit the current i has to rise from zero to its final value i0. If the circuit contained only resistance but no inductance, this would take place instantly, that is, there would be no transition period. Every circuit, however, contains some inductance. The induc- tance L of the circuit means L interlinkages of the circuit with lines of magnetic force produced by unit current in the circuit, or iL interlinkages by current i. That is, in establishing current i0 in the circuit, the magnetic flux iQL must ...", "... 1 / 1 1 \\ I, = • 01 en r.v- 1° \\ I a a \\ 1 < \\ / V / \\ / \\ s ' — , -*^. -0- ( 1 I I , 5 ! i j ; L I 1 ! I 5 Seconds Fig. 1. Rise and decay of continuous current in an inductive circuit. continuous current in an inductive circuit: the exciting current of an alternator field, or a circuit having the constants r = 12 ohms; L = 6 henrys, and eQ = 240 volts; the abscissas being seconds of time. 13. If an electrostatic condenser of ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-25", "section_label": "Chapter 3: Inductance And Resistance In Continuous Current Circuits", "section_title": "Inductance And Resistance In Continuous Current Circuits", "kind": "chapter", "sequence": 25, "number": 3, "location": "lines 2659-3514", "status": "candidate", "occurrence_count": 29, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-25/", "snippets": [ "CHAPTER III. INDUCTANCE AND RESISTANCE IN CONTINUOUS- CURRENT CIRCUITS. 20. In continuous-current circuits the inductance does not •enter the equations of stationary condition, but, if e0 = impressed e.m.f., r = resistance, L = inductance, the permanent value of /> current ...", "CHAPTER III. INDUCTANCE AND RESISTANCE IN CONTINUOUS- CURRENT CIRCUITS. 20. In continuous-current circuits the inductance does not •enter the equations of stationary condition, but, if e0 = impressed e.m.f., r = resistance, L = inductance, the permanent value of /> current is ia = — • r Therefore less care is taken in direct-current circuits to reduce the inductance th ...", "CHAPTER III. INDUCTANCE AND RESISTANCE IN CONTINUOUS- CURRENT CIRCUITS. 20. In continuous-current circuits the inductance does not •enter the equations of stationary condition, but, if e0 = impressed e.m.f., r = resistance, L = inductance, the permanent value of /> current is ia = — • r Therefore less care is taken in direct-current circuits to reduce the inductance than in alternating-current circuits, where the inductance usually causes a drop of voltage, and direct-current circuit ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-21", "section_label": "Chapter 21: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 22302-23970", "status": "candidate", "occurrence_count": 28, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-21/", "snippets": [ "... he resultant e.m.f., will take place in this case only when the magnetic densities are so near to saturation that the rise of density at the leading pole corner will be less than the decrease of density at the trailing pole corner. Since the internal self-inductive reactance of the alternator itself causes a certain lag of the current behind the generated e.m.f., this condition of no displacement can exist only in a circuit with external negative reactance, as capacity, etc. ALTERNATING-CURRENT GENERATOR 2G1 If ...", "... generated in the armature by the resultant magnetic flux, produced by the resultant m.m.f. of the field and of the armature, is not the terminal voltage of the machine; the terminal voltage is the resultant of this generated e.m.f. and the e.m.f. of self-inductive reactance and the e.m.f. representing the power loss by resistance in the alternator armature. That is, in other words, the armature current not only opposes or assists the field m.m.f. in creating the resultant magnetic flux, but sends a second magnetic ...", "... only opposes or assists the field m.m.f. in creating the resultant magnetic flux, but sends a second magnetic flux in a local circuit through the armature, which flux does not pass through the field-spools, and is called the magnetic flux of armature self-inductive reactance. 262 ALTERNATING-CURRENT PHENOMENA Thus we have to distinguish in an alternator between armature reaction, or the magnetizing action of the armature upon the field, and armature self-inductive reactance, or the e.m.f. gener- ated in the arma ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-09", "section_label": "Chapter 9: Kbsistanci: And Kbactance Of Transmission Iine8", "section_title": "Kbsistanci: And Kbactance Of Transmission Iine8", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 6371-8268", "status": "candidate", "occurrence_count": 28, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "snippets": [ "... ance is small if the current is in phase with the E.M.F., while a drop of potential is produced with a lagging, and a rise of potential with a leading, current in the receiver circuit. Thus the change of potential due to a line of given re- sistance and inductance depends upon the phase difference in the receiver circuit, and can be varied and controlled by varying this phase difference; that is, by varying the admittance, Y = g + Jb, of the receiver circuit. The conductance, g, of the receiver circuit depends upo ...", "... upon the consumption of power, — that is, upon the load on the circuit, — and thus cannot be varied for the purpose of reg- ulation. Its susceptance, by however, can be changed by shunting the circuit with a reactance, and will be increased by a shunted inductance, and decreased by a shunted con- densance. Hence, for the purpose of investigation, the 84 AL TERN A TIXG-CURRENT PHENOMENA, [§ 68 receiver circuit can be assumed to consist of two branches, a conductance, g^ — the non-inductive part of the circuit, — ...", "... ncreased by a shunted inductance, and decreased by a shunted con- densance. Hence, for the purpose of investigation, the 84 AL TERN A TIXG-CURRENT PHENOMENA, [§ 68 receiver circuit can be assumed to consist of two branches, a conductance, g^ — the non-inductive part of the circuit, — shunted by a susceptance, by which can be varied without expenditure of energy. The two components of current can thus be considered separately, the energy component as determined by the load on the circuit, and the wattless compon ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 28, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "... current in the conductor produces a magnetic field, not only outside of the conductor, but inside of it also ; and the lines of magnetic force which close themselves inside of the conductor induce E.M.Fs. in their interior only. Thus the counter E.M.F. of self- inductance is largest at the axis of the conductor, and least at its surface ; consequently, the current density at the surface will be larger than at the axis, or, in extreme cases, the current may not penetrate at all to the center, or a reversed current flow ther ...", "... ctor, or the highest frequency, where this phenomenon is still negligible. In the interior of the conductor, the current density is not only less than at the surface, but the current lags behind the current at the surface, due to the increased effect of self-inductance. This lag of the current causes the magnetic fluxes in the conductor to be out of phase with each other, making their resultant less than their sum, while the lesser current density in the center reduces the total flux inside of the conductor. Thus, by as ...", "... /> = 10xlO-6, ft = 500 it is, permitting 5% difference between center and outside of wire; k = 3.2 X 10 ~6 and NR* = .46, hence when, N = 125 100 60 25 X = .061 .068 .088 .136 cm. thus the effect is noticeable even with relatively small iron wire. Mutual Inductance. 97. When an alternating magnetic field of force includes a secondary electric conductor, it induces therein an E.M.F. which produces a current, and thereby consumes energy if the circuit of the secondary conductor is closed. A particular case of such ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-17", "section_label": "Chapter 17: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16362-17596", "status": "candidate", "occurrence_count": 28, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "snippets": [ "... his case only when the magnetic densities are so near to saturation that the rise of density at the leading-pole corner will be less than the decrease of AL TERN A TING-CURRENT GENERA TOR. 299 density at the trailing-pole corner. Since the internal self- inductance of the alternator itself causes a certain lag of the current behind the induced E.M.F., this condition of no displacement can exist only in a circuit with external nega- tive reactance, as capacity, etc. If the armature current lags, it reaches the maxim ...", "... E.M.F. induced in the armature by the re- sultant magnetic flux, produced by the resultant M.M.F. of the field and of the armature, is not the terminal voltage of the machine ; the terminal voltage is the resultant of this induced E.M.F. and the E.M.F. of self-inductance and the E.M.F. representing the energy loss by resistance in the alternator armature. That is, in other words, the armature current not only opposes or assists the field M.M.F. in cre- ating the resultant magnetic flux, but sends a second mag- netic flux ...", "... only opposes or assists the field M.M.F. in cre- ating the resultant magnetic flux, but sends a second mag- netic flux in a local circuit through the armature, which flux does not pass through the field spools, and is called the magnetic flux of armature self-inductance. Thus we have to distinguish in an alternator between armature reaction, or the magnetizing action of the arma- ture upon the field, and armature self-inductance, or the E.M.F. induced in the armature conductors by the current flowing therein. This E.M. ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-31", "section_label": "Chapter 9: Divided Circuit", "section_title": "Divided Circuit", "kind": "chapter", "sequence": 31, "number": 9, "location": "lines 9228-10474", "status": "candidate", "occurrence_count": 27, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "snippets": [ "... IDED CIRCUIT. 72. A circuit consisting of two branches or multiple circuits 1 and 2 may be supplied, over a line or circuit 3, with an impressed e.m.f., e0. Let, in such a circuit, shown diagrammatically in Fig 31, rv Lv Cl and r2, L2, Cz — resistance, inductance, and capacity, respectively, of the two branch circuits 1 and 2; r0, L0, C0 = Co Fig. 31. Divided circuit. resistance, inductance, and capacity of the undivided part of the circuit, 3. Furthermore let e = potential difference at terminals of branch ...", "... impressed e.m.f., e0. Let, in such a circuit, shown diagrammatically in Fig 31, rv Lv Cl and r2, L2, Cz — resistance, inductance, and capacity, respectively, of the two branch circuits 1 and 2; r0, L0, C0 = Co Fig. 31. Divided circuit. resistance, inductance, and capacity of the undivided part of the circuit, 3. Furthermore let e = potential difference at terminals of branch circuits 1 and 2, it and i2 respectively = currents in branch circuits 1 and 2, and i3 = current in undivided part of circuit, 3. Then ...", "... of circuit 2 is e = di 121 (2) (3) 122 TRANSIENT PHENOMENA and of circuit 3 is (4) Instead of the inductances, L, and capacities, C, it is usually preferable, even in direct-current circuits, to introduce the reactances, x = 2 nfL = inductive reactance, xc = = con- 2 7T/G densive reactance, referred to a standard frequency, such as / = 60 cycles per second. Instead of the time t, then, an angle 0 = 2 nft (5) is introduced, and then we have di x di dd di ^ * (6) i/iift - 2 Kfo f Id0 ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 27, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... SSION LINE 281 contain from about one-half to 11 complete waves of the im- pressed frequency. For long-distance telephony the phenomena occurring in the line thus can be investigated only by consider- ing the complete equation of distributed capacity and inductance as so-called \"wave transmission\" and the phenomena thus essentially differ from those in a short energy transmission line. 4. Therefore in very long circuits, as in lines conveying alter- nating currents of high value at high potential over extremely lo ...", "... es or decreases the main current, according to the relative phase of the main current and the e.m.f. As a consequence the current changes in intensity, as well as in phase, in the line from point to point; and the e.m.fs. con- sumed by the resistance and inductance, therefore, also change in phase and intensity from point to point, being dependent upon the current. Since no insulator has an infinite resistance, and since at high potentials not only leakage but even direct escape of electricity into the air takes p ...", "... ze the existence of a current approximately proportional and in phase with the e.m.f. of the line. This current represents consumption of power, and is therefore analogous to the e.m.f. consumed by resistance, while the condenser current and the e.m.f. of inductance are wattless or reactive. Furthermore, the alternating current passing over the line pro- duces in all neighboring conductors secondary currents, which react upon the primary current and thereby introduce e.m.fs. of mutual inductance into the primary cir ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2485-3386", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-04/", "snippets": [ "... e, as shown in Fig. 15C, that is, at a point one-quarter period or 90 degrees distant from the intersec- tion of ii and 12. 32 ELECTRIC DISCHARGES, WAVES AND IMPULSES. If the current ii is zero, we get the starting of the alternating current in an inductive circuit, as shown in Figs. 16, A, B,C. The starting transient is zero, if the circuit is closed at the moment when the permanent current would be zero (Fig. 165), and is a maximum when closing the circuit at the maximum point of the permanent-current wave ...", "... ar, similar as in starting transformers of high magnetic density. In polyphase rotary SINGLE-ENERGY TRANSIENTS. 37 apparatus, however, these momentary starting currents usually are far more limited than in transformers, by the higher stray field (self-inductive reactance), etc., of the apparatus, resulting from the air gap in the magnetic circuit. 19. As instance of the use of the single-energy transient in engineering calculations may be considered the investigation of the momentary short-circuit phenomena of ...", "... with reasonable exactness. In an alternator, the voltage under load is affected by armature reaction and armature self-induction. Under permanent condi- tion, both usually act in the same way, reducing the voltage at noninductive and still much more at inductive load, and increasing it at antiinductive load; and both are usually combined in one quantity, the synchronous reactance Xq. In the transients result- ing from circuit changes, as short circuits, the self-inductive armature reactance and the magnetic armat ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-22", "section_label": "Chapter 22: Armature Reactions Of Alternators", "section_title": "Armature Reactions Of Alternators", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 23971-25134", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-22/", "snippets": [ "... armature reaction, the e.m.f. considered, which would be generated by the magnetic flux, which the arma- ture reaction would produce. That is, both effects are com- bined in an effective reactance, the \"synchronous reactance.\" While armature reaction and self-inductance are similar in ARMATURE REACTIONS OF ALTERNATORS 273 effect, in some cases they differ in their action; the e.m.f. of self-inductance is instantaneous, that is, appears and disappears with the current to which it is due. The effect of the armature rea ...", "... is, both effects are com- bined in an effective reactance, the \"synchronous reactance.\" While armature reaction and self-inductance are similar in ARMATURE REACTIONS OF ALTERNATORS 273 effect, in some cases they differ in their action; the e.m.f. of self-inductance is instantaneous, that is, appears and disappears with the current to which it is due. The effect of the armature reaction, however, requires time; the change of the magnetic field resulting from the combination of the counter m.m.f. of arma- ture reactio ...", "... ircuit conditions, at a rate of speed depending upon the constants of the field-exciting circuit, etc. The extreme case hereof takes place when suddenly short- circuiting an alternator; at the first moment the short-circuit current is limited only by the self-inductance, and the magnetic field still has full strength, the field-exciting current has greatly increased by the e.m.f. generated in the field circuit by the arma- ture reaction. Gradually the field-exciting current and there- with the field magnetism die down to ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 25, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... current in the conductor produces a magnetic field, not only outside of the conductor, but inside of it also ; and the lines of magnetic force which dose themselves inside of the conductor induce E.M.Fs. in their interior only. Thus the counter E.M.F. of self- inductance is largest at the axis of the conductor, and least at its surface ; consequently, the current density at the surface will be larger than at the axis, or, in extreme cases, the current may not penetrate at all to the center, or a reversed current flow ther ...", "... tor, or the highest frequency, where this jDhenomenon is still negligible. In the interior of the conductor, the current density is not only less than at the surface, but the current lags behind the current at the surface, due to the increased effect of self-inductance. This lag of the current causes the magnetic fluxes in the conductor to be out of phase with each other, making their resultant less than their sum, while the lesser current density in the center reduces the total flux inside of the conductor. Thus, by as ...", "... conductor. Conductors of this size are, however, excluded from use at this frequency by the exter- nal selfrinduction, which is several times larger than the resistance. We thus see that unequal current distribution is usually negligible in practice. Mutual Inductance, 97. When an alternating magnetic field of force includes a secondary electric conductor, it induces therein an E.M.F. which produces a current, and thereby consumes energy if the circuit of the secondary conductor is closed. A particular case of such ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-02", "section_label": "Chapter 2: Potential Series And Exponential Function", "section_title": "Potential Series And Exponential Function", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3492-6063", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-02/", "snippets": [ "... n-l)(n-2) ^ If II 4 where |w«-lX2x3X. . .Xm. Thus, for instance, in an alternating-current circuit of resistance r, reactance x, and supply voltage e, the curi-ent is. ^■v^T7^ \"^) 60 ENGINEERING MATHEMATICS. If this circuit is practically non-inductive, as an incandescent lighting circuit; that is, if x is small compared with r, (15) can be written in the form, ._ e e h©T', . . . ae, and the square root can be developed by the binomial (14), thus, u= yyj ; n= --, and gives h(r)T*=-i(7)\"-s(r)'- ...", "... ages are dealt with as functions of time. The current and c.m.f. giving the power lost in resistance are related to each other by Ohm's law. Current also produces a magnetic field, and this magnetic field by its changes generates an e.m.f. — the e.m.f. of self- inductance. In this case, e.m.f. is related to the change of current; that is, the differential coefficient of the current, and thus also to the differential coefficient of e.m.f., since the e.m.f. POTENTIAL SERIES AND EXPONENTIAL FUNCTION. 65 is related to the c ...", "... nd therefore, b}^ Ohm's law, the e.m.f., depends upon and is proportional to the rate of change of the e.m.f. impressed upon the condenser; that is, it is proportional to the differential coefficient of e.m.f. Therefore, in circuits having resistance and inductance, or resistance and capacity, a relation exists between currents and e.m.f s., and their differential coefficients, and in circuits having resistance, inductance and capacity, a double relation of this kind exists; that is, a relation between current or e. ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-04", "section_label": "Chapter 4: Vector Representation", "section_title": "Vector Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2149-2759", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-04/", "snippets": [ "... rrent, I, £3 Eo upon the e.m.f., or by IE cos d, where A ^,--^^'' ^ ~ angle of phase displacement. ^J,.^--^ / 19. Suppose, as an example, that in ^^ *E ^' a line having the resistance, r, and the reactance, x = 2 irfL — where / = fre- quency and L = inductance — there p, ,r> exists a current of / amp., the line being connected to a non-inductive circuit operating at a voltage of E volts. What will be the voltage required at the generator end of the line? In the vector diagram. Fig. 12, let the phase of the c ...", "... splacement. ^J,.^--^ / 19. Suppose, as an example, that in ^^ *E ^' a line having the resistance, r, and the reactance, x = 2 irfL — where / = fre- quency and L = inductance — there p, ,r> exists a current of / amp., the line being connected to a non-inductive circuit operating at a voltage of E volts. What will be the voltage required at the generator end of the line? In the vector diagram. Fig. 12, let the phase of the current be assumed as the initial or zero line, 01. Since the receiving cir- cuit is non- ...", "... circuit operating at a voltage of E volts. What will be the voltage required at the generator end of the line? In the vector diagram. Fig. 12, let the phase of the current be assumed as the initial or zero line, 01. Since the receiving cir- cuit is non-inductive, the current is in phase with its voltage. Hence the voltage, E, at the end of the line, impressed upon the receiving circuit, is represented by a vector, OE. To overcome VECTOR REPRESENTATION 23 the resistance, r, of the hne, a voltage, Ir, is require ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "CHAPTER XIII. DISTRIBUTED CAPACITY, INDUCTANCE, RESISTANCE, AND LEAKAGE. 107. As far as capacity has been considered in the foregoing chapters, the assumption has been made that the condenser or other source of negative reactance is shunted across the circuit at a definite point. In many cases, how- ...", "... ensers infi nitely near together, as diagrammatically shown in Fig. 83. iiiimiiiiumiiiT TTTTTTTTTT.TTTTTTTTTT i Fig. 83. Distributed Capacity. In this case the intensity as well as phase of the current, and consequently of the counter E.M.F. of inductance and resistance, vary from point to point ; and it is no longer possible to treat the circuit in the usual manner by the vector diagram. This phenomenon is especially noticeable in long-distance lines, in underground cables, and to a certain degree in th ...", "... taining the same denotations as in A.), We have, 7 = 2\" = 1' - As will be seen, the first terms in the expression of E0 and of I0 are the same in A.) and in B.). DISTRIBUTED CAPACITY. 163 111. C.) Complete investigation of distributed capacity, inductance, leakage, and resistance. In some cases, especially in very long circuits, as in lines conveying alternating power currents at high potential over extremely long distances by overhead conductors or un- derground cables, or with very feeble currents at ex ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-101", "section_label": "Apparatus Section 4: Alternating-current Transformer: Regulation", "section_title": "Alternating-current Transformer: Regulation", "kind": "apparatus-section", "sequence": 101, "number": 4, "location": "lines 17538-18397", "status": "candidate", "occurrence_count": 23, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-101/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-101/", "snippets": [ "... y and secondary through which the primary current can send magnetic flux which does not interlink with the secondary winding, but is a self-induc- tive or leakage flux and in the same manner the secondary current sends self-inductive or leakage flux through the space between primary and secondary winding. These fluxes give rise to the self -inductive or leakage reactances x\\ and Xz of the transformer. Or in other words, two paths exist for magnetic fl ...", "... inding, but is a self-induc- tive or leakage flux and in the same manner the secondary current sends self-inductive or leakage flux through the space between primary and secondary winding. These fluxes give rise to the self -inductive or leakage reactances x\\ and Xz of the transformer. Or in other words, two paths exist for magnetic flux in the transformer: the path surrounding primary and secondary coils, through which flows the mutual magnetic flux o ...", "... mutual magnetic flux of the transformer, which is the useful flux, that is, the flux which transfers the power from primary to secondary circuit; and the space between pri- mary and secondary winding through which the self-inductive or leakage flux passes, that is, the flux interlinked with one wind- ing only, but not the other one. The latter flux thus does not transmit power, but consumes reactive voltage and thereby pro- duces a voltage drop and a ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-16", "section_label": "Chapter 16: Aiitebnatingh-Current Osnebator", "section_title": "Aiitebnatingh-Current Osnebator", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 17025-18828", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "snippets": [ "... ase only when the magnetic densities are so near to saturation that the rise of density at the leading-pole corner will be less than the decrease of 236 AL TERNA TING-CURRENT PHENOMENA. [§ 160 density at the trailing-pole corner. Since the internal self- inductance of the alternator alone causes a certain lag of the current behind the induced E.M.F., this condition of no displacement can exist only in a circuit with external nega- tive reactance, as capacity, etc. If the armature current lags, it reaches the maximu ...", "... E.M.F. induced in the armature by the re- sultant magnetic flux, produced by the resultant M.M.F. of the field and of the armature, is not the terminal voltage of the machine; the terminal voltage is the resultant of this induced E.M.F. and the E.M.F. of self-inductance and the E.M.F. representing the energy loss by resistance in the alternator armature. That is, in other words, the armature current not only opposes or assists the field M.M.F. in cre- ating the resultant magnetic flux, but sends a second mag- netic flux ...", "... only opposes or assists the field M.M.F. in cre- ating the resultant magnetic flux, but sends a second mag- netic flux in a local circuit through the armature, which flux does not pass through the field spools, and is called the magnetic flux of armature self -inductance. Thus we have to distinguish in an alternator between: armature reaction, or the magnetizing action of. the arma- ture upon the field, and armature self-inductance, or the E.M.F. induced in the armature conductors by the current flowing therein. This E. ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-02", "section_label": "Chapter 2: Multiple Squirrel-Cage Induction Motor", "section_title": "Multiple Squirrel-Cage Induction Motor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3543-5554", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-02/", "snippets": [ "CHAPTER II MULTIPLE SQUIRREL-CAGE INDUCTION MOTOR 18. In an induction motor, a high-resistance low-reactance secondary is produced by the use of an external non-inductive resistance in the secondary, or in a motor with squirrel-cage secondary, by small bars of high-resistance material located clow* to the periphery of the rotor. Such a motor has a great slip of speed under load, therefore poor efficiency and poor speed reg ...", "... small, therefore effi- ciency and speed regulation good, but the starting torque arid torque at low and intermediate speeds is low, and the current in starting and at low speed is large. To combine good start- ing with good running characteristics, a non-inductive resistance is used in the secondary, which is cut out during acceleration. This, however, involves a complication, which is undesirable in many cases, such as in ship propulsion, etc. By arranging then two squirrel cages, one high-resistance low-reactance ...", "... ce, gives its torque at full speed, near synchronism. Mechanically, the rotor iron may be slotted down to the inner- most squirrel cage, so as to avoid the excessive reactance of a closed magnetic circuit, that is, have the magnetic leakage flux or self-inductive flux pass an air gap. 19. In the calculation of the standard induction motor, it is usual to start with the mutual magnetic flux, *, or rather with the voltage induced by this flux, the mutual inductive voltage E — e, as it is most convenient, with the m ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-12", "section_label": "Chapter 14: Phase Conversion And Single-Phase Generation", "section_title": "Phase Conversion And Single-Phase Generation", "kind": "chapter", "sequence": 12, "number": 14, "location": "lines 17125-18412", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-12/", "snippets": [ "... ingle-phase system and polyphase system, a storage of energy thus must take place, as the balance factor of the single-phase system is zero or negative, while that of the balanced polyphase system is unity. For such energy storage may be used capacity, or inductance, or momentum or a combination thereof: Energy storage by capacity, that is, in the dielectric fu Id, required per kilovolt-ampere at 60 cycles about 200O <-.•■. ol space, at a cost of about $10. Inductance, that is. energy storage by the magnetic field, ...", "... or such energy storage may be used capacity, or inductance, or momentum or a combination thereof: Energy storage by capacity, that is, in the dielectric fu Id, required per kilovolt-ampere at 60 cycles about 200O <-.•■. ol space, at a cost of about $10. Inductance, that is. energy storage by the magnetic field, requires about 1000 c.e. per kilo- volt-ampere at 60 cycles, at a cost of $1, while energy storage by momentum, as kinetic mechanical energy, assuming iron moving at 30 meter-seconds, stores 1 kva. at 60 cyc ...", "... increases with decroaniBg kilovolt-ampere capacity. Furthermore, the use of mechanical momentum means moving machinery, requiring more or less attention, thus becomes less suitable, for smaller values of power. Hence, for smaller amounts of stored energy, inductance and capacity may become more economical than momentum, and for very small amounts of energy, the condenser may lie the cheapest device. The above figures thus give only the approxi- • \"Theorv and Calculation of Alterwi ting-current Phenomena,\" edition, ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2162-2971", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "snippets": [ "... nce, that is, at a point one-quarter period or 90 degrees distant from the intersection of i\\ and 12, as shown in Fig. 15C. 32 ELECTRIC DISCHARGES, WAVES AND IMPULSES. If the current ii is zero, we get the starting of the alternating current in an inductive circuit, as shown in Figs. 16, A, B, C. The starting transient is zero, if the circuit is closed at the moment when the permanent current would be zero (Fig. 16B), and is a maximum when closing the circuit at the maximum point of the permanent-current wav ...", "... ar, similar as in starting transformers of high magnetic density. In polyphase rotary SINGLE-ENERGY TRANSIENTS. 37 apparatus, however, these momentary starting currents usually are far more limited than in transformers, by the higher stray field (self-inductive reactance), etc., of the apparatus, resulting from the air gap in the magnetic circuit. 19. As instance of the use of the single-energy transient in engineering calculations may be considered the investigation of the momentary short-circuit phenomena of ...", "... with reasonable exactness. In an alternator, the voltage under load is affected by armature reaction and armature self-induction. Under permanent condi- tion, both usually act\" in the same way, reducing the voltage at noninductive and still much more at inductive load, and increasing it at antiinductive load; and both are usually combined in one quantity, the synchronous reactance XQ. In the transients result- ing from circuit changes, as short circuits, the self-inductive armature reactance and the magnetic armat ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "CHAPTER VI. OSCILLATING CURRENTS, 44. The charge and discharge of a condenser through an inductive circuit produces periodic currents of a frequency depending upon the circuit constants. The range of frequencies which can be produced by electro- dynamic machinery is rather limited: synchronous machines or ordinary alternators can give economically and ...", "... ly is this energy dissipated, that is, the faster the oscillation dies out. With a resistance of the circuit sufficiently low to give a fairly well sustained oscillation, the frequency is, with sufficient approximation, 45. The constants, capacity, C, inductance, L, and resistance, r, have no relation to the size or bulk of the apparatus. For instance, a condenser of 1 mf., built to stand continuously a potential of 10,000 volts, is far larger than a 200-volt condenser of 100 mf. capacity. The energy which the fo ...", "... ts, is far larger than a 200-volt condenser of 100 mf. capacity. The energy which the former is able to Ce2 store is -77-= 50 joules, while the latter stores only 2 joules, 2 and therefore the former is 25 times as large. A reactive coil of 0.1 henry inductance, designed to carry continuously 100 amperes, stores— = 500 joules; a reactive coil of 1000 times the inductance, 100 henrys, but of a current- carrying capacity of 1 ampere, stores 5 joules only, therefore is only about one-hundredth the size of the for ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-43", "section_label": "Chapter 3: The Natural Period Of The Transmission Line", "section_title": "The Natural Period Of The Transmission Line", "kind": "chapter", "sequence": 43, "number": 3, "location": "lines 21721-23178", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "snippets": [ "... d charge of atmospheric electricity (lightning), or oscillates because of a sudden change of load, as a break of circuit, or in general a change of circuit conditions, as closing the circuit, etc. The discharge of a condenser through a circuit containing self- inductance and resistance is oscillating (provided the resistance does not exceed a certain critical value depending upon the capacity and the self-inductance) ; that is, the discharge current alternates with constantly decreasing intensity. The frequency of this os ...", "... rcuit conditions, as closing the circuit, etc. The discharge of a condenser through a circuit containing self- inductance and resistance is oscillating (provided the resistance does not exceed a certain critical value depending upon the capacity and the self-inductance) ; that is, the discharge current alternates with constantly decreasing intensity. The frequency of this oscillating discharge depends upon the capacity C and the self -inductance L of the circuit, and to a much lesser extent upon the resistance, so that, ...", "... does not exceed a certain critical value depending upon the capacity and the self-inductance) ; that is, the discharge current alternates with constantly decreasing intensity. The frequency of this oscillating discharge depends upon the capacity C and the self -inductance L of the circuit, and to a much lesser extent upon the resistance, so that, if the resistance of the circuit is not excessive, the frequency of oscillation can, by neglecting the resistance, be expressed with fair, or even close, approximation by the form ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-04", "section_label": "Chapter 4: Graphic Befrisxintation", "section_title": "Graphic Befrisxintation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2122-2743", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "snippets": [ "... M.F., Ey upon the current, or by the E.M.F., E, into the projection of the current, /, upon the E.M.F., or IE cos (/j^). 17. Suppose, as an instance, that over a line having the resistance, r, and the reactance, x = 2irNLy — where A^ = frequency and L = inductance, — a current of / amperes be sent into a non-inductive circuit at an E.M.F. of E ,Er E • ^^ J • \\ 1 Vi \\ E. \"e. — ~^^E. Fig. 12. volts. What will be the E.M.F. required at the generator end of the line ? In the polar d ...", "... projection of the current, /, upon the E.M.F., or IE cos (/j^). 17. Suppose, as an instance, that over a line having the resistance, r, and the reactance, x = 2irNLy — where A^ = frequency and L = inductance, — a current of / amperes be sent into a non-inductive circuit at an E.M.F. of E ,Er E • ^^ J • \\ 1 Vi \\ E. \"e. — ~^^E. Fig. 12. volts. What will be the E.M.F. required at the generator end of the line ? In the polar diagram. Fig. 12, let the phase of the cur- rent be assu ...", "... E. \"e. — ~^^E. Fig. 12. volts. What will be the E.M.F. required at the generator end of the line ? In the polar diagram. Fig. 12, let the phase of the cur- rent be assumed as the initial or zero line. Of. Since the receiving circuit is non-inductive, the current is in phase with its E.M.F. Hence the E.M.F., E, at the end of the line, impressed upon the receiving circuit, is represented by a vector, OE. To overcome the resistance, r, of the line, an E.M.F., /r, is required in phase with the current, r ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-04", "section_label": "Chapter 4: Graphic Representation", "section_title": "Graphic Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 1743-2321", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "snippets": [ "... e E.M.F., E, upon the current, or by the E.M.F., E, into the projection of the current, /, upon the E.M.F., or by IE cos 17. Suppose, as an instance, that over a line having the resistance, r, and the reactance, x = ZirNL, — where N = frequency and L = inductance, — a current of / amperes be sent into a non-inductive circuit at an E.M.F. of E Fig. 12. volts. What will be the E.M.F. required at the generator end of the line ? In the polar diagram, Fig. 12, let the phase of the cur- rent be assumed as the init ...", "... the projection of the current, /, upon the E.M.F., or by IE cos 17. Suppose, as an instance, that over a line having the resistance, r, and the reactance, x = ZirNL, — where N = frequency and L = inductance, — a current of / amperes be sent into a non-inductive circuit at an E.M.F. of E Fig. 12. volts. What will be the E.M.F. required at the generator end of the line ? In the polar diagram, Fig. 12, let the phase of the cur- rent be assumed as the initial or zero line, Of. Since the receiving circuit is no ...", "... ircuit at an E.M.F. of E Fig. 12. volts. What will be the E.M.F. required at the generator end of the line ? In the polar diagram, Fig. 12, let the phase of the cur- rent be assumed as the initial or zero line, Of. Since the receiving circuit is non-inductive, the current is in phase with its E.M.F. Hence the E.M.F., E, at the end of the line, impressed upon the receiving circuit, is represented by a vector, OE. To overcome the resistance, r, of the line, an E.M.F., Ir, is required in phase with the current, r ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "section_label": "Chapter 16: Induction Motor", "section_title": "Induction Motor", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "... f primary and a number of secondary circuits are used, angularly displaced around the periphery of the motor, and containing E.M.Fs. displaced in phase by the same angle. This multi-circuit arrangement has the object always to retain secondary circuits in inductive relation to primary circuits and vice versa, in spite of their relative motion. The result of the relative motion between primary and secondary is, that the E.M.Fs. induced in the secondary or the motor armature are not of the same frequency as the E.M. ...", "... ance, and thus Vrx + r0)2 + (x^ + x0}z = z is the total impedance of the motor. Hence is the maximum output of the induction motor, at the slip, The same value has been derived in Chapter IX., as the maximum power which can be transmitted into a non- inductive receiver circuit over a line of resistance r, and impedance z, or as the maximum output of a generator, or of a stationary transformer. Hence : The maximum output of an induction motor is expressed by the same formula as the maximum output of a generator ...", "... f a generator, or of a stationary transformer. Hence : The maximum output of an induction motor is expressed by the same formula as the maximum output of a generator, or of a stationary transformer, or the maximum output which can be transmitted over an inductive line into a non-inductive- receiver circuit. The torque corresponding to the maximum output Pp is,. 254 ALTERNATING-CURRENT PHENOMENA. This is not the maximum torque ; but the maximum torque, Tt, takes place at a lower speed, that is, greater slip, ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-36", "section_label": "Chapter 14: Short-Circuit Currents Of Alternators", "section_title": "Short-Circuit Currents Of Alternators", "kind": "chapter", "sequence": 36, "number": 14, "location": "lines 14549-15353", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "snippets": [ "CHAPTER XIV. SHORT-CIRCUIT CURRENTS OF ALTERNATORS. 112. The short-circuit current of an alternator is limited by armature reaction and armature self-inductance; that is, the current in the armature represents a m.m.f. which with lagging current, as at short circuit, is demagnetizing or opposing the impressed m.m.f. of field excitation, and by combining therewith to a resultant m.m.f. reduces the magnetic flux fr ...", "... the generated e.m.f. from the nominal generated e.m.f., eOJ to the virtual generated e.m.f., er The armature current also produces a local magnetic flux in the armature iron and pole- faces which does not interlink with the field coils, but is a true self-inductive flux, and therefore is represented by a reactance xr Combined with the effective resistance, rv of the armature winding, this gives the self-inductive impedance Zl = rl — or zt = Vr* + x*. Vectorially subtracted from the virtual generated e.m.f., ev the ...", "... x in the armature iron and pole- faces which does not interlink with the field coils, but is a true self-inductive flux, and therefore is represented by a reactance xr Combined with the effective resistance, rv of the armature winding, this gives the self-inductive impedance Zl = rl — or zt = Vr* + x*. Vectorially subtracted from the virtual generated e.m.f., ev the voltage consumed by the armature current in the self-inductive impedance Zl then gives the ter- minal voltage, e. At short circuit, the virtual gene ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "LECTURE VII. LINE OSCILLATIONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy surges between magnetic — and dielectric — , and a transient component, by which the total stored energy decreases. Considering only the periodic component, the ...", "... eo, and io follow from the initial values e' and i' of the transient, 2bt t = 0 or (t> = 0: hence ^ = ^o cos 7 e' = —eo sin 7 tan 7 (9) (10) The preceding equations of the double-energy transient apply to the circuit in which capacity and inductance are massed, as, for instance, the discharge or charge of a condenser through an in- ductive circuit. Obviously, no material difference can exist, whether the capacity and the inductance are separately massed, or whether they are intermixed, a piece of i ...", "... double-energy transient apply to the circuit in which capacity and inductance are massed, as, for instance, the discharge or charge of a condenser through an in- ductive circuit. Obviously, no material difference can exist, whether the capacity and the inductance are separately massed, or whether they are intermixed, a piece of inductance and piece of capacity alternating, or uniformly distributed, as in the transmission line, cable, etc. Thus, the same equations apply to any point of the transmission line. j ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3956-4744", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "snippets": [ "LECTURE VII. LINE OSCILLATIONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy 7\" /j'2 f^ r/>2 surges between magnetic -^- and dielectric — , and a transient £i A component, by which the total stored energy decreases. Considering only t ...", "... voltage is i = loe-^cos (0 - 7) 6 = eoe-^sinfa - 7) 7, e0, and i.Q follow from the initial values ef and i' of the transient, at £ = Oor 0 = 0: hence The preceding equations of the double-energy transient apply to the circuit in which capacity and inductance are massed, as, for instance, the discharge or charge of a condenser through an in- ductive circuit. Obviously, no material difference can exist, whether the capacity and the inductance are separately massed, or whether they are intermixed, a piece of i ...", "... double-energy transient apply to the circuit in which capacity and inductance are massed, as, for instance, the discharge or charge of a condenser through an in- ductive circuit. Obviously, no material difference can exist, whether the capacity and the inductance are separately massed, or whether they are intermixed, a piece of inductance and piece of capacity alternating, or uniformly distributed, as in the transmission line, cable, etc. Thus, the same equations apply to any point of the transmission line. A ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-13", "section_label": "Chapter 13: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 13484-14333", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-13/", "snippets": [ "... by unit current in that conductor; Xi — 2 tt/Li = reactance of secondary circuit; that is, Li = total number of interlinkages with the secondary conductor, of the lines of magnetic force produced by unit current in that con- ductor; Xm = 2x/Li = mutual inductive reactance of the circuits; that is, L„i = total number of interlinkages with the secondary conductor, of the lines of magnetic force produced by unit cur- rent in the main conductor, or total number of interlinkages with the main conductor of the lines of ...", "... or, of the lines of magnetic force produced by unit cur- rent in the main conductor, or total number of interlinkages with the main conductor of the lines of magnetic force produced by unit current in the secondary conductor. Obviously: x^^ ^ xxi.^ 1 As self-inductance L, Li, the total flux surrounding the conductor is here meant. Usually in the discussion of inductive apparatus, especiallj^ of trans- formers, as the self-inductance of circuit is denoted that part of the mag- netic flux which surrounds one circuit but no ...", "... rlinkages with the main conductor of the lines of magnetic force produced by unit current in the secondary conductor. Obviously: x^^ ^ xxi.^ 1 As self-inductance L, Li, the total flux surrounding the conductor is here meant. Usually in the discussion of inductive apparatus, especiallj^ of trans- formers, as the self-inductance of circuit is denoted that part of the mag- netic flux which surrounds one circuit but not the other circuit; and as mutual inductance flux which passes between both circuits. Hence, the tot ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-48", "section_label": "Chapter 8: Velocity Of Propagation Of Electric Field", "section_title": "Velocity Of Propagation Of Electric Field", "kind": "chapter", "sequence": 48, "number": 8, "location": "lines 26095-27002", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "snippets": [ "... ency and of conductors without return conductor, hence with electric fields decreasing relatively slowly with the distance, requires an introduction of the velocity of propagation into the circuit equations. As illustrations will be discussed : (A) The inductance of a finite section of an infinitely long con- ductor without return conductor. (B) The mutual inductance between two finite conductors without return conductors, at considerable distance from each other. ((7) The capacity of a sphere in free space. ...", "... owly with the distance, requires an introduction of the velocity of propagation into the circuit equations. As illustrations will be discussed : (A) The inductance of a finite section of an infinitely long con- ductor without return conductor. (B) The mutual inductance between two finite conductors without return conductors, at considerable distance from each other. ((7) The capacity of a sphere in free space. (D) The capacity of a sphere against ground, in space. Cases A and B deal with the electromagnetic, C and ...", "... onsiderable distance from each other. ((7) The capacity of a sphere in free space. (D) The capacity of a sphere against ground, in space. Cases A and B deal with the electromagnetic, C and D with the electrostatic component of the electric field. A. Inductance of a length I of an infinitely long conductor without return conductor. 70. The inductance of a length I of a straight conductor is usually given by the equation L = 2Zlog^XlO-9, (6) lr where V = the distance of return conductor, lr = the radius of ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-05", "section_label": "Lecture 5: Long Distance Transmission", "section_title": "Long Distance Transmission", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2562-3132", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-05/", "snippets": [ "... e character of the load, that is, whether the power is used for alternating current distribution — 60 cycles^-or for conversion to direct current — 25 cycles. For the transmission line, 25 cycles has the advantage that the charging current is less and the inductive drop is less, because charging current and inductance voltage are proportional to the frequency. VOLTAGE 11,000 to 13,200 volts and more recently, even 22,000 volts is most common for shorter distances, as 10 to 20 miles, since this is about the highe ...", "... s used for alternating current distribution — 60 cycles^-or for conversion to direct current — 25 cycles. For the transmission line, 25 cycles has the advantage that the charging current is less and the inductive drop is less, because charging current and inductance voltage are proportional to the frequency. VOLTAGE 11,000 to 13,200 volts and more recently, even 22,000 volts is most common for shorter distances, as 10 to 20 miles, since this is about the highest voltage for which generators can be built; its use ...", "... At very high voltages it is therefore necessary to have the system statically balanced or symmetrical, that is, have the same potential differences from all the conductors to the ground. Any electric circuit, and so also the transmission line, contains inductance and capacity, and therefore stores energy as electromagnetic energy in the magnetic field due to the cur- rent, and as electrostatic energy, or electrostatic charge, due to the voltage. LONG DISTANCE TRANSMISSION 69 If: e = voltage, C = capacity. ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... ing wave, JS? = tt\"*** cos { — 6), can be expressed by the symbol, JjJ = e(cos 6 — j sin 0) dec a = (ei — je2) dec a, where a = tan a is the exponential decrement, a the angular decrement, e\"^'** the numerical decrement. OSCILLATING CURRENTS 347 Inductance 186. Let r = resistance, L = inductance, and x = 27r/L = reactance, in a circuit excited by the oscillating current, I = fc\"\"** cos (0 — ^) = i{cos d + j sin 6) dec a = (ii + jii) dec a, where ii = i cos ^, 12 = i sin 6j a = tan a. We have then, ...", "... be expressed by the symbol, JjJ = e(cos 6 — j sin 0) dec a = (ei — je2) dec a, where a = tan a is the exponential decrement, a the angular decrement, e\"^'** the numerical decrement. OSCILLATING CURRENTS 347 Inductance 186. Let r = resistance, L = inductance, and x = 27r/L = reactance, in a circuit excited by the oscillating current, I = fc\"\"** cos (0 — ^) = i{cos d + j sin 6) dec a = (ii + jii) dec a, where ii = i cos ^, 12 = i sin 6j a = tan a. We have then, the e.m.f. consumed by the resistance, r, ...", "... ting current, I = fc\"\"** cos (0 — ^) = i{cos d + j sin 6) dec a = (ii + jii) dec a, where ii = i cos ^, 12 = i sin 6j a = tan a. We have then, the e.m.f. consumed by the resistance, r, of the circuit, Er = rl dec a. The e.m.f. consumed due to the inductance, L, of the circuit, n T dl rk TT dl dl Hence E^ = — a;i€-\"*{sin (0 — ^) + a cos (0 — ^)} = sm (0 — ^ + a). cos a Thus, in symbolic expression, jFx = I — sin {B — a) — j cos (^ — a) } dec a cos a / ^ \\ /I = — xtXa — j) (cos ^ — j sin ^) dec a; ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1120-1683", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-01/", "snippets": [ "... The resistance, r, in circuits where energy is expended only in heating the conductor, is the same as the ohmic resistance of continuous-current circuits. In circuits, however, where energy is also expended outside of the conductor by magnetic hysteresis, mutual inductance, dielectric hysteresis, etc., r is larger than the true ohmic resistance of the conductor, since it refers to the total expenditure of energy. It may be called then the effective re- sistance. It may no longer be a constant of the circuit. The reactance, ...", "... now $ = the magnetic flux produced by, and interlinked with, the current, i (where those lines of magnetic force which are interlinked ?i-fold, or pass around n turns of the conductor, are counted n times), the ratio, —, is denoted by L, and called the inductance of the circuit. It is numerically equal, in absolute units, to the interlinkages of the circuit with the magnetic flux produced by unit current, and is, in the system of abso- lute units, of the dimension of length. Instead of the inductance, L, sometimes ...", "... d called the inductance of the circuit. It is numerically equal, in absolute units, to the interlinkages of the circuit with the magnetic flux produced by unit current, and is, in the system of abso- lute units, of the dimension of length. Instead of the inductance, L, sometimes its ratio with the ohmic resistance, r, is used, and is called the time-constant of the circuit, r If a conductor surrounds with n turns a magnetic circuit of reluctance, (R, the current, i, in the conductor represents the m.m.f. of ni am ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-06", "section_label": "Chapter 6: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 11051-12221", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-06/", "snippets": [ "... e.m.f., which consumes (or produces) the electric energy, and also the stored magnetic energy, depend on MAGNETISM 93 the current and the mductance of the electric circuit, and in alternating-current circuits the impressed voltage also depends on the inductance of the circuit, the inductance can frequently be expressed by supply voltage and current; and by substituting this in equation (1), the mechanical work of the magnetic forces can thus be expressed, in alternating-ciu'rent apparatus, by sup- ply voltage an ...", "... uces) the electric energy, and also the stored magnetic energy, depend on MAGNETISM 93 the current and the mductance of the electric circuit, and in alternating-current circuits the impressed voltage also depends on the inductance of the circuit, the inductance can frequently be expressed by supply voltage and current; and by substituting this in equation (1), the mechanical work of the magnetic forces can thus be expressed, in alternating-ciu'rent apparatus, by sup- ply voltage and current. In this manner, it ...", "... ion of the armatm'e of the electromagnet, from its initial position 1, to its final position 2,1 = the length of this motion, or the stroke of the electromagnet, in centimeters, and n = number of turns of the magnet winding. The magnetic flux ^, and the inductance L=-^10-8 (2) to of the magnet, vary during the motion of its armature, from a ^^fiiiumum value, $, = Mil 108 (3) n ^ the initial position, to a maximum value, ^, = 12^ 108 (4) n ^ the end position of the armature. 94 ELECTRIC CIRCUITS ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-27", "section_label": "Chapter 5: Resistance, Inductance, And Capacity In Series Condenser Charge And Discharge", "section_title": "Resistance, Inductance, And Capacity In Series Condenser Charge And Discharge", "kind": "chapter", "sequence": 27, "number": 5, "location": "lines 4072-5311", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "snippets": [ "CHAPTER V. RESISTANCE, INDUCTANCE, AND CAPACITY IN SERIES. CONDENSER CHARGE AND DISCHARGE. 29. If a continuous e.m.f . e is impressed upon a circuit contain- ing resistance, inductance, and capacity in series, the stationary condition of the circuit is zero current, i = o, and the poten- ...", "CHAPTER V. RESISTANCE, INDUCTANCE, AND CAPACITY IN SERIES. CONDENSER CHARGE AND DISCHARGE. 29. If a continuous e.m.f . e is impressed upon a circuit contain- ing resistance, inductance, and capacity in series, the stationary condition of the circuit is zero current, i = o, and the poten- tial difference at the condenser equals the impressed e.m.f., et =• e, no permanent current exists, but only the transient current of charge or dischar ...", "... of increase of its e.m.f. and to the capacity. It is therefore and e-^-lidt (1) is the potential difference at the terminals of a condenser of capacity C with current i in the circuit to the condenser. Let then, in a circuit containing resistance, inductance, and capacity in series, e = impressed e.m.f., whether continuous, alternating, pulsating, etc.; i = current in the circuit at time t; r = resistance; L = inductance, and C = capacity; then the e.m.f. consumed by resistance r is n; the e.m.f. consumed ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-30", "section_label": "Chapter 8: Low Frequency Surges In High Potential Systems", "section_title": "Low Frequency Surges In High Potential Systems", "kind": "chapter", "sequence": 30, "number": 8, "location": "lines 7826-9227", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "snippets": [ "... ntial systems, as long distance transmission lines and underground cable systems, occasionally destructive high potential low frequency surges occur; that is, oscillations of the whole system, of the same character as in the case of localized capacity and inductance discussed in the preceding chapter. While a system of distributed capacity has an infinite number of frequencies, which usually are the odd multiples of a funda- mental frequency of oscillation, in those cases where the fundamental frequency predominate ...", "... n of a system of distributed capacity. Such low frequency surges comprise the total system, not only the transmission lines but also the step-up transformers, gen- erators, etc., and in an underground cable system in such an oscillation the capacity and inductance are indeed localized to a certain extent, the one in the cables, the other in the generating system. In an underground cable system, therefore, of the infinite series of frequencies of oscillations which theoretically exist, only the fundamental frequency ...", "... begins, s c is the decrement of the oscillation. 66. The frequency of oscillation is where / is the impressed frequency. That is, the frequency of oscillation equals the impressed frequency times the square root of the ratio of condensive reactance and inductive reactance of the circuit, or is the impressed frequency divided by the square root of inductance voltage and capacity current, as fraction of impressed voltage and full-load current. Since the frequency of oscillation is that is, is independent of t ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-07", "section_label": "Theory Section 7: Inductance in Alternating-current Circuits", "section_title": "Inductance in Alternating-current Circuits", "kind": "theory-section", "sequence": 7, "number": 7, "location": "lines 2250-2717", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-07/", "snippets": [ "7. INDUCTANCE IN ALTERNATING-CURRENT CIRCUITS 34. An alternating current i = IQ sin 2irft or i — I0 sin 0 can be represented graphically in rectangular coordinates by a curved line as shown in Fig. 10, with the instantaneous values ...", "... where tQ is time of one 1 complete period, = -v or by the time angle 6 = 90°. FIG. 11. — Self-induction effects produced by an alternating sine wave of current. This e.m.f. is called the counter e.m.f. of inductance. It is .'•'• '•••• e'*=-Ljt = - 2 TT/L/O cos 2 irft. It is shown in dotted line in Fig. 11 as e'2. The quantity 2 irfL is called the inductive reactance of the circuit, and denoted by x. It is of the na ...", "... ve of current. This e.m.f. is called the counter e.m.f. of inductance. It is .'•'• '•••• e'*=-Ljt = - 2 TT/L/O cos 2 irft. It is shown in dotted line in Fig. 11 as e'2. The quantity 2 irfL is called the inductive reactance of the circuit, and denoted by x. It is of the nature of a resistance, and expressed in ohms. If L is given in 109 absolute units or henrys, x appears in ohms. The counter e.m.f. of inductance of the curren ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-109", "section_label": "Apparatus Section 3: Induction Machines: Single -phase Induction Motor", "section_title": "Induction Machines: Single -phase Induction Motor", "kind": "apparatus-section", "sequence": 109, "number": 3, "location": "lines 20428-21157", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-109/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-109/", "snippets": [ "... nt of the main magnetic flux plus the current producing in the secondary the exciting current of the cross magnetic flux. In reality it is slightly less, especially in small motors, due to the drop of voltage in the self-inductive impedance and the drop of quadrature mag- netic flux below the impressed primary magnetic flux caused thereby. In the secondary at synchronism this secondary exciting current is a current of twice the primary frequency; at a ...", "... r resolves itself into the investigation of the polyphase motor operating on single-phase circuits. 2. LOAD AND SPEED CURVES 147. Comparing thus a three-phase motor of exciting admit- tance per circuit Y = g — jb and self-inductive impedances ZQ = rQ + jxQ and Zi = TI + jxi per circuit with the same motor operating as single-phase motor from one pair of termi- nals, the single-phase exciting admittance is Y' = 3 Y (so as to give, the same volt- ...", "... ating as single-phase motor from one pair of termi- nals, the single-phase exciting admittance is Y' = 3 Y (so as to give, the same volt-amperes excitation 3 eF), the primary 330 ELEMENTS OF ELECTRICAL ENGINEERING self-inductive impedance is the same, ZQ = r0 + jxo', the sec- ondary self-inductive impedance single-phase, however, is only y Z'i = -5-, since all three secondary circuits correspond to the same primary circuit, and thus the total im ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-25", "section_label": "Apparatus Section 4: Synchronous Machines: Self-inductance", "section_title": "Synchronous Machines: Self-inductance", "kind": "apparatus-section", "sequence": 25, "number": 4, "location": "lines 8907-9034", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-25/", "snippets": [ "IV. Self-inductance 12. The effect of self -inductance is ^ similar to that of armature reaction, FlQ 50._Diagram of e m fs> and depends upon the phase relation in loaded generator, in the same manner. If EI = real generated vo ...", "IV. Self-inductance 12. The effect of self -inductance is ^ similar to that of armature reaction, FlQ 50._Diagram of e m fs> and depends upon the phase relation in loaded generator, in the same manner. If EI = real generated voltage, 0i = lag of current behind ...", "... in the same manner. If EI = real generated voltage, 0i = lag of current behind generated voltage EI, the magnetic flux produced by the arma- ture current I is in phase with the current, and thus the counter e.m.f. of self-inductance is in quadrature behind the current, and therefore the e.m.f. consumed by self-inductance is in quadrature ahead of the current. Thus in Fig. 50, denoting OEi = EI the generated e.m.f., the current is 01 = 7; lagging 61 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... loss with distorted wave, 377 of power, 136 Effective circuit constants, 168 Effective circuit conductance, 111 power, 180 reactance, 112 resistance, 2, 5, 9, 111 susceptance, 112 value of wave, 11 in polar diagram, 53 Efficiency of circuit with inductive line, 88, 95 induction motor, 234 Electrostatic, see Dielectric E.m.f. of self-induction, 123 Energy distance of dielectric field, 165 flow in polyphase system, 406 and torque as component of double frequency vector, 186 Epoch, 6 Equivalent circu ...", "... ginary power, 186 Impedance, 2, 9 apparent, of transformer, 201 of induction motor, 211 in series with circuit, 69 series and parallel connections, 55, 59 in symbolic expression, 35 synchronous, of alternator, 277 Independent polyphase system, 397 Inductance, 3, 9 factor of general wave, 382 Induction generator, 237 machine as inductive reactance, 96 motor, 208 on distorted wave, 392 Inductive devices, starting single- phase induction motor, 246 line, maximum power, 82 Inductor alternator, unsymmetr ...", "... , 211 in series with circuit, 69 series and parallel connections, 55, 59 in symbolic expression, 35 synchronous, of alternator, 277 Independent polyphase system, 397 Inductance, 3, 9 factor of general wave, 382 Induction generator, 237 machine as inductive reactance, 96 motor, 208 on distorted wave, 392 Inductive devices, starting single- phase induction motor, 246 line, maximum power, 82 Inductor alternator, unsymmetrical magnetic cycle, 135 Influence, electrostatic, from line, 174 Instantaneous ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-108", "section_label": "Apparatus Section 2: Induction Machines: Polyphase Induction Motor", "section_title": "Induction Machines: Polyphase Induction Motor", "kind": "apparatus-section", "sequence": 108, "number": 2, "location": "lines 19166-20427", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-108/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-108/", "snippets": [ "... r admit- tance of the primary circuit with open secondary circuit; that is, ge = magnetic power current, be = wattless magnetizing current, where e = counter-generated e.m.f. of the motor; ZQ = r0 + jxQ = primary self -inductive impedance, and Zi = 7*1 + jxi = secondary self-inductive impedance, reduced to the primary by the ratio of turns.1 All these quantities refer to one primary circuit and one corre- sponding secondary circuit. Thus in a ...", "... rcuit; that is, ge = magnetic power current, be = wattless magnetizing current, where e = counter-generated e.m.f. of the motor; ZQ = r0 + jxQ = primary self -inductive impedance, and Zi = 7*1 + jxi = secondary self-inductive impedance, reduced to the primary by the ratio of turns.1 All these quantities refer to one primary circuit and one corre- sponding secondary circuit. Thus in a three-phase induction motor the total power, etc., is three ...", "... l standstill of the motor. We then have 1 — s = speed of the motor secondary as fraction of syn- chronous speed, sf = frequency of the secondary currents, where / = frequency impressed upon the primary; 1 The self -inductive reactance refers to that flux which surrounds one of the electric circuits only, without being interlinked with the other circuits. 312 ELEMENTS OF ELECTRICAL ENGINEERING hence, . se = e.m.f. generated in the secondar ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "CHAPTER XV DISTRIBUTED CAPACITY, INDUCTANCE, RESISTANCE, AND LEAKAGE 127. In the foregoing, the phenomena causing loss of energy in an alternating-current circuit have been discussed; and it has been shown that the mutual relation between current and e.m.f. can be expressed by two of the four con ...", "... ely small condensers infinitely near together, as diagrammatically shown in Fig, 100. liiilliiiiiiiiiiiiiiiiiii JTTTTTTTTTTTTTTTTTTTTTTT- Fig. 100. In this case the intensity as well as phase of the current, and consequently of the counter e.m.f. of inductive reactance and resistance, vary from point to point; and it is no longer possible to treat the circuit in the usual manner by the vector diagram. This phenomenon is especially noticeable in long-distance lines, in underground cables, and to a certain degr ...", "... ^ 4 1 ' 172 ALTERNATING-CURRENT PHENOMENA or, expanding, /o = ^[ j^ + ^^{rb - xg)] - j[{b - h) - ^^{rg + xb)] } ; Eo = ^^ jl + (r+jx) (g - jb) +^^ (r+jx) = e{ 1 + (r + jx) [g - jb + ^-^) + ^-jir+jxY (g-jb) 131. Distributed condensive reactance, inductive reactance, leak- age, and resistance. In some cases, especially in very long circuits, as in lines conveying alternating-power currents at high potential over extremely long distances by overhead conductors or under- ground cables, or with very feeble c ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-27", "section_label": "Chapter 27: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 33011-34776", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-27/", "snippets": [ "... . is thus represented by E = 2:2n-i(e„i4-j„e„ii), 1 the general wave of current by 1 If Zi = r -^ j (x„, -{- xo -\\- Xc) is the impedance of the fundamental harmonic, where Xm is that part of the reactance which is proportional to the frequency (inductance, etc.), ^ Xo is that part of the reactance which is independent of the frequency (mutual inductance, synchronous motion, etc.). Xc is that part of the reactance which is inversely propor- tional to the frequency (capacity, etc.). The impedance for the ...", "... Zi = r -^ j (x„, -{- xo -\\- Xc) is the impedance of the fundamental harmonic, where Xm is that part of the reactance which is proportional to the frequency (inductance, etc.), ^ Xo is that part of the reactance which is independent of the frequency (mutual inductance, synchronous motion, etc.). Xc is that part of the reactance which is inversely propor- tional to the frequency (capacity, etc.). The impedance for the nth harmonic is + jn (nxr^ + a^o + -^ ) This term can be considered as the general symbolic expr ...", "... ad and lag, since some harmonics may be leading, others lagging. The apparent power, or total volt-amperes, of the circuit is P, = EI = JX2n-i{ej\" + e„i022n-i(4i' + *V^'). \\ 1 1 The power-factor of the circuit is, P^ 1 P =w = \\ 1 1 The term \"inductance factor,\" however, has no meaning any more, since the reactive powers of the different harmonics are not directly comparable. The quantity go = Vl — p^ , ,.,..„ , . reactive power has no physical sigmncance, and is not . , , : total apparent power ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-23", "section_label": "Chapter 1: The Constants Of The Electric Circuit", "section_title": "The Constants Of The Electric Circuit", "kind": "chapter", "sequence": 23, "number": 1, "location": "lines 1317-1992", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "snippets": [ "... it, as is usually the case, or may increase, as in an alternating-current circuit with leading current, and while the current may remain constant throughout the circuit, or decrease, as in a transmission line of considerable capacity with a leading or non-inductive receiver circuit, the flow of energy always decreases from generating to receiving circuit, and the power gradient therefore is characteristic of the direc- tion of the flow of energy.) In the space outside of the conductor, during the flow of energy th ...", "... current i by the voltage e and measuring this current i by its magnetic action, in the usual voltmeter. The coefficients L and (7, which are the proportionality factors of the magnetic and of the dielectric component of the electric field, are called the inductance and the capacity of the circuit, respectively. As electric power P is resolved into the product of current i and voltage e, the power loss in the conductor, Ph therefore can also be resolved into a product of current i and voltage et which is consumed i ...", "... nd (7, where r = circuit constant representing the power gradient, or the loss of power in the conductor, called resistance. L = circuit constant representing the intensity of the electro- magnetic component of the electric field of the circuit, called inductance. C = circuit constant representing the intensity of the electro- static component of the electric field of the circuit, called capacity. 3. A change of the magnetic field of the conductor, that is, of the number of lines of magnetic force surroundi ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-38", "section_label": "Apparatus Section 17: Synchronous Machines: Short-circuit Currents of Alternators", "section_title": "Synchronous Machines: Short-circuit Currents of Alternators", "kind": "apparatus-section", "sequence": 38, "number": 17, "location": "lines 10190-10429", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-38/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-38/", "snippets": [ "... , and even less in very large high-speed steam turbine alternators. It is where EQ = nominal generated e.m.f., ZQ = synchronous impe- dance of alternator, representing the combined effect of arma- ture reaction and armature self-inductance. In the first moment after short circuiting, however, the current frequently is many times larger than the permanent short- circuit current, that is, where z = self-inductive impedance of the alternator. That is, in the ...", "... effect of arma- ture reaction and armature self-inductance. In the first moment after short circuiting, however, the current frequently is many times larger than the permanent short- circuit current, that is, where z = self-inductive impedance of the alternator. That is, in the first moment after short circuiting the poly- phase alternator the armature current is limited only by the arma- ture self-inductance, and not by the armature reaction, and some ...", "... short- circuit current, that is, where z = self-inductive impedance of the alternator. That is, in the first moment after short circuiting the poly- phase alternator the armature current is limited only by the arma- ture self-inductance, and not by the armature reaction, and some appreciable time — occasionally several seconds — elapses before the armature reaction becomes effective. At short circuit, the magnetic field flux is greatly reduced by the demag ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-39", "section_label": "Chapter 3: Mechanical Rectification", "section_title": "Mechanical Rectification", "kind": "chapter", "sequence": 39, "number": 3, "location": "lines 15963-17754", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-39/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-39/", "snippets": [ "... value of alternating current, and i0 = instantaneous value of rectified current, then we have, before reversal, i0 = i, and after reversal, i0 = — i\\ that is, during the reversal of the circuit one of the currents must reverse. Since, however, due to the self-inductance of the circuits, neither current can reverse instantly, the reversal occurs gradually, so that for a while during rectification the instantaneous value of the alternating and of the rectified current differ from each other. Thus means have to be provided ...", "... occurs gradually, so that for a while during rectification the instantaneous value of the alternating and of the rectified current differ from each other. Thus means have to be provided either to shunt the difference between the two currents through a non-inductive bypath, or, the difference of the two currents exists as arc over the surface of the rectifying commutator.* The general phenomenon of single-phase rectification thus is : The alternating and the rectified circuit are in series. Both circuits are closed ...", "... rectification both circuits are short circuited. Such short-circuit rectification is feasible only in limited-current circuits, as on arc lighting machines, or in * If the circuit is reversed at the moment when the alternating current passes zero, due to self-inductance of the rectified circuit its current differs from zero, and an arc still appears at the rectifier. 229 230 TRANSIENT PHENOMENA cases where the voltage of the rectified circuit is only a small part of the total voltage, and thus the current not contro ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-appendix-01-synchronous-operation", "section_label": "Mathematical Appendix 5: Appendix: Synchronous Operation", "section_title": "Appendix: Synchronous Operation", "kind": "mathematical-appendix", "sequence": 5, "number": 5, "location": "PDF pages 27-68, lines 2165-5013", "status": "pdf-text-extracted-candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "snippets": [ "... ons.] In equation (4), the first term: E 2 . Pi sin co sin (2c> a co) is of double the frequency 2f. It thus does not represent energy transfer between the two alternators, but merely represents the energy storage and return, twice per cycle, occurring in any inductive circuit. It thus is of no further interest. The second term p\"i=- cos a [[END_PDF_PAGE:29]] [[PDF_PAGE:30]] 24 Report of Charles P. Steinmetz gives, substituting cos a = - ; z E 2g P\"i=2? 2 where g is the conductance of the circuit. That is, this term is the ...", "... by : 2F\" 2 = - sin s< sin ($ a) cos (1 s) E 2 f | = sin s0 < sin [(2 s) a]+sin (s< a) > z I J TT 2 TT 2 TT 2 = sin sin [(2 s) <4 a]-}-s- cos a ^- cos (2sd> a) z 2z 2z The first term again is the double frequency term representing the energy storage by inductance; the second term is the power consumed by the resistance of the circuit. Neither thus represents energy transfer between the alternators. The third term : E2 (sj,_ \\ (i2\\ is a slow pulsation of energy, which alternately accelerates the machine and thus tends ...", "... ant, since the magnetic field cannot follow the relatively rapid fluctuation of armature reaction. The magnetic effect of the armature reaction is represented electrically in the synchronous reactance XQ. The synchronous reactance thus consists of a true self-inductive reactance Xi, which is instantaneous, and an effective reactance of armature reaction x, [[END_PDF_PAGE:41]] [[PDF_PAGE:42]] 36 Report of Charles P. Steinmetz which requires appreciable time to develop, and does not correspond to any real magnetic flux. In t ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1659-2484", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-03/", "snippets": [ "... limited extent of the circuit, resulting from the low voltage, and at the low voltage the dielectric energy thus is negligible, that is, the circuit stores appreciable energy only by the magnetic field. A circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectric field. The usual high-voltage capacity circuit, as that of an electrostatic machine, while of very small inductance, also is of very small resistance, and the momen ...", "... circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectric field. The usual high-voltage capacity circuit, as that of an electrostatic machine, while of very small inductance, also is of very small resistance, and the momentary discharge currents may be very consider- able, so that in spite of the very small inductance, considerable magnetic-energy storage may oc- cur; that is, the system is one storing energy in two forms, ...", "... ric field. The usual high-voltage capacity circuit, as that of an electrostatic machine, while of very small inductance, also is of very small resistance, and the momentary discharge currents may be very consider- able, so that in spite of the very small inductance, considerable magnetic-energy storage may oc- cur; that is, the system is one storing energy in two forms, and oscillations appear, as in the dis- charge of the Leyden jar. Let, as represented in Fig. 10, a continuous voltage eo be im- pressed upon a ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1531-2161", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "snippets": [ "... limited extent of the circuit, resulting from the low voltage, and at the low voltage the dielectric energy thus is negligible, that is, the circuit stores appreciable energy only by the magnetic field. A circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectric field. The usual high-voltage capacity circuit, as that of an electrostatic machine, while of very small inductance, also is of very small resistance, and the momen ...", "... circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectric field. The usual high-voltage capacity circuit, as that of an electrostatic machine, while of very small inductance, also is of very small resistance, and the momentary discharge currents may be very consider- able, so that in spite of the very small inductance, considerable __ magnetic-energy storage may oc- cur; that is, the system is one eo storing energy in tw ...", "... ic field. The usual high-voltage capacity circuit, as that of an electrostatic machine, while of very small inductance, also is of very small resistance, and the momentary discharge currents may be very consider- able, so that in spite of the very small inductance, considerable __ magnetic-energy storage may oc- cur; that is, the system is one eo storing energy in two forms, and ^ oscillations appear, as in the dis- ' ~ charge of the Leyden jar. Fig 10._Magnetie Single.energy Let, as represented in Fig. 10, T ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-20", "section_label": "Chapter 20: Single-Phase Induction Motors", "section_title": "Single-Phase Induction Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 21538-22301", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-20/", "snippets": [ "... side e.m.f., as in the monocyclic starting device, or by displacing the circuits of two or more primary coils from each other, either by mutual induc- tion between the coils — that is, by using one as secondary to the other — or by impedances of different inductance factors connected with the different primary coils. 178. The starting devices of the single-phase induction motor by producing a quadrature magnetic flux can be subdivided into three classes: 1. Phase-Splitting Devices. Two or more primary circuits ar ...", "... n them. This can be done either by inserting external impedances in the circuits, as a condenser and a reactive coil, or by making the internal impedances of the motor circuits different, as by making one coil of high and the other of low resistance. 2. Inductive Devices. The different primary circuits of the motor are inductively related to each other in such a way as to produce a phase displacement between them. The induct- ive relation can be outside of the motor or inside, by having the one coil submitted to t ...", "... vices. The different primary circuits of the motor are inductively related to each other in such a way as to produce a phase displacement between them. The induct- ive relation can be outside of the motor or inside, by having the one coil submitted to the inductive action of the other; and in this latter case the current in the secondary coil may be made leading, accelerating coil, or lagging, shading coil. 3. Monocyclic Devices. External to the motor an essentially wattless e.m.f. is produced in quadrature ' with ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "section_title": "Dibtbisnted Capacity, Inductance, Besistance, And", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "CHAPTER XII. DIBTBISnTED CAPACITY, INDUCTANCE, BESISTANCE, AND liEAKAGE. 102. As far as capacity has been considered in the foregoing chapters, the assumption has been made that the condenser or other source of negative reactance is shunted across the circuit at a definite point. In many cases, ho ...", "... e number of infinitely small condensers infi. nitely near together, as diagrammatically shown in Fig. 83. 8 3 S Fig, 83. Distributed Capacity. In this case the intensity as well as phase of the current,, and consequently of the counter E.M.F. of inductance and resistance, vary from point to point ; and it is no longer possible to treat the circuit in the usual manner by the vector diagram. This phenomenon is especially noticeable in long-distance lines, in underground cables, especially concentric cables, ...", "... or decrease the main current, according to the relative phase of the main current and the E.M.F. As a consequence, the current will change in intensity as well as in phase, in the line from point to point ; and the E.M.Fs. consumed by the resistance and inductance will therefore also change in phase and intensity from point to point, being dependent upon the current. Since no insulator has an infinite resistance, and as at high potentials not only leakage, but even direct escape of electricity into the air, takes ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "section_label": "Chapter 30: Quartbr-Fhase System", "section_title": "Quartbr-Fhase System", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... illating wave E=^et~^^ cos (<^ — w) can be expressed by the symbol E = e (cos a> +y sin ui) dec a = {e^ +jc^ dec a, where a = tan a is the exponential decrement, a the angular decrement, t~^^** the numerical decrement. 414 APPENDIX //. [§§ 284, 286 Inductance. 284. Let r = resistance, L = inductance, and x = 2 IT N L = reactance. In a circuit excited by the oscillating current, /= /c\"^*^ cos ( — co) = /(cos tu +/ sin o>) dec a = {h +Jh) dec a, where t\\ == / cos oj, /j = / sin o>, a = tan a. We have t ...", "... expressed by the symbol E = e (cos a> +y sin ui) dec a = {e^ +jc^ dec a, where a = tan a is the exponential decrement, a the angular decrement, t~^^** the numerical decrement. 414 APPENDIX //. [§§ 284, 286 Inductance. 284. Let r = resistance, L = inductance, and x = 2 IT N L = reactance. In a circuit excited by the oscillating current, /= /c\"^*^ cos ( — co) = /(cos tu +/ sin o>) dec a = {h +Jh) dec a, where t\\ == / cos oj, /j = / sin o>, a = tan a. We have then. The electromotive force consumed by ...", "... ^*^ cos ( — co) = /(cos tu +/ sin o>) dec a = {h +Jh) dec a, where t\\ == / cos oj, /j = / sin o>, a = tan a. We have then. The electromotive force consumed by the resistance r of the circuit 7?, = ,- /dec a. The electromotive force consumed by the inductance L of the circuit, 77 r d I o A- r if f d I Ex = /' — = 2 TT A Z = .V . lit i/ ii Hence Ej, = — xit\"*'^ {sin ( — w) + ^ cos ( — w)} = -— — - -- sin ( — (u + «)• cos tt Thus, in symbolic expression, ^x = — {— sin (w — a) +ycos (w ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-32", "section_label": "Chapter 32: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 25904-27405", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "snippets": [ "... he oscillating wave E = ee~a cos ( — w) can be expressed by the symbol E = e (cos w -\\-j sin w) dec a = (e± -\\-j'e^) dec a, where a = tan a is the exponential decrement, a the angular decrement, e~27ra the numerical decrement. 502 APPENDIX II. Inductance. 313. Let r = resistance, L = inductance, and x = 2 IT N L = reactance. In a circuit excited by the oscillating current, /= /£-«* cos (<£ — w) = /(cos to +y sin w) dec a = (*i -\\-J*z) dec a, where /i = / cos w, /2 = / sin £>, a = tan a. We have th ...", "... w) can be expressed by the symbol E = e (cos w -\\-j sin w) dec a = (e± -\\-j'e^) dec a, where a = tan a is the exponential decrement, a the angular decrement, e~27ra the numerical decrement. 502 APPENDIX II. Inductance. 313. Let r = resistance, L = inductance, and x = 2 IT N L = reactance. In a circuit excited by the oscillating current, /= /£-«* cos (<£ — w) = /(cos to +y sin w) dec a = (*i -\\-J*z) dec a, where /i = / cos w, /2 = / sin £>, a = tan a. We have then, The electromotive force consumed by t ...", "... rrent, /= /£-«* cos (<£ — w) = /(cos to +y sin w) dec a = (*i -\\-J*z) dec a, where /i = / cos w, /2 = / sin £>, a = tan a. We have then, The electromotive force consumed by the resistance r of the circuit ^ The electromotive force consumed by the inductance L of the circuit, Ef**L—~*iNI&t = *—. dt d<$> d<$> Hence Ex = — xif.~a^> (sin ( — fy -\\- a cos (<£ — w)} xi(.~a^ . ,. „ , N = sin (^> — w -f- a). COS a Thus, in symbolic expression, £x = - °^—{— sin (w — a) +/ cos (w — a)} dec a COS a ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-26", "section_label": "Chapter 26: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 32540-33010", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-26/", "snippets": [ "... ce the distortion of the wave-shape consists in the superposition of higher harmonics, that is, waves of higher fre- quency, the phenomena taking place in a circuit supplied by such a wave will be the combined effect of the different waves. Thus in a non-inductive circuit the current and the potential difference across the different parts of the circuit are of the same shape as the impressed e.m.f. If inductive reactance is inserted in series with a non-inductive circuit, the self-inductive reactance consumes more ...", "... e in a circuit supplied by such a wave will be the combined effect of the different waves. Thus in a non-inductive circuit the current and the potential difference across the different parts of the circuit are of the same shape as the impressed e.m.f. If inductive reactance is inserted in series with a non-inductive circuit, the self-inductive reactance consumes more e.m.f. of the higher harmonics, since the reactance is proportional to the frequency, and thus the current and the e.m.f. in the non-inductive part of ...", "... mbined effect of the different waves. Thus in a non-inductive circuit the current and the potential difference across the different parts of the circuit are of the same shape as the impressed e.m.f. If inductive reactance is inserted in series with a non-inductive circuit, the self-inductive reactance consumes more e.m.f. of the higher harmonics, since the reactance is proportional to the frequency, and thus the current and the e.m.f. in the non-inductive part of the circuit show the higher harmonics in a reduced a ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "... es, and thus cannot be combined. The general wave of E.M.F. is thus represented by, the general wave of current by, if, is the impedance of the fundamental harmonic, where xm is that part of the reactance which is proportional to the frequency (inductance, etc.). x0 is that part of the reactance which is independent of the frequency (mutual induction, synchronous motion, etc.). xc is that part of the reactance which is inversely pro- portional to the frequency (capacity, etc.). The impedance for the n ...", "... in the general alternating circuit no distinction can be made be- tween lead and lag, since some harmonics may be leading, others lagging. The apparent power, or total volt-amperes, of the circuit is, The power factor of the circuit is, The term \"inductance factor,\" however, has no mean- ing any more, since the wattless powers of the different harmonics are not directly comparable. The quantity, ,...._ ... wattless power has no physical significance, and is not = total apparent power REPRESENTATION ...", "... ics are not directly comparable. The quantity, ,...._ ... wattless power has no physical significance, and is not = total apparent power REPRESENTATION OF ALTERNATING WAVES. 4] > The term, /#. El = 2/n~17 where, consists of a series of inductance factors qn of the individual harmonics. As a rule, if (1) be impressed upon a non-inductive load, giving the current i = I cos (2) The power then is where p = ei = EI cos^ = ^ (1 + cos 2 ) = Q + Q cos 2 « (3) = f (4) that is, in a non-inductive single-phase circuit, the power consists of a constant component, Q--2' and an ...", "... or or condenser. 164. Let a voltage, e = E cos (1) be impressed upon a non-inductive load, giving the current i = I cos (2) The power then is where p = ei = EI cos^ = ^ (1 + cos 2 ) = Q + Q cos 2 « (3) = f (4) that is, in a non-inductive single-phase circuit, the power consists of a constant component, Q--2' and an alternating component, EI = \"2- cos 2 0, of twice the frequency of the supply voltage, and a maximum value equal to that of the constant component. The instantane- ou ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-33", "section_label": "Chapter 40: General System Of Circuits", "section_title": "General System Of Circuits", "kind": "chapter", "sequence": 33, "number": 40, "location": "lines 12217-12884", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-33/", "snippets": [ "CHAPTER XL GENERAL SYSTEM OF CIRCUITS. (A) Circuits containing resistance and inductance only. 95. Let, upon a general system or network of circuits con- nected with each other directly or inductively, and containing resistance and inductance, but no capacity, a system of e.m.fs., ey be impressed. These e.m.fs. may be of any frequency or wa ...", "CHAPTER XL GENERAL SYSTEM OF CIRCUITS. (A) Circuits containing resistance and inductance only. 95. Let, upon a general system or network of circuits con- nected with each other directly or inductively, and containing resistance and inductance, but no capacity, a system of e.m.fs., ey be impressed. These e.m.fs. may be of any frequency or wave shape, or may be continuous or anything else, but are supposed to be given by their equations. They may be free of transient terms, or may contain transi ...", "... the dependency of the e.m.f. upon the currents must obviously be given. Then, in each branch circuit, ^5~=0, (1) where e = total impressed e.m.f.; r. = resistance; L = induc- tance, of the circuit or branch of circuit traversed by current i, and Ms = mutual inductance of this circuit with any circuit in inductive relation thereto and traversed by current is. The currents in the different branch circuits of the system depend upon each other by Kirchhoff's law, D i - 0 (2) at every branching point of the system. By ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-13", "section_label": "Theory Section 13: Alternating-current Transformer", "section_title": "Alternating-current Transformer", "kind": "theory-section", "sequence": 13, "number": 13, "location": "lines 4465-5263", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-13/", "snippets": [ "... rent transformer consists of one mag- netic circuit interlinked with two electric circuits, the primary circuit which receives energy, and the secondary circuit which delivers energy. Let TI = resistance, x\\ = 2TrfSz = self-inductive or leakage reactance of secondary circuit, r0 = resistance, XQ = 2irfSi = self -inductive or leakage reactance of primary circuit, where S2 and Si refer to that magnetic flux which is interlinked with the one but no ...", "... rimary circuit which receives energy, and the secondary circuit which delivers energy. Let TI = resistance, x\\ = 2TrfSz = self-inductive or leakage reactance of secondary circuit, r0 = resistance, XQ = 2irfSi = self -inductive or leakage reactance of primary circuit, where S2 and Si refer to that magnetic flux which is interlinked with the one but not with the other circuit. Let a ratio of — — • — - turns (ratio of transformation), prima ...", "... with OE\"'Q gives OEQ = EQj the primary im- pressed e.m.f., and angle 0o = -#o#/o, the phase angle of the primary circuit. Figs. 35, 36, and 37 give the polar diagrams of 0i = 45° or lagging current, 0i = zero or non-inductive circuit, and 6 = — 45° or leading current. 61. As seen, the primary impressed e.m.f. E0 required to pro- duce the same secondary terminal voltage E at the same current 1 1 is larger with lagging or inductive and smaller ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-15", "section_label": "Theory Section 15: Load Characteristic of Transmission Line", "section_title": "Load Characteristic of Transmission Line", "kind": "theory-section", "sequence": 15, "number": 15, "location": "lines 5832-6221", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-15/", "snippets": [ "... jx. Let EQ = e.m.f. impressed upon the line. Choosing the e.m.f. at the end of the line as horizontal com- ponent in the vector diagram, it can be denoted by E = e. 86 ELEMENTS OF ELECTRICAL ENGINEERING At non-inductive load the line current is in phase with the e.m.f. e, thus denoted by 7 = i. The e.m.f. consumed by the line impedance Z — r + jx is E! = ZI = (r + jx) i = ri+jxi. (1) Thus the impressed voltage, ' Eo = E + ...", "... h open circuit i = 0, e = E0 and P = 0, as is to be expected. At short circuit, e = 0, 0 = \\/#o2 — xzi2 — ri, and ° ; (6) X' that is, the maximum line current which can be established with a non-inductive receiver circuit and negligible line capacity. 71. The condition of maximum 'power delivered over the line '• i| f-* on that is, substituting (3): '! V#o2 - x*i* = e + ri, and expanding, gives e* = (r2 + ...", "... z2i2; hence, e — zi, and - = z. (9) -T- = 7*1 is the resistance or effective resistance of the receiving circuit; that is, the maximum power is delivered into a non- LOAD CHARACTERISTIC OF TRANSMISSION LINE 87 inductive receiving circuit over an inductive line upon which is impressed a constant e.m.f., if the resistance of the receiving circuit equals the impedance of the line, TI = z. In this case the total impedance of the system is ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-17", "section_label": "Chapter 17: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16521-17716", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-17/", "snippets": [ "... being interlinked with the other. This magnetic cross-flux is proportional to the current in the electric circuit, or rather, the ampere-turns or m.m.f., and so increases with the increasing load on the transformer, and constitutes what is called the self-inductive or leakage reactance of the trans- former; while the flux surrounding both coils may be con- sidered as mutual inductive reactance. This cross-flux of self-induction does not generate e.m.f. in the secondary circuit, 187 188 ALTERNATING-CURRENT PHENOM ...", "... her, the ampere-turns or m.m.f., and so increases with the increasing load on the transformer, and constitutes what is called the self-inductive or leakage reactance of the trans- former; while the flux surrounding both coils may be con- sidered as mutual inductive reactance. This cross-flux of self-induction does not generate e.m.f. in the secondary circuit, 187 188 ALTERNATING-CURRENT PHENOMENA and is thus, in general, objectionable, by causing a drop of voltage and a decrease of output. It is this cross-flux ...", "... self-induction does not generate e.m.f. in the secondary circuit, 187 188 ALTERNATING-CURRENT PHENOMENA and is thus, in general, objectionable, by causing a drop of voltage and a decrease of output. It is this cross-flux, how- ever, or flux of self-inductive reactance, which is utilized in special transformers, to secure automatic regulation, for con- stant power, or for constant current, and in this case is exagger- ated by separating primary and secondary coils. In the con- stant potential transformer, howe ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-30", "section_label": "Chapter 30: Balanced And Unbalanced Polyphase Systems", "section_title": "Balanced And Unbalanced Polyphase Systems", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 35256-35691", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-30/", "snippets": [ "... t is called an unbalanced system if the flow of energy varies periodically, as in the single-phase system; and the ratio of the minimum value to the maximum value of power is called the halance-J actor of the system. Hence in a single-phase system on non-inductive circuit, that is, at no-phase displacement, the balance-factor is zero; and it is negative in a single-phase system with lagging or leading current, and becomes equal to — 1 if the phase displace- ment is 90° — that is, the circuit is wattless. 275. Obv ...", "... the current in the middle wire first decreases, reaches a V3 minimum value of -^ = 0.866 of its original value, and then increases again, reaching at no-load the same value as at full-load. The balance factor of the inverted three-phase system on non- inductive load is 0.333. 278. In Figs. 196 to 203 are shown the e.m.fs., as e and currents as i in full hues, and the power as y in dotted lines, for balance- factor, 0; balance-factor,— 0.333; balance-factor, -1- 1; balance- factor, -}- 1 ; balance-factor, + 1 ; ...", "... e systems may be classified into: Monocyclic systems, or systems with a balance-factor zero or negative. Polycyclic systems, with a positive balance-factor. Balance-factor —1 corresponds to a wattless single-phase circuit, balance-factor zero to a non-inductive single-phase circuit, balance-factor +1 to a balanced polyphase system. 280. In polar coordinates the flow of energy of an alternating current system is represented by using the instantaneous value of power as radius vector, with the angle, /3, correspon ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-27", "section_label": "Chapter 27: Balanced And Unbalanced Polyphase Systems", "section_title": "Balanced And Unbalanced Polyphase Systems", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 24054-24488", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-27/", "snippets": [ "... flow of energy varies periodically, as in the single-phase sys- tem ; and the ratio of the minimum value to the maximum value of power is called the balance factor of the system. 442 ALTERNATING-CURRENT PHENOMENA. Hence in a single-phase system on non-inductive circuit, that is, at no-phase displacement, the balance factor is zero ; and it is negative in a single-phase system with lagging or leading current, and becomes = — 1, if the phase displace- ment is 90° — that is, the circuit is wattless. 269. Obviousl ...", "... ero, the current in the middle wire first decreases, reaches a minimum value of 87 per cent of its original value, and then increases again, reaching at no load the same value as at full load. The balance factor of the inverted three-phase system on non-inductive load is .333. 272. In Figs. 185 to 192 are shown the E.M.Fs. as e and currents as i in drawn lines, and the power as / in dotted lines, for : Fig. 185. Single-phase System on Non-inductive Load. Balance Factor, 0. BALANCED POLYPHASE SYSTEMS. 445 ...", "... The balance factor of the inverted three-phase system on non-inductive load is .333. 272. In Figs. 185 to 192 are shown the E.M.Fs. as e and currents as i in drawn lines, and the power as / in dotted lines, for : Fig. 185. Single-phase System on Non-inductive Load. Balance Factor, 0. BALANCED POLYPHASE SYSTEMS. 445 Fig. 186. Single-phase System on Inductiue Load of 60° Lag. Balance Factor, - .333. Fig. 187. Quarter-phase System on Non-inductiui Load. Balance Factor, + 1. Fig. 183. Quarter-phase S ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-53", "section_label": "Chapter 4: Traveling Waves", "section_title": "Traveling Waves", "kind": "chapter", "sequence": 53, "number": 4, "location": "lines 30244-31450", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "snippets": [ "... sly applies only for waves of con- stant velocity, that is, such waves in which q is large compared with s, u, and m, and therefore does not strictly apply to ex- tremely long waves, as discussed in 13. 22. By changing the line constants, as by inserting inductance L in such a manner as to give the effect of uniform distribution (loading the line), the attenuation of the wave can be reduced, that is, the wave caused to travel a greater distance / with the same decrease of amplitude. As function of the inductance L ...", "... g inductance L in such a manner as to give the effect of uniform distribution (loading the line), the attenuation of the wave can be reduced, that is, the wave caused to travel a greater distance / with the same decrease of amplitude. As function of the inductance L, the attenuation constant (155) is a minimum for — °=o- dL hence, rO - gL = 0, or (156) and if the conductance g = 0 we have L = ; hence, in a per- fectly insulated circuit, or rather a circuit having no energy losses depending on the vo ...", "... — °=o- dL hence, rO - gL = 0, or (156) and if the conductance g = 0 we have L = ; hence, in a per- fectly insulated circuit, or rather a circuit having no energy losses depending on the voltage, the attenuation decreases with increase of the inductance, that is, by \"loading the line,\" and the more inductance is inserted the better the telephonic transmission. TRAVELING WAVES 463 In a leaky telephone line increase of inductance decreases the attenuation, and thus improves the telephonic transmission, ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... c can be calculated, without calculating the preceding harmonics. For instance, let the generator e.m.f. wave, Fig. 44, Table II, column 2, be impressed upon an underground cable system Fig. 44. Generator e.m.f. wave. of such constants (capacity and inductance), that the natural frequency of the system is 670 cycles per second, while the generator frequency is 60 cycles. The natural frequency of the TRIGONOMETRIC SERIES. 115 circuit is then close to that of the 11th harmonic of the generator wave, 660 c ...", "... °) + 0.13 sin (7^-6.2°)}, . (2) would be the voltage supplied to the transmission line at the high potential terminals of the step-up transformers. From the wire tables, the resistance per mile of No. 0 B. & S. copper line wire is ro = 0.52 ohm. The inductance per mile of wire is given by the formula : Lo = 0.7415 log ^+0.0805mh, .... (3) where h is the distance between the wires, and Z^ the radius of the wire. In the present case, this gives Z^ = 5 ft. = 60 in. Z^ = 0 . 1625 in. L() = l .9655 mh., and, her ...", "... e, a:,=|i»=2770ohms; *\" 60 ' 30 miles, or half the line (from the generating station to the middle of the line, where the line capacity is represented by a shunted condenser) give: the resistance, r = 30ro = 16.6 ohms TRIGONOMETRIC SERIES. 141 the inductive reactance, a; = 30xo = 22.5 ohms, and the equiva- lent circuit of the line now consists of the resistance r, inductive reactance x and condensive reactance Xc, in series with each other in the circuit of the supply voltage e. 95. If i= current in the lin ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-10", "section_label": "Lecture 10: Regulation And Control", "section_title": "Regulation And Control", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 4595-4930", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-10/", "snippets": [ "... s compounding and over-compounding without any elaborate apparatus. Disadvantages — Only limited power can be rectified, therefore suitable only for smaller machines. Compounds correctly only for constant power factoi ; that is, if compounded for non-inductive load, the voltage drops on inductive load, since inductive load requires a greater field excitation than non-inductive load. 130 GENERAL LECTURES Brushes have to be shifted with change of power factor, that is, change from motor load to lighting load, ...", "... hout any elaborate apparatus. Disadvantages — Only limited power can be rectified, therefore suitable only for smaller machines. Compounds correctly only for constant power factoi ; that is, if compounded for non-inductive load, the voltage drops on inductive load, since inductive load requires a greater field excitation than non-inductive load. 130 GENERAL LECTURES Brushes have to be shifted with change of power factor, that is, change from motor load to lighting load, etc. ; other- wise commutator sparks ...", "... paratus. Disadvantages — Only limited power can be rectified, therefore suitable only for smaller machines. Compounds correctly only for constant power factoi ; that is, if compounded for non-inductive load, the voltage drops on inductive load, since inductive load requires a greater field excitation than non-inductive load. 130 GENERAL LECTURES Brushes have to be shifted with change of power factor, that is, change from motor load to lighting load, etc. ; other- wise commutator sparks badly. These machin ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-06", "section_label": "Theory Section 6: Self-inductance of Continuous-current Circuits", "section_title": "Self-inductance of Continuous-current Circuits", "kind": "theory-section", "sequence": 6, "number": 6, "location": "lines 1785-2249", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-06/", "snippets": [ "6. SELF-INDUCTANCE OF CONTINUOUS-CURRENT CIRCUITS 30. Self-inductance makes itself felt in continuous-current circuits only in starting and stopping or, in general, when the current changes in value. Starting of Current. If r = resistance, L ...", "6. SELF-INDUCTANCE OF CONTINUOUS-CURRENT CIRCUITS 30. Self-inductance makes itself felt in continuous-current circuits only in starting and stopping or, in general, when the current changes in value. Starting of Current. If r = resistance, L = inductance of circuit, E = continuous e.m.-f. i ...", "... F CONTINUOUS-CURRENT CIRCUITS 30. Self-inductance makes itself felt in continuous-current circuits only in starting and stopping or, in general, when the current changes in value. Starting of Current. If r = resistance, L = inductance of circuit, E = continuous e.m.-f. impressed upon circuit, i = current in circuit at time t after impressing e.m.f. E, and di the increase of current during time moment dt, then the increase of magnetic interlinkages duri ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-22", "section_label": "Chapter 20: Ri", "section_title": "Ri", "kind": "chapter", "sequence": 22, "number": 20, "location": "lines 24560-25119", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "snippets": [ "... superposition of higher harmonics, that is, waves of higher frequency, the phenomena taking place in a circuit / 3o8 AL TERNA TIXG-CURREXT PHEXOMEXA. [§ 225 supplied by such a wave will be the combined effect of the different waves. Thus in a non-inductive circuit, the current and the potential difference across the different parts of the circuit are of the same shape as the impressed E.M.F\". If self- induction is inserted in series to a non-inductive circuit, the self-induction consumes more E.M.F. of the ...", "... combined effect of the different waves. Thus in a non-inductive circuit, the current and the potential difference across the different parts of the circuit are of the same shape as the impressed E.M.F\". If self- induction is inserted in series to a non-inductive circuit, the self-induction consumes more E.M.F. of the higher harmon- ics, since the reactance is proportional to the frequency, and thus the current and the E.M.F. in the non-inductive part of the circuit shows the higher harmonics in a reduced amplitu ...", "... impressed E.M.F\". If self- induction is inserted in series to a non-inductive circuit, the self-induction consumes more E.M.F. of the higher harmon- ics, since the reactance is proportional to the frequency, and thus the current and the E.M.F. in the non-inductive part of the circuit shows the higher harmonics in a reduced amplitude. That is, self-induction in series to a non-induc- tive circuit reduces the higher harmonics or smooths out the wave to a closer resemblance with sine shape. In- versely, capacity in s ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-14", "section_label": "Chapter 14: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 11605-12682", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "snippets": [ "... r, the ampere- turns or M.M.F. increase with the increasing load on the transformer, and constitute what is called the self-induc- tance of the transformer ; while the flux surrounding both 194 ALTERNATING-CURRENT PHENOMENA. coils may be considered as mutual inductance. This cross- flux of self-induction does not induce E.M.F. in the second- ary circuit, and is thus, in general, objectionable, by causing a drop of voltage and a decrease of output. It is this cross-flux, however, or flux of self-inductance, which is uti- ...", "... onsidered as mutual inductance. This cross- flux of self-induction does not induce E.M.F. in the second- ary circuit, and is thus, in general, objectionable, by causing a drop of voltage and a decrease of output. It is this cross-flux, however, or flux of self-inductance, which is uti- lized in special transformers, to secure automatic regulation, for constant power, or for constant current, and in this case is exaggerated by separating primary and secondary coils. In the constant potential transformer however, the prima ...", "... case is exaggerated by separating primary and secondary coils. In the constant potential transformer however, the primary and secondary coils are brought as near together as possible, or even interspersed, to reduce the cross-flux. As will be seen by the self-inductance of a circuit, not the total flux produced by, and interlinked with, the circuit is understood, but only that (usually small) part of the flux which surrounds one circuit without interlinking with the other circuit. 128. The alternating magnetic flux of ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-23", "section_label": "Chapter 23: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 21983-22448", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "snippets": [ "... nsists in the superposition of higher harmonics, that is, waves of higher frequency, the phenomena taking place in a circuit 402 ALTERNATING-CURRENT PHENOMENA. supplied by such a wave will be the combined effect of the different waves. Thus in a non-inductive circuit, the current and the potential difference across the different parts of the circuit are of the same shape as the impressed E.M.F. If self- induction is inserted in series to a non-inductive circuit, the self-induction consumes more E.M.F. of the h ...", "... e combined effect of the different waves. Thus in a non-inductive circuit, the current and the potential difference across the different parts of the circuit are of the same shape as the impressed E.M.F. If self- induction is inserted in series to a non-inductive circuit, the self-induction consumes more E.M.F. of the higher harmon- ics, since the reactance is proportional to the frequency, and thus the current and the E.M.F. in the non-inductive part of the circuit shows the higher harmonics in a reduced amplitu ...", "... e impressed E.M.F. If self- induction is inserted in series to a non-inductive circuit, the self-induction consumes more E.M.F. of the higher harmon- ics, since the reactance is proportional to the frequency, and thus the current and the E.M.F. in the non-inductive part of the circuit shows the higher harmonics in a reduced amplitude. That is, self-induction in series to a non-induc- tive circuit reduces the higher harmonics or smooths out the wave to a closer resemblance with sine shape. In- versely, capacity in s ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-10", "section_label": "Chapter 10: Instability Of Circuits : The Arc", "section_title": "Instability Of Circuits : The Arc", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 17632-21381", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-10/", "snippets": [ "... ithout voltage drop, and the voltage thus has to be taken up by the shunt resistance, ri, giving the same con- dition of stability as with an arc in a constant-current circuit, shunted by a resistance, paragraph 89. If, in addition to the capacity, C, an inductance, L, and some re- sistance, r, are shunted across the circuit. A, of a rising volt-ampere characteristic, as shown in Fig. 87, the readjustment occurring at a sudden change of the supply current, 7, is not exponential, as in Fig. 86, but oscillatory, as in ...", "... istance, r, current and voltage vary simultaneously or in phase, current and voltage in the condenser branch circuit also must be in phase with each other, that is, the Fig. 87. frequency of the oscillation in Fig. 87 is that at which capacity, C, and inductance, L, balance, or is the resonance frequency. If circuit. A, in Fig. 87 is an arc circuit, and the resistance, r, in the shunt circuit small, instability again results, in the same man- ner as discussed before. 93. Another way of looking at the phenomena ...", "... rc. This gives C < 26 mf. Let: (b) to = 10-«, which is probably the approximate magnitude in the mercury arc. This gives C<0.26 mf. 95. Consider the case of a circuit, A, Fig. 87, supplied by a constant ciu-rent, /, but shunted by a capacity, C, inductance, L, and resistance, r, in series. RESONATING CIRCUIT SHUNTING ARC Fig. 89. As long as the current in the circuit, A — whether resistance or arc — is steady, no current passes the condenser circuit, and the current and voltage in A thus are constan ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-26", "section_label": "Chapter 4: Inductance And Resistance In Alternating Current Circuits", "section_title": "Inductance And Resistance In Alternating Current Circuits", "kind": "chapter", "sequence": 26, "number": 4, "location": "lines 3515-4071", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-26/", "snippets": [ "CHAPTER IV. INDUCTANCE AND RESISTANCE IN ALTERNATING- CURRENT CIRCUITS. • 26. In alternating-current circuits, the inductance L, or, as it is usually employed, the reactance x = 2 nfL, where / = fre- quency, enters the expression of the transient as well as the permanent term ...", "CHAPTER IV. INDUCTANCE AND RESISTANCE IN ALTERNATING- CURRENT CIRCUITS. • 26. In alternating-current circuits, the inductance L, or, as it is usually employed, the reactance x = 2 nfL, where / = fre- quency, enters the expression of the transient as well as the permanent term. At the moment 0 = 0, let the e.m.f. e = E cos (0 — 00) be impressed upon a circuit of resistance r an ...", "... , or, as it is usually employed, the reactance x = 2 nfL, where / = fre- quency, enters the expression of the transient as well as the permanent term. At the moment 0 = 0, let the e.m.f. e = E cos (0 — 00) be impressed upon a circuit of resistance r and inductance L, thus inductive reactance x = 2 xfL; let the time 6 = 2 xft be counted from the moment of closing the circuit, and 00 be the phase of the impressed e.m.f. at this moment. In this case the e.m.f. consumed by the resistance = ir, where i = instantaneous ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-52", "section_label": "Chapter 3: Standing Waves", "section_title": "Standing Waves", "kind": "chapter", "sequence": 52, "number": 3, "location": "lines 29316-30243", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "snippets": [ "... = 0, (126) or - = §J (127) that is, the ratio of the energy coefficients is equal to the ratio of the reactive coefficients of the circuit. The standing wave can never be oscillatory, but is always exponential, or gradually dying out, if either the inductance L or the capacity 0 vanishes ; that is, the circuit contains no capacity or contains no inductance. In all other cases the standing wave is oscillatory for waves shorter than the critical value L = -— , where 0 V - 9 V §} > (128) and is exponentia ...", "... of the reactive coefficients of the circuit. The standing wave can never be oscillatory, but is always exponential, or gradually dying out, if either the inductance L or the capacity 0 vanishes ; that is, the circuit contains no capacity or contains no inductance. In all other cases the standing wave is oscillatory for waves shorter than the critical value L = -— , where 0 V - 9 V §} > (128) and is exponential or gradual for standing waves longer than the critical wave length lWo; or for k < ko the standing ...", "... n the critical wave length lWo; or for k < ko the standing wave is exponential, for k > ka it is oscillatory.0 The value kQ = m VLC thus takes a similar part in the theory of standing waves as the value r02 = 4 L0C0 in the condenser discharge through an inductive circuit; that is, it separates the exponential or gradual from trigonometric or oscillatory conditions. The difference is that the condenser discharge through an inductive circuit is gradual, or oscillatory, depending on the circuit constants, while in ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "LECTURE VIII. TRAVELING WAVES. 33. In a stationary oscillation of a circuit having uniformly distributed capacity and inductance, that is, the transient of a circuit storing energy in the dielectric and magnetic field, current and voltage are given by the expression i = ioe-\"^ cos ((/> T CO — 7), ^ . . e = eoe~\"' sin ((^ =F co — 7), where T co — 7), ) where 0 is the time angle, co the distance angle, ...", "... witches, at 89 kilo- volts. Frequently traveling waves are of such high frequency — reaching into the millions of cycles — that the oscillograph does not record them, and their existence and approximate magnitude are determined by inserting a very small inductance into the TRAVELING WAVES. 103 104 ELECTRIC DISCHARGES, WAVES AND IMPULSES. circuit and measuring the voltage across the inductance by spark gap. These traveling waves of very high frequency are extremely local, often extending over a few hundred ...", "... ograph does not record them, and their existence and approximate magnitude are determined by inserting a very small inductance into the TRAVELING WAVES. 103 104 ELECTRIC DISCHARGES, WAVES AND IMPULSES. circuit and measuring the voltage across the inductance by spark gap. These traveling waves of very high frequency are extremely local, often extending over a few hundred feet only. An approximate estimate of the effective frequency of these very high frequency local traveling waves can often be made from the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-23", "section_label": "Apparatus Section 2: Synchronous Machines: Electromotive Forces", "section_title": "Synchronous Machines: Electromotive Forces", "kind": "apparatus-section", "sequence": 23, "number": 2, "location": "lines 8658-8740", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-23/", "snippets": [ "... x corre- sponding to the resultant m.m.f., that is, the resultant of the SYNCHRONOUS MACHINES 129 m.m.fs. of field excitation and of armature reaction. Since the magnetic flux produced by the armature, or flux of armature self-inductance, combines with the field flux to the resultant flux, the flux produced by the field poles does not pass through the armature completely, and the virtual e.m.f. and the real gener- ated e.m.f. differ from each other by the ...", "... field flux to the resultant flux, the flux produced by the field poles does not pass through the armature completely, and the virtual e.m.f. and the real gener- ated e.m.f. differ from each other by the e.m.f. of armature self- inductance; but the virtual generated e.m.f., as well as the e.m.f. generated in the armature by self-inductance, have no real and independent existence, but are merely fictitious components of the real or resultant generated e.m.f. EI ...", "... ure completely, and the virtual e.m.f. and the real gener- ated e.m.f. differ from each other by the e.m.f. of armature self- inductance; but the virtual generated e.m.f., as well as the e.m.f. generated in the armature by self-inductance, have no real and independent existence, but are merely fictitious components of the real or resultant generated e.m.f. EI. The virtual generated e.m.f. is Ei = Et + jlx, where x is the self -inductive armature reactance, ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-85", "section_label": "Apparatus Section 6: Synchronous Converters: Reactive Currents and Compounding", "section_title": "Synchronous Converters: Reactive Currents and Compounding", "kind": "apparatus-section", "sequence": 85, "number": 6, "location": "lines 15476-15585", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-85/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-85/", "snippets": [ "... of variable ratio of transformation, or by a synchronous machine of the same number of poles as the converter, on the same shaft and con- nected in series (\"synchronous booster\") or by the effect of watt- less currents on self-inductance. The latter method is especially suited for converters, due to their ability of producing wattless currents by change of .field excitation. The e.m.f. of self -inductance lags 90 deg. behind the current; thus, if the curren ...", "... booster\") or by the effect of watt- less currents on self-inductance. The latter method is especially suited for converters, due to their ability of producing wattless currents by change of .field excitation. The e.m.f. of self -inductance lags 90 deg. behind the current; thus, if the current is lagging 90 deg. behind the impressed e.m.f., the e.m.f. of self-inductance is 180 deg. behind, or in opposition to, the impressed e.m.f., and thus reduces it. If t ...", "... heir ability of producing wattless currents by change of .field excitation. The e.m.f. of self -inductance lags 90 deg. behind the current; thus, if the current is lagging 90 deg. behind the impressed e.m.f., the e.m.f. of self-inductance is 180 deg. behind, or in opposition to, the impressed e.m.f., and thus reduces it. If the current is 90 deg. ahead of the e.m.f., the e.m.f. of self-inductance is in phase with the impressed e.m.f., thus adds itself th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-24", "section_label": "Chapter 24: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 25682-29374", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-24/", "snippets": [ "... nd then increases again, reaches once more Ei = Eo at Ei^, and then increases beyond Eq. The current is always ahead of the generated e.m.f., Ei, of the motor, and by its lead compensates for the self-induction of the system, making the total circuit non- inductive. The power is a maximum at Ei^, where OEi* = Ei'^Eo = 0.5 X OWo, and is then = 7 X ^\"- Since OE^' = Ir = ^, I = ^^ Eo^ and P = -r~, hence = the maximum power which, over a non- 4 r' inductive line of resistance ?• can be transmitted, at 50 per cent. ...", "... f-induction of the system, making the total circuit non- inductive. The power is a maximum at Ei^, where OEi* = Ei'^Eo = 0.5 X OWo, and is then = 7 X ^\"- Since OE^' = Ir = ^, I = ^^ Eo^ and P = -r~, hence = the maximum power which, over a non- 4 r' inductive line of resistance ?• can be transmitted, at 50 per cent. efficiency, into a non-inductive circuit. In this case, 7-1 ■> ^ -^0 ^ \"^/^e) In general, it is, taken from the diagram, at the condition of maximum efficiency, El = V{Eo - Iry-\\- Px^- ...", "... at Ei^, where OEi* = Ei'^Eo = 0.5 X OWo, and is then = 7 X ^\"- Since OE^' = Ir = ^, I = ^^ Eo^ and P = -r~, hence = the maximum power which, over a non- 4 r' inductive line of resistance ?• can be transmitted, at 50 per cent. efficiency, into a non-inductive circuit. In this case, 7-1 ■> ^ -^0 ^ \"^/^e) In general, it is, taken from the diagram, at the condition of maximum efficiency, El = V{Eo - Iry-\\- Px^- Comparing these results with those in Chapter XI on Induct- ive and Condensive Reactance, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1224-1727", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "snippets": [ "... resistance, r, in circuits where energy is expended only in heating the conductor, is the same as the ohmic resistance of continuous-current circuits. In circuits, how- ever, where energy is also expended outside of the con- ductor by magnetic hysteresis, mutual inductance, dielectric hysteresis, etc., r is larger than the true ohmic resistance of the conductor, since it refers to the total expenditure of energy. It may be called then the effective resistance. It is no longer a constant of the circuit. The reactance, ;r, ...", "... now <> = the magnetic flux produced by, and inter, linked with, the current / (where those lines of magnetic force, which are interlinked //-fold, or pass around n turns of the conductor, are counted ;/ times), the ratio, o//, is denoted by Z, and called self -inductance^ or the coejficient of sclfindiiction of the circuit. It is numerically equal, in absolute units, to the interlinkagcs of the circuit with the magnetic flux produced by unit current, and is, in the system of absolute units, of the dimension of length. In- ...", "... cient of sclfindiiction of the circuit. It is numerically equal, in absolute units, to the interlinkagcs of the circuit with the magnetic flux produced by unit current, and is, in the system of absolute units, of the dimension of length. In- stead of the self-inductance, Z, sometimes its ratio with the ohmic resistance, r, is used, and is called the Tivie- Constant of the circuit : r 4 ALTERNATING-CURRENT PHENOMENA, [§3 If a conductor surrounds with n turns a magnetic cir- cuit of reluctance, (R, the current, /, in ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 963-1366", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "snippets": [ "... resistance, r, in circuits where energy is expended only in heating the conductor, is the same as the ohmic resistance of continuous-current circuits. In circuits, how- ever, where energy is also expended outside of the con- ductor by magnetic hysteresis, mutual inductance, dielectric hysteresis, etc., r is larger than the true ohmic resistance of the conductor, since it refers to the total expenditure of energy. It may be called then the effective resistance. It is no longer a constant of the circuit. The reactance, x, d ...", "... now 4> = the magnetic flux produced by, and inter- linked with, the current i (where those lines of magnetic force, which are interlinked w-fold, or pass around n turns of the conductor, are counted n times), the ratio, $ / z, is denoted by L, and called self -inductance, or the coefficient of self-induction of the circuit. It is numerically equal, in absolute units, to the interlinkages of the circuit with the magnetic flux produced by unit current, and is, in the system of absolute units, of the dimension of length. In- ...", "... cient of self-induction of the circuit. It is numerically equal, in absolute units, to the interlinkages of the circuit with the magnetic flux produced by unit current, and is, in the system of absolute units, of the dimension of length. In- stead of the self-inductance, L, sometimes its ratio with the ohmic resistance, r, is used, and is called the Time- Constant of the circuit : 4 ALTERNATING-CURRENT PHENOMENA. If a conductor surrounds with ;/ turns a magnetic cir- cuit of reluctance, (R, the current, i, in the con ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-19", "section_label": "Chapter 19: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 18053-19457", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "snippets": [ "... acement of phase of the impressed SYNCHRONOUS MOTOR. 329 E.M.F., or self-induction of the circuit compensated by the effect of the lead of the motor current. This condition of maximum efficiency of a circuit we have found already in the Chapter on Inductance and Capacity. 202. B. EQ and El constant, I variable. Obviously EQ lies again on the circle eQ with EQ as radius and O as center. Fig. 143. E lies on a straight line e, passing throtigh the origin; Since in the parallelogram OE E0 Ev EEQ = E^ we ...", "... reases again, reaches once more Fig. 146. El = EQ at E?, and then increases beyond E0. The cur- rent is always ahead of the induced E.M.F. El of the motor, and by its lead compensates for the self-induction of the system, making the total circuit non-inductive. The power is a maximum at Ef, where OEf = EfEQ = 1/2 x ~OE^ and is then = / x \"^7/2. Hence, since OEf = EJ2,f=E()/2randP hence = the maxi- mum power which, over a non-inductive line of resistance r can be transmitted, at 50 per cent, efficiency, ...", "... s for the self-induction of the system, making the total circuit non-inductive. The power is a maximum at Ef, where OEf = EfEQ = 1/2 x ~OE^ and is then = / x \"^7/2. Hence, since OEf = EJ2,f=E()/2randP hence = the maxi- mum power which, over a non-inductive line of resistance r can be transmitted, at 50 per cent, efficiency, into a non- inductive circuit. -334 ALTERNATING-CURRENT PHENOMENA. In this case, In general, it is, taken from the diagram, at the condi- tion of maximum efficiency : Comparing ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-09", "section_label": "Chapter 9: Wave Screens. Even Harmonics", "section_title": "Wave Screens. Even Harmonics", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 16964-17631", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-09/", "snippets": [ "... o their order, n. Even if r is large compared with x, and thus c^>lj iSnally c^ becomes negligible with n^, and the harmonics decrease with their order. 77. The screening effect of the series reactance is increased by shunting a capacity, C, beyond the inductance, L, that is, across the resistance, r, as shown in Fig. 73. By consuming current jTRRRRRTl e 1 rmmM Fig. 73. r e Fig. 74. proportional to frequency and voltage, the condenser shimts the more of the current passing through the reactan ...", "... current in the resistance, r, and thus of voltage across this re- sistance. Its effect is limited, however, by the decreasing voltage distortion at r and thus at the condenser, C. Thus the screening effect is still further increased by inserting a second inductance, L, beyond the condenser, C, in series to the resistance, r, as shown in Fig. 74. By making the second induct- ance equal to the first one, and making the condenser, C, of the same reactance, for the fundamental wave, as each of the two inductances, we ge ...", "... uctances, we get what probably is the most effective wave screen. This T-connection or resonating circuit will be discussed more fully in Chapter XIV, in its feature of constant-potential constant-current transformation. Under the condition, that the two inductive reactances and the WAVE SCREENS. EVEN HARMONICS 156 capacity reactance are equal, the equation of the current in the resistance, r, is (page 291), for the nth harmonic. or, absolute. / = ?^ (34) xn(n^ - 2) - jr{n^ - 1) ^ ^ i = -° X ^ (35) ^ ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-47", "section_label": "Chapter 7: Distribution Of Alternating-Current Density In Conductor", "section_title": "Distribution Of Alternating-Current Density In Conductor", "kind": "chapter", "sequence": 47, "number": 7, "location": "lines 24981-26094", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "snippets": [ "... hich carries the current is very large, or its electric conductivity or its magnetic per- meability high, the current density is not uniform throughout the conductor section, but decreases towards the interior of the conductor, due to the higher e.m.f. of self-inductance in the interior of the conductor, caused by the magnetic flux inside of the conductor. The phase of the current inside of the conductor also differs from that on the surface and lags behind it. In consequence of this unequal current distribution in a lar ...", "... gs behind it. In consequence of this unequal current distribution in a large conductor traversed by ^alternating currents, the effective resist- ance of the conductor may be far higher than the ohmic resist- ance, and the conductor also contains internal inductance. In the extreme case, where the current density in the interior of the conductor is very much lower than on the surface, or even negligible, due to this \"screening effect/' as it has been called, the current can be 'assumed to exist only in a thin surfac ...", "... the center line of the conductor, and 2 10 = the thickness of conductor. Furthermore, let E0 = the impressed e.m.f. per unit length of conductor, that is, the voltage consumed per unit length in the conductor after subtracting the e.m.f. consumed by the self- inductance of the external magnetic field of the conductor; thus, if El = the total supply voltage per unit length of conductor 372 TRANSIENT PHENOMENA and E2 = the external reactance voltage, or voltage consumed by the magnetic field outside of the conductor, be ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-10", "section_label": "Theory Section 10: Hysteresis and Effective Resistance", "section_title": "Hysteresis and Effective Resistance", "kind": "theory-section", "sequence": 10, "number": 10, "location": "lines 3234-3585", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-10/", "snippets": [ "... irfL and of negligible resistance, the HYSTERESIS AND EFFECTIVE RESISTANCE 49 magnetic flux produced by the current, 0$ = $, is in phase with the current, and the e.m.f. generated by this flux, or counter e.m.f. of self-inductance, OE'\" = E'\" = xl, lags 90 degrees be- hind the current. The e.m.f. consumed by self-inductance or impressed e.m.f. OE\" = E\" = xl is thus 90 degrees ahead of the current. Inversely, if the e.m.f. OE\" = E\" is impressed ...", "... produced by the current, 0$ = $, is in phase with the current, and the e.m.f. generated by this flux, or counter e.m.f. of self-inductance, OE'\" = E'\" = xl, lags 90 degrees be- hind the current. The e.m.f. consumed by self-inductance or impressed e.m.f. OE\" = E\" = xl is thus 90 degrees ahead of the current. Inversely, if the e.m.f. OE\" = E\" is impressed upon a circuit of reactance x = 2 irfL and of negligible resistance, the current E\" 01 = I ...", "... th the e.m.f. E\" due to it, angle a is the phase difference between the magnet- ism and the m.m.f., or the lead of the m.m.f., that is, the exciting 4 FIG. 21.— Phase re- lations of magnetizing current, flux and self- inductive e.m.f. 50 ELEMENTS OF ELECTRICAL ENGINEERING current, before the magnetism. It is called the angle of hysteretic lead. In this case the exciting current 01 = I can be resolved in two components: the magnetizing cur ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-27", "section_label": "Apparatus Section 6: Synchronous Machines: Characteristic Curves of Alternating-current Generator", "section_title": "Synchronous Machines: Characteristic Curves of Alternating-current Generator", "kind": "apparatus-section", "sequence": 27, "number": 6, "location": "lines 9170-9291", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-27/", "snippets": [ "... urrent Generator 15. In Fig. 59 are shown, at constant terminal voltage E, the values of nominal generated e.m.f. E0, and thus of field excitation FQ, with the current 7 as abscissas and for the three conditions, 1. Non-inductive load, p = 1, q = 0. 2. Inductive load of 0 = 60 degrees lag, p = 0.5, q = 0.866. 3. Anti-inductive load of — 6 = 60 degrees lead, p = 0.5, q = -0.866. SYNCHRONOUS MACHINES 139 The values r = 0.1, XQ = ...", "... shown, at constant terminal voltage E, the values of nominal generated e.m.f. E0, and thus of field excitation FQ, with the current 7 as abscissas and for the three conditions, 1. Non-inductive load, p = 1, q = 0. 2. Inductive load of 0 = 60 degrees lag, p = 0.5, q = 0.866. 3. Anti-inductive load of — 6 = 60 degrees lead, p = 0.5, q = -0.866. SYNCHRONOUS MACHINES 139 The values r = 0.1, XQ = 5, E = 1000, are assumed. These curv ...", "... e.m.f. E0, and thus of field excitation FQ, with the current 7 as abscissas and for the three conditions, 1. Non-inductive load, p = 1, q = 0. 2. Inductive load of 0 = 60 degrees lag, p = 0.5, q = 0.866. 3. Anti-inductive load of — 6 = 60 degrees lead, p = 0.5, q = -0.866. SYNCHRONOUS MACHINES 139 The values r = 0.1, XQ = 5, E = 1000, are assumed. These curves are called the compounding curves of the synchronous generator. In ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-05", "section_label": "Chapter 5: Symbolic Method", "section_title": "Symbolic Method", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2760-3266", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-05/", "snippets": [ "... which make an exact diagram- matic determination impossible. For instance, in the trans- former diagrams (c/. Figs. 18-20), the different magnitudes have numerical values in practice somewhat like the following: Ei = 100 volts, and 7i = 75 amp. For a non-inductive second- ary load, as of incandescent lamps, the only reactance of the secondaiy circuit thus is that of the secondary coil, or Xi = 0.08 ohms, giving a lag of ^i = 3.6°. We have also, rii = 30 turns. rio = 300 turns. Fi = 2250 ampere-turns. F =100 ...", "... antities. 31. If / = I + ji' is a sine wave of alternating current, and r is the resistance, the voltage consumed by the resistance is in phase with the current, and equal to the product of the current and resistance. Or rl = ri -\\- jri'. If L is the inductance, and x = 2x/L the inductive react- ance, the e.m.f. produced by the reactance, or the counter e.m.f. 1 In this representation of the sine wave by the exponential expression of the complex quantity, the angle 0 necessarily must be expressed in radians, an ...", "... ' is a sine wave of alternating current, and r is the resistance, the voltage consumed by the resistance is in phase with the current, and equal to the product of the current and resistance. Or rl = ri -\\- jri'. If L is the inductance, and x = 2x/L the inductive react- ance, the e.m.f. produced by the reactance, or the counter e.m.f. 1 In this representation of the sine wave by the exponential expression of the complex quantity, the angle 0 necessarily must be expressed in radians, and not in degrees, that is, w ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-13", "section_label": "Chapter 13: Ths Alternating^Cnrrent Traxsfobmer", "section_title": "Ths Alternating^Cnrrent Traxsfobmer", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 12673-14088", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "snippets": [ "... mpere- turns or M.M.F. increase with the increasing load on the transformer, and constitute what is called the self-induc- tance of the transformer; while the flux surrounding both 168 AL TERN A TING-CURRENT PHENOMENA. [§118 coils may be considered as mutual inductance. This cross- flux of self-induction does not induce E.M.F. in the second- ary circuit, and is thus, in general, objectionable, by causing a drop of voltage and a decrease of output ; and, therefore, in the constant potential transformer the primary and se ...", "... ausing a drop of voltage and a decrease of output ; and, therefore, in the constant potential transformer the primary and sec- ondary coils are brought as near together as possible, or even interspersed, to reduce the cross-flux. As will be seen, by the self-inductance of a circuit, not the total flux produced by, and interlinked with, the circuit is understood, but only that (usually small) part of the flux w^hich surrounds one circuit without interlinking with the other circuit. 118. The alternating magnetic flux of ...", "... lead \" 93. 20° lag •' 90. 80° lead \" 94. O, or in phase, ** 91. As shown with a change of (3^, Eo^Siygo^ ^^c., change in intensity and direction. The locus described by them are circles, and are shown in Fig. 95, with the point corre- sponding to non-inductive load marked. The part of the . locus corresponding to a lagging secondary current is 174 AL TEKXA TING-CURRENT PHENOMENA. [§121 f /g. 90, Tnuitfwnwr Diagram with 2Cr Lag In Secondary Circuit ^ Fig. 91. Transfornwr Diagram with Secondary Curren ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-18", "section_label": "Chapter 16: Il", "section_title": "Il", "kind": "chapter", "sequence": 18, "number": 16, "location": "lines 19346-21338", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-18/", "snippets": [ "... iW A/. TKHA-A rti\\G-CURRE.VT P//F..VO.VKXA. [| 181 Iv.M.I\"'., or Kclf-induction of the circuit compensated by the effect of the lead of the motor current. This condition of iiiiiximum t-fficiency of a circuit we have found already in Chapter VIII. on Inductance and Capacity. 181. B. r.g aiiel J-\\ constant, I variable. < >l)vi(iitlHU9 Syttem on inductlue Load of 90* Lag. Fig. 169. Quart€r-ph€is9 System on Non^inductioe Loot. Fig. 170. Quarter-phase System on inductive Load of 60' Lag, AL TEKNA nXC-CUI^RENT PHENOMENA. [ % 244 « 245, 246] BALANCED POL YPIIASE SYSTEMS. 245. The flow of power in an alternating-current system is a most important and characteristic feature of the system, and by its nature the systems ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-21", "section_label": "Chapter 23: Review", "section_title": "Review", "kind": "chapter", "sequence": 21, "number": 23, "location": "lines 32138-32819", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-21/", "snippets": [ "... case of the same phase rotation of exciter and main machine, the generated frequency is higher than the speed, and the exciter also is generator. This synchronous induction generator has peculiar regulation characteristics, as the armature reaction of non-inductive load is absent. 3. A Synchronous Commutating Machine. — 112. The couple is synchronous, and called motor converter. It has the advantage of lower frequency commutation, and permits phase control by the internal reactance of the induction machine. It has ...", "... p at double synchronism. The machine requires a supply of lagging current for excitation, just tike ;itr. induction machine. It may be used as synchronous induction generator, or as synchronous motor. As generator, the armature reaction neutralizes at non-inductive, but not at inductive load, REVIEW 463 and thus gives peculiar regulation characteristics, similar as the Stanley induction generator. It has been proposed for steam- turbine alternators, as it would permit higher turbine speed (3000 revolutions at 25 ...", "... m. The machine requires a supply of lagging current for excitation, just tike ;itr. induction machine. It may be used as synchronous induction generator, or as synchronous motor. As generator, the armature reaction neutralizes at non-inductive, but not at inductive load, REVIEW 463 and thus gives peculiar regulation characteristics, similar as the Stanley induction generator. It has been proposed for steam- turbine alternators, as it would permit higher turbine speed (3000 revolutions at 25 cycles) but has not y ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-34", "section_label": "Chapter 12: Magnetic Saturation And Hysteresis In Alternat Ing-Current Circuits", "section_title": "Magnetic Saturation And Hysteresis In Alternat Ing-Current Circuits", "kind": "chapter", "sequence": 34, "number": 12, "location": "lines 12885-13935", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-34/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-34/", "snippets": [ "CHAPTER XII. MAGNETIC SATURATION AND HYSTERESIS IN ALTERNAT- ING-CURRENT CIRCUITS. 99. If an alternating e.m.f. is impressed upon a circuit con- taining resistance and inductance, the current and thereby the magnetic flux produced by the current immediately assume their final or permanent values only in case the circuit is closed at that point of the e.m:f. wave at which the permanent current is zero. Closing the circuit at any ot ...", "... agnetic flux. So for instance, if the circuit is closed when the current i should have its negative maximum value - 70, and therefore the magnetic flux and the magnetic flux density also be at their negative maximum value - ^>0 and - (B0 — that is, in an inductive circuit, near the zero value of the decreasing e.m.f. wave — during the first half wave of e.m.f. the magnetic flux, which generates the counter e.m.f., should vary from — 4>0 to + 0, or by 2 4>0; hence, starting with 0, to generate the same counter e. ...", "... lux, which generates the counter e.m.f., should vary from — 4>0 to + 0, or by 2 4>0; hence, starting with 0, to generate the same counter e.m.f., it must rise to + 2 0, that is, twice its permanent value, and so the current i also rises, at constant inductance L, from zero to twice its maximum permanent value, 2 70. Since the e.m.f. consumed by the current during the variation from 0 to 2 70 is greater than during the normal variation from — 70 to + 70, less .e.m.f. is to be generated by the change of magnetic ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-50", "section_label": "Chapter 1: General Equations", "section_title": "General Equations", "kind": "chapter", "sequence": 50, "number": 1, "location": "lines 27761-28694", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "snippets": [ "... sistance, representing the power or rate of energy consumption depending upon the current, tfr; or the power component of the e.m.f. consumed in the circuit, that is, with an alternating current, the voltage, ir, in phase with the current. L = effective inductance, representing the energy storage i2L depending upon the current, - — , as electromagnetic component & of the electric field; or the voltage generated due to the change of the current, L — , that is, with an alternating current, the at reactive vo ...", "... OMENA In the investigation of electric circuits, these four constants, r, L, g, C, usually are assumed as located separately from each other, or localized. Although this assumption can never be per- fectly correct, — for instance, every resistor has some inductance and every reactor has some resistance, — nevertheless in most cases it is permissible and necessary, and only in some classes of phenomena, and in some kinds of circuits, such as high-frequency phenomena, voltage and current distribution in long-distance, ...", "... rent distribution in long-distance, high-potential circuits, cables, telephone circuits, etc., this assumption is not permissible, but r, L, g, C must be treated as distributed throughout the circuit. In the case of a circuit with distributed resistance, inductance, conductance, and capacity, as r, L, g, C, are denoted the effec- tive resistance, inductance, conductance, and capacity, respec- tively, per unit length of circuit. The unit of length of the circuit- may be chosen as is convenient, thus : the centimeters ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1003-1658", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-02/", "snippets": [ "... included in the term electric field, and are the two components of the electric field of the conductor. 8. The magnetic field or magnetic flux of the circuit, $, is pro- portional to the current, i, with a proportionality factor, L, which is called the inductance of the circuit. $ = L^.* (1) The magnetic field represents stored energy ly. To produce it, power, p, must therefore be supplied by the circuit. Since power is current times voltage : P = e'i, (2) * n^, if the flux interlinks the circuit n fold. ...", "... GES, WAVES AND IMPULSES. to produce the magnetic field $ of the current i, a voltage e' must be consumed in the circuit, which with the current i gives the power p, which supplies the stored energy w of the magnetic field $. This voltage e' is called the inductance voltage, or voltage consumed hy self-induction. Since no power is required to maintain the field, but power is required to produce it, the inductance voltage must be propor- tional to the rate of increase of the magnetic field : or by (1), e' = L§ (4 ...", "... the power p, which supplies the stored energy w of the magnetic field $. This voltage e' is called the inductance voltage, or voltage consumed hy self-induction. Since no power is required to maintain the field, but power is required to produce it, the inductance voltage must be propor- tional to the rate of increase of the magnetic field : or by (1), e' = L§ (4) di If i and therefore $ decrease, j- and therefore e' are negative; that is, p becomes negative, and power is returned into the circuit. The ener ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-05", "section_label": "Lecture 5: Single-Energy Tra.Nsient Of Ironclad Circuit", "section_title": "Single-Energy Tra.Nsient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3387-3720", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-05/", "snippets": [ "... lectric field reaches densities beyond the dielectric strength of the carrier of the field, etc.; and the proportionality between current or voltage and their respective fields, the magnetic and the dielectric, thus ceases, or, as it may be expressed, the inductance L is not constant, but varies w^ith the current, or the capacity is not constant, but varies with the voltage. The most important case is that of the ironclad magnetic cir- cuit, as it exists in one of the most important electrical apparatus, the alterna ...", "... alues where magnetic saturation begins. Below saturation values of current, the tran- sient thus is the simple exponential discussed before. If the magnetic circuit is closed entirely by iron, the magnetic flux is not proportional to the current, and the inductance thus not constant, but varies over the entire range of currents, following the permeability curve of the iron. Furthermore, the transient due to a decrease of the stored magnetic energy differs in shape and in value from that due to an increase of magneti ...", "... series with the iron, and d is the part of the flux passing through nonmagnetic material. Denoting now Z/i = na 10-^ ) U = nc 10-s, ) ^ ^ where n = number of turns of the electric circuit, which is inter- linked with the magnetic circuit, L2 is the inductance of the air part of the magnetic circuit, Li the (virtual) initial inductance, that is, inductance at very small currents, of the iron part of the mag- SINGLE-ENERGY TRANSIENT OF IRONCLAD CIRCUIT. 55 netic circuit, and j- the saturation value of the flux ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 883-1530", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "snippets": [ "... included in the term electric field, and are the two components of the electric field of the conductor. 8. The magnetic field or magnetic flux of the circuit, <£, is pro- portional to the current, i, with a proportionality factor, L, which is called the inductance of the circuit. = Li. (1) The magnetic field represents stored energy w. To produce it, power, p, must therefore be supplied by the circuit. Since power is current times voltage, p = e'i. (2) 12 ELECTRIC DISCHARGES, WAVES AND IMPULSES. To pr ...", "... S, WAVES AND IMPULSES. To produce the magnetic field $ of the current i, a voltage ef must be consumed in the circuit, which with the current i gives the power p, which supplies the stored energy w of the magnetic field . This voltage er is called the inductance voltage, or voltage consumed by self-induction. Since no power is required to maintain the field, but power is required to produce it, the inductance voltage must be propor- tional to the increase of the magnetic field: :' ; (3) or by (1), (4) If ...", "... the power p, which supplies the stored energy w of the magnetic field . This voltage er is called the inductance voltage, or voltage consumed by self-induction. Since no power is required to maintain the field, but power is required to produce it, the inductance voltage must be propor- tional to the increase of the magnetic field: :' ; (3) or by (1), (4) If i and therefore $ decrease, -r and therefore e' are negative; that is, p becomes negative, and power is returned into the circuit. The energy supplied ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-05", "section_label": "Lecture 5: Single-Energy Transient Of Ironclad Circuit", "section_title": "Single-Energy Transient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2972-3286", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "snippets": [ "... ectric field reaches densities beyond the dielectric strength of the carrier of the field, etc. ; and the proportionality between current or voltage and their respective fields, the magnetic and the dielectric, thus ceases, or, as it may be expressed, the inductance L is not constant, but varies with the current, or the capacity is not constant, but varies with the voltage. The most important case is that of the ironclad magnetic cir- cuit, as it exists in one of the most important electrical apparatus, the alternat ...", "... alues where magnetic saturation begins. Below saturation values of current, the tran- sient thus is the simple exponential discussed before. If the magnetic circuit is closed entirely by iron, the magnetic flux is not proportional to the current, and the inductance thus not constant, but varies over the entire range of currents, following the permeability curve of the iron. Furthermore, the transient due to a decrease of the stored magnetic energy differs in shape and in value from that due to an increase of magneti ...", "... air space may be in series with the iron, and a is the part of the flux passing through nonmagnetic material. Denoting now L2 = nc 10-8, i where n = number of turns of the electric circuit, which is inter- linked with the magnetic circuit, L2 is the inductance of the air part of the magnetic circuit, LI the (virtual) initial inductance, that is, inductance at very small currents, of the iron part of the mag- SINGLE-ENERGY TRANSIENT OF IRONCLAD CIRCUIT. 55 netic circuit, and =- the saturation value of the flux ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-06", "section_label": "Lecture 6: Higher Harmonics Of The Generator Wave", "section_title": "Higher Harmonics Of The Generator Wave", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3133-3507", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-06/", "snippets": [ "... HIGHER HARMONICS OF THE GENERATOR WAVE mHE open circuit reactance of the transformer is the only reactance high enough to give resonance with the line capacity at fundamental frequency. All other reactances are too low for this. Since, however, the inductive reactance increases and the capacity reactance decreases proportionally to the frequency, the two reactances come nearer together for higher frequency; that is, for the higher harmonics of the generator wave, and for some of the higher harmonics of the ge ...", "... two reactances come nearer together for higher frequency; that is, for the higher harmonics of the generator wave, and for some of the higher harmonics of the generator wave resonance rise of voltage so may occur between the line capacity and the circuit inductance. The origin and existence of higher harmonics therefore bears investigation in transformers, transmlission lines and cable systems. ORIGIN OF HIGHER HARMONICS Higher harmonics may originate in synchronous machines, as generators, synchronous motors a ...", "... insulation strain. For this single-phase voltage all three lines go together, and so may cause static induction on other circuits, as telephone lines. A circuit of this single-phase triple frequency voltage then exists frcmi the generator neutral over the inductance of all three generator circuits in multiple, and over the capacity of all three lines to ground, back to the generator neutral ; that is, we have capacity and inductance in series in a circuit of the triple har- monic, and if capacity and inductance are h ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-17", "section_label": "Theory Section 17: Impedance and Admittance", "section_title": "Impedance and Admittance", "kind": "theory-section", "sequence": 17, "number": 17, "location": "lines 6814-7380", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-17/", "snippets": [ "... - to alternating-current circuits, e is the IMPEDANCE AND ADMITTANCE ' 99 total e.m.f. resulting from the impressed e.m.f. and all e.m.fs. produced by the current i in the circuit. Such counter e.m.fs. may be due to inductance, as self-induc- tance, or mutual inductance, to capacity, chemical polarization, etc. The counter e.m.f. of self-induction, or e.m.f. generated by the magnetic field produced by the alternating current i, is repre- sented by a ...", "... e is the IMPEDANCE AND ADMITTANCE ' 99 total e.m.f. resulting from the impressed e.m.f. and all e.m.fs. produced by the current i in the circuit. Such counter e.m.fs. may be due to inductance, as self-induc- tance, or mutual inductance, to capacity, chemical polarization, etc. The counter e.m.f. of self-induction, or e.m.f. generated by the magnetic field produced by the alternating current i, is repre- sented by a quantity of the same dimensions as resist ...", "... the quantity 21 = Vr!2 + x2 or, in symbolic representation, Zi = ri + jxi is the impedance of the circuit. If power is consumed in the circuit only by the ohmic resist- ance r, and counter e.m.f. produced only by self-inductance, the effective resistance TI is the true or ohmic resistance r, and the effective reactance Xi is the true or inductive reactance x. 100 ELEMENTS OF ELECTRICAL ENGINEERING By means of the terms effective resistance, e ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 3267-3618", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-06/", "snippets": [ "... rding to the direction considered, 38. If now the three branches, OEi, OE2 and OE3, of the three-phase system are loaded equally by three currents equal in intensity and in difference of phase against their voltages, BAtANCED THREE-PHASE SYSTEtif NON-INDUCTIVE LOAD Fig. 29. Fig. 30. these currents are represented in Fig. 29 by the vectors 01 1 = 01 2 = 01 3 = I, lagging behind the voltages by angles EiOIi = £20/2 = EsOh = d. Let the three-phase circuit be supplied over a line of impedance, Zi = ri -{- ...", "... impedance of the generator, we get E^^E^^^ = /ro, and parallel to OTi, W^^'^ = Ixo, and 90° ahead of OIi, and thus as triangle of (nominal) gen- erated e.m.fs. of the generator, Ei^E2°Ez^. In Fig. 29 the diagram is shown for 45° lag, in Fig. 30 for non- inductive load, and in Fig. 31 for 45° lead of the currents with regard to their voltages. As seen, the generated e.m.f. and thus the generator excitation with lagging current must be higher, and with leading current lower, than at non-inductive load, or conversel ...", "... Fig. 30 for non- inductive load, and in Fig. 31 for 45° lead of the currents with regard to their voltages. As seen, the generated e.m.f. and thus the generator excitation with lagging current must be higher, and with leading current lower, than at non-inductive load, or conversely with the same generator excitation, that is, the same internal generator e.m.f. SINGLE-PHASE CIRCUIT 60' LAG CABLE OF DISTRIBUTED CAPACIir AND RESISTANCE Fig. 31. Fig. 32. triangle, Ei^E^^Ez^, the voltages at the receive ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-11", "section_label": "Chapter 11: Phase Control", "section_title": "Phase Control", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 9767-10717", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-11/", "snippets": [ "... ng circuit, causes the voltage, e, at the receiver circuit to decrease with increasing current, /, through the resistance. The decrease of the voltage, e, is greatest if the current, /, is in phase with the voltage, e — less if the current is not in phase. Inductive reactance in series with the receiving circuit, e, at constant impressed e.m.f., eo, causes the voltage, e, to drop less with a unity power-factor current, 7, but far more with a lagging current, and causes the voltage, e, to rise with a leading current. ...", "... pressed e.m.f., eo, causes the voltage, e, to drop less with a unity power-factor current, 7, but far more with a lagging current, and causes the voltage, e, to rise with a leading current. While series resistance always causes a drop of voltage, series inductive reactance, x, may cause a drop of voltage or a rise of voltage, depending on whether the current is lagging or leading. If the supply line contains resistance, r, as well as reactance, x, and the phase of the current, I, can be varied at will, by producin ...", "... o 30 per cent, of the power component of the current would give an PHASE CONTROL 99 increase of 4.4 per cent, only, that is, could be carried by the motor armature without any appreciable increase of the motor heating. Phase control depends upon the inductive reactance of the line or circuit between generating and receiving voltage, So and e, and where the inductive reactance of the transmission line is not sufficient, additional reactance may be inserted in the form of reactive coils or high internal reactanc ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-12", "section_label": "Chapter 12: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 10718-13483", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-12/", "snippets": [ "... ts, it is necessarj-, therefore, to substitute everywhere the values \"effective re- sistance,\" \"effective reactance,\" \"effective conductance,\" and \"effective susceptance,\" to make the calculation applicable to general alternating-current circuits, such as inductive reactances containing iron, etc. While the true ohmic resistance is a constant of the circuit, depending only upon the temperature, but not upon the e.m.f., etc., the effective resistance and effective reactance are, in gen- eral, not constants, but dep ...", "... on. EFFECTIVE RESISTANCE AND REACTANCE 113 -» 3. Secondary or induced currents, as, (a) Eddy or Foucault currents in surrounding magnetic materials; (b) Eddy or Foucault currents in surrounding conducting materials ; (c) Secondary currents of mutual inductance in neighboring circuits. 4. Induced electric charges, electrostatic induction or influence. While all these losses can be included in the terms effective resistance, etc., the magnetic hysteresis and the eddy currents are the most frequent and importa ...", "... when the energy is supplied electrically, appears as magnetic hysteresis, and is caused by the cyclic reversals of magnetic flux in the iron in the alternating magnetic field. To examine this phenomenon, first a circuit may be con- sidered, of very high inductive reactance, but negligible true ohmic resistance; that is, a circuit entirely surrounded by iron, as, for instance, the primary circuit of an alternating-current transformer with open secondary circuit. The wave of current produces in the iron an alternat ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-18", "section_label": "Chapter 18: Polyphase Induction Motors", "section_title": "Polyphase Induction Motors", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17717-20445", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-18/", "snippets": [ "... f primary and a number of secondary circuits are used, angularly displaced around the periphery of the motor, and containing e.m.fs. displaced in phase by the same angle. This multi-circuit arrangement has the object always to retain secondary circuits in inductive rela- tion to primary circuits and vice versa, in spite of their relative motion. The result of the relative motion between primary and secondary is, that the e.m.fs. generated in the secondary or the motor armature are not of the same frequency as the ...", "... he total impedance of the motor. Hence P Pi^o^ , ^^ ~2(r + z} is the maximum output of the induction motor, at the slip, ri 5» = ri + 2 The same value has been derived in Chapter X, as the maxi- mum power which can be transmitted into a non-inductive receiver circuit over a line of resistance, r, and impedance, z, or as the maximum output of a generator, or of a stationary transformer. Hence: The maximum output of an induction motor is expressed by the same formula as the maximum output of a generat ...", "... f a generator, or of a stationary transformer. Hence: The maximum output of an induction motor is expressed by the same formula as the maximum output of a generator, or of a stationary transformer, or the maximum output ivhich can he transmitted over an inductive line into a non-inductive receiver circuit. POLYPHASE INDUCTION MOTORS 223 The torque corresponding to the maximum output, Pp, is ^ qVxE,\\r, + z) ^^ ^irfzir + z) This is not the maximum torque; but the maximum torque, Dt, takes place at a lower sp ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-01", "section_label": "Chapter 1: Speed Control Of Induction Motors", "section_title": "Speed Control Of Induction Motors", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1368-3542", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-01/", "snippets": [ "... considerable extent, this disadvantage of inconstancy of speed can be overcome: (a) By the use of capacity or effective capacity in the motor secondary, which contracts the range of torque into that of approximate resonance of the capacity with the motor inductance, and thereby gives fairly constant speed, independent of the load, at various speed values determined by the value of the capacity. (6) By the use of a resistance of very high negative tempera- ture coefficient in the armature, so that with increase of l ...", "... ctric resistances is the difficulty of producing stable pyro-electric conductors, and permiiiiriit terminal connections on such conductors. B. Condenser Speed Control 11. The reactance of a condenser is inverse proportional to the frequency, that of an inductance is directly proportional to the frequency. In the secondary of the induction motor, the Frequency varies from zero at synchronism, to full frequency at standstill. If, therefore, a suitable capacity is inserted into the Secondary of an induction motor, th ...", "... requency. In the secondary of the induction motor, the Frequency varies from zero at synchronism, to full frequency at standstill. If, therefore, a suitable capacity is inserted into the Secondary of an induction motor, there is a definite speed, at which inductive reactance and capacity reactance are equal and Opposite, that is, balance, and at and near this speed, a large current is taken by the motor and thus large torque developed, while at speeds considerably above or below this resonance speed, the current and ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-14", "section_label": "Chapter 16: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 14, "number": 16, "location": "lines 19374-20293", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-14/", "snippets": [ "... 3\"u, in its two components, the armature reaction and the true armature reactance, and once more resolving the armature reaction into a magnetizing and a distorting component, and msidering only the former, in its effect, on the field. The true armature self-inductance then is usually assumed as constant. Or, both armature reactance and self-inductance, are resolved into the two quadrature components, in line and in quadrature with the field poles, as shown in Chapters XXI and XXIV of \"Alternating-Current Phenomena,\" 5t ...", "... nd once more resolving the armature reaction into a magnetizing and a distorting component, and msidering only the former, in its effect, on the field. The true armature self-inductance then is usually assumed as constant. Or, both armature reactance and self-inductance, are resolved into the two quadrature components, in line and in quadrature with the field poles, as shown in Chapters XXI and XXIV of \"Alternating-Current Phenomena,\" 5th edition. 160. However, while a machine comprising a stationary single- phase \"fie ...", "... in the first, to alternating current in the second winding. The maximum voltage in the second winding can not exceed the voltage, per turn, in the exciting winding, thus is very limited, and so is the current. Higher values are secured by inserting a high inductance in series in the direct-current winding. In this case, a single winding may be used and the alternating-circuit, shunted across the machine terminals, inside of the inductance. 161. Obviously, if the reactance or reluctance is variable, it will perform a ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3721-4369", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-06/", "snippets": [ "... urrent, etc., would last if maintained at its initial value. The duration To is the ratio of the energy-storage coefficient to the power-dissipation coefficient. Thus, if energy is stored by the current i, as magnetic field. To = -, (2) r where L = inductance = coefficient of energy storage by the cur- rent, r = resistance = coefficient of power dissipation by the current. If the energy is stored by the voltage e, as dielectric field, the duration of the transient would be TV - -, (3) g 59 60 ELECTRIC D ...", "... 5> 9 where Vq = limiting velocity, g = acceleration of gravity, and would be given by v = Vo[l-e~'^). (6) In a system in which energy can be stored in two different forms, as for instance as magnetic and as dielectric energy in a circuit containing inductance and capacity, in addition to the gradual decrease of stored energy similar to that represented by the single-energy transient, a transfer of energy can occur between its two different forms. Thus, if i = transient current, e = transient voltage (that is, ...", "... st momentary voltages, is e^, the maximum discharge current in the line is limited to Iq = eoyo. If L is high but C low, as in the high-potential winding of a high-voltage transformer (which winding can be considered as a circuit of distributed capacity, inductance, and resistance), Zq is high and 2/0 low. That is, a high transient voltage can produce only moderate transient currents, but even a small transient cur- rent produces high voltages. Thus reactances, and other reactive apparatus, as transformers, stop the ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3287-3955", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "snippets": [ "... e, current, etc., would last if maintained at its initial value. The duration T0 is the ratio of the energy-storage coefficient to the power-dissipation coefficient. Thus, if energy is stored by the current i, as magnetic field, T0 = £, (2) where L = inductance = coefficient of energy storage by the cur- rent, r = resistance = coefficient of power dissipation by the current. If the energy is stored by the voltage e, as dielectric field, the duration of the transient would be TJ = -, (3) s/ 59 60 ELECTRIC ...", "... -°, (5) where VQ = limiting velocity, g = acceleration of gravity, and would be given by v = v0(l-6~r}. (6) In a system in which energy can be stored in two different forms, as for instance as magnetic and as dielectric energy in a circuit containing inductance and capacity, in addition to the gradual decrease of stored energy similar to that represented by the single-energy transient, a transfer of energy can occur between its two different forms. Thus, if i = transient current, e = transient voltage (that is, ...", "... t momentary voltages, is e0, the maximum discharge current in the line is limited to i0 = e<>yo. If L is high but C low, as in the high-potential winding of a high-voltage transformer (which winding can be considered as a circuit of distributed capacity, inductance, and resistance), z0 is high and T/O low. That is, a high transient voltage can produce only moderate transient currents, but even a small transient cur- rent produces high voltages. Thus reactances, and other reactive apparatus, as transformers, stop the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-08", "section_label": "Theory Section 8: Power in Alternating-current Circuits", "section_title": "Power in Alternating-current Circuits", "kind": "theory-section", "sequence": 8, "number": 8, "location": "lines 2718-2864", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-08/", "snippets": [ "... + 00)). Since the average cos (20 + 00) = zero, the average power is P = zP cos 00 = rP = EJ-, that is, the power in the circuit is that consumed by the resistance, and independent of the reactance. Reactance or self-inductance consumes no power, and the e.m.f. of self-inductance is a wattless or reactive e.m.f., while the e.m.f. of resistance is a power or active e.m.f. The wattless e.m.f. is in quadrature, the power e.m.f. in phase with the ...", "... he average power is P = zP cos 00 = rP = EJ-, that is, the power in the circuit is that consumed by the resistance, and independent of the reactance. Reactance or self-inductance consumes no power, and the e.m.f. of self-inductance is a wattless or reactive e.m.f., while the e.m.f. of resistance is a power or active e.m.f. The wattless e.m.f. is in quadrature, the power e.m.f. in phase with the current. In general, if 0 = angle of time-phase dis ...", "... VECTOR DIAGRAMS 41 EXAMPLES 41. (1) What is the power received over the transmission line in Section 7, Example 2, the power lost in the line, the power put into the line, and the efficiency of transmission with non- inductive load, with 45-time-degree lagging load and 45-degree leading load? The power received per line with non-inductive load is P = El = 3170 X 44 = 139 kw. With a load of 45 degrees phase displacement, P = El cos 45° = ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-26", "section_label": "Apparatus Section 5: Synchronous Machines: Synchronous Reactance", "section_title": "Synchronous Machines: Synchronous Reactance", "kind": "apparatus-section", "sequence": 26, "number": 5, "location": "lines 9035-9169", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-26/", "snippets": [ "V. Synchronous Reactance 14. In general, both effects, armature self-inductance and armature reaction, can be combined by the term \" synchronous reactance.\" FIG. 55. — Diagram showing effect of synchronous reactance. FIG. 56. — Diagram of generator e.m.f s. showing affect of synchronous reactance with ...", "... \" poly- phase synchronous reactance.\" The resultant armature reac- tion of all phases of the polyphase machine is higher than that with the same current in one phase only, and so also the self- SYNCHRONOUS MACHINES 137 inductive flux, as resultant flux of several phases, and thus rep- resents a higher synchronous reactance. Let r = effective resistance, XQ = synchronous reactance of armature, as discussed in Section II. Let E = terminal voltage, ...", "... .m.f. consumed by the synchronous impedance. Combining OE'i, OE'o, OE gives the nominal generated e.m.f. OEo = EQ, corresponding to the field excitation FQ. In Figs. 56, 57, 58, are shown the diagrams for 6 = 0 or non- inductive load, 6 = 60 degrees lag or inductive load, and & — — 60 degrees or anti-inductive load. Resolving all e.m.fs. into components in phase and in quad- rature with the current, or into power and reactive components, in sym ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-35", "section_label": "Chapter 35: Balanced Symmetrical Polyphase Systems", "section_title": "Balanced Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 35, "number": 35, "location": "lines 37453-37957", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-35/", "snippets": [ "... ght of 1680 lb. per mile. Choosing this size of wire so requires for the 300 miles of line conductor, 300 X 1680 = 500,000 lb. of copper. At 0.52 ohms per mile, the resistance per transmission line or circuit of 100 miles length is, r — 52 ohms. The inductance of wire No. 0, with d = 0.325 in. diameter, and 6 ft. = 72 in. distance from the return conductor, is calculated from the formula of line inductance^ as, 2.3 mil-henrys per mile; hence, per circuit, L - 0.23 henry, and herefrom the reactance, X = 2Tr ...", "... ohms per mile, the resistance per transmission line or circuit of 100 miles length is, r — 52 ohms. The inductance of wire No. 0, with d = 0.325 in. diameter, and 6 ft. = 72 in. distance from the return conductor, is calculated from the formula of line inductance^ as, 2.3 mil-henrys per mile; hence, per circuit, L - 0.23 henry, and herefrom the reactance, X = 2TrfL = 88 ohms. The capacity of the transmission line may be calculated directly, or more conveniently it may be derived from the inductance. If C i ...", "... of line inductance^ as, 2.3 mil-henrys per mile; hence, per circuit, L - 0.23 henry, and herefrom the reactance, X = 2TrfL = 88 ohms. The capacity of the transmission line may be calculated directly, or more conveniently it may be derived from the inductance. If C is the capacity of the circuit, of which the inductance is L, then is the fundamental frequency of oscillation, or natural period, that is, the frequency which makes the length, I, of the line a quarter-wave length. Since the velocity of propaga ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-05", "section_label": "Chapter 5: Symbouc Mbthod", "section_title": "Symbouc Mbthod", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2744-3229", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "snippets": [ "... am, which make an exact diagram- matic determination impossible. For instance, in the trans- former diagrams (cf. Figs. 18-20), the different magnitudes •will have numerical values in practice, somewhat like E-^ = 100 volts, and /j = 75 amperes, for a non-inductive secon- dary load, as of incandescent lamps. Thus the only reac- tance of the secondary circuit is that of the secondary coil, or, x\\ = .08 ohms, giving a lag of eSj = 3.6^. We have also, fty = 30 turns. Uf, = 300 turns. (Fi = 2250 ampere-turns. $ ...", "... ntities. 29. If /= / +ji' is a sine wave of alternating current, and r is the resistance, the E.M.F. consumed by the re- sistance is in phase with the current, and equal to the prod- uct of the current and resistance. Or — r/= ri '\\' jri\\ If L is the inductance, and j: = 2 tt NL the reactance, the E.M.F. produced by the reactance, or the counter §20] SYMBOLIC METHOD. 39' E.M.F. of self-inductance, is the product of the current and reactance, and lags 90° behind the current; it is, therefore, represented by t ...", "... phase with the current, and equal to the prod- uct of the current and resistance. Or — r/= ri '\\' jri\\ If L is the inductance, and j: = 2 tt NL the reactance, the E.M.F. produced by the reactance, or the counter §20] SYMBOLIC METHOD. 39' E.M.F. of self-inductance, is the product of the current and reactance, and lags 90° behind the current; it is, therefore, represented by the expression — jxl =jxi — xi\\ The E.M.F. required to overcome the reactance is con- sequently 90° ahead of the current (or, as usually exp ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "section_label": "Chapter 10: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "... in the conductor or unequal current distribution. 3.) Secondary or induced currents, as, a.) Eddy or Foucault currents in surrounding mag- netic materials ; b.} Eddy or Foucault currents in surrounding conducting materials ; c.} Sec- ondary currents of mutual inductance in neigh- boring circuits. 4.) Induced electric charges, electrostatic influence. While all these losses can be included in the terms effec- tive resistance, etc., only the magnetic hysteresis and the eddy currents in the iron will form the subject of w ...", "... when the energy is supplied electrically, appears as magnetic hysteresis, and is caused by the cyclic reversals of magnetic flux in the iron in the alternating magnetic field. To examine this phenomenon, first a circuit may be con- sidered, of very high inductance, but negligible true ohmic resistance ; that is, a circuit entirely surrounded by iron, as, for instance, the primary circuit of an alternating-current transformer with open secondary circuit. The wave of current produces in the iron an alternating magn ...", "... zing current is as large as shown here only in an iron-closed magnetic circuit expending energy by hysteresis only, as in an iron- clad transformer on Open secondary circuit. As soon as the circuit expends energy in any other way, as in resistance, or by mutual inductance, or if an air-gap is introduced in the magnetic circuit, the distortion of the current wave rapidly decreases and practically disappears, and the current becomes more sinusoidal. That is, while the distorting component remains the same, the sinusoidal com ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-07", "section_label": "Chapter 7: Shaping Of Waves : General", "section_title": "Shaping Of Waves : General", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 12222-12961", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-07/", "snippets": [ "... s, or in certain parts of the circuit, it may change to a shape which is undesirable or even Figs. 46 to 49. dangerous. Voltage, e, and current, i, are related to each other \\>y proportionality, by differentiation and by integration, with sistance, r, inductance, L, and capacity, C, as factors, e = n, r di e = cl idt, and as the differentials and integrals of sines are sines, as long SB r, L and C are constant — which is mostly the case — sine waves of SHAPING OF WAVES 113 voltage produce sine waves ...", "... waves of SHAPING OF WAVES 113 voltage produce sine waves of current and inversely, that is, the sine wave shape of the electrical quantities remains constant. A flat-topped current wave like Fig. 47, however, would by differentiation give a self-inductive voltage wave, which is peakedj like Fig. 48, A voltage wave like Fig. 48, which is more efficient in transformation, may by further distortion, as by intensifica- tion of the triple harmonic by line capacity, assume the shape, Fig. 49, and the latter th ...", "... enth, etc. They are due to the pulsation of the magnetic field flux caused by the pulsation of the SHAPING OF WAVES 121 field reluctance by the passage of the armature slots, and occa- sionally, under load, by magnetic saturation of the armature self- inductive flux, that is, flux produced by the current in an arma- ture slot and surrounding this slot, in cases where very many ampere conductors are massed in one slot, and the slot opening bridged or nearly so. The low harmonics, third, fifth, seventh, are relat ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-40", "section_label": "Chapter 4: Arc Rectification", "section_title": "Arc Rectification", "kind": "chapter", "sequence": 40, "number": 4, "location": "lines 17755-19259", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "snippets": [ "... des, and the constant- Fig. 60. Constant-current mercury arc rectifier. Fig. 61. Constant-potential mercury arc rectifier. current transformer is replaced by a constant-potential trans- former or compensator (auto-transformer) having considerable inductance between the two half coils II and III, as shown in Fig. 61. Two reactive coils are inserted between the outside terminals of the transformer and rectifier tube respectively, for the purpose of producing an overlap between the two rectifying arcs, ca and c ...", "... ial rectifier, instead of the transformer ACS and the reactive coils A a and Ba, generally a compensator or auto-transformer is used, as shown in Fig. 61, in which the 252 TRANSIENT PHENOMENA two halves of the coil, AC and BC, are made of considerable self-inductance against each other, as by their location on different magnet cores, and the reactive coil at c frequently omitted. The modification of the equations resulting herefrom is obvious. Such auto-transformer also may raise or lower the impressed voltage, as sho ...", "... ; that is, 2 e sin 6 = total secondary generated e.m.f. of the constant-current transformer; Z1 = r1 -- jx1 = imped- ance of the reactive coil in each anode circuit of the rectifier (\" alternating- current reactive coil\")? inclusive of the internal self-inductive impedance be- tween the two halves of the transformer secondary coil; t\\ and i2 = anode cur- rents, counted in the direction from anode to cathode; ea = counter e.m.f. Fig. 64. Constant-current of rectifying arc, which is constant; Z0 = mercury arc rect ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-49", "section_label": "Chapter 9: High-Frequency Conductors", "section_title": "High-Frequency Conductors", "kind": "chapter", "sequence": 49, "number": 9, "location": "lines 27003-27760", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "snippets": [ "... nts of very high frequency, as lightning discharges, high frequency oscillations of transmission lines, the currents used in wireless telegraphy, etc., cannot be calculated by the use of the constants derived at low frequency, but effective resistance and inductance, and therewith the power consumed by the conductor, and the voltage drop, may be of an entirely different magnitude from the values which would be found by using the usual values of resistance and induc- tance. In conductors such as are used in the connec ...", "... sistance of the conductor does not appear as heating of the conductor, but a large part of it may be sent out into space as electric radiation, which accounts for the power exerted upon bodies near the path of a lightning stroke, as \"side discharge.\" The inductance is reduced by the unequal current distribution in the conductor, which, by deflecting most of the current into the outer layer of the conductor, reduces or practically eliminates the magnetic field inside of the conductor. The lag of the mag- netic field ...", "... t into the outer layer of the conductor, reduces or practically eliminates the magnetic field inside of the conductor. The lag of the mag- netic field in space, behind the current in the conductor, due to the finite velocity of radiation, also reduces the inductance to less than that from the conductor surface to a distance of one- half wave. An exact determination of the inductance is, how- ever, not possible; the inductance is represented by the electro- magnetic field of the conductor, and this depends upon the p ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 6125-6803", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-09/", "snippets": [ "... n coil of the step-up transformer, the two lines, and the load. Let then Xi = length of line, X2 = length of transformer circuit, and X3 = length of load circuit, in velocity measure.* If then * If Zi = length of circuit section in any measure, and Lo = inductance, Co = capacity per unit of length U, then the length of the circuit in velocity measure is Xi = aoh, where o-q = v LoCo. Thus, if L = inductance, C = capacity per transformer coil, n = number of transformer coils, for the transformer the unit of length i ...", "... of load circuit, in velocity measure.* If then * If Zi = length of circuit section in any measure, and Lo = inductance, Co = capacity per unit of length U, then the length of the circuit in velocity measure is Xi = aoh, where o-q = v LoCo. Thus, if L = inductance, C = capacity per transformer coil, n = number of transformer coils, for the transformer the unit of length is the coil; hence the 110 ELECTRIC DISCHARGES, WAVES AND IMPULSES. Ui = 900 = power- dissipation constant of the line, W2 = 100 = power-dissipa ...", "... e rate e^^^^; that is, in the line: p = 79ie\"2oox^ the energy of the wave decreases slowly; in the transformer: p = p2€+^''°°^, the energy of the wave increases rapidly; length li = n, and the length in velocity measure, X = aou = n ^ LC. Or, if L = inductance, C = capacity of the entire transformer, its length in velocity measure is \\ = ^ LC. Thus, the reduction to velocity measure of distance is very simple. Oscillations of the compound circuit. Ill in the load: p = pse~^^^^^, the energy of the wave ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 5521-6088", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "snippets": [ "... n coil of the step-up transformer, the two lines, and the load. Let then Xi = length of line, X2 = length of transformer circuit, and Xs = length of load circuit, in velocity measure.* If then * If Zi = length of circuit section in any measure, and L0 = inductance, Co = capacity per unit of length Zi, then the length of the circuit in velocity measure is Xi = o-oZi, where 1, that is, when passing from ci a section of low inductance and high capacity into a section of high inductance and low capacity, as from a transmission line into a transformer or a reactive coil, the voltage of the wave is s* increased; if — < 1, that is, when passing from a section of high ci inductance a ...", "... sult thereof,\" in passing from one section C2 of a circuit to another section, the voltage of the wave may ^ . decrease or may increase. If — > 1, that is, when passing from ci a section of low inductance and high capacity into a section of high inductance and low capacity, as from a transmission line into a transformer or a reactive coil, the voltage of the wave is s* increased; if — < 1, that is, when passing from a section of high ci inductance and low capacity into a section of low inductance and ...", "... w inductance and high capacity into a section of high inductance and low capacity, as from a transmission line into a transformer or a reactive coil, the voltage of the wave is s* increased; if — < 1, that is, when passing from a section of high ci inductance and low capacity into a section of low inductance and high capacity, as from a transformer to a transmission line, the voltage of the wave is decreased. This explains the frequent increase to destructive voltages, when entering a station from the transmi ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-05", "section_label": "Chapter 6: Empirical Curves", "section_title": "Empirical Curves", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 16483-21988", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-05/", "snippets": [ "... sion from some general law of nature, or as an approxima- tion thereof, but is an empirical equation if no theoretical reason can be seen for the particular form of the equation. For instance, when representing the dying out of an electrical current in an inductive circuit by an exponential function of time, we have a rational equation: the induced voltage, and therefore, by Ohm's law, the current, varies proportionally to the rate of change of the current, that is, its differential quotient, and as the exponential ...", "... of change of the current, that is, its differential quotient, and as the exponential function has the characteristic of being proportional to its differential quotient, the exponential function thus rationally represents the dying out of the current in an inductive circuit. On the other hand, the relation between the loss by magnetic hysteresis and the magnetic density: W=-q(^^'^, is an empirical equation since no reason can be seen for this law of the 1.6th power, except that it agrees with the observa- tions. A ...", "... tions, for the reason that in nature the conditions on which the rational law is based are rarely perfectly fulfilled. For instance, the representation of a decaying current by an exponential fimction is based on the assumption that the resistance and the inductance of the cu'cuit are constant, and capacity absent, and none of these conditions can ever be perfectly satisfied, and thus a deviation occurs from the theoretical condition, by what is called \" secondary effects.\" 143. To derive an equation, which represen ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-07", "section_label": "Lecture 7: High Frequency Oscillations And Surges", "section_title": "High Frequency Oscillations And Surges", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3508-3780", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-07/", "snippets": [ "... he power consump- tion by the resistance of the lines, an energy storage ■^ occurs as electrostatic energy, or electrostatic charge due to the voltage on the line (capacity) ; and as electromag- netic energy, or magnetic field of the current in the line (inductance). In the long distance transmission line, both amounts of stored energy are very considerable, and of about equal magnitude; the former varying with the voltage, the latter with the current in the line. Any change of the voltage on the line, or the curren ...", "... he generators, it is not the generator wave nor one of its harmonics which builds up, as discussed in the previous lectures; but the generator merely supplies the energy, which is stored as electrostatic charge of the capacity and as magnetic field of the inductance, and the readjustment of this stored energy to the change of circuit conditions then gives the oscillation. These oscillating voltages and currents, adding to the generator voltage and current, thus increase the voltage and the current the more, the gre ...", "... ines therefore oscillate in voltage against ground, that is, charge and discharge also at a frequency of 2300 cycles. They receive their charge, however, over the transformers at the two ends of the line, and their capacity therefore is in series with the self-inductance of these trans- formers in the circuit of the surge frequency of 2300 cycles; and the voltage of the other two lines thus may build up by the combination of capacity and inductance in series, to excessive values ; that is, a destructive breakdown occurs f ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-08", "section_label": "Lecture 8: Arc Lamps And Arc Lighting", "section_title": "Arc Lamps And Arc Lighting", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 7141-8510", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-08/", "snippets": [ "... is, the FIG. current drifts; small variations of the resistance of the arc stream, and thereby of the voltage consumed by the arc, cause excessive fluctuations of the current. These pulsations of cur- rent can be essentially reduced by using a large inductance in series with the arc, and an arc can be operated very much closer to its stability limit if its series resistance is constructed highly inductive, that is, wound on an iron core. Obviously, 144 RADIATION, LIGHT, AND ILLUMINATION. no series inductanc ...", "... ive fluctuations of the current. These pulsations of cur- rent can be essentially reduced by using a large inductance in series with the arc, and an arc can be operated very much closer to its stability limit if its series resistance is constructed highly inductive, that is, wound on an iron core. Obviously, 144 RADIATION, LIGHT, AND ILLUMINATION. no series inductance can extend stable operation beyond the stability point %. At the stability limit iQJ the resultant characteristic III in Fig. 48 is horizontal, t ...", "... nductance in series with the arc, and an arc can be operated very much closer to its stability limit if its series resistance is constructed highly inductive, that is, wound on an iron core. Obviously, 144 RADIATION, LIGHT, AND ILLUMINATION. no series inductance can extend stable operation beyond the stability point %. At the stability limit iQJ the resultant characteristic III in Fig. 48 is horizontal, that is, the slope of the resistance curve ef II, r = - i is equal but opposite to the slope of the arc char ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-12", "section_label": "Theory Section 12: Impedance of Transmission Lines", "section_title": "Impedance of Transmission Lines", "kind": "theory-section", "sequence": 12, "number": 12, "location": "lines 3761-4464", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-12/", "snippets": [ "... at vol- tage E} and the voltage drop in the line, do not depend upon current and line constants only, but depend also upon the angle of phase displacement of the current delivered over the line. If 0 = o, that is, non-inductive receiving circuit, FIG. 29. — Locus of the generator and receiver e.m.fs. in a transmission line with varying load phase angle. E0 = - 4 EIz sin21; that is, less than E + Iz, and thus the line drop is less than ...", "... n The values of E corresponding to the generator voltages E'Q, E\"0, E'\"Q, #IV0 are shown by the points E' E\" Ef\" E™ respectively. The voltages E\"Q and Elv$ correspond to a wattless receiver cir- cuit E\" and E™. For non-inductive receiver circuit W the generator voltage is OEvo. 56. That is, in an inductive transmission line the drop of voltage is maximum and equal to Iz if the phase angle 0 of the receiving circuit equals the phase angle 00 o ...", "... are shown by the points E' E\" Ef\" E™ respectively. The voltages E\"Q and Elv$ correspond to a wattless receiver cir- cuit E\" and E™. For non-inductive receiver circuit W the generator voltage is OEvo. 56. That is, in an inductive transmission line the drop of voltage is maximum and equal to Iz if the phase angle 0 of the receiving circuit equals the phase angle 00 of the line. The drop of voltage in the line decreases with increasing difference ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-14", "section_label": "Theory Section 14: Rectangular Coordinates", "section_title": "Rectangular Coordinates", "kind": "theory-section", "sequence": 14, "number": 14, "location": "lines 5264-5831", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-14/", "snippets": [ "... (1) In a 20-kw. transformer the ratio of turns is 20 : 1, and 100 volts are required at the secondary terminals at full load. What is the primary current, the primary impressed e.m.f., and the primary lag, (a) at non-inductive load, 0i = 0; (6) with 0i = 60 degrees time lag in the external secondary circuit; (c) with 61 = — 60 degrees time lead in the external secondary circuit? 82 ELEMENTS OF ELECTRICAL ENGINEERING i i «!s 32 ...", "... What is the secondary current and secondary terminal voltage and the primary current if the total impedance of the secondary circuit (internal impedance plus external load) consists of (a) resistance, Z = r = 0.5 — non-inductive circuit. (6) impedance, Z = r + jx = 0.3 + 0.4 j — inductive circuit. (c) impedance, Z = r -\\- jx = 0.3 — 0.4 j — anti-inductive circuit. Let e = secondary e.m.f., assumed as real axis in symbolic expression, an ...", "... the primary current if the total impedance of the secondary circuit (internal impedance plus external load) consists of (a) resistance, Z = r = 0.5 — non-inductive circuit. (6) impedance, Z = r + jx = 0.3 + 0.4 j — inductive circuit. (c) impedance, Z = r -\\- jx = 0.3 — 0.4 j — anti-inductive circuit. Let e = secondary e.m.f., assumed as real axis in symbolic expression, and carrying out the calculation in tabulated form, on page 83. 69. ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-20", "section_label": "Theory Section 20: Nomenclature", "section_title": "Nomenclature", "kind": "theory-section", "sequence": 20, "number": 20, "location": "lines 7991-8291", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-20/", "snippets": [ "... agnetic / conductivity) Magnetic gradient Ampere-turns per centi- Electrical F Magnetizing force Magnetomotive force meter. Ampere-turns Electrical R Reluctance (magnetic Electrical L M S .. . resistance) Inductance Mutual inductance Self-inductance Henry; milhenry Henry; milhenry Henry; milhenry Magnetic Magnetic Magnetic *,Q D K Leakage inductance Dielectric flux Electric quantity or charge Dielectric density Dielectric fiel ...", "... conductivity) Magnetic gradient Ampere-turns per centi- Electrical F Magnetizing force Magnetomotive force meter. Ampere-turns Electrical R Reluctance (magnetic Electrical L M S .. . resistance) Inductance Mutual inductance Self-inductance Henry; milhenry Henry; milhenry Henry; milhenry Magnetic Magnetic Magnetic *,Q D K Leakage inductance Dielectric flux Electric quantity or charge Dielectric density Dielectric field inten- Lines o ...", "... gnetic gradient Ampere-turns per centi- Electrical F Magnetizing force Magnetomotive force meter. Ampere-turns Electrical R Reluctance (magnetic Electrical L M S .. . resistance) Inductance Mutual inductance Self-inductance Henry; milhenry Henry; milhenry Henry; milhenry Magnetic Magnetic Magnetic *,Q D K Leakage inductance Dielectric flux Electric quantity or charge Dielectric density Dielectric field inten- Lines of dielectric fo ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-65", "section_label": "Apparatus Section 13: Direct-current Commutating Machines: Commutation", "section_title": "Direct-current Commutating Machines: Commutation", "kind": "apparatus-section", "sequence": 65, "number": 13, "location": "lines 11905-11980", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-65/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-65/", "snippets": [ "... during which the current in A reverses. Thus, considering the reversal as a 1 S single alternation, tQ is a half period, and thus /0 = ^-7- = ;ry- is 4 »o z iw the frequency of commutation; hence, if L = inductance of the armature coil A, the e.m.f. generated in the armature coil during commutation is eo = 2irfoLiot where io = current reversed, and the energy which has to be dissipated during commutation is i ^ ...", "... reflected wave. 51. The energy stored by the inductance L of a circuit element dXj that is, in the magnetic field of the circuit, is 'LV dwl =-^~A where U = inductance per unit length of circuit expressed by the distance coordinate A. Since L = the inductance per unit length of circuit, of distance coordinate Z, and X = ^ (ouyj In general, the circuit constants r, L, 0, C, per unit length, I = 1 give, per unit le ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-04", "section_label": "Chapter 5: Methods Of Approximation", "section_title": "Methods Of Approximation", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 15156-16482", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-04/", "snippets": [ "... F = ^i/2xa3/4(l+|il)x4(l-|82)xaV4x(l+2^)(l-2j) (1 _ \\4a2 a a J a3/2(l-3s2+2-- + S2--) \\ a a / \\ 4 a. a J 138. As further example may be considered the equations of an alternating-current electric circuit, containing distributed resistance, inductance, capacity, and shunted conductance, for instance, a long-distance transmission line or an underground high-potential cable. Equations of the Transmission Line. Let I be the distance along the line, from some starting point; E^ the voltage; 7, the curre ...", "... current at point I, expressed as vector quantities or general numbers; Zo^ro—jxo, the line impedance per unit length (for instance, per mile); Yo=^go—jhQ = Hne admittance, shunted, per unit length; then, rn is the ohmic effective resistance; .To, the self-inductive reactance; &o, the condensive susceptance, that is, wattless charging current divided by volts, and go = energy component of admit- tance, that is, energy component of charging current, divided by volts, per unit length, as, per mile. Considering a line ...", "... term can also usually be neglected, which givet> /,= /o(l+^)±y^o, (16) and the error made hereby is of the magnitude of less than — of the line impedance voltage and line charging current. 141. Example. Assume 200 miles of 60-cycle line, on non- inductive load of ^0 = 100,000 volts; and io = 100 amperes. The line constants, as taken from tables are Z = 104 — 140/ ohms and F=— 0.0013/ ohms; hence, Zy=- (0.182 +0.136/); ^1 = 100000(1-0.091-0.068/) +100(104-104/) = 101400 - 20800/, in volts ; fi = 100(1 ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... usly by a proper arrangement of the work. The most convenient way usually is the arrangement in tabular form. As example, consider the problem of calculating the regula- tion of a 6(),000-volt transmission line, of r = 60 ohms resist- ance, a;= 135 ohms inductive reactance, and 6 = 0.0012 conden- sive susceptance, for various values of non-inductive, inductive, and condensive load. Starting with the complete equations of the long-distance transmission line, as given in \"Theory and Calculation of Transient Electr ...", "... ment in tabular form. As example, consider the problem of calculating the regula- tion of a 6(),000-volt transmission line, of r = 60 ohms resist- ance, a;= 135 ohms inductive reactance, and 6 = 0.0012 conden- sive susceptance, for various values of non-inductive, inductive, and condensive load. Starting with the complete equations of the long-distance transmission line, as given in \"Theory and Calculation of Transient Electric Phenomena and Oscillations,\" Section III, paragraph 9, and considering that for every ...", "... bular form. As example, consider the problem of calculating the regula- tion of a 6(),000-volt transmission line, of r = 60 ohms resist- ance, a;= 135 ohms inductive reactance, and 6 = 0.0012 conden- sive susceptance, for various values of non-inductive, inductive, and condensive load. Starting with the complete equations of the long-distance transmission line, as given in \"Theory and Calculation of Transient Electric Phenomena and Oscillations,\" Section III, paragraph 9, and considering that for every one of the ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-02", "section_label": "Lecture 2: Conclusions From The Relativity Theory", "section_title": "Conclusions From The Relativity Theory", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 736-2388", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... (as two beams of light or two alternating currents) may be anything between their sum and their difference. Thus the two alternating currents consumed by two incandescent lamps add, being in phase; the two alternating currents consumed respectively by an inductance and by a capacity subtract, giving a resultant equal to their difference; that is, if they are equal, they extinguish each other. The phenomenon of interference thus leads to the wave theory of light. If light is a wave motion, there must be something to ...", "... an fill up the space with the field energy. The field energy is proportional to the energy radiation of the source of the field (transmission line, radio antenna, incandescent body) and to the electromagnetic constants of space (permeability, or specific inductance, and permittivity, or specific capac- ity), and the velocity of propagation of the electromagnetic field — that is, the velocity of light — ^thus is: 1 c = ~7E=^ = 3 X IQio cm., where L is the inductance, C the capacity per unit space. As has been ...", "... constants of space (permeability, or specific inductance, and permittivity, or specific capac- ity), and the velocity of propagation of the electromagnetic field — that is, the velocity of light — ^thus is: 1 c = ~7E=^ = 3 X IQio cm., where L is the inductance, C the capacity per unit space. As has been seen, the velocity of light has nothing to do with any rigidity and elasticity constants of matter, but is merely a function of the electromagnetic field constants of space. Lack of familiarity with the conce ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-01", "section_label": "Lecture 1: General Review", "section_title": "General Review", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 154-565", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-01/", "snippets": [ "... han rotary converter substations in a direct current system, and the i^r loss is then reduced by the greatly reduced distance of second- ary distribution. 2. In the alternating current system, the drop of voltage in the conductors is greater by the self-inductive drop than the GENERAL REVIEW 19 ir drop ; the ir drop is therefore only a part of the total voltage drop; and with the same voltage drop and therefore the same regulation as a direct current system, the i^r loss in the alternat- ing current system wou ...", "... e only a part of the total voltage drop; and with the same voltage drop and therefore the same regulation as a direct current system, the i^r loss in the alternat- ing current system would be smaller than in the direct current system. 3. Due to the self-inductive drop, smaller and therefore more numerous low tension distribution circuits must be used with alternating current than with direct current, and a separ- ate and independent voltage regulation of each low tension cir- cuit— ^that is — each transformer, the ...", "... alternating current than with direct current, and a separ- ate and independent voltage regulation of each low tension cir- cuit— ^that is — each transformer, therefore usually becomes im- practicable. This means that the total voltage drop, resistance and inductance, in the alternating current low tension distribu- tion circuits must be kept within a few percent., that is, within the range permissible by the incandescent lamp. As a result thereof, the voltage regulation of an alternating current low tension distribut ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-02", "section_label": "Lecture 2: General Distribution", "section_title": "General Distribution", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 566-982", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-02/", "snippets": [ "... concentrated load, as in the interior of a large city, since the independent voltage regulation of each one of numerous feeders is economically permissible only where each feeder represents a large amount of power; with alternating cur- rent systems, the inductive drop forbids the concentration of such large currents in a single conductor. That is, conductors of one million circular mils cannot be used economically in an alternating current system. The resistance of a conductor is inversely proportional to the si ...", "... ter is half that of one conductor No. i, or .058 ohms, provided that the two con- ductors are used as separate circuits. In alternating current low tension distribution, the size of the conductor and so the current per conductor, is limited by the self -inductive drop, and alternating current low tension networks are therefore of necessity of smaller size than those of direct current distribution. As regards economy of distribution, this is not a serious objection, as the alternating current transformer and prima ...", "... lternating current distribution therefore re- quires the use of secondary distribution mains of as large an extent as possible, fed by large transformers. The distance, however, to which a transformer can supply secondary current, is rather limited by the inductive drop of voltage ; therefore, for supplying secondary mains, transformers of larger size than 30 kw. are rarely used, but rather several transformers are em- ployed, to feed in the same main at different points. GENERAL DISTRIBUTION 31 Extending th ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-04", "section_label": "Theory Section 4: Power and Effective Values", "section_title": "Power and Effective Values", "kind": "theory-section", "sequence": 4, "number": 4, "location": "lines 1244-1572", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-04/", "snippets": [ "... X 10~6 r = - — -rT^ — \" = 0.71 ohms per circuit. 44.2 amp. X 0.71 ohms gives 31.5 volts per circuit and (44.2)2 X 0.71 = 1400 watts per circuit, or a total of 3 X 1400 = 4200 watts loss. 24. (3) What is the self-inductance per wire of a three- phase line of 14 miles length consisting of three wires No. 0 (Id = 0.82 cm.), 45 cm. apart, transmitting the output of this 450 kw. 5900- volt three-phase machine? 18 ELEMENTS OF ELECTRICAL ...", "... ines in Fig. 9. The area of a parabolic curve is width times one-third of height, or OAE2 hence, the mean square of voltage is 0 and the actual effective voltage is _,4 1/280 ~ e, ~ TT V 27 L°25' SELF-INDUCTANCE AND MUTUAL INDUCTANCE 21 hence, the form factor is 7 r or, 2.5 per cent, higher than with a sine wave.", "... he area of a parabolic curve is width times one-third of height, or OAE2 hence, the mean square of voltage is 0 and the actual effective voltage is _,4 1/280 ~ e, ~ TT V 27 L°25' SELF-INDUCTANCE AND MUTUAL INDUCTANCE 21 hence, the form factor is 7 r or, 2.5 per cent, higher than with a sine wave." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-112", "section_label": "Apparatus Section 6: Induction Machines: Phase Converter", "section_title": "Induction Machines: Phase Converter", "kind": "apparatus-section", "sequence": 112, "number": 6, "location": "lines 21647-21812", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-112/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-112/", "snippets": [ "... secondary to the ter- tiary or generator circuit. Thus, in a quarter-phase motor connected to single-phase mains with one of its circuits, if Y = g — jb = primary polyphase exciting admittance, ZQ = TQ -f- JXQ = self -inductive impedance per primary or ter- tiary circuit, Zi = ri + jxi = resultant single-phase self-inductive impe- dance of secondary circuits. Let e = e.m.f. generated by the mutual flux and Z = r + jx = impedance of the exter ...", "... e-phase mains with one of its circuits, if Y = g — jb = primary polyphase exciting admittance, ZQ = TQ -f- JXQ = self -inductive impedance per primary or ter- tiary circuit, Zi = ri + jxi = resultant single-phase self-inductive impe- dance of secondary circuits. Let e = e.m.f. generated by the mutual flux and Z = r + jx = impedance of the external circuit supplied by the phase converter as generator of second phase. We then have /> I = ...", "... arranged on an angle of 60 deg. with the primary circuit, and in starting a powerful torque is thereby developed, with a torque efficiency superior to any other single-phase motor starting device, and when com- bined with inductive reactance in a second tertiary circuit, the apparent starting torque efficiency can be made even to exceed that of the polyphase induction motor (see page 336). For further discussion hereof, see A. I. E. E. Transactions, ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-44", "section_label": "Apparatus Subsection 44: Direct-current Commutating Machines: C. Commutating Machines 175", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 175", "kind": "apparatus-subsection", "sequence": 44, "number": null, "location": "lines 10685-10736", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-44/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-44/", "snippets": [ "... ENGINEERING over only four or five teeth instead of over six. As five-sixths fractional-pitch multiple drum winding it is shown in Fig. 91. Fractional-pitch windings have the advantage of shorter end connections and less self-inductance in commutation, since commutation of corresponding coils under different poles does not take place in the same, but in different, slots, and the flux of self-inductance in commutation is thus more subdivided. Fig. 91 shows ...", "... have the advantage of shorter end connections and less self-inductance in commutation, since commutation of corresponding coils under different poles does not take place in the same, but in different, slots, and the flux of self-inductance in commutation is thus more subdivided. Fig. 91 shows the multiple drum winding of Fig. 81 as a frac- FIG. 91. — Multiple drum five-sixth fractional pitch winding. tional-pitch winding with five teeth spread, or five-sixth ...", "... five-sixths pitch. During commutation the coils a b c d e f commutate simultane- ously. In Fig. 81 these coils lie by twos in the same slots, in Fig. 91 they lie in separate slots. Thus, in the former case the flux of self-inductance interlinked with the commutated coil is due to two coils; that is, twice that in the latter case. Frac- tional-pitch windings, however, have the disadvantage of reduc- ing the width of the neutral zone, or zone without gene ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-66", "section_label": "Apparatus Subsection 66: Direct-current Commutating Machines: C. Commutating Machines 201", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 201", "kind": "apparatus-subsection", "sequence": 66, "number": null, "location": "lines 11981-12083", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-66/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-66/", "snippets": [ "... magnetic field of armature reaction, or the reverse magnetic field of a commutating pole, or the fringe of the main field of the machine, into which the brushes are shifted. In this case the commutation depends upon the inductance and the resistance of the armature coil and the e.m.f. generated therein by the main magnetic field, and if this magnetic field is a corn- mutating field, is called voltage commutation. In either case the resistance of t ...", "... n to minimum, and then up again to infinity at the end of commutation. 65. (a) Negligible resistance of brush and brush contact. This is more or less approximately the case with copper brushes. Let iQ = current, L = inductance, r — resistance of armature coil, to = -£• = time of commutation, and — e = e.m.f. generated in the armature coil by its rotation through the magnetic field, where e is negative for the magnetic field of armature re ...", "... the magnetic field, where e is negative for the magnetic field of armature reaction and positive for the commutating field. Denoting the current in the coil A at time t after beginning of commutation by i, the e.m.f. of self-inductance is _ di Thus the total e.m.f. acting in coil A, di — e -\\- ei = — e — L -77* at and the current is e Ldi r r dt 202 ELEMENTS OF ELECTRICAL ENGINEERING Transposing, this expression becomes rdt ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-80", "section_label": "Apparatus Subsection 80: Direct-current Commutating Machines: C. Commutating Machines 221", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 221", "kind": "apparatus-subsection", "sequence": 80, "number": null, "location": "lines 13120-13188", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-80/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-80/", "snippets": [ "D. C. COMMUTATING MACHINES 221 economy of high voltage alternating-current transmission and distribution. For railroading generally the series motor type is used, either the plain compensated series motor, or inductive modifications thereof, as the repulsion motor etc. In the repul- sion motor the armature, instead of being connected in series with field and compensating winding, is closed on itself and thus traversed by a secondary curren ...", "... secondary is of the frequency of slip, the speed controlling e.m.f. must either be supplied through the commutator or de- rived from a low frequency commutating machine as source. 4. For power-factor compensation. In an inductive circuit, the current lags behind the voltage or, what is the same, the voltage leads the current, and the power-factor thus can be raised by compensation either by introducing a leading current, as from condenser or overe ...", "... ade to give unity power-factor or even leading current. Such phase compensation is frequently used in alternating- current commutator motors to get good power-factor. Thus in the series motor, by shunting the field by a non-inductive re- sistance, and thereby lagging the field exciting component of the current and with it the field flux and the voltage induced in the armature by its rotation, behind the main current, the series motor can at higher spe ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-20", "section_label": "Chapter 20: Beactiox Machines", "section_title": "Beactiox Machines", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 22388-23273", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "snippets": [ "... double frequency, and its higher harmonics, in first approximation the assump- tion can be made that the reactance or the reluctance vary with double frequency of the main current ; that is, are represented in the form, X =^ a -\\- b cos 2 <^. Let the inductance, or the coefficient of self-induction, be represented by — Z = / + <^ cos 2 <^ = /(I -f y cos 2 <^) where y = amplitude of variation of inductance. Let , inclosed by the circuit is produced by the current flowing in the circuit, the ratio — flux X number of turns X 10~8 current . is called the inductance, L, of the circuit, in henrys. The product of the number of turns, n, into the maxi- mum flux, , produced by a current of / amperes effective, or / V2 amperes maximum, is therefore — n® =Z/V2 108; and consequently the effective E.M.F. of self-induct ...", "... inductance, L, of the circuit, in henrys. The product of the number of turns, n, into the maxi- mum flux, , produced by a current of / amperes effective, or / V2 amperes maximum, is therefore — n® =Z/V2 108; and consequently the effective E.M.F. of self-inductance is: E = V2 =' 2 TT NLI volts. The product, x = 2 vNL, is of the dimension of resistance, and is called the reactance of the circuit ; and the E.M.F. of self-inductance of the circuit, or the reactance voltage, is E = Ix, and lags 90° behind the c ...", "... maximum, is therefore — n® =Z/V2 108; and consequently the effective E.M.F. of self-inductance is: E = V2 =' 2 TT NLI volts. The product, x = 2 vNL, is of the dimension of resistance, and is called the reactance of the circuit ; and the E.M.F. of self-inductance of the circuit, or the reactance voltage, is E = Ix, and lags 90° behind the current, since the current is in phase with the magnetic flux produced by the current, and the E.M.F. lags 90° behind the magnetic flux. The E.M.F. lags 90° behind the magneti ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-21", "section_label": "Chapter 21: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 20502-21189", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-21/", "snippets": [ "... of double frequency, and its higher harmonics, in first approximation the assump- tion can be made that the reactance or the reluctance vary with double frequency of the main current ; that is, are represented in the form, x = a + b cos 2 /8. Let the inductance, or the coefficient of self-induction, be represented by — L = I + <£ cos 2 /3 = /(I + y COS 2 0) where y = amplitude of variation of inductance. Let u> = angle of lag of zero value of current behind maximum value of inductance L. It is then, as ...", "... uble frequency of the main current ; that is, are represented in the form, x = a + b cos 2 /8. Let the inductance, or the coefficient of self-induction, be represented by — L = I + <£ cos 2 /3 = /(I + y COS 2 0) where y = amplitude of variation of inductance. Let u> = angle of lag of zero value of current behind maximum value of inductance L. It is then, assuming the current as sine wave, or repla- cing it by the equivalent sine wave of effective intensity /, Current, * = I V2 sin (/? - £). The magn ...", "... cos 2 /8. Let the inductance, or the coefficient of self-induction, be represented by — L = I + <£ cos 2 /3 = /(I + y COS 2 0) where y = amplitude of variation of inductance. Let u> = angle of lag of zero value of current behind maximum value of inductance L. It is then, assuming the current as sine wave, or repla- cing it by the equivalent sine wave of effective intensity /, Current, * = I V2 sin (/? - £). The magnetism produced by this current is, where n = number of turns. Hence, substituted, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-22", "section_label": "Chapter 22: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 21190-21982", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "snippets": [ "... th the harmonics due to the varying reluctance of the magnetic circuit. In ironclad alternators with few slots and teeth per pole, the passage of slots across the field poles causes a pulsation of the magnetic reluc- tance, or its reciprocal, the magnetic inductance of the circuit. In consequence thereof the magnetism per field pole, or at least that part of the magnetism passing through the armature, will pulsate with a frequency 2 y if y = num- ber of slots per pole. Thus, in a machine with one slot per pole, the ...", "... aused by pulsation of the reluc- tance. 390 ALTERNATING-CURRENT PHENOMENA. V 100 50 60 70 80 90 1 00 30 140 150 160 170 180 Fig. 172. No-load Wave of E.M.F. of Unitooth Three-phase Alternator. In general, if the pulsation of the magnetic inductance is denoted by the general expression : l + ^\"cYcos(2yj8-aY), 1 the instantaneous magnetic flux is : 00 = $ cos 13 ey cos (2 y ff - cos((2y+l) hence, the E.M.F. 2 ; sm(P — DISTORTION OF WAVE-SHAPE. 391 Pulsation of Reactance. 237. ...", "... etrical distortion of the wave which makes the wave of induced E.M.F. differ by more than 90° from the current wave and thereby represents power, — the power consumed by hysteresis. In practice both effects are always superimposed ; that is, in a ferric inductance, a distortion of wave-shape takes place due to the lack of proportionality between magnetism and M.M.F. as expressed by the variation in the hysteretic cycle. This pulsation of reactance gives rise to a distortion consisting mainly of a triple harmonic. ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-22", "section_label": "Chapter 24: Conclusion", "section_title": "Conclusion", "kind": "chapter", "sequence": 22, "number": 24, "location": "lines 32820-33531", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-22/", "snippets": [ "... yland motor, 92 Higher harmonic torques in induc- tion motor, 144 Homopolar, see Unipolar. Hunt motor, 49 Hunting, see Surging. Hysteresis generator, 169 motor, 168 starting device of induction motor, 5 I Independent phase rectifier, 251 Inductance storing energy in phase conversion, 212 Inductive compensation of single- phase commutator motor, 343 devices starting singlephase in- duction motor, 97, 111 Inductive excitation of singlephase commutator motor, 343 •Induction frequency converter ...", "... ion motor, 144 Homopolar, see Unipolar. Hunt motor, 49 Hunting, see Surging. Hysteresis generator, 169 motor, 168 starting device of induction motor, 5 I Independent phase rectifier, 251 Inductance storing energy in phase conversion, 212 Inductive compensation of single- phase commutator motor, 343 devices starting singlephase in- duction motor, 97, 111 Inductive excitation of singlephase commutator motor, 343 •Induction frequency converter, 191 generator, 473 motor inductor frequency con- ...", "... starting device of induction motor, 5 I Independent phase rectifier, 251 Inductance storing energy in phase conversion, 212 Inductive compensation of single- phase commutator motor, 343 devices starting singlephase in- duction motor, 97, 111 Inductive excitation of singlephase commutator motor, 343 •Induction frequency converter, 191 generator, 473 motor inductor frequency con- verter, 284 phase balancer stationary, 228 phase converter, 220 Inductor machines, 274 Interlocking pole type of machin ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-17", "section_label": "Chapter 17: Circuits With Distributed Leakage", "section_title": "Circuits With Distributed Leakage", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 30429-31656", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-17/", "snippets": [ "... ent circuits, the induetance and the capacity of the conductor do not come into consideration except in the transients of current change, and in stationary con- ditions such a circuit thus is one of distributed series resistance and shunted conductance. Inductance also is absent with the current induced in the cable armor by an alternating current traversing the cable conductor, 330 CIRCUITS WITH DISTRIBUTED LEAKAGE 331 and with all low- and medium-voltage conductors, with the com- mercial frequencies of alter ...", "... 31 and with all low- and medium-voltage conductors, with the com- mercial frequencies of alternating currents, the capacity effects are so small as to be negligible. In high-voltage conductors, such as transmission lines, etc., in general, capacity and inductance require consideration as well as resistance and shunted conductance. This general case is fully discussed in \"Theory and Calculation of Transient Electric Phe- nomena and Oscillations,\" and in \"Electric Discharges, Waves and Impulses,\" more particularly i ...", "... 1.5 0.155 2.0 0.086 2.5 0.046 3.0 0.025 4.0 0.0074 5 km. 0.0021 As seen, beyond 2 km. distance, the current in the conductor is practically nothing. 177. If the current, i, is an alternating current, and the con- dition such that inductance and capacity are negligible, the equations (7), (9), (10), (11) and (13) remain the same, except that i, 6 and A are vector quantities, or general numbers: J, ^, A. Considering thus the more general case, where a voltage is in- duced in the leaky conduct ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-22", "section_label": "Chapter 9: Inductive Discharges. 535", "section_title": "Inductive Discharges. 535", "kind": "chapter", "sequence": 22, "number": 9, "location": "lines 1286-1316", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-22/", "snippets": [ "CHAPTER IX. INDUCTIVE DISCHARGES. 535 64. Massed inductance discharging into distributed circuit. Combination of generating station and transmission line. 535 65. Equations of inductance, and change of constants at transition point. 536 66. Line open or grounded at end. ...", "CHAPTER IX. INDUCTIVE DISCHARGES. 535 64. Massed inductance discharging into distributed circuit. Combination of generating station and transmission line. 535 65. Equations of inductance, and change of constants at transition point. 536 66. Line open or grounded at end. Evaluation of frequency constant and ...", "CHAPTER IX. INDUCTIVE DISCHARGES. 535 64. Massed inductance discharging into distributed circuit. Combination of generating station and transmission line. 535 65. Equations of inductance, and change of constants at transition point. 536 66. Line open or grounded at end. Evaluation of frequency constant and resultant decrement. 538 67. The final equations, and their discussion. 540 68. Numerical example. Calculation of the first six ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-41", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 41, "number": 1, "location": "lines 19260-19338", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "snippets": [ "... phone circuits, multiple spark-gaps, as used in some forms of high potential lightning arresters (multi-gap arrester), etc. (b) The distribution of alternating current in solid conductors and the increase of effective resistance and decrease of effective inductance resulting therefrom. (c) The distribution of alternating magnetic flux in solid iron, or the screening effect of eddy currents produced in the iron, and the apparent decrease of permeability and increase of power consumption resulting therefrom. (d) Th ...", "... pparent decrease of permeability and increase of power consumption resulting therefrom. (d) The distribution of the electric field of a conductor through space, resulting from the finite velocity of propagation of the electric field, and the variation of self-inductance and mutual inductance and of capacity of a conductor without return, as function of the frequency, in its effect on wireless telegraphy. (e) Conductors conveying very high frequency currents, as lightning discharges.", "... ermeability and increase of power consumption resulting therefrom. (d) The distribution of the electric field of a conductor through space, resulting from the finite velocity of propagation of the electric field, and the variation of self-inductance and mutual inductance and of capacity of a conductor without return, as function of the frequency, in its effect on wireless telegraphy. (e) Conductors conveying very high frequency currents, as lightning discharges." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-45", "section_label": "Chapter 5: Distributed Series Capacity", "section_title": "Distributed Series Capacity", "kind": "chapter", "sequence": 45, "number": 5, "location": "lines 23586-23947", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "snippets": [ "... onnected between line L and ground G. This arrangement, Fig. 90, can be represented diagrammatically by Fig. 91. Each cylinder has a capacity (70 against ground, a capacity C against the adja- cent cylinder, a resistance r, — usually very small, — and an inductance L. If such a series of n equal spark gaps is connected across a & constant supply voltage e0, each gap has a voltage e = — . If, Tl however, the supply voltage is alternating, the voltage does not divide uniformly between the gaps, but the potential ...", "... ted series capacity thus leads to an under- standing of the phenomena occurring in the thunder cloud during the lightning discharge.* Only a general outline can be given in the following. 45. In a circuit containing distributed resistance, conductance, inductance, shunt, and series capacity, as the multigap lightning arrester, Fig. 90, represented electrically as a circuit in Fig. 91, let r = the effective resistance per unit length of circuit, or per circuit element, that is, per arrester cylinder; g = the shunt ...", "... ircuit in Fig. 91, let r = the effective resistance per unit length of circuit, or per circuit element, that is, per arrester cylinder; g = the shunt conductance per unit length, representing leakage, brush dis- charge, electrical radiation, etc.; L = the inductance per unit length of circuit; C = the series capacity per unit length of cir- cuit, or circuit element, that is, capacity between adjacent arrester cylinders, and <70 = the shunt capacity per unit length of circuit, or circuit element, that is, capacity bet ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-51", "section_label": "Chapter 2: Discussion Of General Equations", "section_title": "Discussion Of General Equations", "kind": "chapter", "sequence": 51, "number": 2, "location": "lines 28695-29315", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "snippets": [ "... xpense of a decrease of amplitude during its propagation, or, in i\", e\" duration in time is sacrificed to duration in distance, and inversely in i', e'. DISCUSSION OF GENERAL EQUATIONS 433 It is interesting to note that in a circuit having resistance, inductance, and capacity, the mathematical expressions of the two cases of energy flow; that is, the gradual or exponential and the oscillatory or trigonometric, are both special cases of the equations (60) and (61), corresponding respectively to q = o, k = 0 and to ...", "... along the DISCUSSION OF GENERAL EQUATIONS 439 circuit, but is a stationary or standing wave. It is an oscillatory discharge of a circuit containing a distributed r, L, g, C, and therefore is analogous to the oscillating condenser discharge through an inductive circuit, except that, due to the distributed capacity, the phase changes along the circuit. The free oscilla- tions of a circuit such as a transmission line are of this character. For A = 0, that is, assuming the wave length of the oscillation as so great ...", "... of the wave length, that the phase of i and e can be assumed as uniform throughout the circuit, the equations (83) and (84) assume the form i = £-^{B0 cos qt + BQ' sin qt\\ and (85) these are the usual equations of the condenser discharge through an inductive circuit, which here appear as a special case of a special case of the general circuit equations. If q equals zero, the functions D and H in equations (74) and (75) become constant, and these equations so assume the form and e = (86) where B= ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-55", "section_label": "Chapter 6: Transition Points And The Complex Circuit", "section_title": "Transition Points And The Complex Circuit", "kind": "chapter", "sequence": 55, "number": 6, "location": "lines 32709-33527", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "snippets": [ "... out the entire circuit, and across transition points, at which the circuit constants change, and the same equations (266) and (267) apply throughout the entire circuit. In this case, however, in any section of the circuit, (268) where Lt and Ct are the inductance and the capacity, respect- ively, of the section i of the circuit, per unit length, for instance, per mile, in a line, per turn in a transformer coil, etc. In a complex circuit the time variable t is the same throughout the entire circuit, or, in other w ...", "... actual linear length of conductor may be unknown. For instance, choosing the total length of conductor in the high-potential transformer as unit length, then the length of the transformer winding in the velocity measure ^ is >10 = \\/L0C0, where L0 — total inductance, C0 = total capacity of transformer. The introduction of the distance variable ^ thus permits the representation in the circuit of apparatus as reactive coils, etc., in which one of the constants is very small compared with the other and therefore is us ...", "... of the distance variable ^ thus permits the representation in the circuit of apparatus as reactive coils, etc., in which one of the constants is very small compared with the other and therefore is usually neglected and the apparatus considered as \"massed inductance,'7 etc., and allows the investi- gation of the effect of the distributed capacity of reactive coils and similar matters, by representing the reactive coil as a finite (frequently quite long) section ^0 of the circuit. 43. Let y*0, Av >^2, ... kn be a num ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 557-1002", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-01/", "snippets": [ "... ircuits, since voltage, current, magnetic flux, etc., are proportional to each other, and the electrical transients therefore are usually of the simplest nature. In those cases, however, where this direct proportionality does not exist, as for instance in inductive circuits containing iron, or in electrostatic fields exceed- ing the corona voltage, the transients also are far more complex, and very little work has been done, and very little is known, on these more complex electrical transients. Assume that in an el ...", "... ed energy — decrease or increase — frequently occurs by a series of successive changes from magnetic to dielectric and back again from dielectric to magnetic stored energy. This for instance is the case in the charge or discharge of a condenser through an inductive circuit. If energy can be stored in more than two different forms, still more complex phenomena may occur, as for instance in the hunt- ing of synchronous machines at the end of long transmission lines, where energy can be stored as magnetic energy in th ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 460-882", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "snippets": [ "... ircuits, since voltage, current, magnetic flux, etc., are proportional to each other, and the electrical transients therefore are usually of the simplest nature. In those cases, however, where this direct proportionality does not exist, as for instance in inductive circuits containing iron, or in electrostatic fields exceed- ing the corona voltage, the transients also are far more complex, and very little work has been done, and very little is known, on these more complex electrical transients. Assume that in an el ...", "... ed energy — decrease or increase — frequently occurs by a series of successive changes from magnetic to dielectric and back again from dielectric to magnetic stored energy. This for instance is the case in the charge or discharge of a condenser through an inductive circuit. If energy can be stored in more than two different forms, still more complex phenomena may occur, as for instance in the hunt- ing of synchronous machines at the end of long transmission lines, where energy can be stored as magnetic energy in th ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-13", "section_label": "Lecture 13: Electric Railway: Motor Characteristics", "section_title": "Electric Railway: Motor Characteristics", "kind": "lecture", "sequence": 13, "number": 13, "location": "lines 7124-8648", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-13/", "snippets": [ "... med by the resistance, still further voltage is consumed by self-induction; and the voltage e available for the armature rotation thus drops still further, as seen in Fig. 41. Since the self-induction consumes voltage in quadrature with the cur- rent, the inductive drop is not proportional to the current, but is small at low currents, and greater at high currents ; e therefore is not a straight line, but curves downwards at higher currents. The speed, Si, is dropped still further by the inductive drop of voltage, to ...", "... the cur- rent, the inductive drop is not proportional to the current, but is small at low currents, and greater at high currents ; e therefore is not a straight line, but curves downwards at higher currents. The speed, Si, is dropped still further by the inductive drop of voltage, to the curve Si, and then raised to the curve S by saturation. The eflFect of saturation in the alternating current motor usually is far less, since the magnetic field is alternating, and good power factor requires a low field excitation, ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... lly, it is interesting to consider the corresponding relations in electric waves. In an electric circuit, the speed of propagation of an electric wave is, when neglecting the energy losses in and by the con- ductor: S = -L= , (5) VLC where L is the inductance, C the capacity of the conductor per unit length (the length measured in the same measure as the speed S). The inductance L is proportional to the permeability /*, and the capacity C proportional to the dielectric constant, or specific capacity K of the ...", "... agation of an electric wave is, when neglecting the energy losses in and by the con- ductor: S = -L= , (5) VLC where L is the inductance, C the capacity of the conductor per unit length (the length measured in the same measure as the speed S). The inductance L is proportional to the permeability /*, and the capacity C proportional to the dielectric constant, or specific capacity K of the medium surrounding the conductor, that is, the medium through which the electric wave propagates; that is, A V p* where ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-09", "section_label": "Theory Section 9: Vector Diagrams", "section_title": "Vector Diagrams", "kind": "theory-section", "sequence": 9, "number": 9, "location": "lines 2865-3233", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-09/", "snippets": [ "... hat at time zero 0=0, its projec- tion on the horizontal, is zero, and at times 0 > 0, but < TT, the projection is positive. Thus this vector 0/0 is the negative vertical, as shown in Fig. 18. The voltage consumed by inductance, ez = x!0 cos 0, is repre- sented by a vector OEZ equal in length to x!Q, and located so that at 0 = 0, its projection on the horizontal is a maximum. That is, it is the zero vector OE2 in Fig. 18. Analogously, th ...", "... is repre- sented by a vector OEZ equal in length to x!Q, and located so that at 0 = 0, its projection on the horizontal is a maximum. That is, it is the zero vector OE2 in Fig. 18. Analogously, the counter e.m.f. of self-inductance E'2 is represented by vector OE'Z on the negative horizontal of Fig. 18; the voltage consumed by the resistance r, e\\ — e!Q sin 0, is represented by vector OEi equal to r/0, and located on the nega- VECTOR DIAGRAMS 4 ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-110", "section_label": "Apparatus Section 4: Induction Machines: Induction Generator", "section_title": "Induction Machines: Induction Generator", "kind": "apparatus-section", "sequence": 110, "number": 4, "location": "lines 21158-21588", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-110/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-110/", "snippets": [ "... in Fig. 230 as function of the impedance of the external circuit z = -?• as abscissas (where eQ = terminal voltage, iQ = 2o current in external circuit), the leading power-factor p = cos 6 required in the load, the inductance factor q = sin 6, and the frequency. Hence, when connected to a circuit of impedance z this induc- tion generator can operate only if the power-factor of its circuit is p', and if this is the case the voltage is indef ...", "... the circuit unstable, even neglecting the impossibility of securing exact equality of the power-factor of the external circuit with that of the induction generator. FIG. 188. — Three-phase induction generator power factor and inductance factor of external circuit. Two possibilities thus exist with such an induction generator circuit. 1st. The power-factor of the external circuit is constant and independent of the voltage, as when the external circuit consi ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-114", "section_label": "Apparatus Section 8: Induction Machines: Concatenation of Induction Motors", "section_title": "Induction Machines: Concatenation of Induction Motors", "kind": "apparatus-section", "sequence": 114, "number": 8, "location": "lines 21923-22191", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-114/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-114/", "snippets": [ "... ; that is, theoretically concatenation doubles the torque and output for a given current, or power input into the motor system. In reality the gain is somewhat less, due to the second motor not being quite equal to a non-inductive resistance for the secondary of the first motor, and due to the drop of voltage in the internal impedance of the first motor, etc. At one-half synchronism, that is, the limiting speed of the con- catenated couple, the cu ...", "... otors with a single motor of double the number of poles. Comparing the concatenated couple with a single motor re- wound for twice the number of poles, that is, one-half speed also, such rewinding does not change the self-inductive impe- INDUCTION MACHINES 359 dance, but quadruples the exciting admittance, since one-half as many turns per pole have to produce the same flux in one-half the pole arc, that is, with twice the density. Thus the char ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-24", "section_label": "Apparatus Section 3: Synchronous Machines: Armature Reaction", "section_title": "Synchronous Machines: Armature Reaction", "kind": "apparatus-section", "sequence": 24, "number": 3, "location": "lines 8741-8906", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-24/", "snippets": [ "... le the arma- ture coil still partly faces the pre- ceding magnet pole, as shown in Fig. 48, C and C\", and thus mag- netizes the field in a generator, Fig. 48, C, and demagnetizes it in a syn- chronous motor C'. With non-inductive load, or with the current in phase with the ter- minal voltage of an alternating- current generator, the current lags behind the nominal generated e.m.f., due to armature reaction and self- inductance, and thus partly de- m ...", "... n- chronous motor C'. With non-inductive load, or with the current in phase with the ter- minal voltage of an alternating- current generator, the current lags behind the nominal generated e.m.f., due to armature reaction and self- inductance, and thus partly de- magnetizes; that is, the voltage is lower under load than at no load with the same field excitation. In other words, lagging current demag- netizes and leading current magne- tizes the field of an alter ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-30", "section_label": "Apparatus Section 9: Synchronous Machines: Magnetic Characteristic or Saturation Curve", "section_title": "Synchronous Machines: Magnetic Characteristic or Saturation Curve", "kind": "apparatus-section", "sequence": 30, "number": 9, "location": "lines 9554-9650", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-30/", "snippets": [ "... the magnetic circuit approach saturation successively. The dependence of the terminal voltage upon the field excita- tion, at constant full-load current through the amature into a 148 ELEMENTS OF ELECTRICAL ENGINEERING non-inductive circuit, is called the load saturation curve of the synchronous machine. It is a curve approximately parallel to the no-load saturation curve, but starting at a definite value of field excitation for zero terminal voltage, ...", "... In addition thereto, due to the counter m.m.f. of the armature current, the magnetic stray field, that is, that magnetic flux which leaks from field pole to field pole through the air, increases under load, especially with inductive load where the armature m.m.f. directly opposes the field, and thus a still further increase of density is required in the field magnetic circuit under load. In consequence thereof, at high saturation the load saturation cu ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-40", "section_label": "Apparatus Subsection 40: Direct-current Commutating Machines: C. Commutating Machines", "section_title": "Direct-current Commutating Machines: C. Commutating Machines", "kind": "apparatus-subsection", "sequence": 40, "number": null, "location": "lines 10475-10519", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-40/", "snippets": [ "... is arranged on the surface of a laminated iron core. In the iron-clad machine the arma- ture winding is sunk into slots. The iron-clad type has the ad- vantage of greater mechanical strength, but the disadvantage of higher self-inductance in commutation, and thus requires high- resistance, carbon or graphite, commutator brushes. The iron- clad type has the advantage of lesser magnetic stray field, due FIG. 78. — Series machine. FIG. 79. — Compound machine. ...", "... multipolar machines the iron- clad type of armature is best adapted; the smooth-core type is hardly ever used nowadays. Either of these types can be drum wound or ring wound. The drum winding has the advantage of lesser self-inductance and lesser distortion of the magnetic field, and is generally less difficult to construct and thus mostly preferred. By the arma- ture winding, commutating machines are divided into multiple- wound and series-wound machines. T ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-53", "section_label": "Apparatus Subsection 53: Direct-current Commutating Machines: C. Commutating Machines 185", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 185", "kind": "apparatus-subsection", "sequence": 53, "number": null, "location": "lines 11132-11213", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-53/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-53/", "snippets": [ "... nt shift of the brushes, the commutation of the constant potential machine, direct-current generator or motor, is best at a certain load, and usually becomes poorer at lighter or heavier loads, and ultimately becomes bad by inductive sparks due to insufficient commutating flux. In machines in which very good commutating constants cannot be secured, as in large high-speed machines (steam turbine driven direct-current generators) , this may lead to bad spark ...", "... point of the armature surface, at which commutation occurs, and excited so as to produce a commutating flux proportional to the load, and thus giving the required commutating field at all loads. Such machines then give no inductive sparking, but regarding commutation are limited in overload capacity only by the current density under the brush. Such commutating poles are excited by series coils, that is, coils connected in series with the armature and ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-79", "section_label": "Apparatus Subsection 79: Direct-current Commutating Machines: C. Commutating Machines 219", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 219", "kind": "apparatus-subsection", "sequence": 79, "number": null, "location": "lines 13019-13119", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-79/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-79/", "snippets": [ "... and thereby reduces output and efficiency and hence requires some method of compensation, as capacity in series with the field winding or excitation of the field from a quadrature phase of voltage. In the series motor the self-inductance of the field causes the main current to lag behind the impressed voltage and thereby lowers the power-factor of the motor. Thus, to get good power-factor, the field self-inductance must be made low, that is, the field as ...", "... phase of voltage. In the series motor the self-inductance of the field causes the main current to lag behind the impressed voltage and thereby lowers the power-factor of the motor. Thus, to get good power-factor, the field self-inductance must be made low, that is, the field as weak and the armature as strong as possible. With such a strong armature, and weak field, the commutating pole is not sufficient to control magnetic distortion by the arma- ture re ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-82", "section_label": "Apparatus Section 3: Synchronous Converters: Variation of the Ratio of Electromotive Forces", "section_title": "Synchronous Converters: Variation of the Ratio of Electromotive Forces", "kind": "apparatus-section", "sequence": 82, "number": 3, "location": "lines 13796-13888", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-82/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-82/", "snippets": [ "... ed direct e.m.f., and the counter-generated alternating e.m.f. less than the impressed, due to the voltage consumed by the armature resistance. If the current in the converter is in phase with the impressed e.m.f., armature self-inductance has little effect, but reduces the counter-generated alternating e.m.f. below the impressed with a lagging and raises it with a leading current, in the same way as in a synchronous motor. Thus in general the ratio of vol ...", "... ating system of very large capacity, the impressed e.m.f. wave will be practically identical with the generator wave, while at the terminals of a converter connected to the generator over long lines with re- active coils or inductive regulators interposed, the wave of im- pressed e.m.f. may be so far modified by that of the counter e.m.f. of the converter as to resemble the latter much more than the generator wave, and thereby the ratio of conversion ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-03", "section_label": "Chapter 3: Law Of Electromagnetic Induction", "section_title": "Law Of Electromagnetic Induction", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 2012-2148", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-03/", "snippets": [ "... al formula of alternating-current induc- tion by sine waves. 15. If, in a circuit of n turns, the magnetic flux, , inclosed by the circuit is produced by the current in the circuit, the ratio, flux X number of turns X 10\"^ current ' is called the inductance, L, of the circuit, in henrys. The product of the number of turns, n, into the maximum flux, $, produced by a current of / amperes effective, or 7^/2 amperes maximum, is therefore n$ = LIV2 108; 18 ALTERNATING-CURRENT PHENOMENA and consequently the ...", "... mperes maximum, is therefore n$ = LIV2 108; 18 ALTERNATING-CURRENT PHENOMENA and consequently the effective e.m.f. of self-induction is E = V2 7rn$/10-8 = 2 wfLI volts. The product, x = 2 7r/L, is of the dimension of resistance, and is called the inductive reactance of the circuit; and the e.m.f. of self-induction of the circuit, or the reactance voltage, is E = Ix, and lags 90° behind the current, since the current is in phase with the magnetic flux produced by the current, and the e.m.f. lags 90° behin ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-19", "section_label": "Chapter 19: Induction Generators", "section_title": "Induction Generators", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 20446-21537", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-19/", "snippets": [ "... ction generator, due regard has to be taken of the decrease of frequency with increase of load, or what may be called the slip of frequency, s. Let, in an induction generator, Yo = go — jho = primary exciting admittance, Zo = To -\\- jxo = primary self-inductive impedance, Zi = ri + jxi = secondary self-inductive impedance, reduced to primary, all these quantities being reduced to the frequency of synchronism with the speed of the machine, /. Let e = generated em.f., reduced to full frequency. s = slip of fr ...", "... crease of frequency with increase of load, or what may be called the slip of frequency, s. Let, in an induction generator, Yo = go — jho = primary exciting admittance, Zo = To -\\- jxo = primary self-inductive impedance, Zi = ri + jxi = secondary self-inductive impedance, reduced to primary, all these quantities being reduced to the frequency of synchronism with the speed of the machine, /. Let e = generated em.f., reduced to full frequency. s = slip of frequency, thus: (1 — s) / = frequency generated by mac ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-03", "section_label": "Chapter 3: Iiaw Of Eucctbo-Maonimc Induction", "section_title": "Iiaw Of Eucctbo-Maonimc Induction", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 1973-2121", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-03/", "snippets": [ "... ent is called the inductanccy Z, of the circuit, in henrys. The product of the number of turns, n, into the maxi- mum flux, *, produced by a current of / amperes effective, or/V2 amperes maximum, is therefore — and consequently the effective E.M.F. of self-inductance is: = 2 IT NLI volts. The product, jr = 2 irNLy is of the dimension of resistance, and is called the reactance of the circuit ; and the E.M.F. of self-inductance of the circuit, or the reactance voltage, is E = Ix, and lags 90** behind the current, ...", "... ffective, or/V2 amperes maximum, is therefore — and consequently the effective E.M.F. of self-inductance is: = 2 IT NLI volts. The product, jr = 2 irNLy is of the dimension of resistance, and is called the reactance of the circuit ; and the E.M.F. of self-inductance of the circuit, or the reactance voltage, is E = Ix, and lags 90** behind the current, since the current is in phase with the magnetic flux produced by the current, and the E.M.F. lags 90° behind the magnetic flux. The E.M.F. lags 90° behind the magnet ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-12", "section_label": "Chapter 12: Power, And Double Frequency Quantities In General", "section_title": "Power, And Double Frequency Quantities In General", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 9381-9740", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "snippets": [ "... 's in graphical or symbolic representation. The graphical methods of treatment of alternating cur- rent phenomena are here extended to include double fre- quency quantities as power, torque, etc. P1 — =p = cos w = power factor. PJ — = q = sin w = inductance factor of the circuit, and the general expression of power is, = Q (cos co -\\-j sin o>) 104. The introduction of the double frequency vector product P = \\E I~\\ brings us outside of the limits of alge- 154 ALTERNATING-CURRENT PHENOMENA. bra, howev ...", "... om is for instance : If in a generator supplying power to a system the cur- rent is out of phase with the E.M.F. so as to give the watt- less power Pi, the current can be brought into phase with the generator E.M.F., or the load on the generator made non-inductive by inserting anywhere in the circuit an appa- ratus producing the wattless power — F$\\ that is, compen- sation for wattless currents in a system takes place regardless of the location of the compensating device. Obviously between the compensating device ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-15", "section_label": "Chapter 17: Inductor Machines", "section_title": "Inductor Machines", "kind": "chapter", "sequence": 15, "number": 17, "location": "lines 20294-20974", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-15/", "snippets": [ "... na?, is not the insignificant power of the telephone current, but is the high-frequency power generated by the alternator with telephonic excitation, and may be many kilowatts, thus permitting long- distance radio telephony. It is obvious, that the high inductance of the field coil, F, of the machine, Fig. 138, would make it impossible to force a tele- phone current through it, but the telephonic exciting current would be sent through the armature winding, which is of very low inductance, and by the use of the capa ...", "... t is obvious, that the high inductance of the field coil, F, of the machine, Fig. 138, would make it impossible to force a tele- phone current through it, but the telephonic exciting current would be sent through the armature winding, which is of very low inductance, and by the use of the capacity the armature made self-exciting by leading current. Instead of sending the high-frequency machine current, which pulsates in amplitude with telephonic frequency, through radio transmission and rectifying the receiving curr ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-11", "section_label": "Chapter 11: Instability Of Circuits: Induction And Syn Chronous Motors", "section_title": "Instability Of Circuits: Induction And Syn Chronous Motors", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 21382-22633", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-11/", "snippets": [ "... synchronizing power ifa and_ the damping power wi, and is shown by the dotted Fio. 104. curve v>. As seen, under the assumption or Pig. 104, in this case a rapid damping occurs. If the damping winding, which consumes a part of all the power, Wi, is inductive — and to a shght extent it always is — the current in the damping winding lags behind the e.m.f. induced in it by the oscillation, that is, lags behind the speed, v. The power, wt, 212 ELECTRIC CIRCUITS or that part of it which is current times voltage ...", "... sly negative or damping, but contains a positive period, and its average is greatly reduced, as shown by the drawn curve, wi, in Fig. 104, that is, inductivity of the damper winding is very harmful, and it is essential to design the damper winding as non- inductive as possible to give efficient damping. With the change of position, p, the current, and thus the ar- mature reaction, and with it the magnetic flux of the machine, changes. A flux change can not be brought about instantly, as it represents energy stored, ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-15", "section_label": "Chapter 15: Constant-Voltage Series Operation", "section_title": "Constant-Voltage Series Operation", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 27996-29301", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-15/", "snippets": [ "... e-shape distortion between current and voltage changes, as with increasing p, more and more saturated reactors are thrown into the circuit and dis- tort the current wave. As 61 is shunted by gf, and carries a small part of the current only, and g is non-inductive, the change of wave shape in 61 will be less, and as 61 carries only a part of the current, the effect of the change of wave shape in 61 thus is practically neg- ligible, so that 61 can be assumed as constant and independent of p. 62, however, carries th ...", "... f p. 62, however, carries the total current, at fairly high saturation, and thus exerts a great distorting effect. At and near full-load, with all or nearly all conductances, g, in 312 ELECTRIC CIRCUITS circuit, the entire circuit is practically non-inductive, that is, the current has the same wave shape as the voltage. Assuming a sine wave of impressed voltage, eo, the current, i, at and near full- load thus is practically a sine wave, and the shunting reactance, 62, thus has the value corresponding to a sine ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-06", "section_label": "Chapter 2: Long Distance Transmission Line. 279", "section_title": "Long Distance Transmission Line. 279", "kind": "chapter", "sequence": 6, "number": 2, "location": "lines 755-835", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-06/", "snippets": [ "... CONTENTS. xix PAGE 11. Example of 60,000-volt 200-mile line. 292 12. Comparison of result with different approximate calcula- tions. 294 13. Wave length and phase angle. 295 14. Zero phase angle and 45-degree phase angle. Cable of negligible inductance. 296 15. Examples of non-inductive, lagging and leading load, and discussion of flow of energy. 297 16. Special case: Open circuit at end of line. 299 17. Special case: Line grounded at end. 304 18. Special case : Infinitely long conductor. 305 19 ...", "... of 60,000-volt 200-mile line. 292 12. Comparison of result with different approximate calcula- tions. 294 13. Wave length and phase angle. 295 14. Zero phase angle and 45-degree phase angle. Cable of negligible inductance. 296 15. Examples of non-inductive, lagging and leading load, and discussion of flow of energy. 297 16. Special case: Open circuit at end of line. 299 17. Special case: Line grounded at end. 304 18. Special case : Infinitely long conductor. 305 19. Special case: Generator feeding int ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-35", "section_label": "Chapter 13: Transient Term Of The Rotating Field", "section_title": "Transient Term Of The Rotating Field", "kind": "chapter", "sequence": 35, "number": 13, "location": "lines 13936-14548", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-35/", "snippets": [ "... is closed, while in all preced- ing investigations the transient term depended upon the point of the wave at which the circuit was closed, and that this tran- sient term is oscillatory. In the preceding chapter, in circuits containing only resistance and inductance, the transient term has always been gradual or logarithmic, and oscillatory phenom- ena occurred only in the presence of capacity in addition to in- ductance. In the rotating field, or the polyphase m.m.f., we thus have a case where an oscillatory transie ...", "... , and oscillatory phenom- ena occurred only in the presence of capacity in addition to in- ductance. In the rotating field, or the polyphase m.m.f., we thus have a case where an oscillatory transient term occurs in a circuit containing only resistance and inductance but not capacity, and where this transient term is independent of the point of the wave at which the circuits were closed, that is, is always the same, regardless of the moment of start of the phe- nomenon. The transient term of the polyphase m.m.f. thu ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-54", "section_label": "Chapter 5: Free Oscillations", "section_title": "Free Oscillations", "kind": "chapter", "sequence": 54, "number": 5, "location": "lines 31451-32708", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "snippets": [ "... f the problem. Upon the values of these integration constants C and C' largely depends the difference between the phenomena occurring in electric circuits, as those due to direct currents or pulsating currents, alternating currents, oscillating currents, inductive dis- charges, etc., and the study of the terminal conditions thus is of the foremost importance. 29. By free oscillations are understood the transient phe- nomena occurring in an electric circuit or part of the circuit to which neither electric energy i ...", "... gy storage in more than one form so as to allow 478 FREE OSCILLATIONS 479 an interchange or surge of energy between its different forms, electromagnetic and electrostatic energy. Free oscillations occur only in circuits containing both capacity C and inductance, L. The absence of energy supply or abstraction defines the free oscillations by the condition that the power p = ei at the two ends of the circuit or section of the circuit must be zero at all times, or the circuit must be closed upon itself. The latt ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-04", "section_label": "Lecture 4: The Characteristics Of Space A. The Geometry Of The Gravitational Field", "section_title": "The Characteristics Of Space A. The Geometry Of The Gravitational Field", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3595-6820", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-04/", "snippets": [ "... in projective Harmonic relation geometry, 108 as non-metric, 110 Hertz, 17, 21 Hyperbolic geometry, 64, 72, 74 Hypersurface, 88 Hypothesis of ether abandoned, 16 Imaginary number, meaning, 38 rotation, meaning, 39 representing relativity, 35 Inductance and wave velocity, 23 Inertial mass, 47 Infinitely distant elements in geom- etry, 96 Intensity of dielectric field, 47 of gravitational field, 47 of magnetic field, 47 Interference of light, 13 K Kinetic energy, 44, 47 Kinks, in space, 90 L ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-03", "section_label": "Lecture 3: Light And Power Distribution", "section_title": "Light And Power Distribution", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 983-1526", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-03/", "snippets": [ "... current motors starting with the same torque on the same voltage; and the current of the alternating current motor is lagging, the voltage drop caused by it in the reactance is therefore far greater than would be caused by the same current taken by a non-inductive load, as lamps. Furthermore, alternating current supply mains usually are of far smaller capacity, and therefore more affected in voltage. Large motors are therefore rarely connected to the lighting mains of an alternating current system, but separate tr ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-08", "section_label": "Lecture 8: Generation", "section_title": "Generation", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 3781-4217", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-08/", "snippets": [ "... moment of short circuiting such an alternator, the field current rises to several times its normal value, and becomes pulsating, of double frequency. Gradually the armature cur- rent and the field current die down to their normal values. By inserting non-inductive resistance in the field circuit of the alternator, the field current, which is induced in the moment of short circuit, can be forced to die out more rapidly, and the armature short circuit current made thereby to reach its final value more quickly, that i ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-11", "section_label": "Lecture 11: Lightning Protection", "section_title": "Lightning Protection", "kind": "lecture", "sequence": 11, "number": 11, "location": "lines 4931-5294", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-11/", "snippets": [ "... arc light circuits, that is, constant current circuits, horn gap arresters with series resistance are generally used, especially on direct current arc circuits, in which the multi-gap is not permissible. In such circuits of limited current, and very high inductance, the series resistance is not objectionable. Other- wise the horn gap arrester is still occasionally used outdoors as emergency arrester on transmission lines, set for a much higher discharge voltage than the station arrester, and then preferably without ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-16", "section_label": "Lecture 16: The Incandescent Lamp", "section_title": "The Incandescent Lamp", "kind": "lecture", "sequence": 16, "number": 16, "location": "lines 9687-9919", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-16/", "snippets": [ "... n the incandescent lamp the current flows through a solid conductor, usually in a vacuum, and the heat produced in the resistance of the conductor makes it incandescent, thus giving the light. Incandescent lamps in an electric circuit therefore act as non-inductive ohmic resistance and can there- fore be operated equally well on constant potential as on con- stant current. As electric distribution systems are always constant potential, most incandescent lamps are operated on constant potential ; and only for outdoor ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "... ensity with _J [ I m v. ^ ,/ YELLOW <^^-^_ ^ BLUE VlO increasing vapor pressure. To show you this I use a U-shaped FlG- 42- mercury lamp constructed as shown half size in Fig. 43. I con- nect the lamp into a 220-volt direct-current circuit, with an inductive resistance in series thereto, to limit the current, and 120 RADIATION, LIGHT, AND ILLUMINATION. start the arc by pouring some mercury over from one side to the other. Immediately after starting the lamp you see no red lines in the low-power spectro ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-01", "section_label": "Theory Section 1: Magnetism and Electric Current", "section_title": "Magnetism and Electric Current", "kind": "theory-section", "sequence": 1, "number": 1, "location": "lines 477-909", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-01/", "snippets": [ "... tance transmission line carrying 7 amperes of current, if Id = 0.82 cm. is the diam- eter of the conductors (No. 0 B. & S.), 18 = 45 cm. the spacing or distance between them? FIG. 2. — Diagram of transmission line for inductance calculation. At distance lr from the center of one of the conductors (Fig. 2), the length of the magnetic circuit surrounding this conductor is 2irlr) the m.m.f., 7 ampere-turns; thus the magnetizing force / = s— r> an ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-16", "section_label": "Theory Section 16: Phase Control of Transmission Lines", "section_title": "Phase Control of Transmission Lines", "kind": "theory-section", "sequence": 16, "number": 16, "location": "lines 6222-6813", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-16/", "snippets": [ "16. PHASE CONTROL OF TRANSMISSION LINES 76. If in the receiving circuit of an inductive transmission line the phase relation can be changed, the drop of voltage in the line can be maintained constant at varying loads or even decreased with increasing load; that is, at constant generator voltage the transmissio ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-31", "section_label": "Apparatus Section 10: Synchronous Machines: Efficiency and Losses", "section_title": "Synchronous Machines: Efficiency and Losses", "kind": "apparatus-section", "sequence": 31, "number": 10, "location": "lines 9651-9718", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-31/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-31/", "snippets": [ "... sistance loss in the field circuit of 800 watts, at EQ = 1000, and a load loss at full load of 600 watts. The loss curves and efficiency curves are plotted in Fig. 70 for the generator, with the current output at non-inductive load or 0 = 0 as abscissas, and in Fig. 71 for the synchronous motor, with the mechanical power output as abscissas." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-32", "section_label": "Apparatus Section 11: Synchronous Machines: Unbalancing of Polyphase Synchronous Machines", "section_title": "Synchronous Machines: Unbalancing of Polyphase Synchronous Machines", "kind": "apparatus-section", "sequence": 32, "number": 11, "location": "lines 9719-9748", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-32/", "snippets": [ "... the current is different in the different branches, the terminal voltage must become different also, more or less. This is called the unbalancing of the polyphase generator. It is due to different load or load of different inductance factor in the different branches. Inversely, in a polyphase synchronous motor, if the terminal voltages of the different branches are unequal, due to an unbal- ancing of the polyphase circuit, the synchronous motor takes mor ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-36", "section_label": "Apparatus Section 15: Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "section_title": "Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "kind": "apparatus-section", "sequence": 36, "number": 15, "location": "lines 9918-10123", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-36/", "snippets": [ "... current. If, however, alternators are operated in parallel over a circuit of appreciable resistance, as two stations at some distance from each other are synchronized, especially if the resistance between the stations is non-inductive, as underground cables, with alter- nators of very low reactance, as turbo alternators, the synchro- nizing power may be insufficient. In this case, reactance has to be inserted between the stations, to lag the cross current ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-37", "section_label": "Apparatus Section 16: Synchronous Machines: Higher Frequency Cross Currents Between Synchronous Machines", "section_title": "Synchronous Machines: Higher Frequency Cross Currents Between Synchronous Machines", "kind": "apparatus-section", "sequence": 37, "number": 16, "location": "lines 10124-10189", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-37/", "snippets": [ "... e system to which they are connected. The intensity of these cross currents is the difference of the corresponding harmonics of the machines divided by the impe- dance between the machines. This impedance includes the self- inductive reactance of the machine armatures. The reactance obviously is that at the frequency of the harmonic, that is, if x = reactance at fundamental frequency, it is nx for the nth harmonic. In most cases these cross currents ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-88", "section_label": "Apparatus Section 10: Synchronous Converters: Frequency", "section_title": "Synchronous Converters: Frequency", "kind": "apparatus-section", "sequence": 88, "number": 10, "location": "lines 15811-15892", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-88/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-88/", "snippets": [ "... are necessary than at 25 cycles, and the 60-cycle converter, though still within conserva- tive limits, does not permit as conservative commutator design, especially at higher voltage, as a low-frequency converter, and a lower self-inductance of commutation thus must be aimed at than permissible in a 25-cycle converter, the more so as the fre- quency of commutation (half the number of commutator seg- ments per pole times frequency of rotation) necessarily is hig ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-89", "section_label": "Apparatus Section 11: Synchronous Converters: Double-current Generators", "section_title": "Synchronous Converters: Double-current Generators", "kind": "apparatus-section", "sequence": 89, "number": 11, "location": "lines 15893-15982", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-89/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-89/", "snippets": [ "... can be overcome by a series field. The reaction on the field of the alternating-current load when feeding converters can be compensated for by a change of phase relation, by means of a series field on the converter, with self- inductance in the alternating lines, or reactive coils at the converters. Thus, a double-current generator feeding on the alternating side converters can be considered as a direct-current generator in which a part of the commutator, w ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-91", "section_label": "Apparatus Section 13: Synchronous Converters: Direct-current Converter", "section_title": "Synchronous Converters: Direct-current Converter", "kind": "apparatus-section", "sequence": 91, "number": 13, "location": "lines 16065-16540", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-91/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-91/", "snippets": [ "... B^ the position of brushes, represent the currents in the individual armature coils. The current changes from A to A' at the moment 0 = r when the respective armature coil passes the brush, twice per period. Due to the inductance of the armature coils, which opposes the change of current, the current waves are not perfectly triangular, but differ somewhat therefrom. With n autotransformers, each autotransformer lead carries the current — , which pass ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-02", "section_label": "Chapter 2: Instantaneous Values And Integral Values", "section_title": "Instantaneous Values And Integral Values", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 1684-2011", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-02/", "snippets": [ "... ave is a wave in which one of the half- waves pre- ponderates, as in Fig. 5. By electromagnetic induction, pulsating waves are produced only by commutating and unipolar machines (or by the super- position of alternating upon direct currents, etc.). All inductive apparatus without commutation give exclusively alternating waves, because, no matter what conditions may exist in the circuit, any line of magnetic force which during a complete period is cut by the circuit, and thereby generates an e.m.f., must during th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-07", "section_label": "Chapter 7: Polar Coordinates And Polar Diagrams", "section_title": "Polar Coordinates And Polar Diagrams", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 3619-4087", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-07/", "snippets": [ "... sformed into it by reversing right and left, or top and bottom. So the crank diagram, Fig. 47, is the image of the polar diagram, Fig. 46. In symbolic representation, based upon the crank diagram, the impedance was denoted by Z = r -\\- jx, where x == inductive reactance. In the polar diagram, the impedance thus is denoted by: Z = r — jx since the latter is the mirror image of the crank diagram, that is, differs from it symbolically by the interchange of + j and — j. A treatise written in the symbolic repre- ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-16", "section_label": "Chapter 16: Power, And Double-Frequency Quantities In", "section_title": "Power, And Double-Frequency Quantities In", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 16077-16520", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-16/", "snippets": [ "... erefrom is, for instance: If in a generator supplying power to a system the current is out of phase with the e.m.f. so as to give the reactive power P', the current can be brought into phase with the generator e.m.f. or the load on the generator made non-inductive by in- serting anywhere in the circuit an apparatus producing the react- ive power — P'; that is, compensation for wattless currents in a system takes place regardless of the location of the compensating device. • Obviously, wattless currents exist betw ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-25", "section_label": "Chapter 25: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 29375-32539", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-25/", "snippets": [ "... rical distor- tion of the wave which makes the wave of generated e.m.f. differ by more than 90° from the current wave and thereby represents power — the power consumed by hysteresis. In practice both effects are always superimposed; that is, in a ferric inductive reactance, a distortion of wave-shape takes place due to the lack of proportionality between magnetism and m.m.f. as expressed by the variation in the hysteretic cycle. This pulsation of reactance gives rise to a distortion con- sisting mainly of a tripl ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-32", "section_label": "Chapter 32: Transformation Of Polyphase Systems", "section_title": "Transformation Of Polyphase Systems", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 36062-36514", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-32/", "snippets": [ "... in the same manner as the primaries in Fig. 210. Since in this system each phase is transformed by a separate transformer, the voltages of the system remain balanced even at unbalanced load, within the limits of voltage variation due to the internal self-inductive impedance (or short-circuit impedance) of the transformers — which is small, while the exciting impedance (or open-circuit impedance) of the transformers, which causes the unbalancing in the Y-delta connection above discussed is enormous. 3. Y-Y connect ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-34", "section_label": "Chapter 34: Metering Of Polyphase Circuit", "section_title": "Metering Of Polyphase Circuit", "kind": "chapter", "sequence": 34, "number": 34, "location": "lines 37128-37452", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-34/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-34/", "snippets": [ "... the three-phase system is the sum of the individual powers of the three branch circuits. 302. In the standard polyphase wattmeter connection of the three-wire, three-phase system, Fig. 219, the voltage coils are out of phase with the current coils at non-inductive load, the one lagging, the other leading by 30°. Therefore, even in a balanced W -OD- Fig. 221. system, if the current lags, the two wattmeter coils do not read alike, as the voltmeter coil in the one lags by the angle of lag of the current plus ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-02", "section_label": "Chapter 2: Chapter II", "section_title": "Chapter II", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 1728-1972", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-02/", "snippets": [ "... lsating wave is a wave in which one of the half- waves preponderates, as in Fig, 5. Pulsating waves are produced only by commutating machines, and by unipolar machines (or by the superposi- tion of alternating waves upon continuous currents, etc.). All inductive apparatus without commutation give ex- clusively alternating waves, because, no matter what con- S. PmmUog WwK. ditions may exist in the circuit, any line of magnetic force, which during a complete period is cut by the circuit, and thereby induces an ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-14", "section_label": "Chapter 14: The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "section_title": "The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14089-14918", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "snippets": [ "... current y El k Hye ^ • ' \"■ Zi + Z \" (ri + r) - yx (x^ + x) ' Secondary terminal voltage E\\ = El — -^Zi = /yZ = snie \\ 1 ri-jsxi ) _ snie{r^jsx) ^ \\ {ri + r)-'js{xi + x)) (ri+r) ^js{xi + x) ♦ This applies to the case where the secondary contains inductive reac- tance only : or, rather, that kind of reactance which is proportional to the fre- quency. In a condenser the reactance is inversely proportional to the frequency in a synchronous motor under circumstances independent of the frequency. Thus, in gener ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-19", "section_label": "Chapter 19: Commutatob Motobs", "section_title": "Commutatob Motobs", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 21339-22387", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "snippets": [ "... in- duced, and thus the action is due to the repulsive thrust between induced current and inducing magnetism. As stated under the heading of induction motors, a multiple circuit armature is required for the purpose of having always secondary circuits in inductive relation to the primary circuit during the rotation. If with a single- coil field, these secondary circuits are constantly closed upon themselves as in the induction motor, the primary circuit will not exert a rotary effect upon the armature while at res ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-02", "section_label": "Chapter 2: Instantaneous Values And Integral Values", "section_title": "Instantaneous Values And Integral Values", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 1367-1605", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-02/", "snippets": [ "... wave is a wave in which one of the half- waves preponderates, as in Fig. 5. By electromagnetic induction, pulsating waves are pro- duced only by commutating and unipolar machines (or by the superposition of alternating upon direct currents, etc.). All inductive apparatus without commutation give ex- clusively alternating waves, because, no matter what con- Fig. 5. Pulsating Wave. ditions may exist in the circuit, any line of magnetic force, which during a complete period is cut by the circuit, and thereby in ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-20", "section_label": "Chapter 20: Commutator Motors", "section_title": "Commutator Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 19458-20501", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "snippets": [ "... n- duced, arid thus the action is due to the repulsive thrust between induced current and inducing magnetism. As stated under the heading of induction motors, a multiple circuit armature is required for the purpose of having always secondary circuits in inductive relation to the primary circuit during the rotation. If with a single- coil field, these secondary circuits are constantly closed upon themselves as in the induction motor, the primary circuit will not exert a rotary effect upon the armature while at res ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-05", "section_label": "Chapter 6: Induction-Motor Regulation And Stability", "section_title": "Induction-Motor Regulation And Stability", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 10583-12397", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-05/", "snippets": [ "... ristic made inferior to that given at constant voltage supply, the more so the higher the voltage drop in the supply circuit. Assuming then a three-phase motor having the following con- stants: primary exciting admittance, Y = 0.01 — 0.1 j; primary self-inductive impedance, Z0 = 0.1 + 0.3 j; secondary self -induc- 123 124 ELECTRICAL APPARATUS tive impedance, Z, = 0.1 + 0.3 j; supply voltage, e0 = 110 volts, and rated output, 5000 waits per phase. Assuming this motor to be operated: 1. By transformers of ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-07", "section_label": "Chapter 8: Synchronizing Induction Motors", "section_title": "Synchronizing Induction Motors", "kind": "chapter", "sequence": 7, "number": 8, "location": "lines 13956-14465", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-07/", "snippets": [ "... ltiple with each other to a common resistance, r, and neglecting for simplicity the exciting current and the vol- tage drop in the impedance of the motor primaries as not mate- rially affecting the synchronizing power. Let Zi — n + ./j-t = secondary self-inductive impedance at full frequency; s = slip of the two motors, as fraction of syn- chronism; Co = absolute value of impressed voltage and thus, when neglecting the primary impedance, of the voltage generated iu the primary by the rotating field. If then Ihe t ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-19", "section_label": "Chapter 21: Regulating Pole Converters", "section_title": "Regulating Pole Converters", "kind": "chapter", "sequence": 19, "number": 21, "location": "lines 30088-31715", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-19/", "snippets": [ "... polarity, the othtf section must be increased by approximately the same amount] to maintain the same alternating voltage. When changing the direct voltage by mechanically shifting the brushes, as soon as the brushes come under the field pole faces, self-inductive sparking on the commutator would result if the iron of the field poles were not kepi away from the brush REGULATING POLE CONVERTERS 425 position by having a slot in the field poles, as indicated in dotted line in Fig. 196 and Fig. 198, B. With the arra ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-01", "section_label": "Chapter 1: Electric Conduction. Soled And Liquid", "section_title": "Electric Conduction. Soled And Liquid", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 959-3894", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-01/", "snippets": [ "... d also inside thereof. The phenomena outside of the conductor are conditions of stress in space which are called the electric field, the two main components of the electric field being the electromagnetic component, characterized by the cir- cuit constant inductance, L, and the electrostatic component, characterized by the electric circuit constant capacity, C. Inside of the conductor we find a conversion of energy into heat; that is, electric power is consumed in the conductor by what may be considered as a kind of ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-16", "section_label": "Chapter 3: Standing Waves. 442", "section_title": "Standing Waves. 442", "kind": "chapter", "sequence": 16, "number": 3, "location": "lines 1087-1111", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-16/", "snippets": [ "... -potential underground power cable. Character of waves. Numerical example. General equations. 452 18. Submarine telegraph cable. Existence of logarithmic waves. 454 19. Long distance telephone circuit. Numerical example. Effect of leakage. Effect of inductance or \"loading.\" 454" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-17", "section_label": "Chapter 4: Traveling Waves. 457", "section_title": "Traveling Waves. 457", "kind": "chapter", "sequence": 17, "number": 4, "location": "lines 1112-1147", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-17/", "snippets": [ "CHAPTER IV. TRAVELING WAVES. 457 20. Different forms of the equations of the traveling wave. 457 CONTENTS. xxiii PAGE 21. Component waves and single traveling wave. Attenua- tion. 459 22. Effect of inductance, as loading, and leakage, on attenu- ation. Numerical example of telephone circuit. 462 23. Traveling sine wave and traveling cosine wave. Ampli- tude and wave front. 464 24. Discussion of traveling wave as function of distance, and of time. 466 2 ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-37", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 37, "number": 1, "location": "lines 15354-15625", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "snippets": [ "... ch change of circuit conditions takes place and is calculated independently of the other change, or the periodic recurrence. A number of such cases have been discussed in Section I, as for instance, the effect of cutting a resistor in and out of a divided inductive circuit, paragraph 75, Fig. 33. In this case, four successive changes are made before the cycle recurs: a resistor is cut in, in two steps, and cut out again in two steps, but at each change, sufficient time elapses to reach practically permanent conditio ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-38", "section_label": "Chapter 2: Circuit Control By Periodic Transient Phenomena", "section_title": "Circuit Control By Periodic Transient Phenomena", "kind": "chapter", "sequence": 38, "number": 2, "location": "lines 15626-15962", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-38/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-38/", "snippets": [ "... riodic transient phenomena, used for the control of electric circuits, may be considered an automatic potential regulator operating in the field circuit of the exciter of an alternating current system. Let, r0 = 40 ohms = resistance and L = 400 henrys = inductance of the exciter field circuit. A resistor, having a resistance, rl = 24 ohms, is inserted in series to r0, L in the exciter field, and a potential magnet, con- trolled by the alternating current system, is arranged so as to short circuit resistance, rv if ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-44", "section_label": "Chapter 4: Distributed Capacity Of High-Potential Transformers", "section_title": "Distributed Capacity Of High-Potential Transformers", "kind": "chapter", "sequence": 44, "number": 4, "location": "lines 23179-23585", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "snippets": [ "... considerably less in small transformers — the high- potential coil contains a large number of turns, a great length of conductor, and therefore its electrostatic capacity is appreciable, and such a coil thus represents a circuit of distributed resistance, inductance, and capacity somewhat similar to a transmission line. The same applies to reactive coils, etc., wound for very high voltages, and even in smaller reactive coils at very high frequency. This capacity effect is more marked in smaller transformers, where ..." ] } ] }, { "id": "frequency", "label": "Frequency", "aliases": [ "Frequency", "cycles per second", "frequencies", "frequency", "periodicity" ], "total_occurrences": 2694, "matching_section_count": 218, "matching_source_count": 14, "source_totals": [ { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 568, "section_count": 21 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 481, "section_count": 38 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 271, "section_count": 22 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 222, "section_count": 25 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 216, "section_count": 7 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 205, "section_count": 38 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 188, "section_count": 8 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 163, "section_count": 20 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 102, "section_count": 6 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 92, "section_count": 14 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 86, "section_count": 6 }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 59, "section_count": 4 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 32, "section_count": 6 }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 9, "section_count": 3 } ], "section_hits": [ { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-11", "section_label": "Chapter 12: Frequency Converter Or General Alternating Current Transformer", "section_title": "Frequency Converter Or General Alternating Current Transformer", "kind": "chapter", "sequence": 11, "number": 12, "location": "lines 14897-17124", "status": "candidate", "occurrence_count": 213, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-11/", "snippets": [ "CHAPTER XII FREQUENCY CONVERTER OR GENERAL ALTERNATING- CURRENT TRANSFORMER 103. In general, an alternating-current transformer conafete of a magnetic circuit, interlinked with two electric circuits or sets of electric circuits, the primary circuit, in which power, sup- plie ...", "... sist* of a magnetic circuit interlinked with two sets of electric circuits, the primary and the secondary, which are mounted rotatably with regards to each other. It transforms between primary electrical and secondary electrical power, and also between FREQUENCY CONVERTER 177 electrical and mechanical power. As the frequency of the re- volving secondary is the frequency of slip, thus differing from the primary, it follows, that the general alternating-current transformer changes not only voltages and current, bu ...", "... circuits, the primary and the secondary, which are mounted rotatably with regards to each other. It transforms between primary electrical and secondary electrical power, and also between FREQUENCY CONVERTER 177 electrical and mechanical power. As the frequency of the re- volving secondary is the frequency of slip, thus differing from the primary, it follows, that the general alternating-current transformer changes not only voltages and current, but also frequencies, and may therefore be called \"frequency conver ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 77, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... body to a 230 GENERAL LECTURES high temperature. Then the heat energy is converted into radi- ation and issues from the heated body, as for instance an incan- descent lamp filament, as a mass of radiations of different wave lengths, that is, different frequencies. All kinds of frequencies appear : from very low frequencies, that is only a few millions of millions of cycles per second, up to many times higher frequencies. We can get, if we desire, still very much lower fre- quencies, as electromagnetic waves, such ...", "... ECTURES high temperature. Then the heat energy is converted into radi- ation and issues from the heated body, as for instance an incan- descent lamp filament, as a mass of radiations of different wave lengths, that is, different frequencies. All kinds of frequencies appear : from very low frequencies, that is only a few millions of millions of cycles per second, up to many times higher frequencies. We can get, if we desire, still very much lower fre- quencies, as electromagnetic waves, such as the radiation sent out ...", "... heat energy is converted into radi- ation and issues from the heated body, as for instance an incan- descent lamp filament, as a mass of radiations of different wave lengths, that is, different frequencies. All kinds of frequencies appear : from very low frequencies, that is only a few millions of millions of cycles per second, up to many times higher frequencies. We can get, if we desire, still very much lower fre- quencies, as electromagnetic waves, such as the radiation sent out by an oscillating current or an alt ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 72, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "... which receives electric power and converts it into mechanical power, and the primary or stator of the induc- tion machine thus corresponds to the armature of the synchro- nous or commutating machine. In the secondary or rotor of the induction machine, low-frequency currents — of the frequency of slip — are induced by the primary, but the magnetic field flux is produced by the exciting current which traverses the primary or armature or stator. Thus the induction machine may be considered as a machine in which the mag ...", "... r and converts it into mechanical power, and the primary or stator of the induc- tion machine thus corresponds to the armature of the synchro- nous or commutating machine. In the secondary or rotor of the induction machine, low-frequency currents — of the frequency of slip — are induced by the primary, but the magnetic field flux is produced by the exciting current which traverses the primary or armature or stator. Thus the induction machine may be considered as a machine in which the magnetic field is produced by ...", "... a lesaer exciting current in the rotor — at least the power-factor increased. Various such methods of secondary excitation have been pro- posed, and to some extent used. 1. Passing a direct current through the rotor for excitation. In this case, as the frequency of the secondary currents is the frequency of slip, with a direct current, the frequency is zero, that is, the motor becomes a synchronous motor. 2. Excitation through commutator, by the alternating supply current, either in shunt or in series to the ar ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 59, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... from each other by a fractional wave length is called iridescence. Iridescent colors, for instance, are those of mother-of-pearl, of opal, of many butterflies, etc. Light, therefore, is a wave motion. NATURE AND DIFFERENT FORMS OF RADIATION. 1 The frequency of radiation follows from the velocity of light, and the wave length. The average wave length of visible radiation, or light, is about lw = 60 microcentimeters,* that is, 60 X 10~8 cm. (or about ^ to), the other the voltage phase (0+w). We may assume the alternators as of equal voltage, since a voltage difference superpos ...", "... n by: 2E 2 = sin co sin (d> a) cos ( co) z E 2 f 1 = sin co sin { (20 a co)+sin (co cm Z I J E 2 E 2 E 2 = sin co sin (2 a 0))+^- cos a jr- cos (2co a) (4) ^7 ^7 The phase angle co of the EMF is not constant, but pulsates with approximately constant low frequency, the frequency of the beat, and decreasing amplitude. co =co oe = maximum value of the phase angle, then may approximately represent the gradually decreasing amplitude of the phase angle, where a = attenuation of the beat or oscillation, and -at . ... co=a>oo ...", "... n co sin (d> a) cos ( co) z E 2 f 1 = sin co sin { (20 a co)+sin (co cm Z I J E 2 E 2 E 2 = sin co sin (2 a 0))+^- cos a jr- cos (2co a) (4) ^7 ^7 The phase angle co of the EMF is not constant, but pulsates with approximately constant low frequency, the frequency of the beat, and decreasing amplitude. co =co oe = maximum value of the phase angle, then may approximately represent the gradually decreasing amplitude of the phase angle, where a = attenuation of the beat or oscillation, and -at . ... co=a>oo sin pc/> (5; w ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2162-2971", "status": "candidate", "occurrence_count": 32, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "snippets": [ "... al or permanent short- circuit current, and this excess current usually decreases very slowly, lasting for many cycles. At the same time, a big cur- rent rush occurs in the field. This excess field current shows curious pulsations, of single and of double frequency, and in the beginning the armature currents also show unsymmetrical shapes. Some oscillograms of three-phase, quarter-phase, and single-phase short circuits of turboalternators are shown in Figs. 25 to 28. By considering the transients of energy storage ...", "... r duration than the short-circuit transient of its field, the more so, the greater m, that is, the larger the ratio of momentary to permanent short-circuit current. In Fig. 21 the decrease of the transient is shown greatly exagger- ated compared with the frequency of the armature currents, and Fig. 22 shows the curves more nearly in their actual proportions. The preceding would represent the short-circuit phenomena, if there were no armature transient. However, the armature cir- cuit contains inductance also, that ...", "... nce its m.m.f. minus the armature reaction gives the resultant field excitation corresponding to flux $>. The starting transient of the polyphase armature reaction thus appears in the field current, as shown in Fig. 22(7, as an oscillation of full machine frequency. As the mutual induction between armature and field circuit is not perfect, the transient pulsation of armature reaction appears with reduced amplitude in the field current, and this reduction is the greater, the poorer the mutual inductance, that is, the ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2485-3386", "status": "candidate", "occurrence_count": 31, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-04/", "snippets": [ "... or permanent short- circuit current, and this excess current usually decreases fairly slowly, lasting for many cycles. At the same time, a big cur- rent rush occurs in the field. This excess field current shows curious pulsations, of single and of double frequency, and in the beginning the armature currents also show unsymmetrical shapes. Some oscillograms of three-phase, quarter-phase, and single-phase short circuits of turboalternators are shov/n in Figs. 25 to 28. By considering the transients of energy storag ...", "... r duration than the short-circuit transient of its field, the more so, the greater m, that is, the larger the ratio of momentary to permanent short-circuit current. In Fig. 21 the decrease of the transient is shown greatly exagger- ated compared with the frequency of the armature currents, and Fig. 22 shows the curves more nearly in their actual proportions. The preceding would represent the short-circuit phenomena, if there were no armature transient. However, the armature cir- cuit contains inductance also, that ...", "... since its m.m.f. minus the armature reaction gives the resultant field excitation corresponding to flux $. The starting transient of the polyphase armature reaction thus appears in the j&eld current, as shown in Fig. 22C, as an oscillation of full machine frequency. As the mutual induction between armature and field circuit is not perfect, the transient pulsation of armature reaction appears with reduced amplitude in the field current, and this reduction is the greater, the poorer the mutual inductance, that is, the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "section_label": "Chapter 14: Dielectric Losses", "section_title": "Dielectric Losses", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 31, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "... densive reactance, which may be repre- sented by an \"effective resistance of dielectric losses\" or an \"effective conductance of dielectric losses.\" In the alternating magnetic field, power is consumed by mag- netic hysteresis. This is proportional to the frequency, and to the 1.6*'' power of the magnetic density, and is considerable, amounting in a closed magnetic circuit to 40 to 60 per cent, of the total volt-amperes. In the dielectric field, the energy losses usually are very much smaller, rarely amounting to ...", "... tial or local breakdown of the electrostatic field, and dielectric hysteresis or phenomena of similar nature. It is doubtful whether a true dielectric hysteresis, that is, a molecular dielectric friction, exists. A dielectric loss, propor- tional to the- frequency and to the 1.6*^' power of the dielectric field: P = njD'-^ has been observed in rotating dielectric fields, but is so small, that it usually is overshadowed by the other losses. In alternating dielectric fields in solid materials, such as in condens ...", "... pproximately constant power-factor of the elec- tric energizing circuit, over a wide range of voltage and of fre- quency, from less than a fraction of 1 per cent, up to a few per cent. 150 DIELECTRIC LOSSES 151 Constancy of the power-factor with the frequency, means that the loss is proportional to the frequency, as the current i, and thus the volt-ampere input, ei, are proportional to the frequency. Constancy of the power-factor with the voltage, means that the loss is proportional to the square of the voltag ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-18", "section_label": "Chapter 20: Single-Phase Commutator Motors", "section_title": "Single-Phase Commutator Motors", "kind": "chapter", "sequence": 18, "number": 20, "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 31, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "... e efficient acceleration under heavy torque is necessary. As generators, they would be of advantage for the generation of very low fre- quency, since in this case synchronous machines are uneconom- ical, due to their very low speed, resultant from the low frequency. The direction of rotation of a direct-current motor, whether shunt or series motor, remains the same at a reversal of the im- pressed e.m.f., as in this case the current in the armature circuit and the current in the field circuit and so the field magne ...", "... not useful but wattless, and therefore harmful in lowering the power- factor, hence must be kept as low as possible. This e.m.f. of self-inductance of the field, e0, is proportional to the field strength, $, to the number of field turns, n0, and to the frequency, /, of the impressed e.m.f. : eo = 2 ir/no* 10\"8, (1) while the useful e.m.f. generated by the field in the armature conductors, or \"e.m.f. of rotation,\" e, is proportional to the field strength, $, to the number of armature turns, nh and to the fre- q ...", "... and (2): tan 6 - { -°- (5) Small angle of lag and therewith good power-factor therefore require high values of /0 and n\\ and low values of / and n0. High /o requires high motor speeds and as large number of poles as possible. Low / means low impressed frequency; there- fore 25 cycles is generally the highest frequency considered for large commutating motors. High ni and low n0 means high armature reaction and low field excitation, that is, just the opposite conditions from that required for good commutator-mot ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-02", "section_label": "Chapter 2: Multiple Squirrel-Cage Induction Motor", "section_title": "Multiple Squirrel-Cage Induction Motor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3543-5554", "status": "candidate", "occurrence_count": 30, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-02/", "snippets": [ "... e first squirrel cage, and thus of higher reactance, a \"double squirrel-cage induction motor\" in derived, which to some extent combines the characteristics of the high- resistance and the low-resistance secondary. That is, at start- ing and low speed, the frequency of the magnetic flux in the arma- ture, and therefore the voltage induced in the secondary winding is high, and the high-resistance squirrel cage thus carries con- siderable current, gives good torque and torque efficiency, while the low-resistance squirr ...", "... ced in the secondary winding is high, and the high-resistance squirrel cage thus carries con- siderable current, gives good torque and torque efficiency, while the low-resistance squirrel cage is ineffective, due to its high reactance at the high armature frequency. At speeds near synchronism, the secondary frequency, being that of slip, is low, and the secondary induced voltage correspondingly low. The high-resistance squirrel cage thus carries little current and gives little torque. In the low-resistance squirrel ...", "... sistance squirrel cage thus carries con- siderable current, gives good torque and torque efficiency, while the low-resistance squirrel cage is ineffective, due to its high reactance at the high armature frequency. At speeds near synchronism, the secondary frequency, being that of slip, is low, and the secondary induced voltage correspondingly low. The high-resistance squirrel cage thus carries little current and gives little torque. In the low-resistance squirrel cage, due to its low reactance at the low frequency o ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-46", "section_label": "Chapter 6: Alternating Magnetic Flux Distribution", "section_title": "Alternating Magnetic Flux Distribution", "kind": "chapter", "sequence": 46, "number": 6, "location": "lines 23948-24980", "status": "candidate", "occurrence_count": 30, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "snippets": [ "... es of magnetic force. Hence, alternating magnetic fields and magnetic structures desired to respond very quickly to changes of m.m.f. are built of thin wires or thin iron sheets, that is, are laminated. Since the generated e.m.fs. are proportional to the frequency of the alternating magnetism, the laminations must be finer the higher the frequency. To fully utilize the magnetic permeability of the iron, it there- fore has to be laminated so as to give, at the impressed frequency, practically uniform magnetic indu ...", "... ed to respond very quickly to changes of m.m.f. are built of thin wires or thin iron sheets, that is, are laminated. Since the generated e.m.fs. are proportional to the frequency of the alternating magnetism, the laminations must be finer the higher the frequency. To fully utilize the magnetic permeability of the iron, it there- fore has to be laminated so as to give, at the impressed frequency, practically uniform magnetic induction throughout its section, that is, negligible secondary currents. This, however, i ...", "... ted e.m.fs. are proportional to the frequency of the alternating magnetism, the laminations must be finer the higher the frequency. To fully utilize the magnetic permeability of the iron, it there- fore has to be laminated so as to give, at the impressed frequency, practically uniform magnetic induction throughout its section, that is, negligible secondary currents. This, however, is no longer the case, even with the thinnest possible laminations, at extremely high frequencies, as oscillating currents, lightning d ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 29, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "... iron wire as the carrier of magnetic flux. Eddy currents are true electric currents, though flowing in minute circuits; and they follow all the laws of electric circuits. Their E.M.F. is proportional to the intensity of magneti- zation, (B, and to the frequency, N. Eddy currents are thus proportional to the magnetization, (B, the frequency, N, and to the electric conductivity, y, of the iron ; hence, can be expressed by The power consumed by eddy currents is proportional to their square, and inversely propor ...", "... nts, though flowing in minute circuits; and they follow all the laws of electric circuits. Their E.M.F. is proportional to the intensity of magneti- zation, (B, and to the frequency, N. Eddy currents are thus proportional to the magnetization, (B, the frequency, N, and to the electric conductivity, y, of the iron ; hence, can be expressed by The power consumed by eddy currents is proportional to their square, and inversely proportional to the electric con- ductivity, and can be expressed by W= 130 ALTERNA ...", "... f the iron ; or, W=aE*y. Hence, that component of the effective conductance which is due to eddy currents, is that is, The equivalent conductance due to eddy currents in the iron is a constant of the magnetic circuit ; it is indepen- dent of ^M..^., frequency, etc., but proportional to the electric conductivity of the iron, y. 87. Eddy currents, like magnetic hysteresis, cause an advance of phase of the current by an angle of advance, ft ; but, unlike hysteresis, eddy currents in general do not dis- tort the ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-01", "section_label": "Chapter 1: Speed Control Of Induction Motors", "section_title": "Speed Control Of Induction Motors", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1368-3542", "status": "candidate", "occurrence_count": 29, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-01/", "snippets": [ "... creasing the secondary resistance with increas- ing slip, to get high torque at low speeds, the same result can be produced by the use of an effective resistance, such as the effect- ive or equivalent resistance of hysteresis, or of eddy currents. As the frequency of the secondary current varies, a magnetic circuit energized by the secondary current operates at the varying frequency of the slip, s. At a given current, i\\, the voltage required to send the current through the magnetic circuit is proportional to the ...", "... ed by the use of an effective resistance, such as the effect- ive or equivalent resistance of hysteresis, or of eddy currents. As the frequency of the secondary current varies, a magnetic circuit energized by the secondary current operates at the varying frequency of the slip, s. At a given current, i\\, the voltage required to send the current through the magnetic circuit is proportional to the frequency, that is, to 8. Hence, the suaceptance is inverse proportional to «: V = 6- (5) 8 The angle of hysteretic ...", "... of the secondary current varies, a magnetic circuit energized by the secondary current operates at the varying frequency of the slip, s. At a given current, i\\, the voltage required to send the current through the magnetic circuit is proportional to the frequency, that is, to 8. Hence, the suaceptance is inverse proportional to «: V = 6- (5) 8 The angle of hysteretic advance of phase, a, and the power- factor, in a closed magnetic circuit, are independent of the frequency, and vary relatively little with the ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-30", "section_label": "Chapter 8: Low Frequency Surges In High Potential Systems", "section_title": "Low Frequency Surges In High Potential Systems", "kind": "chapter", "sequence": 30, "number": 8, "location": "lines 7826-9227", "status": "candidate", "occurrence_count": 29, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "snippets": [ "CHAPTER VIII. LOW FREQUENCY SURGES IN HIGH POTENTIAL SYSTEMS. 64. In electric circuits of considerable capacity, that is, in extended high potential systems, as long distance transmission lines and underground cable systems, occasionally destructive high potential low frequency sur ...", "... LOW FREQUENCY SURGES IN HIGH POTENTIAL SYSTEMS. 64. In electric circuits of considerable capacity, that is, in extended high potential systems, as long distance transmission lines and underground cable systems, occasionally destructive high potential low frequency surges occur; that is, oscillations of the whole system, of the same character as in the case of localized capacity and inductance discussed in the preceding chapter. While a system of distributed capacity has an infinite number of frequencies, which us ...", "... tential low frequency surges occur; that is, oscillations of the whole system, of the same character as in the case of localized capacity and inductance discussed in the preceding chapter. While a system of distributed capacity has an infinite number of frequencies, which usually are the odd multiples of a funda- mental frequency of oscillation, in those cases where the fundamental frequency predominates and the effect of the higher frequencies is negligible, the oscillation can be approxi- mated by the equations of ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 28, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... ron wire as the carrier of magnetic flux. Eddy currents are true electric currents, though flowing in minute circuits ; and they follow all the laws of electric circuits. Their E.M.F. is proportional to the intensity of magneti- zation, (B, and to the frequency, N. Eddy currents are thus proportional to the magnetization, (B, the frequency, A^, and to the electric conductivity, y, of the iron ; hence, can be expressed by The power consumed by eddy currents is proportional to their square, and inversely propor ...", "... ts, though flowing in minute circuits ; and they follow all the laws of electric circuits. Their E.M.F. is proportional to the intensity of magneti- zation, (B, and to the frequency, N. Eddy currents are thus proportional to the magnetization, (B, the frequency, A^, and to the electric conductivity, y, of the iron ; hence, can be expressed by The power consumed by eddy currents is proportional to their square, and inversely proportional to the electric con- ductivity, and can be expressed by 130 ALTERNATING- ...", "... e iron ; or, H^=aJS^y. Hence, that component of the effective conductance which is due to eddy currents, is that is. The equivalent conductance due to eddy currents in the iron is a constant of the magnetic circuit ; it is indepen- dent of 1£.M.,Y ,y frequency y etCy but proportiotml to the electric conductivity of the iropi, y. 87. Eddy currents, like magnetic hysteresis, cause an advance of phase of the current by an a?tgle of advanccy p ; but, unlike hysteresis, eddy currents in general do not dis- tort th ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-06", "section_label": "Lecture 6: Higher Harmonics Of The Generator Wave", "section_title": "Higher Harmonics Of The Generator Wave", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3133-3507", "status": "candidate", "occurrence_count": 27, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-06/", "snippets": [ "SIXTH LECTURE HIGHER HARMONICS OF THE GENERATOR WAVE mHE open circuit reactance of the transformer is the only reactance high enough to give resonance with the line capacity at fundamental frequency. All other reactances are too low for this. Since, however, the inductive reactance increases and the capacity reactance decreases proportionally to the frequency, the two reactances come nearer together for higher frequency; that is, for the higher harm ...", "... r is the only reactance high enough to give resonance with the line capacity at fundamental frequency. All other reactances are too low for this. Since, however, the inductive reactance increases and the capacity reactance decreases proportionally to the frequency, the two reactances come nearer together for higher frequency; that is, for the higher harmonics of the generator wave, and for some of the higher harmonics of the generator wave resonance rise of voltage so may occur between the line capacity and the ci ...", "... line capacity at fundamental frequency. All other reactances are too low for this. Since, however, the inductive reactance increases and the capacity reactance decreases proportionally to the frequency, the two reactances come nearer together for higher frequency; that is, for the higher harmonics of the generator wave, and for some of the higher harmonics of the generator wave resonance rise of voltage so may occur between the line capacity and the circuit inductance. The origin and existence of higher harmonic ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-09", "section_label": "Lecture 9: Hunting Of Synchronous Machines", "section_title": "Hunting Of Synchronous Machines", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 4218-4594", "status": "candidate", "occurrence_count": 27, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-09/", "snippets": [ "... sing energy losses. This kind of hunting is stopped by increasing the energy losses due to the oscillation, by copper bridges between the poles, by aluminum collars around the pole faces, or by a com- plete squirrel cage winding in the pole faces. The frequency of this hunting depends on the magnetic attraction, that is, on the field excitation, and on the weight of the rotating mass. The higher the field excitation the greater is the magnetic force, that is, quicker the motion of the ma- chine and therefore the ...", "... ting depends on the magnetic attraction, that is, on the field excitation, and on the weight of the rotating mass. The higher the field excitation the greater is the magnetic force, that is, quicker the motion of the ma- chine and therefore the higher the frequency. The greater the weight, the slower it is set in motion, that is, the lower the frequency. Characteristic of this hunting therefore is that its fre- quency is changed by changing the field excitation. 2nd. If the speed of the engine varies during the r ...", "... t of the rotating mass. The higher the field excitation the greater is the magnetic force, that is, quicker the motion of the ma- chine and therefore the higher the frequency. The greater the weight, the slower it is set in motion, that is, the lower the frequency. Characteristic of this hunting therefore is that its fre- quency is changed by changing the field excitation. 2nd. If the speed of the engine varies during the rota- tion, rising and falling with the steam impulses, then the alternator speed and the f ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-03", "section_label": "Lecture 3: Physiological Effects Of Radiation", "section_title": "Physiological Effects Of Radiation", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2366-3638", "status": "candidate", "occurrence_count": 27, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-03/", "snippets": [ "... d to produce the record, otherwise the lower portions of the speech are not recorded, while at the louder portions the recording point jumps and the voice breaks in the reproduction. 21. The sensitivity of the eye to radiation obviously changes with the frequency, as it is zero in the ultra-red, and in the ultra- violet — where the radiation is not visible — and thus gradually increases from zero at the red end of the spectrum to a maximum somewhere near the middle of the spectrum and then decreases again to zero ...", "... n produce visibility. It thus varies about as indicated in Fig. 22. The mechanical power equivalent of light, thus, is not constant, as the mechanical energy equivalent of heat — which is 426 kgm. or 4.25 kile-joule per calorie — but is a function of the frequency, that is, of the color of radiation, with a maximum, probably not very far from 0.01 watt per candle power in the middle of the spectrum. When comparing, however, the physiological effects of different frequencies of radiation, that is, different colors ...", "... le per calorie — but is a function of the frequency, that is, of the color of radiation, with a maximum, probably not very far from 0.01 watt per candle power in the middle of the spectrum. When comparing, however, the physiological effects of different frequencies of radiation, that is, different colors of light, the diffi- culty arises that different colored lights cannot be compared photometrically, as all photometers are based on making the illu- mination produced by the two different sources of light equal, and ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-04", "section_label": "Lecture 4: Chemical And Physical Effects Of Radiation", "section_title": "Chemical And Physical Effects Of Radiation", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3639-3945", "status": "candidate", "occurrence_count": 25, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-04/", "snippets": [ "... ther radiation is heat, but it may become heat when it ceases to be radiation. Thus all radiations are chemical rays, that is, produce chemical action, if they strike a body which is responsive to them. The chemical action of radiation is specific to its frequency and seems to be some kind of a resonance effect. We may picture to ourselves that the frequency of vibration of a silver atom is that of violet or ultra-violet light, and therefore, when struck by a wave of this frequency, is set in vibration by resonance ...", "... s are chemical rays, that is, produce chemical action, if they strike a body which is responsive to them. The chemical action of radiation is specific to its frequency and seems to be some kind of a resonance effect. We may picture to ourselves that the frequency of vibration of a silver atom is that of violet or ultra-violet light, and therefore, when struck by a wave of this frequency, is set in vibration by resonance, just as a tuning fork is set in vibration by a sound wave of the frequency with which it can v ...", "... n of radiation is specific to its frequency and seems to be some kind of a resonance effect. We may picture to ourselves that the frequency of vibration of a silver atom is that of violet or ultra-violet light, and therefore, when struck by a wave of this frequency, is set in vibration by resonance, just as a tuning fork is set in vibration by a sound wave of the frequency with which it can vibrate, and if the vibration of the silver atom, in response to the frequency of radiation, becomes sufficiently intense, it b ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-113", "section_label": "Apparatus Section 7: Induction Machines: Frequency Converter or General Alternating-current Transformer", "section_title": "Induction Machines: Frequency Converter or General Alternating-current Transformer", "kind": "apparatus-section", "sequence": 113, "number": 7, "location": "lines 21813-21922", "status": "candidate", "occurrence_count": 25, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-113/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-113/", "snippets": [ "VH. Frequency Converter or General Alternating-current Transformer 159. The e.m.fs. generated in the secondary of the induction machine are of the frequency of slip, that is, synchronism minus speed, thus of lower frequency than the impre ...", "VH. Frequency Converter or General Alternating-current Transformer 159. The e.m.fs. generated in the secondary of the induction machine are of the frequency of slip, that is, synchronism minus speed, thus of lower frequency than the impressed e.m.f. in the range from standstill to double synchronism; of higher frequency outside of this range. ' Thus, by opening the secondary c ...", "VH. Frequency Converter or General Alternating-current Transformer 159. The e.m.fs. generated in the secondary of the induction machine are of the frequency of slip, that is, synchronism minus speed, thus of lower frequency than the impressed e.m.f. in the range from standstill to double synchronism; of higher frequency outside of this range. ' Thus, by opening the secondary circuits of the induction machine and connecting them to an external ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 25, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... of one half wave of impressed e.m.f. is the time required by light to travel twice the length of the line, or the time of one complete period is the time light requires to travel four times the length of the line; in other words, the number of periods, or frequency of the impressed alternating e.m.fs., in resonance condition, is the velocity of light divided by four times the length of the line; or, in free oscillation or resonance condition, the length of the line is one quarter wave length. 279 280 TRANSIENT ...", "... is the velocity of light divided by four times the length of the line; or, in free oscillation or resonance condition, the length of the line is one quarter wave length. 279 280 TRANSIENT PHENOMENA If then I = length of line, S = speed of light, the frequency of oscillations or natural period of the line is — '• \"4? or, with I given in miles, hence S = 188,000 miles per second, it is , 47,000 /o = — j- cycles. (2) To get a resonance frequency as low as commercial frequencies, as 25 or 60 cycles, would ...", "... ENOMENA If then I = length of line, S = speed of light, the frequency of oscillations or natural period of the line is — '• \"4? or, with I given in miles, hence S = 188,000 miles per second, it is , 47,000 /o = — j- cycles. (2) To get a resonance frequency as low as commercial frequencies, as 25 or 60 cycles, would require Z == 1880 miles for /0 = 25 cycles, and Z = 783 miles for./, - 60 cycles. It follows herefrom that many existing transmission lines are such small fractions of a quarter-wave length of t ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-14", "section_label": "Chapter 14: The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "section_title": "The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14089-14918", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "snippets": [ "... izing current and large self-induction ; that is, comparatively large primary susceptance and large reactance. The general alternating-current transformer transforms between electrical and mechanical power, and changes not only E.M.Fs. and currents, but frequencies also. 132. Besides the magnetic flux interlinked with both primary and secondary electric circuit, a magnetic cross- flux passes in the transformer between primary and second- ary, surrounding one coil only, without being interlinked with the other. Thi ...", "... with the other, and is thus produced by the M.M.F. of one circuit only. 133. The common magnetic flux of the transformer is produced by the resultant M.M.F. of both electric circuits. It is determined by the counter E.M.F., the number of turns, and the frequency of the electric circuit, by the equation : ^ Where E = effective E.M.F. iV= frequency. n = number of turns. * = maximum magnetic flux. The M.M.F. producing this flux, or the resultant M.M.F. of primary and secondary circuit, is determined by shape ...", "... magnetic flux of the transformer is produced by the resultant M.M.F. of both electric circuits. It is determined by the counter E.M.F., the number of turns, and the frequency of the electric circuit, by the equation : ^ Where E = effective E.M.F. iV= frequency. n = number of turns. * = maximum magnetic flux. The M.M.F. producing this flux, or the resultant M.M.F. of primary and secondary circuit, is determined by shape and magnetic characteristic of the material composing the magnetic circuit, and by the mag ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 23, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "... the zero of voltage, and inversely, if the one is represented by the cosine function, the other is the sine function; hence the periodic com- ponents of the transient are ii = Iq cos (0 — 7) ei = eo sm (0 — 7) ) where 0 = 2 Tft, (4) and is the frequency of oscillation. The dissipative or \" transient \" component is M = €-\"', (6) 72 LINE OSCILLATIONS. T6 where u 2 U ^ C; hence the total expression of transient current and voltage is ^ = ^oe~ \"^ cos (0 — 7) e = eoe~ ^^ sin (0 — 7) ...", "... urrent and voltage are 360 degrees displaced from their values at the starting point, that is, are again in the same phase. This distance Zo is called the wave length, and is the distance which the electric field travels during one period to — -j. of the frequency of oscillation. As current and voltage vary in phase progressively along the line, the effect of inductance and of capacity, as represented by the inductance voltage and capacity current, varies progressively, and the resultant effect of inductance and c ...", "... e double- energy oscillation of the line the values — and — ^ IT IT In the same manner, instead of the total resistance r and the total conductance g, the values — and —^ appear. TT IT The values of Zq, yo, u, 4>, and co are not changed hereby. The frequency /, however, changes from the value correspond- ing to the circuit of massed capacity, / = 7= , to the value 2 7r vLC 4:VLC Thus the frequency of oscillation of a transmission line is / = — 7= = T-^ ■ (20) where a = VlC. (21) If h is the length ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-47", "section_label": "Chapter 7: Distribution Of Alternating-Current Density In Conductor", "section_title": "Distribution Of Alternating-Current Density In Conductor", "kind": "chapter", "sequence": 47, "number": 7, "location": "lines 24981-26094", "status": "candidate", "occurrence_count": 23, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "snippets": [ "CHAPTER VII. DISTRIBUTION OF ALTERNATING-CURRENT DENSITY IN CONDUCTOR. 59. If the frequency of an alternating or oscillating current is high, or the section of the conductor which carries the current is very large, or its electric conductivity or its magnetic per- meability high, the current density is not uniform throughout the conductor sectio ...", "... iderable, the conductor section is not fully utilized, but the material in the interior of the conductor is more or less wasted. It is of importance, therefore, in alternating- current circuits, especially in dealing with very large currents, or with high frequency, or materials of very high permeability, as iron, to investigate this phenomenon. An approximate determination of this effect for the purpose of deciding whether the unequal current distribution is so small as to be negligible in its effect on the resist ...", "... hen using iron as conductor, as for instance iron wires in high potential transmissions for branch lines of smaller power, or steel cables for long spans in transmission lines. (3) In the rail return of single-phase railways. (4) When carrying very high frequencies, such as lightning discharges, high frequency oscillations. In the last two cases, which probably are of the greatest impor- tance, the unequal current distribution usually is such that practically no current exists at the conductor center, and the effe ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 23, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... } s = - (u - u0). (395) 540 TRANSIENT PHENOMENA From equations (394) q is calculated by approximation, and then from (395) u0 and s. As seen, in all these expressions of q, uw s, etc., the integration constants M and N eliminate; that is, the frequency, time atten- uation constant, power transfer, etc., depend on the circuit con- stants only, but not on the distribution of current and voltage in the circuit. 67. At any point X of the circuit, the voltage is given by equa- tion (376), which, transposed ...", "... sil|s=(-l) + 1 2~2 INDEX PAGE Acceleration constant of traveling wave 466 Air blast, action in oscillating-current generator 75 pressure required in oscillating-current generator 75 Alternating-current circuit and transient term of fundamental frequency 473 distribution in conductor 369 transformer operating oscillating-current generator 87 transmission, equations of traveling wave 477 wave as traveling wave without attenuation 472 Alternator control by periodic transient term of field excitation 2 ...", "... at transition point 532 Condenser, also see Capacity. charge, inductive 18 noninductive 18 circuit of negligible inductance 55 equations 48 oscillation, effective value of voltage, current and power. ... 70 efficiency, decrement and output 72 frequency 62 general equations 60 size and rating 69 starting on alternating voltage 94 voltage in inductive circuit 49 Conductance, shunted, effective 12 Conductors at high frequency 403 Constant-current mercury arc rectifier 250 rectification 221, 230 ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3956-4744", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "snippets": [ "... oltage, and inversely, if the one is represented by the cosine function, the other is the sine function; hence the periodic com- ponents of the transient are ii = IQ cos ( — 7) ei = e0 sin (0 — 7) l where # = 2»ft (4) and ' = 27^ (5) is the frequency of oscillation. The transient component is hk = e-*, (6) 72 LINE OSCILLATIONS. 73 where e = — €Q sin 7 hence the total expression of transient current and voltage is i = loe-^cos (0 - 7) 6 = eoe-^sinfa - 7) 7, e0, and i.Q follow from the i ...", "... current and voltage are 360 degrees displaced from their values at the starting point, that is, are again in the same phase. This distance Z0 is called the wave length, and is the distance which the electric field travels during one period to = j of the frequency of oscillation. As current and voltage vary in phase progressively along the line, the effect of inductance and of capacity, as represented by the inductance voltage and capacity current, varies progressively, and the resultant effect of inductance and c ...", "... gy oscillation of the line the values - - and — . 7T 7T In the same manner, instead of the total resistance r and the 2 T 2 Q total conductance g, the values - — and - - appear. 7T 7T The values of z0, y0, u, 0, and co are not changed hereby. The frequency /, however, changes from the value correspond- ing to the circuit of massed capacity, / = - . , to the value 2 IT VLC f = 4 Vic * Thus the frequency of oscillation of a transmission line is where (7 = VLC. (21) If h is the length of the line, or ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "... length of conductor = 5 x 106 cm. ; d = distance of conductors from each other = 50 cm. ; 8 = diameter of conductor = 1 cm. Since C = .3 microfarads, the capacity reactance is x — 106 / 2 TT NC ohms, 160 ALTERNATING-CURRENT PHENOMENA. where N '= frequency; hence, at N = 60 cycles, x = 8,900 ohms ; and the charging current of the line, at E = 20,000 volts, becomes, ^ = E / x = 2.25 amperes. The resistance of 100 km of line of 1 cm diameter is 22 ohms ; therefore, at 10 per cent = 2,000 volts loss in the ...", "... resistance. In some cases, especially in very long circuits, as in lines conveying alternating power currents at high potential over extremely long distances by overhead conductors or un- derground cables, or with very feeble currents at extremely high frequency, such as telephone currents, the consideration of the line resistance — which consumes E.M.Fs. in phase with the current — and of the line reactance — which con- sumes E.M.Fs. in quadrature with the current — is not sufficient for the explanation of the p ...", "... gnetic hysteresis, or an expenditure of E.M'.F. in phase with the current, which acts as an increase of re- sistance. This electromagnetic hysteretic loss may take place in the conductor proper if iron wires are used, and will then be very serious at high frequencies, such as those of telephone currents. The effect of eddy currents has already been referred to under \"mutual inductance,\" of which it is an energy component. The alternating electrostatic field of force expends energy in dielectrics by what is called ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "section_label": "Lecture 10: Continual And Cumulative Oscillations", "section_title": "Continual And Cumulative Oscillations", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... increas- ing in amplitude, until either the system breaks down or, by the increase of the energy dissipation, it becomes equal to the energy supply, and the oscillation becomes continual. A continual or cumulative oscillation thus involves an energy and frequency transformation, from the low-frequency or con- tinuous-current energy of the power supply of the system to the high-frequency energy of the oscillation. 119 120 ELECTRICAL DISCHARGES, WAVES AND IMPULSES This energy transformation may be brought about ...", "... r the system breaks down or, by the increase of the energy dissipation, it becomes equal to the energy supply, and the oscillation becomes continual. A continual or cumulative oscillation thus involves an energy and frequency transformation, from the low-frequency or con- tinuous-current energy of the power supply of the system to the high-frequency energy of the oscillation. 119 120 ELECTRICAL DISCHARGES, WAVES AND IMPULSES This energy transformation may be brought about by the transient of energy readjustme ...", "... to the energy supply, and the oscillation becomes continual. A continual or cumulative oscillation thus involves an energy and frequency transformation, from the low-frequency or con- tinuous-current energy of the power supply of the system to the high-frequency energy of the oscillation. 119 120 ELECTRICAL DISCHARGES, WAVES AND IMPULSES This energy transformation may be brought about by the transient of energy readjustment, resulting from a change of circuit conditions, producing again a change of circuit c ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-07", "section_label": "Lecture 7: High Frequency Oscillations And Surges", "section_title": "High Frequency Oscillations And Surges", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3508-3780", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-07/", "snippets": [ "SEVENTH LECTURE HIGH FREQUENCY OSCILLATIONS AND SURGES 1\"^ N an electric circuit, in addition to the power consump- tion by the resistance of the lines, an energy storage ■^ occurs as electrostatic energy, or electrostatic charge due to the voltage on the line (capacity) ; and as el ...", "... ity, that is, dies out. ' These oscillating voltages and currents are the result of the readjustment of the stored energy of the circuit to a sudden change of conditions, and are dependant upon the stored energy of the circuit, but not upon the generator frequency or wave shape ; therefore they occur in the same manner, and are of the same frequency, in a 25 cycle system as in a 60 cycle system, or a high potential direct current transmission; and occur with sine waves of generator voltage equally as with distorted ...", "... e readjustment of the stored energy of the circuit to a sudden change of conditions, and are dependant upon the stored energy of the circuit, but not upon the generator frequency or wave shape ; therefore they occur in the same manner, and are of the same frequency, in a 25 cycle system as in a 60 cycle system, or a high potential direct current transmission; and occur with sine waves of generator voltage equally as with distorted 92 GENERAL LECTURES generator waves. While the power of these oscillations ulti- m ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-38", "section_label": "Apparatus Section 17: Synchronous Machines: Short-circuit Currents of Alternators", "section_title": "Synchronous Machines: Short-circuit Currents of Alternators", "kind": "apparatus-section", "sequence": 38, "number": 17, "location": "lines 10190-10429", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-38/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-38/", "snippets": [ "... t from zero in all phases and gradually approach their symmetrical appear- ance, i.e., in a three-phase machine three currents displaced by 120 degrees. Hereby the field current is made pulsating, with nor- mal or synchronous frequency, that is, with the same frequency as the armature current. This full frequency pulsation gradually dies out and the field current becomes constant with a polyphase short circuit, while with a single-phase short circuit it r ...", "... dually approach their symmetrical appear- ance, i.e., in a three-phase machine three currents displaced by 120 degrees. Hereby the field current is made pulsating, with nor- mal or synchronous frequency, that is, with the same frequency as the armature current. This full frequency pulsation gradually dies out and the field current becomes constant with a polyphase short circuit, while with a single-phase short circuit it remains 162 ELEMENTS OF ELECTRIC ...", "... i.e., in a three-phase machine three currents displaced by 120 degrees. Hereby the field current is made pulsating, with nor- mal or synchronous frequency, that is, with the same frequency as the armature current. This full frequency pulsation gradually dies out and the field current becomes constant with a polyphase short circuit, while with a single-phase short circuit it remains 162 ELEMENTS OF ELECTRICAL ENGINEERING pulsating with double frequency ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-12", "section_label": "Chapter 12: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 10718-13483", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-12/", "snippets": [ "... wave in this case, but is distorted by hysteresis. It is possible, however, to plot the cur- rent wave in this case from the hysteretic cycle of magnetic flux. From the number of turns, n, of the electric circuit, the effective counter e.m.f., E, and the frequency, /, of the current, the maxi- mum magnetic flux, ^, is found by the formula: E = \\/2 7r7(/$ 10-^; 8 114 ALTERNATING-CURRENT PHENOMENA hence, ElO^ $ = —-= V 2 7rr?; A maximiiin flux, , and magnetic cross-section, A, give the ... $ maxim ...", "... e distorted wave of current can be resolved into two components: A true sine ivave of equal effective intensity and equal 'power to the distorted wave, called the equivalent sine wave, and a wattless higher harmonic, consisting chiefly of a term of triple frequency. In Figs. 80, 81 and 83 are shown, as /, the equivalent sine waves, and as i, the difference between the equivalent sine wave and the real distorted wave, which consists of wattless complex higher harmonics. The equivalent sine wave of m.m.f. or of curr ...", "... to neglect the higher harmonics altogether, and replace the dis- torted wave by its equivalent sine wave, keeping in mind, however, the existence of a higher harmonic as a possible dis- turbing factor which may become noticeable in those cases where the frequency of the higher harmonic is near the frequency of resonance of the circuit, that is, in circuits containing conden- sive as well as inductive reactance, or in those circuits in which the higher harmonic of currrent is suppressed, and thereby the voltage is ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-16", "section_label": "Chapter 16: Power, And Double-Frequency Quantities In", "section_title": "Power, And Double-Frequency Quantities In", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 16077-16520", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-16/", "snippets": [ "CHAPTER XVI POWER, AND DOUBLE-FREQUENCY QUANTITIES IN GENERAL 135. Graphically, alternating currents and voltages are repre- sented by vectors, of which the length represents the intensity, the direction the phase of the alternating wave. The vectors generally issue from the center of coordi ...", "... of current, voltage, impedance, do not give a correct result in the inter-relation of voltage, current, power. The reason is, that E and / are vectors of the same fre- quency, and Z a constant numerical factor or \"operator,\" which thus does not change the frequency. 179 180 ALTERNATING-CURRENT PHENOMENA The power, P, however, is of double frequency compared with E and /, that is, makes a complete wave for every half wave of E or 7, and thus cannot be represented by a vector in the same diagram with E and I. ...", "... ge, current, power. The reason is, that E and / are vectors of the same fre- quency, and Z a constant numerical factor or \"operator,\" which thus does not change the frequency. 179 180 ALTERNATING-CURRENT PHENOMENA The power, P, however, is of double frequency compared with E and /, that is, makes a complete wave for every half wave of E or 7, and thus cannot be represented by a vector in the same diagram with E and I. Po = EI is a quantity of the same frequency with E and /, and thus cannot represent the po ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-18", "section_label": "Chapter 18: Polyphase Induction Motors", "section_title": "Polyphase Induction Motors", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17717-20445", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-18/", "snippets": [ "... lectric power to the secondary, while in the induction motor the secondary is movable with regards to the primary, and the mechanical forces between the primary, and secondary utilized to produce motion. In the general alternating-current trans- former or frequency converter we shall find an apparatus trans- mitting electric as well as mechanical energy, and comprising both, induction motor and transformer, as the two limiting cases. In the induction motor, only the mechanical force be- tween primary and secondary i ...", "... uits in inductive rela- tion to primary circuits and vice versa, in spite of their relative motion. The result of the relative motion between primary and secondary is, that the e.m.fs. generated in the secondary or the motor armature are not of the same frequency as the e.m.fs. impressed upon the primary, but of a frequency which is the difference between the impressed frequency and the frequency of rotation, or equal to the \"slip,\" that is, the difference between synchronism and speed (in cycles). 208 POLYPH ...", "... a, in spite of their relative motion. The result of the relative motion between primary and secondary is, that the e.m.fs. generated in the secondary or the motor armature are not of the same frequency as the e.m.fs. impressed upon the primary, but of a frequency which is the difference between the impressed frequency and the frequency of rotation, or equal to the \"slip,\" that is, the difference between synchronism and speed (in cycles). 208 POLYPHASE INDUCTION MOTORS 209 Hence, if / = frequency of main or ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-27", "section_label": "Chapter 27: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 33011-34776", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-27/", "snippets": [ "... NATING WAVES 259. The vector representation, A — a'^ -{- ja^'^ = a (cos d -\\- j sin 6) of the alternating wave, A = tto cos {(f) — 6) apphes to the sine wave only. The general alternating wave, however, contains an infinite series of terms, of odd frequencies, A = Aicos( 0- ^i) + ^3 cos (3 (^ - 63) + As cos (5 <^ - ^5) + thus cannot be directly represented by one complex vector quantity. The replacement of the general wave by its equivalent sine wave, as before discussed, that is, a sine wave of equal effec ...", "... , each term can be represented by a complex symbol, and the equations of the general wave then are the resultants of those of the individual harmonics. This can be represented symbolically by combining in one formula symbolic representations of different frequencies, thus, A = 22n-i(a„i+i„a„ii),^ 1 1 The index 2n — 1 in the S sign denotes that only the odd values of n are considered. If the wave contained even harmonics, the even vahies of n would also be considered, and the index in the 2 sign would be n. 379 ...", "... onsidered, and the index in the 2 sign would be n. 379 380 ALTERNATING-CURRENT PHENOMENA where jn = V - 1, and the index of the j„ merely denotes that the j's of differ- ent indices, n, while algebraically identical, physically represent different frequencies, and thus cannot be combined. The general wave of e.m.f. is thus represented by E = 2:2n-i(e„i4-j„e„ii), 1 the general wave of current by 1 If Zi = r -^ j (x„, -{- xo -\\- Xc) is the impedance of the fundamental harmonic, where Xm is that part o ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-17", "section_label": "Chapter 19: Alternating- Current Motors In General", "section_title": "Alternating- Current Motors In General", "kind": "chapter", "sequence": 17, "number": 19, "location": "lines 21713-23905", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-17/", "snippets": [ "... y with their relative positions, ami those in which they vary with the relatifl positions of stator and rotor. In the latter a cycle of rotation exists, and therefrom the tendency of the motor results to lock at a speed giving a definite ratio between the frequency of rotation and the frequency of impressed e.m.f. Such motors, therefore, are synchronous motors. The main types of synchronous motors are as follows: 1. One member supplied with alternating and the other with direct current — polyphase or single-phase ...", "... s, ami those in which they vary with the relatifl positions of stator and rotor. In the latter a cycle of rotation exists, and therefrom the tendency of the motor results to lock at a speed giving a definite ratio between the frequency of rotation and the frequency of impressed e.m.f. Such motors, therefore, are synchronous motors. The main types of synchronous motors are as follows: 1. One member supplied with alternating and the other with direct current — polyphase or single-phase synchronous motors, 2. One m ...", "... tion motors. 3. One member excited by alternating current, the other of different magnetic reluctance iii different direction! construction) — reaction motors. 4. One member excited by alternating current, the other by altcrnating current of different frequency or different direction of rotation- — general alternating-current transformer or fre- quency converter and synchronous-induction generator. ALTERNATING-CURRENT MOTORS 301 (II is the synchronous motor of the electrical industry. (2) and (3) are used oc ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-14", "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "section_title": "Constant-Potential Constant-Current Trans Formation", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "... ctance of the constant-cmrent transformer, varies auto- matically between a maximum, with the primary and secondary coils at their maximum distance apart, and a minimum with the coils touching each other. Obviously, this automatic action is independent of frequency, impressed voltage, and character of load. If the two coils P and S in Fig. 114 are wound with the same number of turns and connected in series with each other and with the circuit, Fig. 114 is a constant-current regulator, or a regulating reactance, th ...", "... ficiency. 140. In alternating-current circuits small variations of fre- quency are unavoidable, as for instance, caused by changes of load, etc., and the inductive reactance is directly proportional, the condensive reactance inversely proportional to the frequency. Wherever inductive and condensive reactances are used in series with each other and of equal or approximately equal reactance, so more or less neutralizing each other, even small changes of frequency may cause very large variations in the result, and in ...", "... he condensive reactance inversely proportional to the frequency. Wherever inductive and condensive reactances are used in series with each other and of equal or approximately equal reactance, so more or less neutralizing each other, even small changes of frequency may cause very large variations in the result, and in 272 ELECTRIC CIRCUITS such cases it is therefore necessary to investigate the effect of a change of frequency on the result: for instance, in a resonating circuit of very small power loss, a small c ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-29", "section_label": "Chapter 7: Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "section_title": "Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "kind": "chapter", "sequence": 29, "number": 7, "location": "lines 6798-7825", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "snippets": [ "... 0 = 0, the e.m.f., e = E cos (0 - 00), (1) be impressed upon a circuit containing in series the resistance, r, the inductance, L, and the capacity, C. The inductive reactance is x = 2 TT/L 1 and the condensive reactance is xc = > 2 7T/C J where/ = frequency and 6 = 2 nft. (3) Then the e.m.f. consumed by resistance is ri\\ the e.m.f. consumed by inductance, is di di Ldt = xJe' and the e.m.f. consumed by capacity is , (4) where i = instantaneous value of the current. di di C Hence, e = ri + x - ...", "... ce at the condenser terminals as cos# cos V -H where cos xc sin , (27) xc, and 7 = - 90°. (28) In this case an oscillating term always exists whatever the value of 00, that is, the point of the wave, where the circuit is started. The frequency of oscillation therefore is /o or, approximately, 2x\" _ 4X2 (29) where/ = fundamental frequency. Substituting x = 2nfL and zc = — -r-, we have CL or, approximately, /o (30) 98 TRANSIENT PHENOMENA 60. The oscillating start, ...", "... In this case an oscillating term always exists whatever the value of 00, that is, the point of the wave, where the circuit is started. The frequency of oscillation therefore is /o or, approximately, 2x\" _ 4X2 (29) where/ = fundamental frequency. Substituting x = 2nfL and zc = — -r-, we have CL or, approximately, /o (30) 98 TRANSIENT PHENOMENA 60. The oscillating start, or, in general, change of circuit conditions, is the most important, since in circuits containing capacity the t ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-22", "section_label": "Chapter 20: Ri", "section_title": "Ri", "kind": "chapter", "sequence": 22, "number": 20, "location": "lines 24560-25119", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "snippets": [ "... rp zero : sin /3 - .15 sin (3 p - 180°) - .10 sin 5 p. Sharp peak with sharp zero : sin 13 - .15 sin 3 /3 - .10 sin (5 /S - 180°). 224. Since the distortion of the wave-shape consists in the superposition of higher harmonics, that is, waves of higher frequency, the phenomena taking place in a circuit / 3o8 AL TERNA TIXG-CURREXT PHEXOMEXA. [§ 225 supplied by such a wave will be the combined effect of the different waves. Thus in a non-inductive circuit, the current and the potential difference across the ...", "... ifferent parts of the circuit are of the same shape as the impressed E.M.F\". If self- induction is inserted in series to a non-inductive circuit, the self-induction consumes more E.M.F. of the higher harmon- ics, since the reactance is proportional to the frequency, and thus the current and the E.M.F. in the non-inductive part of the circuit shows the higher harmonics in a reduced amplitude. That is, self-induction in series to a non-induc- tive circuit reduces the higher harmonics or smooths out the wave to a clos ...", "... , self-induction in series to a non-induc- tive circuit reduces the higher harmonics or smooths out the wave to a closer resemblance with sine shape. In- versely, capacity in series to a non-inductive circuit con- sumes less E.M.F. at higher than at lower frequency, and thus makes the higher harmonics of current and of poten- tial difference in the non-inductive part of the circuit more pronounced — intensifies the harmonics. Self-induction and capacity in series may cause an in- crease of voltage due to complete ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-23", "section_label": "Chapter 23: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 21983-22448", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "snippets": [ "... harp zero : sin (3 - .15 sin (30- 180°) - .10 sin 5 /?. Sharp peak with sharp zero : sin {3 — .15 sin 3 0 — .10 sin (5 (3 — 180°). 245. Since the distortion of the wave-shape consists in the superposition of higher harmonics, that is, waves of higher frequency, the phenomena taking place in a circuit 402 ALTERNATING-CURRENT PHENOMENA. supplied by such a wave will be the combined effect of the different waves. Thus in a non-inductive circuit, the current and the potential difference across the different par ...", "... different parts of the circuit are of the same shape as the impressed E.M.F. If self- induction is inserted in series to a non-inductive circuit, the self-induction consumes more E.M.F. of the higher harmon- ics, since the reactance is proportional to the frequency, and thus the current and the E.M.F. in the non-inductive part of the circuit shows the higher harmonics in a reduced amplitude. That is, self-induction in series to a non-induc- tive circuit reduces the higher harmonics or smooths out the wave to a clos ...", "... , self-induction in series to a non-induc- tive circuit reduces the higher harmonics or smooths out the wave to a closer resemblance with sine shape. In- versely, capacity in series to a non-inductive circuit con- sumes less E.M.F. at higher than at lower frequency, and thus makes the higher harmonics of current and of poten- tial difference in the non-inductive part of the circuit more pronounced — intensifies the harmonics. Self-induction and capacity in series may cause an in- crease of voltage due to complete ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-22", "section_label": "Chapter 24: Conclusion", "section_title": "Conclusion", "kind": "chapter", "sequence": 22, "number": 24, "location": "lines 32820-33531", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-22/", "snippets": [ "... primary cir- cuit, the other the secondary circuit. The magnetic field of the induction machine inherently must be an alternating field (usually a polyphase rotating field) excited by alternating currents. Synchronous machines are machines in which the frequency of rotation has a fixed and rigid relation to the frequency of the supply voltage. Usually the frequency of rotation is the same as the frequency of the. supply voltage: in the standard synchronous machine, with direct-current field excitation. The tw ...", "... netic field of the induction machine inherently must be an alternating field (usually a polyphase rotating field) excited by alternating currents. Synchronous machines are machines in which the frequency of rotation has a fixed and rigid relation to the frequency of the supply voltage. Usually the frequency of rotation is the same as the frequency of the. supply voltage: in the standard synchronous machine, with direct-current field excitation. The two frequencies, however, may be different: in the double sync ...", "... must be an alternating field (usually a polyphase rotating field) excited by alternating currents. Synchronous machines are machines in which the frequency of rotation has a fixed and rigid relation to the frequency of the supply voltage. Usually the frequency of rotation is the same as the frequency of the. supply voltage: in the standard synchronous machine, with direct-current field excitation. The two frequencies, however, may be different: in the double synchronous generator, the frequency of rotation is ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-48", "section_label": "Chapter 8: Velocity Of Propagation Of Electric Field", "section_title": "Velocity Of Propagation Of Electric Field", "kind": "chapter", "sequence": 48, "number": 8, "location": "lines 26095-27002", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "snippets": [ "... r, in other words, the electric field lags the more, the greater the distance from the conductor. Since the velocity of propagation is very high — about 3 X 1010 centimeters per second — the wave of an alternating or oscillating current even of very high frequency is of considerable length ; at 60 cycles the wave length is 0.5 X 109 centimeters, and even at a million cycles the wave length is 30,000 centimeters, or about 1000 feet, that is, very great compared with the distance to which electric fields usually exte ...", "... with the flow of energy in the conductor, that is, the velocity of propagation has no appreciable effect. Thus, the finite velocity of propagation of the electric field requires consideration only: 387 388 TRANSIENT PHENOMENA (a) At extremely high frequencies, hundreds of millions of cycles per second, as given by Hertzian resonators. (6) In high frequency discharges having no return circuit or no well defined return circuit, as lightning discharges. In this case the effective resistance of radiation may be s ...", "... tor, that is, the velocity of propagation has no appreciable effect. Thus, the finite velocity of propagation of the electric field requires consideration only: 387 388 TRANSIENT PHENOMENA (a) At extremely high frequencies, hundreds of millions of cycles per second, as given by Hertzian resonators. (6) In high frequency discharges having no return circuit or no well defined return circuit, as lightning discharges. In this case the effective resistance of radiation may be so large com- pared with the ohmic resistanc ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-26", "section_label": "Chapter 26: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 32540-33010", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-26/", "snippets": [ "... s of the circuit are of the same shape as the impressed e.m.f. If inductive reactance is inserted in series with a non-inductive circuit, the self-inductive reactance consumes more e.m.f. of the higher harmonics, since the reactance is proportional to the frequency, and thus the current and the e.m.f. in the non-inductive part of the circuit show the higher harmonics in a reduced amplitude. That is, self-inductive react- ance in series with a non-inductive circuit reduces the higher harmonics or smooths out the wave ...", "... -inductive react- ance in series with a non-inductive circuit reduces the higher harmonics or smooths out the wave to a closer resemblance to sine-shape. Inversely, capacity in series to a non-inductive circuit consumes less e.m.f. at higher than at lower frequency, and thus makes the higher harmonics of current and of potential EFFECTS OF HIGHER HARMONICS 373 difference in the non-inductive part of the circuit more pro- nounced— intensifies the harmonics. Self-induction and capacity in series may cause an incr ...", "... after. 253. In long-distance transmission over lines of noticeable inductive and condensive reactance, rise of voltage due to reso- nance may occur with higher harmonics, as waves of higher fre- quency, while the fundamental wave is usually of too low a frequency to cause resonance. An approximate estimate of the possible rise by resonance with various harmonics can be obtained by the investigation of a numerical example. Let in a long-distance line, fed by step-up transformers at 60 cycles. The resistance drop ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-10", "section_label": "Chapter 10: F", "section_title": "F", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 8269-10499", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "snippets": [ "... e wave in this case, but is distorted by hysteresis. It is possible, however, to plot the current wave in this case from the hysteretic cycle of magnetic flux. From the number of turns, «, of the electric circuit, the effective counter E.M.F., E, and the frequency, iV, of the current, the maximum magnetic flux, *, is found by the formula: ^= V2 7r//iV*10-8; hence, . ^}^^ -s/2irnN A maximum flux, *, and magnetic cross-section, 5, give the maximum magnetic induction, (SS = ^ / S. If the magnetic induction v ...", "... o components : A true sine wave of equal effective intensity and equal power to the distorted wave, called the equivalent 112 ALTERNATING-CURRENT PHENOMENA. IS 77 sine wave, and a -wattless higher harmonic, consisting chiefly of a term of triple frequency. In Figs. 66 to 71 are shown, in full lines, the equiva- Y ■^ / \\ \\ M A ■' 'v 1 ,-' V \\ ^ \\i / , \"i^ . '■\\ ~ ~^ 1 / — \\ \\ '\\ 1 ,-' k \\ ■-/ ,^ -' / ...", "... glect the higher harmonic altogether, and replace the dis- torted wave by its equivalent sine wave, keeping in mind, however, the existence of a higher harmonic as a possible disturbing factor which may become noticeable in those very rare cases where the frequency of the higher harmonic is near the frequency of resonance of the circuit. 79. The equivalent sine wave of exciting current leads the sine wave of magnetism by an angle a, which is called the angle of hysteretic advance of phase. Hence the cur- rent lags ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-15", "section_label": "Chapter 15: Induction Motob", "section_title": "Induction Motob", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 14919-17024", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "snippets": [ "... in secondary cir- cuits in inductive relation to primary circuits, in spite of their relative motion. The result of the relative motion between primary and secondary is, that the E.M.Fs. induced in the secondary or the motor armature are not of the same frequency as the E.M.F. impressed upon the primary, but of a frequency which is the difference between the impressed frequency and the frequency of rotation, or equal to the ** slip,\" that is, the difference between synchronism and speed (in cycles). Hence, if ...", "... uits, in spite of their relative motion. The result of the relative motion between primary and secondary is, that the E.M.Fs. induced in the secondary or the motor armature are not of the same frequency as the E.M.F. impressed upon the primary, but of a frequency which is the difference between the impressed frequency and the frequency of rotation, or equal to the ** slip,\" that is, the difference between synchronism and speed (in cycles). Hence, if N = frequency of main or primary E.M.F., and s = percentage ...", "... the relative motion between primary and secondary is, that the E.M.Fs. induced in the secondary or the motor armature are not of the same frequency as the E.M.F. impressed upon the primary, but of a frequency which is the difference between the impressed frequency and the frequency of rotation, or equal to the ** slip,\" that is, the difference between synchronism and speed (in cycles). Hence, if N = frequency of main or primary E.M.F., and s = percentage slip ; sN = frequency of armature or secondary E.M.F., ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "section_label": "Chapter 10: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "... ne wave in this case, but is distorted by hysteresis. It is possible, however, to plot the current wave in this case from the hysteretic cycle of magnetic flux. From the number of turns, n, of the electric circuit, the effective counter E.M.F., E, and the frequency, N, of the current, the maximum magnetic flux, , is found by the formula : hence, E 108 A maximum flux, <£, and magnetic cross-section, S, give the maximum magnetic induction, (B = $ / 6\". If the magnetic induction varies periodically between ...", "... into two components : A true sine wave of equal effective intensity nnd equal power to the distorted wave, called the equivalent 112 ALTERNATING-CURRENT PHENOMENA. sine wave, and a wattless JiigJier harmonic, consisting chiefly of a term of triple frequency. In Figs. 66 to 71 are shown, as /, the equivalent sine' \\ \\ v \\ Figs. 70 and 71. Distortion of Current Wave by Hysteresis. waves and as i, the difference between the equivalent sine wave and the real distorted wave, which consists of watt ...", "... ble to neglect the higher harmonic altogether, and replace the dis- torted wave by its equivalent sine wave, keeping in mind, however, the existence of a higher harmonic as a possible disturbing factor which may become noticeable in those cases where the frequency of the higher harmonic is near the fre- quency of resonance of the circuit, that is, in circuits con- taining capacity besides the inductance. 79. The equivalent sine wave of exciting current leads the sine wave of magnetism by an angle a, which is calle ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-12", "section_label": "Chapter 12: Power, And Double Frequency Quantities In General", "section_title": "Power, And Double Frequency Quantities In General", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 9381-9740", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "snippets": [ "CHAPTER XII. POWER, AND DOUBLE FREQUENCY QUANTITIES IN GENERAL. 102. Graphically alternating currents and E.M.F's are represented by vectors, of which the length represents the intensity, the direction the phase of the alternating wave. The vectors generally issue from the center of co-ordina ...", "... resistance, and conductance are related by Ohms law in direct current circuits. In direct current circuits, power is the product of cur- rent into E.M.F. In alternating current circuits, if The product, P0 = EI= (Ml - *\"/\") +j (W POWER, AND DOUBLE FREQUENCY QUANTITIES. 151 is not the power; that is, multiplication and division, which are correct in the inter-relation of current, E.M.F., impe- dance, do not give a correct result in the inter-relation of E.M.F., current, power. The reason is, that El are vec- ...", "... is not the power; that is, multiplication and division, which are correct in the inter-relation of current, E.M.F., impe- dance, do not give a correct result in the inter-relation of E.M.F., current, power. The reason is, that El are vec- tors of the same frequency, and Z a constant numerical factor which thus does not change the frequency. The power P, however, is of double frequency compared with E and /, that is, makes a complete wave for every half wave of E or 7, and thus cannot be represented by a vector in ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "... LTERNATING WAVES. 253. The vector representation, A = a1 +y = 2 7rft, (13) where / = the frequency of this transfer (which is still undeter- mined), and y the phase angle at the starting moment of the transient; that is, ^l = ^o cos 7 = initial transient current. (14) As the current iissi maximum at the moment when the magnetic energy is a maximum a ...", "... rrent is a maximum, and inversely; and if the current is represented by the cosine function, the voltage thus is represented by the sine function, that is, e = eo sin (0 — 7), (15) where ei = — 60 sin 7 = initial value of transient voltage. (16) The frequency / is still unknown, but from the law of propor- tionality it follows that there must be a frequency, that is, the suc- cessive conversions between the two forms of energy must occur in equal time intervals, for this reason: If magnetic energy converts to ...", "... tage thus is represented by the sine function, that is, e = eo sin (0 — 7), (15) where ei = — 60 sin 7 = initial value of transient voltage. (16) The frequency / is still unknown, but from the law of propor- tionality it follows that there must be a frequency, that is, the suc- cessive conversions between the two forms of energy must occur in equal time intervals, for this reason: If magnetic energy converts to dielectric and back again, at some moment the proportion be- tween the two forms of energy must be t ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "... ) and the average power flow is Po = avg p, (3) = 0. Hence, in a stationary oscillation, or standing wave of a uni- form circuit, the average flow of power, po, is zero, and no power flows along the circuit, but there is a surge of power, of double frequency. That is, power flows first one way, during one-quarter cycle, and then in the opposite direction, during the next quarter- cycle, etc. Such a transient wave thus is analogous to the permanent wave of reactive power. As in a stationary wave, current an ...", "... he phenomenon may start with a traveling wave or impulse, and this, by reflection at the ends of the circuit, and combination of the, reflected waves and the main waves, gradually changes to a stationary wave. In this case, the traveling wave has the same frequency as the stationary wave resulting from it. In Fig. 47 is shown the reproduction of an oscillogram of the formation of a stationary oscillation in a transmission line by the repeated re- Fig. 47. — CD11168. — Reproduction of an Oscillogram of Stationary Li ...", "... ch the energy stored magnetically or dielectrically in the different circuit sections adjusts itself to the proportion cor- responding to the stationary oscillation of the complete circuit. Such traveling waves then are local, and therefore of much higher frequency than the final oscillation of the complete circuit, and thus die out at a faster rate. Occasionally they are shown by the oscillograph as high-frequency oscillations intervening between 102 ELECTRIC DISCHARGES, WAVES AND IMPULSES. the alternating waves ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3287-3955", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "snippets": [ "... ient current i and the transient voltage e successively increase, decrease, and become zero. The current thus may be represented by i = locosfa -7), (12) where iQ is the maximum value of current, discussed above, and = 27Tft, (13) where / = the frequency of this transfer (which is still undeter- mined), and 7 the phase angle at the starting moment of the transient; that is, ii = IQ cos 7 = initial transient current. (14) As the current i is a maximum at the moment when the magnetic energy is a maximum ...", "... rrent is a maximum, and inversely; and if the current is represented by the cosine function, the voltage thus is represented by the sine function, that is, e = e0 sin (0 - 7), (15) where ei = — e0 sin 7 = initial value of transient voltage. (16) The frequency / is still unknown, but from the law of propor- tionality it follows that there must be a frequency, that is, the suc- cessive conversions between the two forms of energy must occur in equal time intervals, for this reason: If magnetic energy converts to ...", "... tage thus is represented by the sine function, that is, e = e0 sin (0 - 7), (15) where ei = — e0 sin 7 = initial value of transient voltage. (16) The frequency / is still unknown, but from the law of propor- tionality it follows that there must be a frequency, that is, the suc- cessive conversions between the two forms of energy must occur in equal time intervals, for this reason: If magnetic energy converts to dielectric and back again, at some moment the proportion be- tween the two forms of energy must be t ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 4745-5520", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "snippets": [ "... ) and the average power flow is Po = avg p, (3) = 0. Hence, in a stationary oscillation, or standing wave of a uni- form circuit, the average flow of power, p0, is zero, and no power flows along the circuit, but there is a surge of power, of double frequency. That is, power flows first one way, during one-quarter cycle, and then in the opposite direction, during the next quarter- cycle, etc. Such a transient wave thus is analogous to the permanent wave of reactive power. As in a stationary wave, current an ...", "... The phenomenon may start with a traveling wave or impulse, and this, by reflection at the ends of the circuit, and combination of the reflected waves and the main waves, gradually changes to a stationary wave. In this case, the traveling wave has the same frequency as the stationary wave resulting from it. In Fig. 47 is shown the reproduction of an oscillogram of the formation of a stationary oscillation in a transmission line by the repeated re- i, Fig. 47. — CD11168. — Reproduction of an Oscillogram of Station ...", "... ch the energy stored magnetically or dielectrically in the different circuit sections adjusts itself to the proportion cor- responding to the stationary oscillation of the complete circuit. Such traveling waves then are local, and therefore of much higher frequency than the final oscillation of the complete circuit, and thus die out at a faster rate. Occasionally they are shown by the oscillograph as high-frequency oscillations intervening between 102 ELECTRIC DISCHARGES, WAVES AND IMPULSES. the alternating waves ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-19", "section_label": "Chapter 19: Induction Generators", "section_title": "Induction Generators", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 20446-21537", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-19/", "snippets": [ "... When operating in parallel with synchronous alternating cur- rent generators, the induction generator obviously takes its leading exciting current from the synchronous alternator, which thus carries a lagging wattless current. 175. To generate constant frequency, the speed of the in- duction generator must increase with the load. Inversely, when driven at constant speed, with increasing load on the induction generator, the frequency of the current generated thereby decreases. Thus, when calculating the characteri ...", "... nator, which thus carries a lagging wattless current. 175. To generate constant frequency, the speed of the in- duction generator must increase with the load. Inversely, when driven at constant speed, with increasing load on the induction generator, the frequency of the current generated thereby decreases. Thus, when calculating the characteristic curves of the constant-speed induction generator, due regard has to be taken of the decrease of frequency with increase of load, or what may be called the slip of freque ...", "... ant speed, with increasing load on the induction generator, the frequency of the current generated thereby decreases. Thus, when calculating the characteristic curves of the constant-speed induction generator, due regard has to be taken of the decrease of frequency with increase of load, or what may be called the slip of frequency, s. Let, in an induction generator, Yo = go — jho = primary exciting admittance, Zo = To -\\- jxo = primary self-inductive impedance, Zi = ri + jxi = secondary self-inductive impedance ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-36", "section_label": "Chapter 14: Short-Circuit Currents Of Alternators", "section_title": "Short-Circuit Currents Of Alternators", "kind": "chapter", "sequence": 36, "number": 14, "location": "lines 14549-15353", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "snippets": [ "... as uni-tooth high frecfUency alternators, this increase of the momentary short-circuit current over the permanent short- circuit current is moderate, but may reach enormous values in machines of low self-inductance and high armature reaction, as large low frequency turbo alternators. 114. Superimposed upon this transient term, resulting from the gradual adjustment of the field flux to a change of m.m.f., is the transient term of armature reaction. In a polyphase alternator, the resultant m.m.f. of the .armature in ...", "... and therefore generates in the field coils Field Current Armature Current Fig. 50. Three-phase short-circuit current of a turbo-alternator. an e.m.f. and causes a corresponding pulsation in the field current and field terminal voltage, of the same frequency as the armature current, as shown by the oscillogram of such a three-phase short-circuit, in Fig. 50. This pulsation of field current is independent of the point in the wave, at which the short-circuit occurs, and dies out gradually, with the dying out o ...", "... ve, at which the short-circuit occurs, and dies out gradually, with the dying out of the transient term of the rotating m.m.f. In a single-phase alternator, the armature reaction is alter- nating with regard to the armature, hence pulsating, with double frequency, with regard to the field, varying between zero and its SHORT-CIRCUIT CURRENTS OF ALTERNATORS 203 maximum value, and therefore generates in the field coils a double frequency e.m.f., producing a pulsation of field current of double frequency. This doub ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-54", "section_label": "Chapter 5: Free Oscillations", "section_title": "Free Oscillations", "kind": "chapter", "sequence": 54, "number": 5, "location": "lines 31451-32708", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "snippets": [ "... ONS. 28. The general equations of the electric circuit, (50) and (51), contain eight terms: four waves: two main waves and their reflected waves, and each wave consists of a sine term and a cosine term. The equations contain five constants, namely: the frequency constant, g; the wave length constant, &; the time attenuation constant, u\\ the distance attenuation constant, h, and the time acceleration constant, s ; among these, the time attenuation, uy is a constant of the circuit, independent of the character of t ...", "... ion, 21, (2n + 2LVW ' (232) L>VW (233) Denoting the length of the circuit in a quarter-wave oscillation by and the length -of the circuit in a half-wave oscillation by (234) (235) the wave length of the fundamental or lowest frequency of oscillation is >10 = 4 ^ = 2 Ja; (236) or the length of the fundamental wave, with the velocity of prop- agation as distance unit, in a quarter-wave oscillation is (237) and in a half-wave oscillation is *, = 2 Z0 VW. FREE OSCILLATIONS ...", "... ; • ,* ^ * == V 7 e 2,n#r> sm nr sin (w0 - jj, * L Y where (245) ko 2^VW (240) ^0 = 4 Z0 v L(7 in a quarter-wave t (237) = 2 Z0 v LC in a half-wave oscillation, J and MV £~w< = e ~ .-^T. (246) ^0 is the wave length, and thus — the frequency, of the funda- mental wave, with the velocity of propagation as distance unit. It is interesting to note that the time decrement of the free oscillation, e~ut, is the same for all frequencies and wave lengths, FREE OSCILLATIONS 491 and that the relat ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-55", "section_label": "Chapter 6: Transition Points And The Complex Circuit", "section_title": "Transition Points And The Complex Circuit", "kind": "chapter", "sequence": 55, "number": 6, "location": "lines 32709-33527", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "snippets": [ "... apacity, respect- ively, of the section i of the circuit, per unit length, for instance, per mile, in a line, per turn in a transformer coil, etc. In a complex circuit the time variable t is the same throughout the entire circuit, or, in other words, the frequency of oscillation, as represented by q, and the rate of decay of the oscillation, as represented by the exponential function of time, must be the same throughout the entire circuit. Not so, however, with the distance variable Z; the wave length of the oscill ...", "... om Xl to X2, etc. At X = ^ it then must be i1 = i2, e1 = e2; thus substituting A = ^ into equations (266) and (267) gives cos q2(^+t-d2. (269) TRANSITION POINTS AND THE COMPLEX CIRCUIT 503 Herefrom it follows that «, = = <^ cos /? { 1 + e cos [2 /3 - = average ...", "... os [2 7/3 - e] ) . Hence the e.m.f. generated thereby, d(j) = - V2Trf^^ {coS|S(l + e cos [2 7^ - 0])}' And, expanded, e = V2 x/n j sin /3 + e \" ^y— sin [(27- 1)13 - 6] + 6^^^^sin[(27+l)^-^] }• Hence, the pulsation of the magnetic flux with the frequency, 2 7, as due to the existence of 7 slots per pole, introduces two harmonics, of the orders (2 7 — 1) and (2 7 + 1). 235. If 7 = 1 it is e = V2 7r/n$ { sin /3 + | sin (/3 - 0) + ~ sin (3/3-0) j ; that is, in a unitooth single-phaser a pronounced triple ...", "... -^' cos [(2 7 + 1) i3 - ^^ + i] hence the wave of generated e.m.f., e = — n-j- — — 2 TTjn -j- dt •' dl3 = a; sin ^ + ^^ sin (^ - 9,) + 2t ^ ^^+ ^ [e^ sin [(2 7 + 1) ^ - g + 62 ^,, sin [(2 y + 1)13 - d^ + 1]] ; that is, the pulsation of reactance of frequency, 2 7, introduces two higher harmonics of the order (2 7 — 1) and (2 7 + 1). If X = x{l -h ecos (2/3 - d)}, it is = 2^{ cos 1(3 + I cos (^ - ^) + |cos (3 /3 - 0) } ; e = a: j sin i3 +^ sin (0 - 9) + -^ sin (3 /3 - 0) • Since the pulsation of rea ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-05", "section_label": "Chapter 6: Induction-Motor Regulation And Stability", "section_title": "Induction-Motor Regulation And Stability", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 10583-12397", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-05/", "snippets": [ "... 00.0; 107.5: 102.0 OH OiO • • • • 0 ^1 H *£ ** ** eM -* 0000 • • • • 0000 »H *-l f>4 <-4 ^as .2 31 00 O CO 00 0000 I I I • • • 000 s CO 00 000*0 I I I O © «\"« • » • 000 INDUCTION-MOTOR REGULATION 131 3. FREQUENCY PULSATION 81. If the frequency of the voltage supply pulsates with sufficient rapidity that the motor speed can not appreciably follow the pulsations of frequency, the motor current and torque also pulsate; that is, if the frequency pulsates by the fract ...", "... • • • • 0 ^1 H *£ ** ** eM -* 0000 • • • • 0000 »H *-l f>4 <-4 ^as .2 31 00 O CO 00 0000 I I I • • • 000 s CO 00 000*0 I I I O © «\"« • » • 000 INDUCTION-MOTOR REGULATION 131 3. FREQUENCY PULSATION 81. If the frequency of the voltage supply pulsates with sufficient rapidity that the motor speed can not appreciably follow the pulsations of frequency, the motor current and torque also pulsate; that is, if the frequency pulsates by the fraction, p, above and below the norm ...", "... s CO 00 000*0 I I I O © «\"« • » • 000 INDUCTION-MOTOR REGULATION 131 3. FREQUENCY PULSATION 81. If the frequency of the voltage supply pulsates with sufficient rapidity that the motor speed can not appreciably follow the pulsations of frequency, the motor current and torque also pulsate; that is, if the frequency pulsates by the fraction, p, above and below the normal, at the average slip, s, the actual slip pulsates between s + p and a — p, and motor current and = =■ - ^pts uw ^ ^^J ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-52", "section_label": "Chapter 3: Standing Waves", "section_title": "Standing Waves", "kind": "chapter", "sequence": 52, "number": 3, "location": "lines 29316-30243", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "snippets": [ "... nd zero g, in which no energy losses occur, the speed of propagation is and if the medium has unit permeability and unit inductivity, it is the speed of light, S0 = 3 X 1010. (124) In an undamped circuit, this wave length lWo would correspond to the frequency, STANDING WAVES 447 hence, from (62), '•-,Vr.- <125> The frequency at the wave length lWo is zero, since at this wave length the phenomenon ceases to be oscillatory ; that is, due to the energy losses in the circuit, by the effective resistance r ...", "... and if the medium has unit permeability and unit inductivity, it is the speed of light, S0 = 3 X 1010. (124) In an undamped circuit, this wave length lWo would correspond to the frequency, STANDING WAVES 447 hence, from (62), '•-,Vr.- <125> The frequency at the wave length lWo is zero, since at this wave length the phenomenon ceases to be oscillatory ; that is, due to the energy losses in the circuit, by the effective resistance r and effective conductance g, the frequency / of the wave is reduced below t ...", "... from (62), '•-,Vr.- <125> The frequency at the wave length lWo is zero, since at this wave length the phenomenon ceases to be oscillatory ; that is, due to the energy losses in the circuit, by the effective resistance r and effective conductance g, the frequency / of the wave is reduced below the value corresponding to the wave length lw, the more, the greater the wave length, until at the wave length lWo the frequency becomes zero and the phenomenon thereby non-oscillatory. This means that with increasing wave l ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1120-1683", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-01/", "snippets": [ "... ove-mentioned fundamental laws of continuous currents, we find in alternating-current circuits the following: Ohm's law assumes the form i = -, where z, the apparent resistance, or impedance, is no longer a constant of the circuit, but depends upon the frequency of the currents; and in circuits containing iron, etc., also upon the e.m.f. Impedance, z, is, in the system of absolute units, of the same dimension as resistance (that is, of the dimension lt~^ = velocity), and is expressed in ohms. It consists of tw ...", "... ce. It may no longer be a constant of the circuit. The reactance, x, does not represent the expenditure of energy as does the effective resistance, r, but merelj^ the surging to and fro of energy. It is not a constant of the circuit, but depends upon the frequency, and frequently, as in circuits containing iron, or in electrolytic conductors, upon the e.m.f. also. Hence while the effective resistance, r, refers to the power or active component of e.m.f., or the e.m.f. in phase with the current, the re- actance, X, ...", "... s the current and L is the inductance of a cir- cuit, the magnetic flux interlinked with a circuit of current, i, is Li, and 4/L* is consequently the average rate of cutting; that is, the number of lines of force cut by the conductor per second, where / = frequency, or number of complete periods (double reversals) of the current per second, i = maximum value of current. Since the maximum rate of cutting bears to the average rate the same ratio as the quadrant to the radius of a circle (a sinu- 4 ALTERNATING-CURR ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-10", "section_label": "Chapter 10: Instability Of Circuits : The Arc", "section_title": "Instability Of Circuits : The Arc", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 17632-21381", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-10/", "snippets": [ "... assumed as constant. The effect of the variation of constants, as found more or less in actual circuits: the change of L with the current in circuits con- taining iron; the change of C and g with the voltage (corona, etc.) ; the change of r and g with the frequency, etc., has been studied to a limited extent only, and in specific cases. In the application of the theory of transients to actual electric circuits, considerable judgment thus is often necessary to allow and correct for these \"secondary\" phenomena which ...", "... all three may occur, under different circuit conditions. The electric arc is the most frequent and most serious cause of instability of electric circuits, and therefore should first be sus- pected, especially if the instability assumes the form of high- frequency disturbances or abrupt changes of current or voltage, such as is shown for instance in the oscillograms. Figs. 80 and 81. Somewhat similar effects of instability are produced by pyro- electric conductors. Induction motors and synchronous motors may show ...", "... elf-destruction of the system results, or the in- creasing energy loss becomes equal to the energy supply, and a stationary condition of oscillation results. The mechanism of this energy supply to an oscillating system from a source of energy differing in frequency from that of the oscillation is still practi- cally unknown, and very little investigating work has been done to clear up the phenomenon. It is not even generally realized that the phenomenon of a permanent or cumulative line surge involves an energy supp ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-40", "section_label": "Chapter 4: Arc Rectification", "section_title": "Arc Rectification", "kind": "chapter", "sequence": 40, "number": 4, "location": "lines 17755-19259", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "snippets": [ "... t-current rectifier will be considered more explicitly in the following paragraphs. The constant-current mercury arc rectifier system, as used for the operation of constant direct-current arc circuits from an alternating constant potential supply of any frequency, is sketched diagrammatically in Fig. 60. It consists of a constant-current transformer with a tap C brought out from the middle of the secondary coil AB. The rectifier tube has two graphite anodes ARC RECTIFICATION 251 a, 6, and a mercury cathode ...", "... to maintain the d. c. current fluctuation within certain given limits. The efficiency, power factor, regulation, etc., of such a mercury arc rectifier system are essentially those of the constant-current transformer feeding- the rectifier tube. Let / = frequency of the alternating-current supply system, i0 = mean value of the rectified direct current, and a = the pulsa- tion of the rectified current from the mean value, i.e., i0 (1 + a) the maximum and i0 (1 - a) the minimum value of direct cur- rent. A pulsation ...", "... per cent is permissible in an arc circuit. The total variation of the rectified current then is 2 aiOJ i.e., the alternating component of the direct current has the maximum value ai0, hence the effective value — i_ i0 (or for a = 0.2, 0.141 10) and the frequency 2/. Hysteresis and eddy losses in the direct-current reactive coil, therefore, correspond to an alternating current of frequency 2f and effective value a -—— i0, or about 0.141 -iQ, i.e., are small even at relatively high densities. 256 TRANSIENT ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-53", "section_label": "Chapter 4: Traveling Waves", "section_title": "Traveling Waves", "kind": "chapter", "sequence": 53, "number": 4, "location": "lines 30244-31450", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "snippets": [ "CHAPTER IV. TRAVELING WAVES. 20. As seen in Chapter III, especially in electric power cir- cuits, overhead or underground, the longest existing standing wave has a wave length which is so small compared with the critical wave length — where the frequency becomes zero — that the effect of the damping constant on the frequency and the wave length is negligible. The same obviously applies also to traveling waves, generally to a still greater extent, since the lengths of traveling waves are commonly only a sm ...", "... cially in electric power cir- cuits, overhead or underground, the longest existing standing wave has a wave length which is so small compared with the critical wave length — where the frequency becomes zero — that the effect of the damping constant on the frequency and the wave length is negligible. The same obviously applies also to traveling waves, generally to a still greater extent, since the lengths of traveling waves are commonly only a small part of the length of the circuit. Usually, therefore, in the discus ...", "... veling waves are commonly only a small part of the length of the circuit. Usually, therefore, in the discussion of traveling waves, the effect of the damping constants on the fre- quency constant q and the wave length constant k can be neglected, that is, frequency and wave length assumed as inde- pendent of the energy loss in the circuit. Usually, therefore, the equations (74) and (75) can be applied in dealing with the traveling wave. In these equations the distance traveled by the wave per second is used as un ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-03-record", "section_label": "Report Record 4: Record of Four Troubles", "section_title": "Record of Four Troubles", "kind": "report-record", "sequence": 4, "number": 4, "location": "PDF pages 16-27, lines 1139-2164", "status": "pdf-text-extracted-candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-03-record/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-03-record/", "snippets": [ "... f about 1 second per beat. d) The tie line reactor B, got very hot. e) The drop of voltage and the voltage fluctuation lasted for 18 minutes, with only slight decrease. Then they suddenly disappeared and normal voltage returned. f) During the disturbance, the frequency of the system fluctuated by about two cycles, that is 8%, and three machines in Fisk A where the trouble originated tripped their excess speed governors and cut off steam. g) Some synchronous machines dropped out of step, but the exact record is no more avail ...", "... of the synchronous impedance), the amplitude of the oscillation steadily diminishes, until the oscillation disappears. That is, the interchange current between two alternators which are in synchronism but out of phase, pulsates, with approximate- ly constant frequency of the beat, but with an amplitude, which grad- ually decreases to nothing. If the EMFs of the two machines are equal, then at the moment when the two machines are in phase, there is no resultant EMF, and thus no current, and when the machines are out of phas ...", "... rested in the magnitude of the effects, we may for simplicity assume equality of EMF of the machines. B If two alternators or groups of alternators such as station sections, are connected together out of synchronism, that is while differing from each other in frequency, they slowly slip past each other, and during each cycle of slip, or beat, a periodic energy transfer takes place, while the interchange current periodically rises and falls. During one-quar- ter the cycle of slip, or beat, the alternators are partly in phase ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-10", "section_label": "Theory Section 10: Hysteresis and Effective Resistance", "section_title": "Hysteresis and Effective Resistance", "kind": "theory-section", "sequence": 10, "number": 10, "location": "lines 3234-3585", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-10/", "snippets": [ "... sheet iron or sheet steel and in silicon steel, rj varies from 0.60 X 10~3 to 2.5 X 10~3, and can in average, for good material, be assumed as 1.5 X 10~3. The loss of power in the volume, V, at flux density B and frequency /, is thus P = VfoB1'6 X 10\"7, in watts, and, if / = the exciting current, the hysteretic effective resist- ance is P B1'6 r\" =J-* = VfrW-^' If the flux density, B, is proportional to the current, /, sub- stitutin ...", "... sub- stituting for B, and introducing the constant k, we have rn V ~ 'PA' that is, the effective hysteretic resistance is inversely propor- tional to the 0.4 power of the current, and directly proportional to the frequency. 49. Besides hysteresis, eddy or Foucault currents contribute to the effective resistance. Since at constant frequency the Foucault currents are pro- portional to the magnetism producing them, and thus approxi- mately proportio ...", "... resistance is inversely propor- tional to the 0.4 power of the current, and directly proportional to the frequency. 49. Besides hysteresis, eddy or Foucault currents contribute to the effective resistance. Since at constant frequency the Foucault currents are pro- portional to the magnetism producing them, and thus approxi- mately proportional to the current, the loss of power by Foucault currents is proportional to the square of the current, the same as ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-20", "section_label": "Chapter 20: Commutator Motors", "section_title": "Commutator Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 19458-20501", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "snippets": [ "... he primary circuit by the ratio of turns, in the same way as done in the chapter on Induction Motors. 217. Let $ = maximum magnetic flux per field pole ; e = effective E.M.F. induced thereby in the field turns ; thus, where ;/ = number of turns, N= frequency. = — -- \\&-anN The instantaneous value of magnetism is = <& sin (3 ; and the flux interlinked with the armature circuit <£x = sin /3 sin X ; when X is the angle between the plane of the armature coil and the direction of ...", "... irection of the magnetic flux. (Usually about 45°.) The E.M.F. induced in the armature circuit, of n turns, (as reduced to primary circuit), is thus, e = _ n ^1 10-8, = - n® 4- sin B sin X lO\"8, at at = - n$> sin X cos (3 + sin (3 cos X 10~8. If N= frequency in cycles per second, N: = frequency of rotation or speed in cycles per second, and k = N^/ N speed we have frequency thus, gl = — 2-TrnJV® {sin X cos /? + k cos X sin B\\ 10~8, or, since $ = — — — — , et = e V2 {sin X cos /3 + k cos X sin fi\\. ...", "... he magnetic flux. (Usually about 45°.) The E.M.F. induced in the armature circuit, of n turns, (as reduced to primary circuit), is thus, e = _ n ^1 10-8, = - n® 4- sin B sin X lO\"8, at at = - n$> sin X cos (3 + sin (3 cos X 10~8. If N= frequency in cycles per second, N: = frequency of rotation or speed in cycles per second, and k = N^/ N speed we have frequency thus, gl = — 2-TrnJV® {sin X cos /? + k cos X sin B\\ 10~8, or, since $ = — — — — , et = e V2 {sin X cos /3 + k cos X sin fi\\. 360 ALTERNATING-CUR ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-02-discussion-of-recommendations", "section_label": "Report Section 3: Discussion of Recommendations", "section_title": "Discussion of Recommendations", "kind": "report-section", "sequence": 3, "number": 3, "location": "PDF pages 12-16, lines 721-1138", "status": "pdf-text-extracted-candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-02-discussion-of-recommendations/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-02-discussion-of-recommendations/", "snippets": [ "Discussion of Recommendations While recommendations 1) to 3) should greatly reduce the frequency of troubles or keep them out of the generating system by isolating or localizing them by the feeder reactors, it obviously is not possible to absolutely guard against the occasional troubles in the generating sys- tem, such as short circuits. But as soon as t ...", "... fore is hardly to be expected that they would promptly drop into synchronism but rather would continue indefinitely to drift out of synchronism with the rest of the system. Two alternators or stations, thrown together out of synchronism, that is, differing in frequency from each other, will promptly, that is, practically instantly, pull each other into step, that is, the slow machine [[END_PDF_PAGE:14]] [[PDF_PAGE:15]] Report of Charles P. Steinmetz speeds up and the fast machine slows down, if their frequency differ- ence ...", "... differing in frequency from each other, will promptly, that is, practically instantly, pull each other into step, that is, the slow machine [[END_PDF_PAGE:14]] [[PDF_PAGE:15]] Report of Charles P. Steinmetz speeds up and the fast machine slows down, if their frequency differ- ence was low enough. This, however, would, with turbo-alternators, require a frequency difference not much exceeding one percent, and it is not probable that the unloaded station, idling on the governors, would be so close in frequency to the loaded s ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-01", "section_label": "Lecture 1: General Review", "section_title": "General Review", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 154-565", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-01/", "snippets": [ "... rrent is usually applied for railroading. For power distribution, both forms of current are used; in electrochemistry, direct current must be used for electrolytic work, while for electric furnace work alternating current is preferable. The two standard frequencies of alternating current are 60 cycles and 25 cycles. The former is used for general distri- bution for lighting and power, the latter for conversion to direct current, for alternating current railways, and for large powers. GENERAL REVIEW ii In Englan ...", "... ycles. The former is used for general distri- bution for lighting and power, the latter for conversion to direct current, for alternating current railways, and for large powers. GENERAL REVIEW ii In England and on the continent, 50 cycles is standard frequency. This frequency still survives in this country in Southern California, where it was introduced before 60 cycles was standard. The frequencies of 125 to 140 cycles, which were standard in the very early days, 20 years ago, have disappeared. The frequenc ...", "... r is used for general distri- bution for lighting and power, the latter for conversion to direct current, for alternating current railways, and for large powers. GENERAL REVIEW ii In England and on the continent, 50 cycles is standard frequency. This frequency still survives in this country in Southern California, where it was introduced before 60 cycles was standard. The frequencies of 125 to 140 cycles, which were standard in the very early days, 20 years ago, have disappeared. The frequency of 40 cycles, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-19", "section_label": "Chapter 19: Commutatob Motobs", "section_title": "Commutatob Motobs", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 21339-22387", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "snippets": [ "... the primary circuit by the ratio of turns, in the same way as done in the chapter on Induction Motors. 196. Let ^ = maximum magnetic flux per field pdle ; e = effective E.M.F. induced thereby in the field turns; thus : ^^ n = number of turns, iV= frequency, thus : ^ , 10» V2irnN The instantaneous value of magnetism is sin )3 ; and the flux interlinked with the armature circuit <^i = 4> sin p, sin X ; when X is the angle between the plane of the armature coil and the direction of the magne ...", "... rection of the magnetic flux. The E.M.F. induced in the armature circuit, of n turns, as reduced to primary circuit, is thus : ^ — _ «^^10-« = — « 4> — sin )3 sin X 10\"* == — « 4> ) sin X cos p dp_ lit + s\\npcos\\—\\ 10 ^ dt ) -8 If iV= frequency in cycles per second, N^ = speed in cycles per second (equal revolutions per second times num- ber of pairs of poles), it is : dt dt ' §197] COMMUTATOR MOTORS, 297 and since A = 45°, or sin X = cos X = 1 / V2, it is, sub- stituted : ^1= - V2fl-« ...", "... e magnetic flux. The E.M.F. induced in the armature circuit, of n turns, as reduced to primary circuit, is thus : ^ — _ «^^10-« = — « 4> — sin )3 sin X 10\"* == — « 4> ) sin X cos p dp_ lit + s\\npcos\\—\\ 10 ^ dt ) -8 If iV= frequency in cycles per second, N^ = speed in cycles per second (equal revolutions per second times num- ber of pairs of poles), it is : dt dt ' §197] COMMUTATOR MOTORS, 297 and since A = 45°, or sin X = cos X = 1 / V2, it is, sub- stituted : ^1= - V2fl-«*{iV^cos)3+^isin)3}10 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 963-1366", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "snippets": [ "... entioned fundamental laws of continuous currents, we find in alternating-current circuits the following : Ohm's law assumes the form, i = e ] s, where z, the apparent resistance, or impedance, is no longer a constant of the circuit, but depends upon the frequency of the cur- rents ; and in circuits containing iron, etc., also upon the E.M.F. Impedance, z, is, in the system of absolute units, of the same dimensions as resistance (that is, of the dimension LT~l = velocity), and is expressed in ohms. It consists ...", "... nger a constant of the circuit. The reactance, x, does not represent the expenditure of power, as does the effective resistance, r, but merely the surging to and fro of energy. It is not a constant of the INTRODUCTION. 3 circuit, but depends upon the frequency, and frequently, as in circuits containing iron, or in electrolytic conductors, upon the E.M.F. also. Hence, while the effective resist- ance, r, refers to the energy component of E.M.F., or the E.M.F. in phase with the current, the reactance, x, refers ...", "... he current, and L is the inductance of a circuit, the magnetic flux interlinked with a circuit of current, z, is Li, and 4 NLi is consequently the average rate of cutting ; that is, the number of lines of force cut by the conductor per second, where N ' = frequency, or number of complete periods (double reversals) of the cur- rent per second. Since the maximum rate of cutting bears to the average rate the same ratio as the quadrant to the radius of a circle (a sinusoidal variation supposed), that is the ratio ir/ ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-09", "section_label": "Chapter 9: Wave Screens. Even Harmonics", "section_title": "Wave Screens. Even Harmonics", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 16964-17631", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-09/", "snippets": [ "... pply wave, that is, the reverse procedure from that discussed in the preceding chapter, is accomplished by what has been called ''wave screens.\" Series reactance alone acts to a considerable extent as wave screen, by consuming voltage proportional to the frequency and the current, and thereby reducing the harmonics of voltage in the rest of the circuit the more, the higher their order. Let the voltage impressed upon the circuit be denoted sym- bolically by e = €i + 63 + es + ej + . . . =^i:en (29) where n de ...", "... gher their order. Let the voltage impressed upon the circuit be denoted sym- bolically by e = €i + 63 + es + ej + . . . =^i:en (29) where n denotes the order of the harmonic of absolute numerical value 6n. If, then, the reactance x (at fundamental frequency) is inserted into the circuit of resistance, r, the impedance is 2i = -y/r^ + x^ for the fundamental frequency, and Zn = y/r^ + n^^ for the nth harmonic, (30) and the current thus is e or, denoting f = ? = y , ^ (31) 2 ^Vr^ + nV ^ = c, (32 ...", "... ej + . . . =^i:en (29) where n denotes the order of the harmonic of absolute numerical value 6n. If, then, the reactance x (at fundamental frequency) is inserted into the circuit of resistance, r, the impedance is 2i = -y/r^ + x^ for the fundamental frequency, and Zn = y/r^ + n^^ for the nth harmonic, (30) and the current thus is e or, denoting f = ? = y , ^ (31) 2 ^Vr^ + nV ^ = c, (32) X it is 66 x^25 + c2 153 + . . . (33) 154 ELECTRIC CIRCUITS if r is small compared with x ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-45", "section_label": "Chapter 5: Distributed Series Capacity", "section_title": "Distributed Series Capacity", "kind": "chapter", "sequence": 45, "number": 5, "location": "lines 23586-23947", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "snippets": [ "... he voltage does not divide uniformly between the gaps, but the potential difference is the greater, that is, the potential gradient steeper the nearer the gap is to the line L, and this distribution of potential becomes the more non-uniform the higher the frequency; that is, the greater the charging current of the capacity of the cylinder against ground. The charging currents against ground, of all 848 DISTRIBUTED SERIES CAPACITY 349 the cylinders from q to the ground G, Figs. 90 and 91, must pass the gap ...", "... ester. formed by these two cylinders, C, this potential difference increases towards L, being, at each point proportional to the vector sum of all the charging currents, against ground, of all the cylinders between this point and ground. The higher the frequency, the more non-uniform is the poten- tial gradient along the circuit and the lower is the total supply voltage required to bring the maximum potential gradient, near the line L, above the disruptive voltage, that is, to initiate the discharge. Thus such a ...", "... ent along the circuit and the lower is the total supply voltage required to bring the maximum potential gradient, near the line L, above the disruptive voltage, that is, to initiate the discharge. Thus such a multigap structure is discriminating regarding frequency; that is, the discharge voltage with increas- 350 TRANSIENT PHENOMENA ing frequency, does not remain constant, but decreases with increase of frequency, when the frequency becomes sufficiently high to give appreciable charging currents. Hence high fre- ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-114", "section_label": "Apparatus Section 8: Induction Machines: Concatenation of Induction Motors", "section_title": "Induction Machines: Concatenation of Induction Motors", "kind": "apparatus-section", "sequence": 114, "number": 8, "location": "lines 21923-22191", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-114/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-114/", "snippets": [ "VIII. Concatenation of Induction Motors 160. In the secondary of the induction motor an e.m.f. is generated of the frequency of slip. Thus connecting the sec- ondary circuit of the induction motor to the primary of a second induction motor, the latter is fed by a frequency equal to the slip of the first motor, and reaches its synchronism at t ...", "... In the secondary of the induction motor an e.m.f. is generated of the frequency of slip. Thus connecting the sec- ondary circuit of the induction motor to the primary of a second induction motor, the latter is fed by a frequency equal to the slip of the first motor, and reaches its synchronism at the frequency of slip of the first motor, the first motor then acting as frequency converter for the second motor. If, then, two equal induction motor ...", "... slip. Thus connecting the sec- ondary circuit of the induction motor to the primary of a second induction motor, the latter is fed by a frequency equal to the slip of the first motor, and reaches its synchronism at the frequency of slip of the first motor, the first motor then acting as frequency converter for the second motor. If, then, two equal induction motors are rigidly connected together and thus caused to revolve at the same speed, the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-21", "section_label": "Apparatus Introduction 21: Introduction", "section_title": "Introduction", "kind": "apparatus-introduction", "sequence": 21, "number": null, "location": "lines 8292-8517", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-21/", "snippets": [ "... mmutator. 121 122 ELEMENTS OF ELECTRICAL ENGINEERING 2d. Synchronous machines, consisting of a undirectional mag- netic field and an armature revolving relatively to the mag- netic field at a velocity synchronous with the frequency of the alternating-current circuit connected thereto. . 3d. Rectifying apparatus, that is, apparatus reversing the direc- tion of an alternating current synchronously with the frequency. 4th. Induction machines, consisting of an ...", "... c field at a velocity synchronous with the frequency of the alternating-current circuit connected thereto. . 3d. Rectifying apparatus, that is, apparatus reversing the direc- tion of an alternating current synchronously with the frequency. 4th. Induction machines, consisting of an alternating mag- netic circuit or circuits interlinked with two electric circuits or sets of circuits moving with regard to each other. 5th. Stationary induction apparatus, consisting ...", "... arc rectifier. (4) Induction machines are generally used as motors, poly- phase or single-phase. In this case they run at practically constant speed, slowing down slightly with increasing load. As generators the frequency of the e.m.f. supplied by them differs from and is lower than the frequency of rotation, but their opera- tion depends upon the phase relation of the external circuit. As phase converters, induction machines can be used ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... tive gradient. 165 Distortion by magnetic field, resist- ance and reactance pulsa- tion. a42 of magnetizing current. 117 of wave, see Harmonics by hysteresis, 116 Distributed capacity. 168 Double delta connections of trans- formers to sis-phase. 428 frequency power and torque with distorted wave, 381 quantities, 180 peak wave. 370 T connections of transformers to six -phase, 430 ^ connection of transformers to six-phase, 429 Drop of voltage in line, 25 Dynamic circuit, 159 Eddy currents, 112 admittan ...", "... .2, f». &. HI valiK? at wav*-. It in i^olar dia|tmm. «^ Kffi«i««MO^ iff drruit wiith indutrtive induction motor. 234 Kl'-' ' trtf K.j: 123 Energy distance oJ dielectric field, 165 flow in polyph&K 9>-9lem. 406 and torque as component of double frequency vector, 186 Epoch. 6 Equivalent circuit of transformer, 202 sine wave in polar diagram, 53 single-phase circuit oi poh\"phase system, 448 Excitation of induction generator, 238 Exciter of induction generator. 238 Exciting admittance of indu ...", "... e induction motor, 247 transformer, 189 Field characteristic of alternator. 265 Fifth harmonic. 370 Five-wire system, efficiency, 466 Flat top wave. 370 zero wave, 370 Foucault ctirrenta, 113 Four-phase system, 397 wire systems, efficiency. 466 Frequency, 6 General w.*ve, symlxilism, 379 Generator, induction, 237 HijrnioiHrs. 7 caused h\\ arr. .liW \"-^AkWMtftkdSv^ ^i^v ■t-«j, .-.>< X ^ .*■% i ^ v-w. -fwt Tjt-^^' STT\" »e '<;--v\\ -yS leai^^^i^ -j^ ^■«r. KS? H I iiftp^ii*f^ ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1224-1727", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "snippets": [ "... entioned fundamental laws of continuous currents, we find in alternating-current circuits the following : Ohm's law assumes the form, i = c j Sy where r, the apparent resistance, or impcdaiue^ is no longer a constant of the circuit, but depends upon the frequency of the cur- rents ; and in circuits containing iron, etc., also upon the E.M.F. Impedance, ^, is, in the system of absolute units, of the same dimensions as resistance (that is, of the dimension L T~ * = velocity), and is expressed in ohms. It consist ...", "... constant of the circuit. The reactance, ;r, does not represent the expenditure of power, as does the effective resistance, r, but merely the surging to and fro of energy. It is not a constant of the §3] I.XTRODUCriO.V, 3 circuit, but depends upon the frequency, and frequently, as in circuits containing iron, or in electrolytic conductors, upon the E.M.F. also. Hence, while the effective resist- ance, /', refers to the energy component of E.M.F., or the E.M.F. in phase with the current, the reactance, ;r, refers ...", "... the current, and L is the inductance of a circuit, the magnetic flux interlinked with a circuit of current, /, is Lt, and 4 NLt is consequently the average rate of cutting ; that is, the number of lines of force cut by the conductor per second, where JV= frequency, or number of complete periods (double reversals) of the cur- rent per second. Since the maximum rate of cutting bears to the average rate the same ratio as the quadrant to the radius of a circle (a sinusoidal variation supposed), that is the ratio IT ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-06", "section_label": "Chapter 7: Higher Harmonics In Induction Motors", "section_title": "Higher Harmonics In Induction Motors", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 12398-13955", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-06/", "snippets": [ "... As seen, these also constitute a quarter-phase system of voltage, but the second wave, which is lagging in the funda- mental, is 90° leading in the third harmonic, or in other words, the third harmonic gives a backward rotation of the poles with triple frequency. It thus produces a torque in opposite direc- tion to the. fundamental, and would reach its synchronism, that is, zero torque, at one-third of synchronism in negative direction, or at the speed - a7 - ^ J + e9 cos (9 4> — ag) + . e\" = 61 cos ( 0 — -s J + e8 cos (3 0 — a8) + e& cos (5 0 — «* + ■ 3*) + e7 cos ( 7 0 - a7 - «- j + e9 cos (9 4> — ag) + • Thus the voltage components of different frequency, impressed upon the three motor phases, are : ei cos * rj COR n cos e? cos r* cos (3 4> - aa) (5* - a4) (7* - a;) (9 * - a») ei cos / 2t\\ ft cos es cos / 2t\\ e 7 cos / 2f\\ r» cos (♦-t) (3 0 - oa) ^♦-« + --j 17* - a ...", "... is, a torque which, starting with zero at standstill, increases to a maximum in positive direction or assisting, and then decreases again to zero at its synchronous speed, and above this, becomes negative as single-phase induction-generator torque. Triple frequency with three times the number of poles gives a synchronous speed of S = +}(>. That is, the third harmonic in a three-phase vol- tage may give a single-phase motor torque with a synchronous speed of one-ninth that of the fundamental torque, and in cither di ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-08", "section_label": "Chapter 9: Synchronous Induction Motor", "section_title": "Synchronous Induction Motor", "kind": "chapter", "sequence": 8, "number": 9, "location": "lines 14466-14550", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-08/", "snippets": [ "... with the rotation of the arma- ture the secondary circuit, corresponding to a primary circuit, varies from short-circuit at coincidence of the axis of the arma- ture coil with the axis of the primary coil, to open-circuit in quadrature therewith, with the periodicity of the armature speed. That is, the apparent admittance of the primary circuit varies periodically from open-circuit admittance to the short- circuited transformer admittance. At synchronism such a motor represents an electric circuit of an admittance v ...", "... d. That is, the apparent admittance of the primary circuit varies periodically from open-circuit admittance to the short- circuited transformer admittance. At synchronism such a motor represents an electric circuit of an admittance varying with twice the periodicity of the primary frequency, since twice per period the axis of the armature coil and that of the primary coil coincide. A varying admittance is obviously identical in effeel with a varying reluctance, which will be discussed in the chapter on reaction machi ...", "... ittance of the primary circuit varies periodically from open-circuit admittance to the short- circuited transformer admittance. At synchronism such a motor represents an electric circuit of an admittance varying with twice the periodicity of the primary frequency, since twice per period the axis of the armature coil and that of the primary coil coincide. A varying admittance is obviously identical in effeel with a varying reluctance, which will be discussed in the chapter on reaction machines. That is, the inducti ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-07", "section_label": "Chapter 7: Shaping Of Waves : General", "section_title": "Shaping Of Waves : General", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 12222-12961", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-07/", "snippets": [ "... in Fig. 52, by connecting B and A in series with each other in such direction that the fundamentals cancel (that is, in opposition for the fundamental wave), we get voltage wave III of Fig. 53, which contains only the even harmonics, that is, is of double frequency. Connecting A and B in series so that the fundamentals add and the second harmonics cancel, gives the wave IV. If the machine is a three-phase F-connected alterna- tor, with ciu^e IV as the voltage per phase, or Y voltage, the delta or terminal voltage, d ...", "... form density under the pole and tapering off at the pole corners, curve I, such as would approximately correspond to actual con- 116 ELECTRIC CIRCUITS ditions. As seen, curve III as well as V are approximately sine waves, but the one of twice the frequency of the other. Thus, such a machine, by reversing connections between the two wind- ings A and B, could be made to give two frequencies, one double the other, or as synchronous motor could run at two speeds, one one-half the other. Fig. 53. 61. Distr ...", "... 116 ELECTRIC CIRCUITS ditions. As seen, curve III as well as V are approximately sine waves, but the one of twice the frequency of the other. Thus, such a machine, by reversing connections between the two wind- ings A and B, could be made to give two frequencies, one double the other, or as synchronous motor could run at two speeds, one one-half the other. Fig. 53. 61. Distribution of the winding over an arc of the periphery^ o^ the armature eliminates or reduces the higher harmonics, so tti^^t the terminal ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-13", "section_label": "Chapter 13: Reactance Of Synchronous Machines", "section_title": "Reactance Of Synchronous Machines", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 23466-24022", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-13/", "snippets": [ "... effect is represented by a self-inductive reactance, x, the gradual or mutual inductive effect by an armatiu'e reaction. The relation between self-inductive component, x, and mutual inductive component, x\\ varies from about 2 -?- 1 in the unitooth- high frequency alternators of old, to about 1 -5- 20 in some of the earlier turbo-alternators. In those synchronous machines, which contain a squirrel-cage induction-motor winding in the field faces, for starting as motors, or as protection against himting, or to equaU ...", "... ctance has no inductive effect on the field, as its resultant is imidirectionaJ with regard to the field flux. In the single-phase machine, however (or polyphase machine on imbalanced load), such inductive effect exists, as a permanent pulsation of double frequency. The mutual inductive flux of the armature circuit on the field circuit is alternating, and the field circuit, revolving synchronously REACTANCE OF SYNCHRONOUS MACHINES 241 through this alternating flux, thus has an e.m.f. of double fre- quency induce ...", "... he armature circuit on the field circuit is alternating, and the field circuit, revolving synchronously REACTANCE OF SYNCHRONOUS MACHINES 241 through this alternating flux, thus has an e.m.f. of double fre- quency induced in it, which produces a double-frequency current in the field circuit, superimposed on the direct ciu-rent from the exciter. The field flux of the single-phase alternator (or poly- phase alternator at imbalanced load) thus pulsates with double frequency, and, by being carried synchronously throu ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-31", "section_label": "Chapter 9: Divided Circuit", "section_title": "Divided Circuit", "kind": "chapter", "sequence": 31, "number": 9, "location": "lines 9228-10474", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "snippets": [ "... circuit 3 is (4) Instead of the inductances, L, and capacities, C, it is usually preferable, even in direct-current circuits, to introduce the reactances, x = 2 nfL = inductive reactance, xc = = con- 2 7T/G densive reactance, referred to a standard frequency, such as / = 60 cycles per second. Instead of the time t, then, an angle 0 = 2 nft (5) is introduced, and then we have di x di dd di ^ * (6) i/iift - 2 Kfo f Id0 - Xc/i dd, t since Hereby resistance, inductance, and capacity are expressed i ...", "... d of the inductances, L, and capacities, C, it is usually preferable, even in direct-current circuits, to introduce the reactances, x = 2 nfL = inductive reactance, xc = = con- 2 7T/G densive reactance, referred to a standard frequency, such as / = 60 cycles per second. Instead of the time t, then, an angle 0 = 2 nft (5) is introduced, and then we have di x di dd di ^ * (6) i/iift - 2 Kfo f Id0 - Xc/i dd, t since Hereby resistance, inductance, and capacity are expressed in the same units, ohms. Time is ...", "... it, the pulsation of current in the load circuit is still zero after 0 = 24°, or after 0.001 seconds, and reaches 1.25 per cent of the pulsation of impressed e.m.f., e0, after 6 = 60°, or t = 0.00275 seconds. A pulsation of the impressed e.m.f., e0, of a frequency higher than 250 cycles, practically cannot penetrate to the load circuit, that is, does not appear at all in the load current it regardless of how much a pulsation of the impressed e.m.f., e0, it is, and a DIVIDED CIRCUIT 139 pulsation of impressed e. ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-37", "section_label": "Apparatus Section 16: Synchronous Machines: Higher Frequency Cross Currents Between Synchronous Machines", "section_title": "Synchronous Machines: Higher Frequency Cross Currents Between Synchronous Machines", "kind": "apparatus-section", "sequence": 37, "number": 16, "location": "lines 10124-10189", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-37/", "snippets": [ "XVI. Higher Frequency Cross Currents between Synchronous Machines 30. If several synchronous machines of different wave shapes are connected into the same circuit, cross currents exist between the machines of frequencies which are odd multiples ...", "XVI. Higher Frequency Cross Currents between Synchronous Machines 30. If several synchronous machines of different wave shapes are connected into the same circuit, cross currents exist between the machines of frequencies which are odd multiples of the circuit frequency, that is, higher harmonics thereof. The machines may be two or more generators, in the same or in different stations, of wave shapes containing higher harmonics of different ...", "... between Synchronous Machines 30. If several synchronous machines of different wave shapes are connected into the same circuit, cross currents exist between the machines of frequencies which are odd multiples of the circuit frequency, that is, higher harmonics thereof. The machines may be two or more generators, in the same or in different stations, of wave shapes containing higher harmonics of different order, intensity or phase, or synchronous motors ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-84", "section_label": "Apparatus Section 5: Synchronous Converters: Armature Reaction", "section_title": "Synchronous Converters: Armature Reaction", "kind": "apparatus-section", "sequence": 84, "number": 5, "location": "lines 15161-15475", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-84/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-84/", "snippets": [ "... — )COB(T-— we have that is, the resultant m.m.f. in any direction T has the phase 6 = r, and the intensity, rcFiA/2 ~^~ thus revolves in space with uniform velocity and constant in- tensity, in synchronism with the frequency of the alternating current. 248 ELEMENTS OF ELECTRICAL ENGINEERING Since in the converter, Fl = ^M, TTU we have the resultant m.m.f. of the power component of the alternating current in the n-phase converter. This ...", "... ions neutralize, a local effect remains which in its relation to the magnetic field oscillates with a period equal to the time of motion of the armature through the angle between adjacent alternating leads; that is, double frequency in a single-phase converter (in which it is equal in magnitude to the direct-current reaction, and is the oscillating armature reaction discussed above), sextuple frequency in a three-phase converter, and quadruple frequency i ...", "... e between adjacent alternating leads; that is, double frequency in a single-phase converter (in which it is equal in magnitude to the direct-current reaction, and is the oscillating armature reaction discussed above), sextuple frequency in a three-phase converter, and quadruple frequency in a four- phase converter. The amplitude of this oscillation in a polyphase converter is small, arid its influence upon the magnetic field is usually neg- ligible, due to ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-23", "section_label": "Chapter 23: Synchronizing Alternators", "section_title": "Synchronizing Alternators", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 25135-25681", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-23/", "snippets": [ "... ; and the power with which it tends to' remain in synchronism is the maximum power which it can furnish as synchronous motor under the conditions of running, 204. The principal and foremost condition of parallel opera- tion of alternators is equality of frequency; that is, the trans- mission of power from the prime movers to the alternators must be such as to allow them to run at the same frequency without slippage or excessive strains on the belts or transmission devices. Rigid mechanical connection of the alter ...", "... ditions of running, 204. The principal and foremost condition of parallel opera- tion of alternators is equality of frequency; that is, the trans- mission of power from the prime movers to the alternators must be such as to allow them to run at the same frequency without slippage or excessive strains on the belts or transmission devices. Rigid mechanical connection of the alternators cannot be con- sidered as synchronizing, since it allows no flexibility or phase adjustment between the alternators, but makes them ...", "... annot be taken care of by phase adjustment of the machines. Thus rigid mechanical connection is not desirable for parallel operation of alternators. 205. The second important condition of parallel operation is uniformity of speed; that is, constancy of frequency. If, for instance, two alternators are driven by independent single- cylinder engines, and the cranks of the engines happen to be crossed, the one engine will pull, while the other is near the dead- point, and conversely. Consequently, alternately the one ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-17", "section_label": "Chapter 17: Synchbonizino Aiitebkatobs", "section_title": "Synchbonizino Aiitebkatobs", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 18829-19345", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-17/", "snippets": [ "... tor ; and the power with which it tends to remain in synchronism is the maximum power which it can furnish as synchronous motor under the conditions of running. 169. The principal and foremost condition of parallel operation of alternators is equality of frequency ; that is, the transmission of power from the prime movers to the alternators must be such as to allow them to run at the same frequency without slippage or excessive strains on the belts or transmission devices. Rigid mechanical connection of the alter ...", "... conditions of running. 169. The principal and foremost condition of parallel operation of alternators is equality of frequency ; that is, the transmission of power from the prime movers to the alternators must be such as to allow them to run at the same frequency without slippage or excessive strains on the belts or transmission devices. Rigid mechanical connection of the alternators cannot be considered as synchronizing ; since it allows no flexibility or phase adjustment between the alternators, but makes them ...", "... ot be taken care of by phase adjustment of the machines. Thus rigid mechanical connection is not desirable for parallel operation of alternators. 170. The second important condition of parallel opera- tion is uniformity of speed ; that is, constancy of frequency. §171] SYNCHRONIZING ALTERNATORS, 249 If, for instance, two alternators are driven by independent single-cylinder engines, and the cranks of the engines hap- pen to be crossed, the one engine will pull, while the other is near the dead-point, and conv ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-18", "section_label": "Chapter 18: Synchronizing Alternators", "section_title": "Synchronizing Alternators", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17597-18052", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-18/", "snippets": [ "... tor ; and the power with which it tends to remain in synchronism is the maximum power which it can furnish as synchronous motor under the conditions of running. 190. The principal and foremost condition of parallel operation of alternators is equality of frequency ; that is, the transmission of power from the prime movers to the alternators must be such as to allow them to run at the same frequency without slippage or excessive strains on the belts or transmission devices. Rigid mechanical connection of the alter ...", "... conditions of running. 190. The principal and foremost condition of parallel operation of alternators is equality of frequency ; that is, the transmission of power from the prime movers to the alternators must be such as to allow them to run at the same frequency without slippage or excessive strains on the belts or transmission devices. Rigid mechanical connection of the alternators cannot be considered as synchronizing ; since it allows no flexibility or phase adjustment between the alternators, but makes them ...", "... ot be taken care of by phase adjustment of the machines. Thus rigid mechanical connection is not desirable for parallel operation of alternators. 191. The second important condition of parallel opera- tion is uniformity of speed ; that is, constancy of frequency. 312 ALTERNATING-CURRENT PHENOMENA. If, for instance, two alternators are driven by independent single-cylinder engines, and the cranks of the engines hap- pen to be crossed, the one engine will pull, while the other is near the dead-point, and conver ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-51", "section_label": "Chapter 2: Discussion Of General Equations", "section_title": "Discussion Of General Equations", "kind": "chapter", "sequence": 51, "number": 2, "location": "lines 28695-29315", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "snippets": [ "... gonometric, are both special cases of the equations (60) and (61), corresponding respectively to q = o, k = 0 and to h = 0, s = 0. 8. In the equations (50) and (51) qt = 2x gives the time of a complete cycle, that is, the period of the wave, and the frequency of the wave is / = -L 2 kl = 27T gives the distance of a complete cycle, that is, the wave length, W 7 7 k (u — s) t = 1 and (u + s) t = 1 give the time, */'- — and t\"= -*—, during which the wave decreases to - = 0.3679 of its value, and ...", "... 7 k (u — s) t = 1 and (u + s) t = 1 give the time, */'- — and t\"= -*—, during which the wave decreases to - = 0.3679 of its value, and hi = 1 gives the distance, over which the wave decreases to - = 0.3679 of its value; £ that is, q is the frequency constant of the wave, f - - I I: «'—'•• (62) > 2V °~' 434 TRANSIENT PHENOMENA k is the wave length constant, (63) (u - s) and (u -f s) are the time attenuation constants of the wave, 1 ) (64) U + S and h is the distance attenuation ...", "... 2V °~' 434 TRANSIENT PHENOMENA k is the wave length constant, (63) (u - s) and (u -f s) are the time attenuation constants of the wave, 1 ) (64) U + S and h is the distance attenuation constant of the wave, L -I. (65) 9. If the frequency of the current and e.m.f. is very high, thousands of cycles and more, as with traveling waves, lightning disturbances, high-frequency oscillations, etc., q is a very large quantity compared with s, u, m, h, k, and k is a large quantity compared with h, th ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... alculating the preceding harmonics. For instance, let the generator e.m.f. wave, Fig. 44, Table II, column 2, be impressed upon an underground cable system Fig. 44. Generator e.m.f. wave. of such constants (capacity and inductance), that the natural frequency of the system is 670 cycles per second, while the generator frequency is 60 cycles. The natural frequency of the TRIGONOMETRIC SERIES. 115 circuit is then close to that of the 11th harmonic of the generator wave, 660 cycles, and if the generator vo ...", "... ics. For instance, let the generator e.m.f. wave, Fig. 44, Table II, column 2, be impressed upon an underground cable system Fig. 44. Generator e.m.f. wave. of such constants (capacity and inductance), that the natural frequency of the system is 670 cycles per second, while the generator frequency is 60 cycles. The natural frequency of the TRIGONOMETRIC SERIES. 115 circuit is then close to that of the 11th harmonic of the generator wave, 660 cycles, and if the generator voltage contains an appreciable 11th har ...", "... .m.f. wave, Fig. 44, Table II, column 2, be impressed upon an underground cable system Fig. 44. Generator e.m.f. wave. of such constants (capacity and inductance), that the natural frequency of the system is 670 cycles per second, while the generator frequency is 60 cycles. The natural frequency of the TRIGONOMETRIC SERIES. 115 circuit is then close to that of the 11th harmonic of the generator wave, 660 cycles, and if the generator voltage contains an appreciable 11th harmonic, trouble may result from a ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-03", "section_label": "Theory Section 3: Generation of E.m.f.", "section_title": "Generation of E.m.f.", "kind": "theory-section", "sequence": 3, "number": 3, "location": "lines 1033-1243", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-03/", "snippets": [ "... OF ELECTRICAL ENGINEERING Thus it cuts during each revolution four times the lines of force inclosed in the position of maximum inclosure. If 3> = the maximum number of lines of force inclosed by the conductor, / = the frequency in revolutions per second or cycles, and n = number of convolutions or turns of the con- ductor, the lines of force cut per second by the conductor, and thus the average generated e.m.f. is, E = 4 fn$ absolute units, ...", "... um of the average values of the e.m.fs. of the individual coils. Thus in a direct-current machine, if $ = maximum flux in- closed per turn, n = total number of turns in series from com- mutator brush to brush, and / = frequency of rotation through the magnetic field. E = 4/n$> = generated e.m.f. ($ in megalines, / in hundreds of cycles per second). This is the formula of the direct-current generator. EXAMPLES 17. (1) A circular wire coil ...", "... flux in- closed per turn, n = total number of turns in series from com- mutator brush to brush, and / = frequency of rotation through the magnetic field. E = 4/n$> = generated e.m.f. ($ in megalines, / in hundreds of cycles per second). This is the formula of the direct-current generator. EXAMPLES 17. (1) A circular wire coil of 200 turns and 40 cm. mean diameter is revolved around a vertical axis. What is the horizontal intensity of th ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-104", "section_label": "Apparatus Section 7: Alternating-current Transformer: Types of Transformers", "section_title": "Alternating-current Transformer: Types of Transformers", "kind": "apparatus-section", "sequence": 104, "number": 7, "location": "lines 18521-18665", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-104/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-104/", "snippets": [ "... splaced in phase from each other by 120°. Their third harmonics therefore are displaced in phase from each other by 3 X 120°, that is, by 360°, or in other words, are in phase with each other. In Fig. 169, such triple frequency fluxes in the three cores would have no magnetic return, except by leakage through the air, that is, cannot exist, except in negligible intensity, and there- fore the core type of three-phase transformer cannot give any ser ...", "... the three cores would have no magnetic return, except by leakage through the air, that is, cannot exist, except in negligible intensity, and there- fore the core type of three-phase transformer cannot give any serious triple frequency voltage. In the shell type Fig. 168, however, the three triple frequency fluxes, being in phase with each other, produce a triple frequency single-phase flux through a closed magnetic circuit. Where the circuit conditions an ...", "... the air, that is, cannot exist, except in negligible intensity, and there- fore the core type of three-phase transformer cannot give any serious triple frequency voltage. In the shell type Fig. 168, however, the three triple frequency fluxes, being in phase with each other, produce a triple frequency single-phase flux through a closed magnetic circuit. Where the circuit conditions and connections are such as to give a triple harmonic — as with YY connecti ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-35", "section_label": "Apparatus Section 14: Synchronous Machines: Division of Load in Parallel Operation", "section_title": "Synchronous Machines: Division of Load in Parallel Operation", "kind": "apparatus-section", "sequence": 35, "number": 14, "location": "lines 9879-9917", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-35/", "snippets": [ "XIV. Division of Load in Parallel Operation 26. Much more important than equality of terminal voltage before synchronizing is equality of frequency. Inequality of frequency, or rather a tendency to inequality of frequency (since by necessity the machines hold each other in step or at equal frequency), causes cross currents which transfer'energy from the machine whose dr ...", "XIV. Division of Load in Parallel Operation 26. Much more important than equality of terminal voltage before synchronizing is equality of frequency. Inequality of frequency, or rather a tendency to inequality of frequency (since by necessity the machines hold each other in step or at equal frequency), causes cross currents which transfer'energy from the machine whose driving power tends to acc ...", "XIV. Division of Load in Parallel Operation 26. Much more important than equality of terminal voltage before synchronizing is equality of frequency. Inequality of frequency, or rather a tendency to inequality of frequency (since by necessity the machines hold each other in step or at equal frequency), causes cross currents which transfer'energy from the machine whose driving power tends to accelerate to the machine whose driving power tends ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-21", "section_label": "Chapter 21: Dibtobtiox Of Wavs-Shafe And Its Causes", "section_title": "Dibtobtiox Of Wavs-Shafe And Its Causes", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 23274-24559", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "snippets": [ "... poles causes a pulsation of the magnetic reluctance, or its reciprocal, the magnetic inductance of the circuit. In consequence thereof the mag- netism per field pole, or at least that part of the magnetism passing through the armature, will pulsate with a frequency 2 y if y = number of slots per pole. Thus, in a machine with one slot per pole, the instanta- neous magnetic flu.x interlinked with the armature con- ductors can be expressed by the equation : <^ = cos)3{l + ccos[2)3- 0)]} where, <^ = average magn ...", "... ll ^-\"■^. ^^ X / s ^ V I 3„ ^ \\ ' ^r- 7 ^ ^\"^ \\ 7 ^ L \\ J 5 F/9^ IH. full-iiMa Want of £.M.F. of MultltootH Tkna-fHattr. 824 AL TERN A TING-CURRENT PHENOMENA, [§216 In case of a pulsation of the magnetic flux with the frequency 2y, due to an existence of y slots per pole in the armature, the instantaneous value of magnetism interlinked with the armature coil is : <^ = cos )3 {1 + c cos [2 y )3 - w]}. Hence the E.M.F. induced thereby : dt = - V2 7riV^« — {cos)3(l + € ...", "... l> cos )3 {1 + c cos [2 y )3 - w]}. Hence the E.M.F. induced thereby : dt = - V2 7riV^« — {cos)3(l + €COS[2y)3~w])}. dp And, expanded : e = V2 TT A'//* {sin P + c ^y~-^ sin [(2 y - 1) ^ _ ] j where, ® = average ...", "... ' 10 50 30 10 g (50 70 SO 90 100 no 120 13(1 140 150 100 170 ISO Fig. 170. Full-Load Waue of E.M.F. of Multitooth Three-phaser. 388 ALTERNATING-CURRENT PHENOMENA. In case of a pulsation of the magnetic flux with the frequency 2y, due to an existence of y slots per pole in the armature, the instantaneous value of magnetism interlinked with the armature coil is : <£ = $ COS ft {1 + e COS [2 y ft — £]}. Hence the E.M.F. induced thereby : e = — n — — dt d *» And, expand ...", "... ked with the armature coil is : <£ = $ COS ft {1 + e COS [2 y ft — £]}. Hence the E.M.F. induced thereby : e = — n — — dt d *» And, expanded : e= V27rA^ (sin /3 + 1 sin (0 — £) + ^ sin (3 /? - £)} ; that is : In a unitooth single-phaser a pronounced tri ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-07", "section_label": "Chapter 8: Synchronizing Induction Motors", "section_title": "Synchronizing Induction Motors", "kind": "chapter", "sequence": 7, "number": 8, "location": "lines 13956-14465", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-07/", "snippets": [ "... , when using two motors in concatena- tion for speeds from standstill to half synchronism, from half synchronism to full speed, the motors may also be operated on a single rheostat by connecting their secondaries in parallel. As in parallel connection the frequency of the secondaries must be the same, and the secondary frequency equals the slip, it follows that the motors in this case must operate at the same slip, that is, at the same frequency of rotation, or in synchronism with each other. If the connection of th ...", "... till to half synchronism, from half synchronism to full speed, the motors may also be operated on a single rheostat by connecting their secondaries in parallel. As in parallel connection the frequency of the secondaries must be the same, and the secondary frequency equals the slip, it follows that the motors in this case must operate at the same slip, that is, at the same frequency of rotation, or in synchronism with each other. If the connection of the induction motors to the load is such that they can not operate ...", "... connecting their secondaries in parallel. As in parallel connection the frequency of the secondaries must be the same, and the secondary frequency equals the slip, it follows that the motors in this case must operate at the same slip, that is, at the same frequency of rotation, or in synchronism with each other. If the connection of the induction motors to the load is such that they can not operate in exact step with each other, obviously separate resistances must be used in the motor secondaries, so as to allow dif ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-14", "section_label": "Chapter 16: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 14, "number": 16, "location": "lines 19374-20293", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-14/", "snippets": [ "... is variable, it will perform a complete cycle during the time the armature coil moves from one field pole to the next field pole, that is, during one-half wave of the main current. That is, in other words, the reluctance and reactance vary with twice the frequency of the alternating main current. Such a case is shown in Figs. 129 and 130. The impressed e.m.f., and thus at negligible resistance, the counter e.m.f., is represented by the sine MVft, REACTION MACHINES E, thus the magnetism produced thereby is a si ...", "... // */J^\"\"Vj \\ / ^^^tn/^'A^^^^v ^ /\\ /A ' / \\V A *» ' \\ y~i^ / v / \\\\ / X ' \\ // ^N / \\ \\ / / ')/ \\\\ / I \\\\/ 1 ■£*,' > *^ s\\' 1 \\ /L ' » - N^-^' i \\ | \"'/■-* i / IT / R / A I IV' vj e shape in reaction machine a varying with the dpuble frequency of E, and shown in Fig. 129 to reach the maximiim value during the rise of magnetism, in 266 ELECTRICAL APPARATUS Fig. 130 during the decrease of magnetism. The current, /, required to produce the magnetism, *, is found from * and x in combination wit ...", "... the periodical variation of reactance will obviously depend upon the nature of the variation, that is, upon the shape of the reactance curve. Since, however, no matter what shape the wave has, it can always be resolved in a series of sine waves of double frequency, and its higher har- monies, in first approximation the assumption can l>e made that the reactance or the reluctance varies with double frequency of the main current ; that is, is represented in the form: x = a + b cos 2 &. Let the inductance be repres ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-19", "section_label": "Chapter 21: Regulating Pole Converters", "section_title": "Regulating Pole Converters", "kind": "chapter", "sequence": 19, "number": 21, "location": "lines 30088-31715", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-19/", "snippets": [ "... former. is not permissible. If, however, the primaries are connected in Y, as in Fig. 206 E, and either three separate single-phase trans- formers, or a three-phase transformer with three independent magnetic circuits, is used, as in Fig. 207, the triple-frequency voltages in the primary are in phase with each other between 28 434 ELECTRICAL APPARATUS the line and the neutral, and thus, with isolated neutral, can not produce any current. With a three-phase transformer as shown in Fig. 208, that is, in whi ...", "... 28 434 ELECTRICAL APPARATUS the line and the neutral, and thus, with isolated neutral, can not produce any current. With a three-phase transformer as shown in Fig. 208, that is, in which the magnetic circuit of the third harmonic is open, triple- frequency currents can exist in the sec- ondary and this arrangement therefore is not satisfactory. In two-phase converters, lugher harmonics can he used for regulation only if the transformers are connected in such a man- ner that the regulating harmonic, which a ...", "... 3 B -0.131 cos 5 0-0.0084 cos 7 0. . \\ (5) - full, c = e,-2<>2 =0.138 A | cos 0+2.07 cos 30 -0.45 cos 5 0-0.008 cos 7 0. . | (6) -1.17, e = c,-2.34e2 = 0.322^jcos 3 0-0.227 cos 5 0. | It is interesling tn note that in the last case the fundamental frequency disappears and the machine is a generator of triple frequency, that is, produces or consumes a frequency equal to three times synchronous frequency. In this ease the sevmUl harmonic also disappears, and only the fifth is appreciable. Iiut could be greatly ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-16", "section_label": "Chapter 16: Load Balance Of Polyphase Systems", "section_title": "Load Balance Of Polyphase Systems", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 29302-30428", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-16/", "snippets": [ "... of all the phases is constant throughout the cycle. In the single-phase system, however, or in a polyphase system with unbalanced load, that is, a system in which the different phases are unequally loaded, the total flow of power is pulsating, with double frequency. To balance an unbalanced polyphase system thus requires a storage of energy, hence can not be done by any method of connection or transformation. Thus mechanical momentum acts as energy-storing device in the use as phase bal- ancer, of the induction or t ...", "... s where p = ei = EI cos^ = ^ (1 + cos 2 ) = Q + Q cos 2 « (3) = f (4) that is, in a non-inductive single-phase circuit, the power consists of a constant component, Q--2' and an alternating component, EI = \"2- cos 2 0, of twice the frequency of the supply voltage, and a maximum value equal to that of the constant component. The instantane- ous power thus pulsates between zero and 2 Q, by equation (3). If the circuit is inductive, of lag angle a, the current is i = I cos (0 — a) (5) and the ...", "... rrent leads the TT impressed voltage by ^, thus is i = / cos (« + I) (10) and the instantaneous power thus, p = EI cos + l) = -Q cos(2 « - ^) • 166. If a number of voltages, ei = Ei cos (<^ — 7i) (12) * \"Engineering Mathematic ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... ally dies out, reaching zero value theoretically at infinite time, prac- tically in a very short time, short usually even in comparison with the time of one alternating half-wave. Characteristic con- stants of the oscillating current are the period, T, or frequency, / = 7p, the first amplitude and the ratio of any two successive amplitudes, the latter being called the decrement of the wave. The oscillating current will thus be represented by the product of a periodic function, and a function decreasing in geometri ...", "... : Z = 0. In this case we have substituting in this equation, x= 2 tt/L; Xc = 2TfC' and expanding, we have 1 a = yjr^c 2^/-^rr aJ^:^ - 1 - 2LMr^C 2aL That is, if in an oscillating-current circuit, the decrement, 1 a = and the frequency / = r — j , the total impedance of the circuit is zero; that is, the oscillating current, when started once, will continue without external energy being impressed upon the circuit. 192. The physical meaning of this is: If upon an electric circuit a cer ...", "... d upon the circuit. 192. The physical meaning of this is: If upon an electric circuit a certain amount of energy is impressed and then the circuit left to itself, the current in the circuit will become oscillat- r ing, and the oscillations assume the frequency, / = t — i^-, and the decrement, 1 a = /4L_ \\r^C That is, the oscillating currents are the phenomenon by which an electric circuit of disturbed equiUbrium returns to equilibrium. This feature shows the origin of the oscillating currents, and t ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-27", "section_label": "Chapter 5: Resistance, Inductance, And Capacity In Series Condenser Charge And Discharge", "section_title": "Resistance, Inductance, And Capacity In Series Condenser Charge And Discharge", "kind": "chapter", "sequence": 27, "number": 5, "location": "lines 4072-5311", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "snippets": [ "... litude are called oscillating waves. Since equations (42) to (47) are periodic, the time t can be represented by an angle 6, so that one complete period is denoted by 2 n or one complete revolution, f) * 4 O -ft (A Q\\ 0 = —t = 2rft. (48) hence, the frequency of oscillation is or, substituting gives the frequency of oscillation as (49) (50) CONDENSER CHARGE AND DISCHARGE 68 This frequency decreases with increasing resistance r, and becomes zero for ( — —\\ = — , that is, r2 = — , or the criti ...", "... o (47) are periodic, the time t can be represented by an angle 6, so that one complete period is denoted by 2 n or one complete revolution, f) * 4 O -ft (A Q\\ 0 = —t = 2rft. (48) hence, the frequency of oscillation is or, substituting gives the frequency of oscillation as (49) (50) CONDENSER CHARGE AND DISCHARGE 68 This frequency decreases with increasing resistance r, and becomes zero for ( — —\\ = — , that is, r2 = — , or the critical \\2 LI L/C C case, where the phenomenon ceases to be os ...", "... od is denoted by 2 n or one complete revolution, f) * 4 O -ft (A Q\\ 0 = —t = 2rft. (48) hence, the frequency of oscillation is or, substituting gives the frequency of oscillation as (49) (50) CONDENSER CHARGE AND DISCHARGE 68 This frequency decreases with increasing resistance r, and becomes zero for ( — —\\ = — , that is, r2 = — , or the critical \\2 LI L/C C case, where the phenomenon ceases to be oscillating. If the resistance is small, so that the second term in equa- tion (50) can be ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-10", "section_label": "Lecture 10: Inductance And Capacity Of Round Parallel Conductors", "section_title": "Inductance And Capacity Of Round Parallel Conductors", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6089-7274", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "snippets": [ "... n inductance, but, if alternating, produces a potential difference between the two sides of conductor B, and thereby a higher current density on the side of B toward A; and as this effect depends on the conduc- tivity of the conductor material, and on the frequency of the current, it cannot be determined without having the frequency, etc., given. The same applies for the flux $1, which is reduced by unequal current density due to its screening effect, so that in the limiting case, for conductors of perfect conductiv ...", "... tween the two sides of conductor B, and thereby a higher current density on the side of B toward A; and as this effect depends on the conduc- tivity of the conductor material, and on the frequency of the current, it cannot be determined without having the frequency, etc., given. The same applies for the flux $1, which is reduced by unequal current density due to its screening effect, so that in the limiting case, for conductors of perfect conductivity, that is, zero resistance, or for infinite, that is, very high fr ...", "... cy, etc., given. The same applies for the flux $1, which is reduced by unequal current density due to its screening effect, so that in the limiting case, for conductors of perfect conductivity, that is, zero resistance, or for infinite, that is, very high frequency, only the magnetic flux $1 exists, which is shown shaded in Fig. 5; but 2 and $3 are zero, and the inductance is . (15) ROUND PARALLEL CONDUCTORS. 125 That is, in other words, with small conductors and moderate currents, the total inductance ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-11", "section_label": "Theory Section 11: Capacity and Condensers", "section_title": "Capacity and Condensers", "kind": "theory-section", "sequence": 11, "number": 11, "location": "lines 3586-3760", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-11/", "snippets": [ "... during rising and from the condenser during decreasing e.m.f., as shown in Fig. 26. That is, the current consumed by the condenser leads the impressed e.m.f. by 90 time degrees, or a quarter of a period. Denoting / as frequency and E as effective alternating e.m.f. impressed upon a condenser of C'mf. capacity, the condenser is charged and discharged twice during each cycle, and the time of one complete charge or discharge is therefore j^- Since ...", "... econds an average current of 4 fCE \\/2 10~6 amp. is required. effective current TT Since average current 2\\/2' the effective current is I = 2-irfCE 10~6; that is, at an impressed e.m.f. of E effective volts and frequency /, a condenser of C mf. capacity consumes a current of 1 = 2 irfCE 10~6 amp. effective, which current leads the terminal voltage by 90 degrees or a quarter period. Transposing, the e.m.f. of the condenser is 106/ ...", "... e capacity is 0.24 X 10~6 X I i ^ t>s logio -7- I'd . , , in mf . The derivation of this equation must be omitted here. The charging current of a line wire is thus 1 = 2 7T/CE 10~6, where / = the frequency, in cycles per second, E = the difference of potential, effective, between the line and the neutral (E — y^ line voltage in a single-phase, or four-wire quarter-phase sys- tem, — -i=. line voltage, or Y voltage, in a th ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-87", "section_label": "Apparatus Section 9: Synchronous Converters: Inverted Converters", "section_title": "Synchronous Converters: Inverted Converters", "kind": "apparatus-section", "sequence": 87, "number": 9, "location": "lines 15735-15810", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-87/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-87/", "snippets": [ "... he distribution of load on the system. Or inverted operation may be used in emergencies to produce alternating current. When converting from alternating to direct current, the speed of the converter is rigidly fixed by the frequency, and cannot be varied by its field excitation, the variation of the latter merely changing the phase relation of the alternating current. When converting, however, from direct to alternating current as the only source of al ...", "... g field strength. As alternating-current generator, however, the field strength depends upon the intensity and phase relation of the alternating current, lagging current reducing the field strength and thus increasing speed and frequency, and leading current increasing the field strength and thus decreasing speed and frequency. Thus, if a load of lagging current is put on an inverted con- verter, as, for instance, by starting an induction motor or another ...", "... the intensity and phase relation of the alternating current, lagging current reducing the field strength and thus increasing speed and frequency, and leading current increasing the field strength and thus decreasing speed and frequency. Thus, if a load of lagging current is put on an inverted con- verter, as, for instance, by starting an induction motor or another converter thereby from the alternating side, the demagnetizing effect of the alternating cu ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-90", "section_label": "Apparatus Section 12: Synchronous Converters: Conclusion", "section_title": "Synchronous Converters: Conclusion", "kind": "apparatus-section", "sequence": 90, "number": 12, "location": "lines 15983-16064", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-90/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-90/", "snippets": [ "... dary of an induction machine is connected to a second induction or synchronous machine on the same shaft, and of the same number of poles, the combination runs at half synchronous speed, and the first induction machine as frequency converter supplies half of its power as electric power of half frequency to the second machine, and changes the other half 262 ELEMENTS OF ELECTRICAL ENGINEERING as motor into mechanical power, driving the second machi ...", "... onous machine on the same shaft, and of the same number of poles, the combination runs at half synchronous speed, and the first induction machine as frequency converter supplies half of its power as electric power of half frequency to the second machine, and changes the other half 262 ELEMENTS OF ELECTRICAL ENGINEERING as motor into mechanical power, driving the second machine as generator. (Or, if the two machines have different number of poles, ...", "... ent but constant ratio) . Using thus a double- current generator as second machine, it receives half of its power mechanically, by the induction machine as motor, and the other half electrically, by the induction machine as frequency converter. Such a machine, then, is intermediate between a converter and a direct-current generator, having an armature reaction equal to half that of a direct-current generator. Such motor converters have been recommended fo ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "... f., and = e.m.f. X effective susceptance, or b. In many cases the exact calculation of the quantities, r, x, g, h, is not possible in the present state of the art. In general, r, x, g, b, are not constants of the circuit, but depend — besides upon the frequency — more or less upon e.m.f., current, etc. Thus, in each particular case it becomes necessary to dis- cuss the variation of r, x, g, b, or to determine whether, and through what range, they can be assumed as constant. In what follows, the quantities r, x, ...", "... usual manner by the vector diagram. This phenomenon is especially noticeable in long-distance lines, in underground cables, and to a certain degree in the high-poten- tial coils of alternating-current transformers for very high vol- tage and also in high frequency circuits. It has the effect that not only the e.m.fs., but also the currents, at the beginning, end, and different points of the conductor, are different in intensity and in phase. Where the capacity effect of the line is small, it may with sufficient a ...", "... nt of the surrounding medium = 1 in air; I = length of conductor = 5 X 10\" cm.; ■ d = distance of conductors from each other = 50 cm.; 5 = diameter of conductor = 1 cm. Hence C = 0.3 microfarad, the condensive reactance is x = ^ — 7f< ohms, where/ = frequency; hence at/ = 60 cycles, X = 8,900 ohms; and the charging current of the line, at £' = 20,000 volts, be- comes, E to = — = 2.25 amp. X The resistance of 100 km. of wire of 1 cm. diameter is 22 ohms; therefore, at 10 per cent. = 2,000 volts loss in ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-17", "section_label": "Chapter 17: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16521-17716", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-17/", "snippets": [ "... of the magnetic circuit surrounding both electric circuits is produced by the combined magnetizing action of the primary and of the secondary current. This magnetic flux is determined by the e.m.f. of the trans- former, by the number of turns, and by the frequency. If $ = maximum magnetic flux, / = frequency, n = number of turns of the coil, the e.m.f. generated in this coil is E = V27r/n$ 10-8 = 4A4fn^ IQ-^ volts; hence, if the e.m.f., frequency, and number of turns are de- termined, the maximum magneti ...", "... circuits is produced by the combined magnetizing action of the primary and of the secondary current. This magnetic flux is determined by the e.m.f. of the trans- former, by the number of turns, and by the frequency. If $ = maximum magnetic flux, / = frequency, n = number of turns of the coil, the e.m.f. generated in this coil is E = V27r/n$ 10-8 = 4A4fn^ IQ-^ volts; hence, if the e.m.f., frequency, and number of turns are de- termined, the maximum magnetic flux is E108 $ = — — V27r/n To produce the ...", "... . of the trans- former, by the number of turns, and by the frequency. If $ = maximum magnetic flux, / = frequency, n = number of turns of the coil, the e.m.f. generated in this coil is E = V27r/n$ 10-8 = 4A4fn^ IQ-^ volts; hence, if the e.m.f., frequency, and number of turns are de- termined, the maximum magnetic flux is E108 $ = — — V27r/n To produce the magnetism, $, of the transformer, a m.m.f. of F ampere-turns is required, which is determined by the shape and the magnetic characteristic of the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-20", "section_label": "Chapter 20: Beactiox Machines", "section_title": "Beactiox Machines", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 22388-23273", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "snippets": [ "... vari- able, it will perform a complete cycle during the time the armature coil moves from one field pole to the next field pole, that is, during one-half wave of the main current. That is, in other words, the reluctance and reactance vary with twice the frequency of the alternating main current. Such a case is shown in Figs. 148 and 149. The impressed E.M.F., and thus at negligible resistance, the counter I'2.M.F., is represented by the sine wave E, thus the magnetism pro- duced thereby is a sine wave J/\", 90^ ahe ...", "... pressed E.M.F., and thus at negligible resistance, the counter I'2.M.F., is represented by the sine wave E, thus the magnetism pro- duced thereby is a sine wave J/\", 90^ ahead of E. The reactance is represented by the sine wave x, varying with the double frequency of if, and shown in Fig. 148 to reach the maximum value during the rise of magnetism, in I'ig. 149 during the decrease of magnetism. The current / re- quired to produce the magnetism * is found from * and x in combination with the cycle of molecular magne ...", "... e periodical variation of reac- tance will obviously depend upon the nature of the variation, that is, upon the shape of the reactance curve. Since, however, no matter what shape the wave has, it can always be dissolved in a series of sine waves of double frequency, and its higher harmonics, in first approximation the assump- tion can be made that the reactance or the reluctance vary with double frequency of the main current ; that is, are represented in the form, X =^ a -\\- b cos 2 <^. Let the inductance, or th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-21", "section_label": "Chapter 21: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 20502-21189", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-21/", "snippets": [ "... vari- able, it will perform a complete cycle during the time the armature coil moves from one field pole to the next field pole, that is, during one-half wave of the main current. That is, in other words, the reluctance and reactance vary with twice the frequency of the alternating main current. Such a case is shown in Figs.. 164 and 165. The impressed E.M.F., and thus at negligible resistance, the counter E.M.F., is represented by the sine wave E, thus the magnetism pro- duced thereby is a sine wave 4>, 90° ahead ...", "... impressed E.M.F., and thus at negligible resistance, the counter E.M.F., is represented by the sine wave E, thus the magnetism pro- duced thereby is a sine wave 4>, 90° ahead of E. The reactance is represented by the sine wave x, varying with the double frequency of E, and shown in Fig. 164 to reach the maximum value during the rise of magnetism, in Fig. 165 during the decrease of magnetism. The current / re- quired to produce the magnetism is found from 3> and-^r in combination with the cycle of molecular mag ...", "... e periodical variation of reac- tance will obviously depend upon the nature of the variation, that is, upon the shape of the reactance curve. Since, however, no matter what shape the wave has, it can always be dissolved in a series of sine waves of double frequency, and its higher harmonics, in first approximation the assump- tion can be made that the reactance or the reluctance vary with double frequency of the main current ; that is, are represented in the form, x = a + b cos 2 /8. Let the inductance, or the c ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-11", "section_label": "Chapter 11: Instability Of Circuits: Induction And Syn Chronous Motors", "section_title": "Instability Of Circuits: Induction And Syn Chronous Motors", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 21382-22633", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-11/", "snippets": [ "... parallel. (6) Hunting of synchronous converters. (c) Hunting of synchronous motors. While considerable theoretical work has been done, practically all theoretical study of the hunting of synchronous machines has been limited to the calculation of the frequency of the transi- ent oscillation of the synchronous machine, at a change of load, frequency or voltage, at synchronizing, etc. However, this transient oscillation is harmless, and becomes dangerous only if the oscillation ceases to be transient, but becomes ...", "... hile considerable theoretical work has been done, practically all theoretical study of the hunting of synchronous machines has been limited to the calculation of the frequency of the transi- ent oscillation of the synchronous machine, at a change of load, frequency or voltage, at synchronizing, etc. However, this transient oscillation is harmless, and becomes dangerous only if the oscillation ceases to be transient, but becomes permanent and cumulative, and the most important problem in the study of hunt- ing thus i ...", "... increase of speed. However, in the synchronous motor the torque is not a function of the speed, but in stationary condition the speed must always be the same, synchronism, and the torque is a function of the relative position of the rotor to the impressed frequency. The increase of speed, due to the excess torque resulting from the decreased load, causes the rotor to run ahead of its previous relative position, and thereby decreases the torque until, by the increased speed, the motor has run ahead from the relative ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-13", "section_label": "Chapter 9: High-Frequency Conductors. 403", "section_title": "High-Frequency Conductors. 403", "kind": "chapter", "sequence": 13, "number": 9, "location": "lines 1014-1042", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-13/", "snippets": [ "CHAPTER IX. HIGH-FREQUENCY CONDUCTORS. 403 80. Effect of the frequency on the constants of a conductor. 403 81. Thermal resistance and radiation resistance, internal and external reactance, as functions of the frequency. 405 82. Total impedance of high frequency conductor, and ...", "CHAPTER IX. HIGH-FREQUENCY CONDUCTORS. 403 80. Effect of the frequency on the constants of a conductor. 403 81. Thermal resistance and radiation resistance, internal and external reactance, as functions of the frequency. 405 82. Total impedance of high frequency conductor, and its components, discussion. 407 83. Exampl ...", "CHAPTER IX. HIGH-FREQUENCY CONDUCTORS. 403 80. Effect of the frequency on the constants of a conductor. 403 81. Thermal resistance and radiation resistance, internal and external reactance, as functions of the frequency. 405 82. Total impedance of high frequency conductor, and its components, discussion. 407 83. Example of copper and iron wire, copper ribbon and iron pipe ; tabulation and discussion of numerical values. 408 84. Continued discussion of results. • 40 ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-32", "section_label": "Chapter 10: Mutual Inductance", "section_title": "Mutual Inductance", "kind": "chapter", "sequence": 32, "number": 10, "location": "lines 10475-12216", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "snippets": [ "... he circuit and the number of lines of magnetic force produced by unit current in the circuit, we have di L{j± = e.m.f. consumed by the inductance, ctt where, t = time. If instead of time t an angle 6 = 2 nft is introduced, where / is some standard frequency, as 60 cycles, di x. 3^ = e.m.f. consumed by the inductance, au where x1 = 2 nfL^ = inductive reactance. If now M = mutual inductance between the circuit and another circuit, that is, number of interlinkages of the circuit with the magnetic flux pr ...", "... in this range as straight line, is given by the equation The impressed e.m.f. of the shunt field is the same, hence, reduced to the main circuit by the ratio of turns, a = 1.2 X 10~3, is e, = 152 TRANSIENT PHENOMENA Assuming now as standard frequency, / = 60 cycles per sec., the constants of the two mutually inductive circuits shown diagrammatically in Fig. 38 are : Main Circuit. Shunt Field Circuit. Current i amp. il amp Impressed e.m.f... Resistance *= 272 1^ VOHS T = 6 ohms e1 = ( ...", "... 6 + 3850 £-°-010' -sin 16.28 6 Approximately therefore we have i\\ = 9.6 £-°-073e cos 50.15 0 + 15.7 £-°-010' cos 16.28 0 ia = - 10 { £-°-0730 cos 50.15 0 - £-°mo0 cos 16.28 0 } e/ = 3850 fi-OJMO« sin 16.28 0 < - -3670 £-°010' sin 16.28 6. The two frequencies of oscillation are 3009 and 977 cycles per sec., hence rather low. The secondary terminal voltage has a maximum of nearly 4000, reduced to the primary, or 400 times as large as corre- sponds to the ratio of turns. In this particular instance, the frequ ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-50", "section_label": "Chapter 1: General Equations", "section_title": "General Equations", "kind": "chapter", "sequence": 50, "number": 1, "location": "lines 27761-28694", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "snippets": [ "... urrent, - — , as electromagnetic component & of the electric field; or the voltage generated due to the change of the current, L — , that is, with an alternating current, the at reactive voltage consumed in the circuit - jxi, where x = 2 nfL and / = frequency. g = effective (shunted) conductance, representing the power or rate of energy consumption depending upon the voltage, e*g; or the power component of the current consumed in the circuit, that is, with an alternating voltage, the current, eg, in phase wit ...", "... he voltage, — , as electrostatic component of the electric field; or the current consumed by a change of the de voltage, C — , that is, with an alternating voltage, the (leading) dt reactive current consumed in the circuit - jbe, where 6 = 2 and / = frequency. 417 418 TRANSIENT PHENOMENA In the investigation of electric circuits, these four constants, r, L, g, C, usually are assumed as located separately from each other, or localized. Although this assumption can never be per- fectly correct, — for insta ...", "... per- fectly correct, — for instance, every resistor has some inductance and every reactor has some resistance, — nevertheless in most cases it is permissible and necessary, and only in some classes of phenomena, and in some kinds of circuits, such as high-frequency phenomena, voltage and current distribution in long-distance, high-potential circuits, cables, telephone circuits, etc., this assumption is not permissible, but r, L, g, C must be treated as distributed throughout the circuit. In the case of a circuit w ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-04", "section_label": "Chapter 5: Methods Of Approximation", "section_title": "Methods Of Approximation", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 15156-16482", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-04/", "snippets": [ "... the current input to an induction motor, at impressed voltage eo and slip s (given as fraction of synchronous speed) if ro — jxo is the impedance of the primary circuit of the motor, and ri — jxi the impedance of the secondary circuit of the motor at full frequency, and the exciting current of the motor is neglected; assuming s to be a small quantity; that is, the motor running at full speed? Let E be the e.m.f. generated by the mutual magnetic flux, that is, the magnetic flux which interlinks with primary and wit ...", "... at full speed? Let E be the e.m.f. generated by the mutual magnetic flux, that is, the magnetic flux which interlinks with primary and with secondary circuit, in the primary circuit. Since the fre- quency of the secondary circuit is the fraction 8 of the frequency 192 ENGINEERING MATHEMATICS. of the primary circuit, the generated e.m.f. of the secondary circuit is sE. Since x\\ is the reactance of the secondary circuit at full frequency, at the fraction s of full frequency the reactance of the secondary circui ...", "... t. Since the fre- quency of the secondary circuit is the fraction 8 of the frequency 192 ENGINEERING MATHEMATICS. of the primary circuit, the generated e.m.f. of the secondary circuit is sE. Since x\\ is the reactance of the secondary circuit at full frequency, at the fraction s of full frequency the reactance of the secondary circuit is sxi, and the impedance of the sec- ondary circuit at slip s, therefore, is ri — jsx\\] hence the secondary current is, • ri-]sxi If the exciting current is neglected, the pri ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-02", "section_label": "Lecture 2: Conclusions From The Relativity Theory", "section_title": "Conclusions From The Relativity Theory", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 736-2388", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... of propagation as the light wave, and has shown that the electromagnetic wave and the (polarized) light wave are identical in all their properties. Hence light is an electromagnetic wave — that is, an alternating electro- magnetic field of extremely high frequency. Electrophysics has been successfully developed to its present high state, and has dealt with alternating currents, voltages and electromag- netic fields, without ever requiring or considering a medium such as the ether. Whatever may be the mechanis ...", "... ectromag- netic fields, without ever requiring or considering a medium such as the ether. Whatever may be the mechanism of the electro- magnetic wave, it certainly is not a mere transverse wave motion of matter, and the light, being shown to be a high-frequency electro- magnetic wave, cannot be considered any more as a wave motion of the ether. The ether thus vanishes. M Fig. 4. 22 RELATIVITY AND SPACE following the phlogiston and other antiquated physical conceptions. The conception of the field of ...", "... romagnetic wave (like that of the radio communication station or that surrounding a power transmission line) are therefore periodic alternations of the electromagnetic energy field in space, and the differ- ences are merely those due to the differences of frequency. Thus the electromagnetic field of the 60-cycle transmission line has a wave length of 3 X lO^V^O cm. = 5000 km. Its extent is limited to the space between the conductors and their immediate surroundings, being therefore extremely small compared with the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-107", "section_label": "Apparatus Section 1: Induction Machines: General", "section_title": "Induction Machines: General", "kind": "apparatus-section", "sequence": 107, "number": 1, "location": "lines 18949-19165", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-107/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-107/", "snippets": [ "... e with the voltage, or the field may be excited from a separate e.m.f. differing 90 deg. in phase from that supplied to the armature. The former arrange- ment has the disadvantage of requiring almost perfect con- stancy of frequency, and therefore is not practicable. In the latter arrangement the armature winding of the motor is fed by one, the field winding by the other phase of a quarter-phase sys- tem, and thus the current in the armature brought ...", "... d the electric energy in the secondary is made use of, while in the latter the secondary is movable regarding the primary, and the me- chanical force acting between primary and secondary is used. In consequence thereof the frequency of the currents in the sec- ondary of the induction motor differs from, and as a rule is very much lower than, that of the currents impressed upon the pri- mary, and thus the ratio of e.m.fs. generated in primary and in ...", "... lower than, that of the currents impressed upon the pri- mary, and thus the ratio of e.m.fs. generated in primary and in secondary is not the ratio of their respective turns, but is the ratio of the product of turns and frequency. Taking due consideration of this difference of frequency be- tween primary and secondary, the theoretical investigation of the induction motor corresponds to that of the stationary trans- former. The transformer feature of the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-108", "section_label": "Apparatus Section 2: Induction Machines: Polyphase Induction Motor", "section_title": "Induction Machines: Polyphase Induction Motor", "kind": "apparatus-section", "sequence": 108, "number": 2, "location": "lines 19166-20427", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-108/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-108/", "snippets": [ "... = slip, with the primary fre- quency as unit; that is, s = 0 denoting synchronous rotation, s = l standstill of the motor. We then have 1 — s = speed of the motor secondary as fraction of syn- chronous speed, sf = frequency of the secondary currents, where / = frequency impressed upon the primary; 1 The self -inductive reactance refers to that flux which surrounds one of the electric circuits only, without being interlinked with the other cir ...", "... hat is, s = 0 denoting synchronous rotation, s = l standstill of the motor. We then have 1 — s = speed of the motor secondary as fraction of syn- chronous speed, sf = frequency of the secondary currents, where / = frequency impressed upon the primary; 1 The self -inductive reactance refers to that flux which surrounds one of the electric circuits only, without being interlinked with the other circuits. 312 ELEMENTS OF ELECTRICAL ENGINEERING ...", "... electric circuits only, without being interlinked with the other circuits. 312 ELEMENTS OF ELECTRICAL ENGINEERING hence, . se = e.m.f. generated in the secondary. The actual impedance of the secondary circuit at the frequency sf is Zi8 = 7*1 +jsxi; hence, the secondary current is se se where the primary exciting current is /oo =eY = e[g — jb], and the total primary current is /o = e I (ai -f g) — j (a2 + b] where The e.m.f. c ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-22", "section_label": "Apparatus Section 1: Synchronous Machines: General", "section_title": "Synchronous Machines: General", "kind": "apparatus-section", "sequence": 22, "number": 1, "location": "lines 8518-8657", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-22/", "snippets": [ "... of the commutating machines with those of the synchronous machines they will be considered separately. In the synchronous machines the terminal voltage and the generated e.m.f. are in synchronism with, that is, of the same frequency as, the speed of rotation. These machines consist of an armature, in which e.m.f. is generated by the rotation relatively to a magnetic field, and a continuous magnetic field, excited either by direct current, or by the ...", "... the e.m.f. generated in synchronous machines, commonly called alternators, is E = S2irn3> = 4. where n is the number of armature turns in series interlinked with the magnetic flux <1> (in megalines per pole), / the frequency of rotation (in hundreds of cycles per second), E the e.m.f. gen- erated in the armature turns. This formula assumes a sine wave of e.m.f. If the e.m.f. wave differs from sine shape, the e.m.f. is E = 4.447/n, 2 ...", "... achines, commonly called alternators, is E = S2irn3> = 4. where n is the number of armature turns in series interlinked with the magnetic flux <1> (in megalines per pole), / the frequency of rotation (in hundreds of cycles per second), E the e.m.f. gen- erated in the armature turns. This formula assumes a sine wave of e.m.f. If the e.m.f. wave differs from sine shape, the e.m.f. is E = 4.447/n, 2 -\\/2 where y = form factor of the wave, or ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-65", "section_label": "Apparatus Section 13: Direct-current Commutating Machines: Commutation", "section_title": "Direct-current Commutating Machines: Commutation", "kind": "apparatus-section", "sequence": 65, "number": 13, "location": "lines 11905-11980", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-65/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-65/", "snippets": [ "... s given in inches, to = -£ is the time during which the current in A reverses. Thus, considering the reversal as a 1 S single alternation, tQ is a half period, and thus /0 = ^-7- = ;ry- is 4 »o z iw the frequency of commutation; hence, if L = inductance of the armature coil A, the e.m.f. generated in the armature coil during commutation is eo = 2irfoLiot where io = current reversed, and the energy which has to be dissipated durin ...", "... = inductance of the armature coil A, the e.m.f. generated in the armature coil during commutation is eo = 2irfoLiot where io = current reversed, and the energy which has to be dissipated during commutation is i10-8, (6) where / = frequency. Denoting 2 irfn 10 ~ ^ by a we have, (7) 62 = a $ (8) and since the generated e.m.f. is 90° behind the generating flux, in symbolic expression, E2= - ja^; (9) hence, substituting (5) in (9), E2 = a(P{fo - ni2) - jaiPnii, . (10) the virtual gen ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-03", "section_label": "Chapter 3: Iiaw Of Eucctbo-Maonimc Induction", "section_title": "Iiaw Of Eucctbo-Maonimc Induction", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 1973-2121", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-03/", "snippets": [ "... or the flux passes in and out of the turns, during each complete alternation or cycle, — the total flux is cut four times, twice passing into, and twice out of, the turns. / §12] LAW OF ELECTRO-MAGNETIC INDUCTION, 17 Hence, if A^= number of complete cycles per second, or the frequency of the relative alternation of flux ♦, the average E.M.F. induced in ;/ turns is, — wfi'.vf . = 4 // ♦ jy 10 - \" volts. This is the fundamental equation of electrical engineer- ing, and applies to continuous-current, as well as to alt ...", "... ut of the turns, during each complete alternation or cycle, — the total flux is cut four times, twice passing into, and twice out of, the turns. / §12] LAW OF ELECTRO-MAGNETIC INDUCTION, 17 Hence, if A^= number of complete cycles per second, or the frequency of the relative alternation of flux ♦, the average E.M.F. induced in ;/ turns is, — wfi'.vf . = 4 // ♦ jy 10 - \" volts. This is the fundamental equation of electrical engineer- ing, and applies to continuous-current, as well as to alter- nating-current ...", "... ion motors, the mag- netic field revolves ; in transformers, the field alternates with respect to the stationary turns. Thus, in the continuous-current machine, if n = num- ber of turns in series from brush to brush, ♦ = flux inclosed per turn, and N =. frequency, the E.M.F. induced in the machine is jE\" = 4«aV10~® volts, independent of the num- ber of poles, or series or multiple connection of the arma- ture, whether of the ring, drum, or other type. In an alternator or transformer, if n is the number of tur ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-13", "section_label": "Chapter 13: Ths Alternating^Cnrrent Traxsfobmer", "section_title": "Ths Alternating^Cnrrent Traxsfobmer", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 12673-14088", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "snippets": [ "... of the magnetic circuit surrounding both electric circuits is produced by the combined magnetizing action of the primary and of the secondary current. This magnetic flux is determined by the E.M.F. of the transformer, by the number of turns, and by the frequency. If 4> = maximum magnetic flux, N-= frequency, n = number of turns of the coil ; the E.M.F. induced in this coil is E = ViirNn^ 10-« volts, = 4.44 AV/* 10 -'volts; hence, if the E.M.F., frequency, and number of turns are determined, the maximu ...", "... ircuits is produced by the combined magnetizing action of the primary and of the secondary current. This magnetic flux is determined by the E.M.F. of the transformer, by the number of turns, and by the frequency. If 4> = maximum magnetic flux, N-= frequency, n = number of turns of the coil ; the E.M.F. induced in this coil is E = ViirNn^ 10-« volts, = 4.44 AV/* 10 -'volts; hence, if the E.M.F., frequency, and number of turns are determined, the maximum magnetic flux is E 1()» W'2.irNn To produc ...", "... transformer, by the number of turns, and by the frequency. If 4> = maximum magnetic flux, N-= frequency, n = number of turns of the coil ; the E.M.F. induced in this coil is E = ViirNn^ 10-« volts, = 4.44 AV/* 10 -'volts; hence, if the E.M.F., frequency, and number of turns are determined, the maximum magnetic flux is E 1()» W'2.irNn To produce the magnetism, *, of the transformer, a M.M.F. of JF ampere-turns is required, which is determined by the shape and the magnetic characteristic of the iron ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-03", "section_label": "Chapter 3: Law Of Electro-Magnetic Induction", "section_title": "Law Of Electro-Magnetic Induction", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 1606-1742", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-03/", "snippets": [ "... through the flux, or the flux passes in and out of the turns, the total flux is cut four times during each complete period or cycle, twice passing into, and twice out of, the turns. LAW OF ELECTRO-MAGNETIC INDUCTION. 17 Hence, if N= number of complete cycles per second, or the frequency of the flux 3>, the average E.M.F. induced in n turns is, £&vg, = 4 « 3> N 10 ~ 8 volts. This is the fundamental equation of electrical engineer- ing, and applies to .continuous-current, as well as to alter- nating-current, apparatus ...", "... lux passes in and out of the turns, the total flux is cut four times during each complete period or cycle, twice passing into, and twice out of, the turns. LAW OF ELECTRO-MAGNETIC INDUCTION. 17 Hence, if N= number of complete cycles per second, or the frequency of the flux 3>, the average E.M.F. induced in n turns is, £&vg, = 4 « 3> N 10 ~ 8 volts. This is the fundamental equation of electrical engineer- ing, and applies to .continuous-current, as well as to alter- nating-current, apparatus. 12. In continuo ...", "... on motors, the mag- netic field revolves ; in transformers, the field alternates with respect to the stationary turns. Thus, in the continuous-current machine, if n = num- ber of turns in series from brush to brush, = flux inclosed per turn, and N = frequency, the E.M.F. induced in the machine is E = 4«4>7V10~8 volts, independent of the num- ber of poles, of series or multiple connection of the arma- ture, whether of the ring, drum, or other type. In an alternator or transformer, if n is the number of turns ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-14", "section_label": "Chapter 14: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 11605-12682", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "snippets": [ "... of the magnetic circuit surrounding both electric circuits is produced by the combined magnetizing action of the primary and of the secondary current. This magnetic flux is determined by the E.M.F. of the transformer, by the number of turns, and by the frequency. If <£ = maximum magnetic flux, N= frequency, n = number of turns of the coil ; the E.M.F. induced in this coil is E= V2 *• JVfc * 10 -8 = 4.44 .Afo* 10 -'volts; hence, if the E.M.F., frequency, and number of turns are determined, the maximum mag ...", "... ic circuits is produced by the combined magnetizing action of the primary and of the secondary current. This magnetic flux is determined by the E.M.F. of the transformer, by the number of turns, and by the frequency. If <£ = maximum magnetic flux, N= frequency, n = number of turns of the coil ; the E.M.F. induced in this coil is E= V2 *• JVfc * 10 -8 = 4.44 .Afo* 10 -'volts; hence, if the E.M.F., frequency, and number of turns are determined, the maximum magnetic flux is To produce the magnetism, $, of ...", "... the transformer, by the number of turns, and by the frequency. If <£ = maximum magnetic flux, N= frequency, n = number of turns of the coil ; the E.M.F. induced in this coil is E= V2 *• JVfc * 10 -8 = 4.44 .Afo* 10 -'volts; hence, if the E.M.F., frequency, and number of turns are determined, the maximum magnetic flux is To produce the magnetism, $, of the transformer, a M.M.F. of 5 ampere-turns is required, which is determined ALTERNATING-CURRENT TRANSFORMER. 195 by the shape and the magnetic charact ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-12", "section_label": "Chapter 14: Phase Conversion And Single-Phase Generation", "section_title": "Phase Conversion And Single-Phase Generation", "kind": "chapter", "sequence": 12, "number": 14, "location": "lines 17125-18412", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-12/", "snippets": [ "... een these two assumptions. 131. Let: Y0 = So _ j°o ■ primary exciting admittance of the induc- tion machine, Zo = r0 + jxq = primary, and thus also tertiary self-induc- tive impedance, Zi ™ Ti + jx, = secondary self-inductive impedance, all at full frequency, and reduced to the same number of turns. Let: Y* = tfi — jbs = admittanceof the load on the second phase; denoting further: z = za + z„ 1 \"Theory and Calculation of Al terns ling-curr edition, page 204. Phenomena,\" 5th PHASE CONVERSION 223 ...", "... n. With balanced •olyphase load, the armature reaction is constant in intensity nd in direction, with regards to the field. With single-phase id, however, the armature reaction is pulsating between zero ind twice its average value, thus may cause a double-frequency pulsation of magnetic flux, which, extending through the field circuit, may give rise to losses and heating by eddy currents in the iron, etc. With the slow-speed multipolar engine-driven alternators of old, due to the large number of poles and low per- ...", "... he phases, and so produce the constant armature reaction of balanced polyphase load, or to eliminate the fluctuation of the armature reaction. The latter is done by the use of an effective squirrel-cage short-circuit winding in the pole faces. The double- frequency pulsation of armature reaction induces double-fre- ! currents in the squirrel cage— just as in the single-phase duetion motor— and these induced currents demagnetize, when 230 ELECTRICAL APPARATUS the armature reaction is above, and magnetize when ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-04", "section_label": "Chapter 4: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 6942-9061", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-04/", "snippets": [ "... cular magnetic friction is meant, and the hysteresis cycle assumed under the con- dition of no other energy conversion, and this assumption will be made in the following, except where expressly stated otherwise. The hysteresis cycle is independent of the frequency within conmiercial frequencies and far beyond this range. Even at frequencies of hundred thousand cycles, experimental evidence seems to show that the hysteresis cycle is not materially changed, except in so far as eddy currents exert a demagnetizing acti ...", "... ant, and the hysteresis cycle assumed under the con- dition of no other energy conversion, and this assumption will be made in the following, except where expressly stated otherwise. The hysteresis cycle is independent of the frequency within conmiercial frequencies and far beyond this range. Even at frequencies of hundred thousand cycles, experimental evidence seems to show that the hysteresis cycle is not materially changed, except in so far as eddy currents exert a demagnetizing action and thereby require a change ...", "... con- dition of no other energy conversion, and this assumption will be made in the following, except where expressly stated otherwise. The hysteresis cycle is independent of the frequency within conmiercial frequencies and far beyond this range. Even at frequencies of hundred thousand cycles, experimental evidence seems to show that the hysteresis cycle is not materially changed, except in so far as eddy currents exert a demagnetizing action and thereby require a change of the impressed m.m.f ., to get the same resu ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-06", "section_label": "Chapter 6: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 11051-12221", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-06/", "snippets": [ "... as well as to the alternating-current electromagnet. In the alternating-current electromagnet, if io is the effective value of the current, F is the effective or average value of the pull, and the pull or force of the electromagnet pulsates with double frequency between and 2F. 63. In the alternating-current electromagnet usually the vol- tage consumed by the resistance of the winding, tV, can be neglected compared with the voltage consumed by the reactance of the winding, ioXy and the latter, therefore, is prac ...", "... onsumed by the reactance of the winding, ioXy and the latter, therefore, is practically equal to the terminal voltage, e, of the electromagnet. We have then, by the general equation of self-induction, e = 27r fLio (20) 96 ELECTRIC CIRCUITS where / = frequency, in cycles per second. From which follows, ij. = 2^ (21) and substituting (21) in equations (14) to (19), gives as the equa- tion of the mechanical workj and the pull of the alternating^current electromagnet. In the metric system: PI = ^ \\ . ^ gram ...", "... reactance of the winding, ioXy and the latter, therefore, is practically equal to the terminal voltage, e, of the electromagnet. We have then, by the general equation of self-induction, e = 27r fLio (20) 96 ELECTRIC CIRCUITS where / = frequency, in cycles per second. From which follows, ij. = 2^ (21) and substituting (21) in equations (14) to (19), gives as the equa- tion of the mechanical workj and the pull of the alternating^current electromagnet. In the metric system: PI = ^ \\ . ^ gram-cm. (22) „ io(e2 — ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-08", "section_label": "Chapter 8: Shaping Of Waves By Magnetic Saturation", "section_title": "Shaping Of Waves By Magnetic Saturation", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 12962-16963", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-08/", "snippets": [ "... 2 per cent, of its previous value. As seen from the reasoning in paragraph and Fig. 67, the SHAPING OF WAVES BY MAGNETIC SATURATION 151 peaked wave of Fig, 72 contains very pronounced harmonics up to about the 701th, which at 60 cycles of fundamental frequency, gives frequencies up to 42,000, or well within the range of the danger frequencies of high- voltage power transformers, that is, -- , / ^ N V B/ \\ ^ // \\t ^^=?rT\" / 1 a^ ^ \\ 5= \" 1 i / r*° U- ...", "... s previous value. As seen from the reasoning in paragraph and Fig. 67, the SHAPING OF WAVES BY MAGNETIC SATURATION 151 peaked wave of Fig, 72 contains very pronounced harmonics up to about the 701th, which at 60 cycles of fundamental frequency, gives frequencies up to 42,000, or well within the range of the danger frequencies of high- voltage power transformers, that is, -- , / ^ N V B/ \\ ^ // \\t ^^=?rT\" / 1 a^ ^ \\ 5= \" 1 i / r*° U- ^ s // ^ ...", "... g. 67, the SHAPING OF WAVES BY MAGNETIC SATURATION 151 peaked wave of Fig, 72 contains very pronounced harmonics up to about the 701th, which at 60 cycles of fundamental frequency, gives frequencies up to 42,000, or well within the range of the danger frequencies of high- voltage power transformers, that is, -- , / ^ N V B/ \\ ^ // \\t ^^=?rT\" / 1 a^ ^ \\ 5= \" 1 i / r*° U- ^ s // ^ ) // ^ V y ! frequencies with which the high-vol ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-12", "section_label": "Chapter 12: Reactance Of Induction Apparatus", "section_title": "Reactance Of Induction Apparatus", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 22634-23465", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-12/", "snippets": [ "... circuit thus has a resistance, and an inductance, however small the latter may be in the so-called \"non-inductive\" circuit. With continuous current in stationary conditions, the inductance, L, has no effect on the energy flow; with alternating current of frequency, /, the inductance, L, consumes a voltage 2 x/Li, and is, therefore, represented by the reactance, x = 2x/L, which is measured in ohms, and differs from the ohmic resistance, r, merely by being wattless or reactive, that is, representing not dissipation o ...", "... /i. 118. Appljdng this to the polyphase induction motor with single squirrel-cage secondary. Let Yo — g — jb = primary exciting admittance; Zo = ro + jxo = primary self-inductive impedance; Zi = ri + jxi = secondary self-inductive impedance at full frequency, reduced to the primary. Let Pi = the true induced voltage in the secondary, at full frequency, corresponding to the magnetic flux in the armature core. The secondary current then is The mutual inductive voltage at full frequency, ^ = ^1 + jxifi ...", "... Yo — g — jb = primary exciting admittance; Zo = ro + jxo = primary self-inductive impedance; Zi = ri + jxi = secondary self-inductive impedance at full frequency, reduced to the primary. Let Pi = the true induced voltage in the secondary, at full frequency, corresponding to the magnetic flux in the armature core. The secondary current then is The mutual inductive voltage at full frequency, ^ = ^1 + jxifi Thus the exciting current, /oo = YoP = ((7-i&)(l+if)^i where sbxi Qi = g + q2 = b — ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-44", "section_label": "Chapter 4: Distributed Capacity Of High-Potential Transformers", "section_title": "Distributed Capacity Of High-Potential Transformers", "kind": "chapter", "sequence": 44, "number": 4, "location": "lines 23179-23585", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "snippets": [ "... and such a coil thus represents a circuit of distributed resistance, inductance, and capacity somewhat similar to a transmission line. The same applies to reactive coils, etc., wound for very high voltages, and even in smaller reactive coils at very high frequency. This capacity effect is more marked in smaller transformers, where the size of the iron core and therewith the voltage per turn is less, and therefore the number of turns greater than in very large transformers, and at the same time the exciting cur- r ...", "... urrent are less; that is, the charging current of the conductor more comparable with the load current of the transformer or reactive coil. However, even in large transformers and at moderately high voltages, capacity effects occur in transformers, if the frequency is sufficiently high, as is the case with the currents produced in overhead lines by lightning discharges, or by arcing grounds resulting from spark discharges between conductor and ground, or in starting or disconnecting the transformer. With such frequ ...", "... uency is sufficiently high, as is the case with the currents produced in overhead lines by lightning discharges, or by arcing grounds resulting from spark discharges between conductor and ground, or in starting or disconnecting the transformer. With such frequencies, of many thousand cycles, the internal capacity of the transformer becomes very marked in its effect on the dis- tribution of voltage and current, and may produce dangerous high-voltage points in the transformer. The distributed capacity of the transform ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... igo- nometric functions, as is seen, but they are more general, depending, as they do, not only on the variable x, but also on the constant c. They have the interesting property of being doubly periodic. The trigonometric functions are periodic, with the periodicity 2;r, that is, repeat the same values after every change of the angle by 2;r. The elliptic functions have two periods pi and p2, that is, sin am{u +npi +w,p2, c) =sin am{u, c), etc.; (26) hence, increasing the variable u by any multiple of either p ...", "... e motion of the pendulum by elliptic functions becomes necessary. In electrical engineering, one has frequently to deal w^ith oscillations similar to those of the pendulum, for instance, in the hunting or surging of synchronous machines. In general, the frequency of oscillation is assumed as constant, but where, as in cumulative hunting of synchronous machines, the amplitude of the swing reaches large values, an appreciable change of the period must be expected, and where the hunting is a resonance effect with som ...", "... tive hunting of synchronous machines, the amplitude of the swing reaches large values, an appreciable change of the period must be expected, and where the hunting is a resonance effect with some other periodic motion, as the engine rotation, the change of frequency with increase of amplitude of the oscillation breaks the complete resonance and thereby tends to limit the amplitude of the swing. 177. As example of the application of elliptic integrals, may be considered the determination of the length of the arc of a ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-03", "section_label": "Lecture 3: Gravitation And The Gravitational Fleld", "section_title": "Gravitation And The Gravitational Fleld", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2389-3594", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-03/", "snippets": [ "... variation of the electromagnetic field^ — and the difference between the alternating fields of our transmission lines, the electro- magnetic waves of our radio stations, the waves of visible light and the X-rays are merely those due to the differences of frequency or wave length. The energy field at any point of space is determined by two constants, the intensity and the direction, and the force exerted by the field on a susceptible body is proportional to the field intensity and is in the direction of the energy ...", "... then the world's radius would be: R^ = 1.08 X 10\" cm. R = S& X 10>2 cm. = 225,000,000 miles. 68 RELATIVITY AND SPACE electrical constants of the hydrogen atom and showing us the exact rate of its vibration in the spectroscope by the wave length or frequency of its spectrum lines. Thus in a strong gravitational field the frequency of luminous vibrations of the atoms should be found slowed down; in other words, the spectrum lines should be shifted towards the red end of the spectrum. The amount of this shift i ...", "... = 225,000,000 miles. 68 RELATIVITY AND SPACE electrical constants of the hydrogen atom and showing us the exact rate of its vibration in the spectroscope by the wave length or frequency of its spectrum lines. Thus in a strong gravitational field the frequency of luminous vibrations of the atoms should be found slowed down; in other words, the spectrum lines should be shifted towards the red end of the spectrum. The amount of this shift is so small that it has not yet been possible to prove its existence beyon ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-08", "section_label": "Lecture 8: Generation", "section_title": "Generation", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 3781-4217", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-08/", "snippets": [ "... verter substations for the interior. In this case, where the transmission line or the main generating station is at 60 cycles, large station transformers are used for the supply of the 2200 volt distribution; where the power supply is at 25 cycles, either frequency converters, or motor generators change to 60 cycles, 2200 volts. 4. For special use, as for electrochemical work, where the electric power is generated directly, different voltages, etc., may be used to suit the requirements. Where the power cannot be ...", "... ment after the short circuit the armature current is limited by self-induction only, and is therefore much larger than afterwards, when self-induction and armature reaction both act. In machines of low armature reaction and high self- induction, as high frequency alternators, the momentary short circuit current is not much larger than the permanent short circuit current. In machines of low self-induction, that is, of a well distributed armature winding, but high armature reac- tion, (that is, very large output per ...", "... times greater than the permanent value of the short circuit cur- rent, which is reached after a few seconds. In the moment of short circuiting such an alternator, the field current rises to several times its normal value, and becomes pulsating, of double frequency. Gradually the armature cur- rent and the field current die down to their normal values. By inserting non-inductive resistance in the field circuit of the alternator, the field current, which is induced in the moment of short circuit, can be forced to die ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-04", "section_label": "Theory Section 4: Power and Effective Values", "section_title": "Power and Effective Values", "kind": "theory-section", "sequence": 4, "number": 4, "location": "lines 1244-1572", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-04/", "snippets": [ "... y some counter e.m.f., E — EI. If an alternating current i = I0 sin 6 passes through a resist- ance r, the power consumed by the resistance is, i*r = 702r sin2 0 = ^r C1 ~ cos 2 0), & thus varies with twice the frequency of the current, between zero and 70V. The average power consumed by resistance r is, avg. since avg. (cos) = 0. 16 ELEMENTS OF ELECTRICAL ENGINEERING Thus the alternating current i = IQ since 0 consumes in a re ...", "... —i is the effective value of the alternating V2 e.m.f., e = EQ sin 6. Since E0 = 2 irfn$, it follows that J' ; = 4.44 fn& ; is the effective alternating e.m.f. generated in a coil of turns n rotating at a frequency of / (in hundreds of cycles per second) through a magnetic field of megalines of force. This is the formula of the alternating-current generator. 21. The formula of the direct-current generator, E = holds even if ...", "... e alternating V2 e.m.f., e = EQ sin 6. Since E0 = 2 irfn$, it follows that J' ; = 4.44 fn& ; is the effective alternating e.m.f. generated in a coil of turns n rotating at a frequency of / (in hundreds of cycles per second) through a magnetic field of megalines of force. This is the formula of the alternating-current generator. 21. The formula of the direct-current generator, E = holds even if the e.m.fs. generated in the individual ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-46", "section_label": "Apparatus Section 3: Direct-current Commutating Machines: Generated E.m.fs.", "section_title": "Direct-current Commutating Machines: Generated E.m.fs.", "kind": "apparatus-section", "sequence": 46, "number": 3, "location": "lines 10778-10835", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-46/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-46/", "snippets": [ "III. Generated E.M.FS. 42. The formula for the generation of e.m.f. in a direct- current machine, as discussed in the preceding, is e = where e = generated e.m.f., / = frequency = number of pairs of poles X hundreds of rev. per sec., n = number of turns in series between brushes, and <£ = magnetic flux passing through the armature per pole, in megalines. In ring-wound machines, is one-half ...", "... e con- ductor lying on the armature surface, or face conductor, while in a drum-wound machine each turn has two face conductors. Thus, with the same . number of face conductors — that is, the same armature surface — the same frequency, and the same flux per field pole, the same e.m.f. is generated in the ring-wound as in the drum-wound armature. The number of turns in series between brushes, n, is one-half the total number of armature turns in a ser ...", "... l number of armature turns in a single-spiral multiple- wound armature with p poles. It is one-half as many in a double- spiral or double-reentrant, one-third as many in a triple-spiral winding, etc. By this formula, from frequency, series turns, and magnetic flux the e.m.f. is found, or inversely, from generated e.m.f., fre- quency, and series turns the magnetic flux per field pole is calculated: *--!-, 4/n From magnetic flux, and section and lengt ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-81", "section_label": "Apparatus Section 1: Synchronous Converters: General", "section_title": "Synchronous Converters: General", "kind": "apparatus-section", "sequence": 81, "number": 1, "location": "lines 13189-13795", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-81/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-81/", "snippets": [ "... ry revolution of the machine (in a 226 ELEMENTS OF ELECTRICAL ENGINEERING bipolar converter, or p periods per revolution in a machine of 2 p poles). Hence, this alternating e.m.f. is e = E sin 2 trft, where / = frequency of rotation, E = e.m.f. between brushes of the machine; thus, the effective value of the alternating e.m.f. is F ;'* El 84. That is, a direct-current machine produces between two collector rings connected with ...", "... is F ;'* El 84. That is, a direct-current machine produces between two collector rings connected with two opposite points of the commutator an alternating e.m.f. of —-= X the direct-current v2 voltage, at a frequency equal to the fre- quency of rotation. Since every alternating- current generator is reversible, such a direct- current machine with two collector rings, when supplied with an alternating e.m.f. of 1 X the direct-current volt ...", "... If now the commutator is connected to a further pair of col- lector rings, D3D4 (Fig. 123), at the points a3 and a4 midway be- tween ai and a2, it is obvious that between Z>3 and D4 an alter- nating voltage of the same frequency and intensity will be produced as between DI and D2, but in quadrature therewith, since at the moment where a3 and a4 coincide with the brushes BiB2 and thus receive the maximum difference of potential, ai and az are at ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-30", "section_label": "Chapter 30: Balanced And Unbalanced Polyphase Systems", "section_title": "Balanced And Unbalanced Polyphase Systems", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 35256-35691", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-30/", "snippets": [ "... tituting this, the instantaneous value of power is found as cos (2/3 - e)^ _ P A _ cos(2)£J- d)\\ \\ cos 0 / ' Hence the power, or the flow of energy, in an ordinary single- phase, alternating-current circuit is fluctuating, and varies with twice the frequency of e.m.f. and current, unlike the power of a continuous-current circuit, which is constant, p = ei. If the angle of lag, ^ = 9, it is, p - P(l - cos 2/3); hence the flow of energy varies between zero and 2 P, where P is the average flow of energy or ...", "... e zero point is quadruple nodal point; in the polycyclic systems quadruple isolated point. Thus these curves are sextics. Since the flow of energy in any single-phase branch of the alternating-current system can be represented by a sine wave of double frequency, sin (2 0 - ey V ~ ^ \\ \"^ cos 0 / ' the total flow of energy of the system as derived by the addition of the powers of the branch circuits can be represented in the form p = P(l +6 sin (2/3 - do)). This is a wave of double frequency also, wit ...", "... f double frequency, sin (2 0 - ey V ~ ^ \\ \"^ cos 0 / ' the total flow of energy of the system as derived by the addition of the powers of the branch circuits can be represented in the form p = P(l +6 sin (2/3 - do)). This is a wave of double frequency also, with e as amplitude of fluctuation of power. This is the equation of the power characteristics of the system in polar coordinates. 287. To derive the equation in rectangular coordinates we introduce a substitution which revolves the system of coo ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-35", "section_label": "Chapter 35: Balanced Symmetrical Polyphase Systems", "section_title": "Balanced Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 35, "number": 35, "location": "lines 37453-37957", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-35/", "snippets": [ "... reactance, X = 2TrfL = 88 ohms. The capacity of the transmission line may be calculated directly, or more conveniently it may be derived from the inductance. If C is the capacity of the circuit, of which the inductance is L, then is the fundamental frequency of oscillation, or natural period, that is, the frequency which makes the length, I, of the line a quarter-wave length. Since the velocity of propagation of the electric field is the ve- ^ \"Theoretical Elements of Electrical Engineering.\" BALANCED SY ...", "... ransmission line may be calculated directly, or more conveniently it may be derived from the inductance. If C is the capacity of the circuit, of which the inductance is L, then is the fundamental frequency of oscillation, or natural period, that is, the frequency which makes the length, I, of the line a quarter-wave length. Since the velocity of propagation of the electric field is the ve- ^ \"Theoretical Elements of Electrical Engineering.\" BALANCED SYMMETRICAL POLYPHASE SYSTEMS 451 locity of light, v, with ...", "... length. Since the velocity of propagation of the electric field is the ve- ^ \"Theoretical Elements of Electrical Engineering.\" BALANCED SYMMETRICAL POLYPHASE SYSTEMS 451 locity of light, v, with a wave-length, 4 I, the number of waves per second, or frequency of oscillation of the line, is f - — and herefrom then follows: hence, for V I Vlc I = 100 miles, V = 186,000 miles per second, L = 0.23 henry, C = 1.26 mf. and the capacity susceptance, 6 = 2 tt/C = 475 X 10-«. Representing, as ap ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-04", "section_label": "Chapter 4: Graphic Befrisxintation", "section_title": "Graphic Befrisxintation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2122-2743", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "snippets": [ "... ojection of the E.M.F., Ey upon the current, or by the E.M.F., E, into the projection of the current, /, upon the E.M.F., or IE cos (/j^). 17. Suppose, as an instance, that over a line having the resistance, r, and the reactance, x = 2irNLy — where A^ = frequency and L = inductance, — a current of / amperes be sent into a non-inductive circuit at an E.M.F. of E ,Er E • ^^ J • \\ 1 Vi \\ E. \"e. — ~^^E. Fig. 12. volts. What will be the E.M.F. required at the generator end of the line ...", "... makes us independent of the ratio of transformation. From the secondary induced E.M.F., E^, we get the flux, 4», required to induce this E.M.F., from the equation — ^i = V2 7r«iA^*10-«. where — El = secondary induced E.M.F., in effective volts, jV — frequency, in cycles per second. f/i = number of secondary turns. 4> = maximum value of magnetic flux, in webers. The derivation of this equation has been given in a preceding chapter. This magnetic flux, 4>, is represented by a vector, O^, at 30 AL TERNA T ...", "... endent of the ratio of transformation. From the secondary induced E.M.F., E^, we get the flux, 4», required to induce this E.M.F., from the equation — ^i = V2 7r«iA^*10-«. where — El = secondary induced E.M.F., in effective volts, jV — frequency, in cycles per second. f/i = number of secondary turns. 4> = maximum value of magnetic flux, in webers. The derivation of this equation has been given in a preceding chapter. This magnetic flux, 4>, is represented by a vector, O^, at 30 AL TERNA TING-CURRENT PHENOMENA, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "section_title": "Dibtbisnted Capacity, Inductance, Besistance, And", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "... / = length of conductor = 5 X 10* cm. ; d = distance of conductors from each other = 50 cm. ; 8 = diameter of conductor = 1 cm. Since C = .3 microfarads, the capacity reactance is 10« . 152 AL TERN A TING-CURRENT PHENOMENA, [$ 104 where N = frequency ; hence, at iV = 60 cycles, X = 8,900 ohms ; and the charging current of the line, at -£* = 20,000 volts, becomes, ^ to = — = 2.25 amperes. X The resistance of 100 km of line of 1 cm diameter is 22 ohms ; therefore, at 10 per cent = 2,000 volts l ...", "... resistattce. In some cases, especially in very long circuits, as in lines conveying alternating power currents at high potential over extremely long distances by overhead conductors or un- derground cables, or with very feeble currents at extremely high frequency, such as telephone currents, the consideration of the line resistance — which consumes E.M.Fs. in phase with the current — and of the line reactatice — which con- sumes E.M.Fs. in quadrature with the current — is not sufficient for the explanation of the ...", "... agnetic hysteresis, or an expenditure of E.M.F. in phase with the current, which acts as an increase of re- sistance. This electromagnetic hysteretic loss may take place in the conductor proper if iron wires are used, and will then be very serious at high frequencies, such as those of telephone currents. The effect of eddy currents has already been referred to under \"mutual inductance,\" of which it is an energy component. The alternating electrostatic field of force expends energy in dielectrics by what is called ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-23", "section_label": "Chapter 23: Generaii Foiitfhase Ststems", "section_title": "Generaii Foiitfhase Ststems", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 25120-25270", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-23/", "snippets": [ "CHAPTER XXIII. GENERAIi FOIiTFHASE STSTEMS. 232. A polyphase system is an alternating-current sys- tem in which several E.M.Fs. of the same frequency, but displaced in phase from each other, produce several currents of equal frequency, but displaced phases. Thus any polyphase system can be considered as con- sisting of a number of single circuits, or branches of the polyphase system, which may be mor ...", "CHAPTER XXIII. GENERAIi FOIiTFHASE STSTEMS. 232. A polyphase system is an alternating-current sys- tem in which several E.M.Fs. of the same frequency, but displaced in phase from each other, produce several currents of equal frequency, but displaced phases. Thus any polyphase system can be considered as con- sisting of a number of single circuits, or branches of the polyphase system, which may be more or less interlinked with each other. In general the investigation of a polyphase s ...", "... M.Fs. displaced by 90°, or one-quarter of a peHod, is an unsymmetrical system. 233. The flow of power in a single-phase system is pulsating ; that is, the watt curve of the circuit is a sine § 233] GENERAL rOLYPHASE SYSTEMS. 347 wave of double frequency, alternating between a maximum value and zero, or a negative maximum value. In a poly- phase system the watt curves of the different branches of the system are pulsating also. Their sum, however, or the total flow of power of the system, may be either con ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-25", "section_label": "Chapter 25: Baiianced And Unbaxiancbd Polyphase Systema", "section_title": "Baiianced And Unbaxiancbd Polyphase Systema", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 25605-26027", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-25/", "snippets": [ "... value of power : 7^= EI cos w. Substituting this, the instantaneous value of power is found as : \\^ cos w J Hence the power, or the flow of energy, in an ordinary single-phase alternating-current circuit is fluctuating, and varies with twice the frequency of E.M.F. and current, unlike the power of a continuous-current circuit, which is constant : p -= €t. If the angle of lag w = it is : / = /^ (1 - sin 2 )3) ; hence the flow of power varies between zero and 2/*, where P is the average flow of ener ...", "... the polycyclic system quadruple isolated point. Thus these curves are sextics. 364 ALTERNATING-CURRENT PHENOMENA, [§247 Since the flow of power in any single-phase branch of the alternating-current system can be represented by a sine wave of double frequency : V cos w J the total flow of power of the system as derived by the addition of the powers of the branch circuits can be rep- resented in the form : / = /'(l + esin(2j8-^)) This is a wave of double frequency also, with c as ampli- tude of fluctua ...", "... e represented by a sine wave of double frequency : V cos w J the total flow of power of the system as derived by the addition of the powers of the branch circuits can be rep- resented in the form : / = /'(l + esin(2j8-^)) This is a wave of double frequency also, with c as ampli- tude of fluctuation of power. This is the equation of the power characteristics of the system in polar coordinates. 247. To derive the equation in rectangular coordinates we introduce a substitution which revolves the system of ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "section_label": "Chapter 30: Quartbr-Fhase System", "section_title": "Quartbr-Fhase System", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... , and gradually dies out, reaching zero value theoreti- cally at infinite time, practically in a very short time, short even in comparison with the time of one alternating half- wave. Characteristic constants of the oscillating current are the period T or frequency .■V= 1/7\", the first ampli- tude and the ratio of any two successive amplitudes, the latter being called the decrement of the wave. The oscil- lating current will thus be represented by the product of s^ s: \"-^^ A 7' S;~-- X\" Ji~ S.' ^i ..-:^-~ ...", "... 0, §291] OSCILLATING CUR RENTS, 419 substituting in this equation A- = 2 IT NL ; AV = 2irNC\" and expanding, we have 1 a = v^ '^ -1 That is, \" If in an oscillating-current circuit, the decrement 1 rt = — v/ 1A_1 and the frequency N =. rj^iiiraLy the total impedance of the circuit is zero ; that is, the oscillating current, when started once, will continue without external energy being impressed upon the circuit.\" 291. The physical meaning of this is: \"If upon an electric circuit ...", "... ischarges. 292. The condition of an oscillating discharge is ^ = 0, that is, ' 2aL 2zVr«C a = c If r = 0, that is, in a circuit without resistance, we have a ^ Oj jV=1/2v VZ C ; that is, the currents are alter- nating with no decrement, and the frequency is that of resonance. If 4 Z/ r« C - 1 < 0, that is, r > 2 VZT^, a and N become imaginary ; that is, the discharge ceases to be os- cillatory. An electrical discharge assumes an oscillating nature only, if r < 2 VZ/ C. In the case r = 2 VZ/ C we have a ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-04", "section_label": "Chapter 4: Graphic Representation", "section_title": "Graphic Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 1743-2321", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "snippets": [ "... e projection of the E.M.F., E, upon the current, or by the E.M.F., E, into the projection of the current, /, upon the E.M.F., or by IE cos 17. Suppose, as an instance, that over a line having the resistance, r, and the reactance, x = ZirNL, — where N = frequency and L = inductance, — a current of / amperes be sent into a non-inductive circuit at an E.M.F. of E Fig. 12. volts. What will be the E.M.F. required at the generator end of the line ? In the polar diagram, Fig. 12, let the phase of the cur- rent be ...", "... en in ampere-turns. makes us independent of the ratio of transformation. From the secondary induced E.M.F., Ely we get the flux» 3>, required to induce this E.M.F., from the equation — where — £i = secondary induced E.M.F. , in effective volts, JV = frequency, in cycles per second, ;/1 = number of secondary turns, 3> = maximum value of magnetic flux, in webers. The derivation of this equation has been given in a preceding chapter. This magnetic flux, 4>, is represented by a vector, O, required to induce this E.M.F., from the equation — where — £i = secondary induced E.M.F. , in effective volts, JV = frequency, in cycles per second, ;/1 = number of secondary turns, 3> = maximum value of magnetic flux, in webers. The derivation of this equation has been given in a preceding chapter. This magnetic flux, 4>, is represented by a vector, O(! + « sin (2 £- a.)) This is a wave of double frequency also, with c as ampli- tude of fluctuation of p ...", "... tem can be represented by a sine wave of double frequency : the total flow of power of the system as derived by the addition of the powers of the branch circuits can be rep- resented in the form : / = />(! + « sin (2 £- a.)) This is a wave of double frequency also, with c as ampli- tude of fluctuation of power. This is the equation of the power characteristics of the system in polar coordinates. 275. To derive the equation in rectangular coordinates we introduce a substitution which revolves the system of ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-32", "section_label": "Chapter 32: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 25904-27405", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "snippets": [ "... , and gradually dies out, reaching zero value theoreti- cally at infinite time, practically in a very short time, short even in comparison with the time of one alternating half- wave. Characteristic constants of the oscillating current are the period T or frequency N = 1/7\", the first ampli- tude and the ratio of any two successive amplitudes, the latter being called the decrement of the wave. The oscil- lating current will thus be represented by the product of V ^ ! I\"**' \\ ^ -. \\ / S r~~ -- ...", "... case we have r - ax 0 ; x -- ^— = 0, - — c 1 + a2 1 + fla OSCILLATING CURRENTS. 507 substituting in this equation x = 2 TT NL • xc = and expanding, we have a That is, \" If in an oscillating-current circuit, the decrement 1 and the frequency N = r/4iraL, the total impedance of the circuit is zero ; that is, the oscillating current, when started once, will continue without external energy being impressed upon the circuit.\" 320. The physical meaning of this is : \" If upon an electric circuit ...", "... es. 321. The condition of an oscillating discharge is Z = 0, that is, ~ ~ / .1 r 2aL 2Z~ ~1' If r = 0, that is, in a circuit without resistance, we have a = 0, Af = 1 / 2 TT VZT ; that is, the currents are alter- nating with no decrement, and the frequency is that of resonance. If 4 H r2 C - 1 < 0, that is, r > 2 V2T/T, a and N become imaginary ; that is, the discharge ceases to be os- cillatory. An electrical discharge assumes an oscillating nature only, if r < 2 V/, / C. In the case r = 2 VZ, / C we ha ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-01", "section_label": "Chapter 1: Electric Conduction. Soled And Liquid", "section_title": "Electric Conduction. Soled And Liquid", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 959-3894", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-01/", "snippets": [ "... has an enormous electrostatic capacity, or \"effective capacity,\" but can stand low voltage only — 1 volt or less — and therefore is of limited industrial value. As chemical action requires appreciable time, such electrolytic condensers show at commercial frequencies high losses of power by what may be called \" chemical hysteresis,\" and therefore low efficiences, but they are alleged to become efficient at very low frequencies. For this reason, they have 10 ELECTRIC CIRCUITS been proposed in the secondaries of ind ...", "... s chemical action requires appreciable time, such electrolytic condensers show at commercial frequencies high losses of power by what may be called \" chemical hysteresis,\" and therefore low efficiences, but they are alleged to become efficient at very low frequencies. For this reason, they have 10 ELECTRIC CIRCUITS been proposed in the secondaries of induction motors, for power- factor compensation. Iron plates in alkaline solution, as sodium carbonate, are often considered for this purpose. Note. — The aluminum ...", "... powdered metal, with non-conductors as clay, carborundum, cement, also have pyroelectric conduction. Such are used, for instance, as \"resistance rods\" in lightning arresters, in some rheostats, as ELECTRIC CONDUCTION 13 cement resistances for high-frequency power dissipation in re- actances, etc. Many, if not all so-called \"insulators\" probably are in reality pyroelectric conductors, in which the maximum voltage point 6 is so high, that the range (3) of decreasing charac- teristic can be reached only by the ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-10", "section_label": "Chapter 6: Alternating Magnetic Flux Distribution. 355", "section_title": "Alternating Magnetic Flux Distribution. 355", "kind": "chapter", "sequence": 10, "number": 6, "location": "lines 904-937", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-10/", "snippets": [ "... ng magnetic flux in a lamina. 356 50. Their integral equations. 357 51. Terminal conditions, and the final equations. 358 52. Equations for very thick laminae. 360 53. Wave length, attenuation, depth of penetration. 361 54. Numerical example, with frequencies of 60, 1000 and 10,000 cycles per second. 362 55. Depth of penetration of alternating magnetic flux in different metals. 363 56. Wave length, attenuation, and velocity of penetration. 365 57. Apparent permeability, as function of frequency, and da ...", "... 50. Their integral equations. 357 51. Terminal conditions, and the final equations. 358 52. Equations for very thick laminae. 360 53. Wave length, attenuation, depth of penetration. 361 54. Numerical example, with frequencies of 60, 1000 and 10,000 cycles per second. 362 55. Depth of penetration of alternating magnetic flux in different metals. 363 56. Wave length, attenuation, and velocity of penetration. 365 57. Apparent permeability, as function of frequency, and damping. 366 58. Numerical example and disc ...", "... e, with frequencies of 60, 1000 and 10,000 cycles per second. 362 55. Depth of penetration of alternating magnetic flux in different metals. 363 56. Wave length, attenuation, and velocity of penetration. 365 57. Apparent permeability, as function of frequency, and damping. 366 58. Numerical example and discussion. 367" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-37", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 37, "number": 1, "location": "lines 15354-15625", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "snippets": [ "... ltage, etc., and the permanent term occasionally is very small compared with the transient term. 4. Periodic transient phenomena are of engineering impor- tance mainly in three cases: (1) in the control of electric circuits; (2) in the production of high frequency currents, and (3) in the rectification of alternating currents. 1. In controlling electric circuits, etc., by some operating mechanism, as a potential magnet increasing and decreasing the resistance of the circuit, or a clutch shifting brushes, etc., the ...", "... any resultant inter- mediary between the two extremes can thus be produced. On this principle, for instance, operated the controlling solenoid of the Thomson-Houston arc machine, and also numerous auto- matic potential regulators. 2. Production of high frequency oscillating currents by period- ically recurring condenser discharges has been discussed under \" oscillating current generator,\" in Section I, paragraph 44. Non-sinusoidal high frequency alternating currents are pro- duced by an arc, when made unstable b ...", "... numerous auto- matic potential regulators. 2. Production of high frequency oscillating currents by period- ically recurring condenser discharges has been discussed under \" oscillating current generator,\" in Section I, paragraph 44. Non-sinusoidal high frequency alternating currents are pro- duced by an arc, when made unstable by shunting it with a condenser, as discussed before. The Ruhmkorff coil or inductorium also represents an appli- cation of periodically recurring transient phenomena, as also does Prof. ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-56", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit", "section_title": "Power And Energy Of The Complex Circuit", "kind": "chapter", "sequence": 56, "number": 7, "location": "lines 33528-34202", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "snippets": [ "... complex circuit differs from that of the uniform circuit in that the former contains exponential functions of the distance A which represent the shifting or transfer of power between the sections of the circuit. Thus the general expression of one term or frequency of current and voltage in a section of a complex circuit is given by equations (290); - £~SA [C cos q (A + 0 + D sin q (J + t)]} and /7 +SA [A cos q (A — t) -f B sin q (A — £)] where q = nq0, q0 = — , A = total length of circuit, expressed in th ...", "... )]2 [C cos q (X + 0 + D sin g (J + O]2} + [e+2sA(A2-£2) cos 2q (X-t) -e~2s* (C2-D2) cos 2 g (l + t)] + 2 [ABe+*s*sm 2 g (X-t) -CDe-2'* sin 2-g (A + *)]} ; (303) that is, the instantaneous value of power consists of a constant term and terms of double frequency in (X - t) and (A + t) or in distance A and time t. Integrating (303) over a complete period in time gives the effective or mean value of power at any point X as p = r*M {fi+2« (A2 + J52) - s-2s (C2 + £>2) } ; (304) .2 * C that is, the effective po ...", "... fore, h (332) and integrating over a complete period ffi._4J^4»4£ (333) dX dX dX the power dissipated in the circuit thus contains a constant term, 4 u — - , and a term which is a periodic function of the distance X, (JLA 4 m — — - , of double frequency. dX Averaged over a half-wave of the circuit, or a multiple thereof, the second term disappears, and dX dX ' or, substituting (314), , (334) thus the power dissipated in a section A' = X2 — Xl of the circuit is, by integrating between limits X\\ ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-01", "section_label": "Chapter 1: The General Number", "section_title": "The General Number", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 915-3491", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-01/", "snippets": [ "... ormed mathematically, IE, and would represent a point C in the vector plane Fig. 21. This point C, however, and the mathematical expression IE, which represents it, does not give the power P of the alternating circuit, since the power P is not of the same frequency as / and E, and therefore cannot be represented in the same polar diagram Fig. 21, which represents 7 and E, If we have a current / and an impedance Z, in Fig. 21; I=ii+ji2 and Z = r—jx, their product is a voltage, and as the voltage is of the same freq ...", "... ency as / and E, and therefore cannot be represented in the same polar diagram Fig. 21, which represents 7 and E, If we have a current / and an impedance Z, in Fig. 21; I=ii+ji2 and Z = r—jx, their product is a voltage, and as the voltage is of the same frequency as the current, it can be repre- sented in the same polar diagram. Fig. 21, and thus is given by the mathematical product of / and Z, ^E = IZ={H+ji2){r-jx), = (iir ■^i2X ) + jfer -iix). 28. Commonly, in the denotation of graphical diagrams by general ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-02", "section_label": "Chapter 2: Potential Series And Exponential Function", "section_title": "Potential Series And Exponential Function", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3492-6063", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-02/", "snippets": [ "... reality, due to the unavoidable resistance in the discharge path, the alterna- tions gradually die out, that is, the discharge is oscillating. The time of one complete period is given by, 1000^0=2;:; or, to=^. Hence the frenquency, /= — = —^ — = 159 cycles per second. As the circuit in addition to the inductance necessarily contains resistance r, besides the voltage consumed by the inductance by equation (112), voltage is consumed by the resistance, thus er = ri, . (117) and the total voltage consumed by resistan ...", "... tions of gradually decreasing amplitude. Such functions are called oscillating functions. Practically all disturbances in electric circuits consist of such oscillating currents and voltages. 600^ = 2;: gives, as the time of one complete period, and the frequency is ^ = ^ = 0.0105 sec; 600 ' /=-^ = 95.3 cycles per sec. In this particular case, as the resistance is relatively high, the oscillations die out rather rapidly. The reader is advised to calculate and plot the numerical values of i and e, and of ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-04", "section_label": "Lecture 4: The Characteristics Of Space A. The Geometry Of The Gravitational Field", "section_title": "The Characteristics Of Space A. The Geometry Of The Gravitational Field", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3595-6820", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-04/", "snippets": [ "... 2 Distance between two events, 32 measure of time, 33 E Earth as elliptic 2-space, 75 Einstein, law of gravitation, 11 Electric field, 47 quantity, 47 Electricity, constancy of speed, 4 Electromagnet, 20 Electromagnetic field, 21 wave, 17, 21 frequency, 22 Electron velocity, 8 Electrostatic charge, 47 field, 18 ElUptic geometry, 64, 72, 74 trigonometry, 77 Energy equivalent of mass, 44 field, 22, 46 kinetic, 47 and mass, 41 of wave, 22 123 124 INDEX Entity energy, 24 Equations ...", "... ric, 18 electromagnetic, 21 electrostatic, 18 gravitational, 18, 46, 47 magnetic, 18 of energy, 22 of force, 12, 18 Finite volume of universe, 63 Force, magnetic, 46 Four-dimensional space with sphere as element, 99 Fraction, meaning of, 38 Frequencies of electromagnetic waves, 22 Friction of ether, 14 G Gauss, 71 General differential space, 115 geometry, 64 or projective geometry space, 115 Geometry, 64 of gravitational field, 69 Gravitation, 46 as accelerated motion, 52 as centrifugal ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-109", "section_label": "Apparatus Section 3: Induction Machines: Single -phase Induction Motor", "section_title": "Induction Machines: Single -phase Induction Motor", "kind": "apparatus-section", "sequence": 109, "number": 3, "location": "lines 20428-21157", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-109/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-109/", "snippets": [ "... e self-inductive impedance and the drop of quadrature mag- netic flux below the impressed primary magnetic flux caused thereby. In the secondary at synchronism this secondary exciting current is a current of twice the primary frequency; at any other speed it is of a frequency equal to speed (in cycles) plus synchronism. Thus, if in a quarter-phase motor running light one phase is open-circuited, the current in the other phase doubles. If in the three- ...", "... quadrature mag- netic flux below the impressed primary magnetic flux caused thereby. In the secondary at synchronism this secondary exciting current is a current of twice the primary frequency; at any other speed it is of a frequency equal to speed (in cycles) plus synchronism. Thus, if in a quarter-phase motor running light one phase is open-circuited, the current in the other phase doubles. If in the three-phase motor two phases are open-circuited, t ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-20", "section_label": "Theory Section 20: Nomenclature", "section_title": "Nomenclature", "kind": "theory-section", "sequence": 20, "number": 20, "location": "lines 7991-8291", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-20/", "snippets": [ "... w.... Energy, work Joule; kilo joule General T,# Temperature Degrees Centigrade General t Time Seconds General $,$,0... Time angle Degrees or radians General <*,T Space angle Degrees or radians General / Frequency Cycles per second General PART II SPECIAL APPARATUS", "... gy, work Joule; kilo joule General T,# Temperature Degrees Centigrade General t Time Seconds General $,$,0... Time angle Degrees or radians General <*,T Space angle Degrees or radians General / Frequency Cycles per second General PART II SPECIAL APPARATUS" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-24", "section_label": "Apparatus Section 3: Synchronous Machines: Armature Reaction", "section_title": "Synchronous Machines: Armature Reaction", "kind": "apparatus-section", "sequence": 24, "number": 3, "location": "lines 8741-8906", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-24/", "snippets": [ "... ine the armature reaction and thereby the resultant m.m.f. of field and armature is pulsating. The pulsation of the resultant m.m.f. of the single-phase machine causes a pulsation of its magnetic field under load, of double frequency, which generates a third harmonic of e.m.f. in the armature conductors. In machines of high armature reaction, as steam-turbine-driven single-phase alternators, the pulsation of the magnetic field may be sufficient to cause se ...", "... rrel- cage induction machine winding in the field pole faces, or by short-circuited conductors laid in the pole faces in electrical space quadrature to the field coils. In these conductors, secondary currents Ei'_ of double frequency are produced which equalize the resultant m.m.f. of the machine." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-29", "section_label": "Apparatus Section 8: Synchronous Machines: Characteristic Curves of Synchronous Motor", "section_title": "Synchronous Machines: Characteristic Curves of Synchronous Motor", "kind": "apparatus-section", "sequence": 29, "number": 8, "location": "lines 9399-9553", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-29/", "snippets": [ "... is, independence of minor fluctuations of impressed voltage or of field excitation. 19. The theoretical maximum output of the synchronous motor, or the load at which it drops out of step, at constant impressed voltage and frequency is, even with very high armature reaction, usually far beyond the heating limits of the machine. 200 100 600 800 1000 1200 UOO 1600 1800 2000 FIG. 66. — Synchronous motor phase characteristics. The ac ...", "... 1600 1800 2000 FIG. 66. — Synchronous motor phase characteristics. The actual maximum output depends on the drop of terminal voltage due to the increase of current, and on the steadiness or uniformity of the impressed frequency, thus upon the individual conditions of operation, but is as a rule far above full load. Hence, by varying the field excitation of the synchronous motor the current can be made leading or lagging at will, and the syn- ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-34", "section_label": "Apparatus Section 13: Synchronous Machines: Parallel Operation", "section_title": "Synchronous Machines: Parallel Operation", "kind": "apparatus-section", "sequence": 34, "number": 13, "location": "lines 9821-9878", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-34/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-34/", "snippets": [ "... nizing one phase of the former with one phase of the latter. Since alternators in parallel must be in step with each other and have the same terminal voltage, the condition of satis- factory parallel operation is that the frequency of the machines is identically the same, and the field excitation such as would give the same terminal voltage. If this is not the case, there will be cross currents between the alternators in a local circuit; that is, ...", "... , and their currents under load are not of the same phase and proportional to their respective capacities. The cross currents between alternators when operated in parallel can be wattless currents or power currents. If the frequencies of two alternators are identically the same, but the field excitation not such as would give equal terminal voltage when operated in parallel, there is a local current between the two machines which is wattless and leading ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-57", "section_label": "Apparatus Subsection 57: Direct-current Commutating Machines: C. Commutating Machines", "section_title": "Direct-current Commutating Machines: C. Commutating Machines", "kind": "apparatus-subsection", "sequence": 57, "number": null, "location": "lines 11401-11540", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-57/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-57/", "snippets": [ "D. C. COMMUTATING MACHINES 191 ture in centimeters per second, lp = pitch of armature slot (that is, width of one slot and one tooth at armature surface), the S frequency is /i = y-. Or, if / = frequency of machine, n — number of armature slots per pair of poles, /i = nf. For instance,/ = 33.3, n = 51, thus/i = 1700. Under the assumption, width of slots equals width of teeth ...", "D. C. COMMUTATING MACHINES 191 ture in centimeters per second, lp = pitch of armature slot (that is, width of one slot and one tooth at armature surface), the S frequency is /i = y-. Or, if / = frequency of machine, n — number of armature slots per pair of poles, /i = nf. For instance,/ = 33.3, n = 51, thus/i = 1700. Under the assumption, width of slots equals width of teeth = 2 X width of air gap, the dis- tr ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-79", "section_label": "Apparatus Subsection 79: Direct-current Commutating Machines: C. Commutating Machines 219", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 219", "kind": "apparatus-subsection", "sequence": 79, "number": null, "location": "lines 13019-13119", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-79/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-79/", "snippets": [ "... xcessive con- centration of heat in the commutating leads in the moment of starting tends to destroy them if the motor does not quickly start. 3. Narrow brushes, to reduce the duration of short circuit. 4. Low impressed frequency, so as to give low values to the induced e.m.f. This is the cause of the desire for abnormally low frequencies, as 15 and even 8 cycles, in alternating-current railway electrification. 5. Low magnetic flux per pole ...", "... or does not quickly start. 3. Narrow brushes, to reduce the duration of short circuit. 4. Low impressed frequency, so as to give low values to the induced e.m.f. This is the cause of the desire for abnormally low frequencies, as 15 and even 8 cycles, in alternating-current railway electrification. 5. Low magnetic flux per pole. This is the reason why alternating-current commutator motors of large power usually have such a large number o ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-80", "section_label": "Apparatus Subsection 80: Direct-current Commutating Machines: C. Commutating Machines 221", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 221", "kind": "apparatus-subsection", "sequence": 80, "number": null, "location": "lines 13120-13188", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-80/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-80/", "snippets": [ "... this e.m.f. is in opposition; raised beyond synchronism, if this e.m.f. is in the same direction as the e.m.f. induced in the motor secondary. As, however, the e.m.f. induced in the induction motor secondary is of the frequency of slip, the speed controlling e.m.f. must either be supplied through the commutator or de- rived from a low frequency commutating machine as source. 4. For power-factor compensation. In an inductive circuit, the current ...", "... in the motor secondary. As, however, the e.m.f. induced in the induction motor secondary is of the frequency of slip, the speed controlling e.m.f. must either be supplied through the commutator or de- rived from a low frequency commutating machine as source. 4. For power-factor compensation. In an inductive circuit, the current lags behind the voltage or, what is the same, the voltage leads the current, and the power-factor thus can be raised ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-89", "section_label": "Apparatus Section 11: Synchronous Converters: Double-current Generators", "section_title": "Synchronous Converters: Double-current Generators", "kind": "apparatus-section", "sequence": 89, "number": 11, "location": "lines 15893-15982", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-89/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-89/", "snippets": [ "... the converter. Obviously the use of the double-current generator is limited to those sizes and speeds at which a good direct-current generator can be built with the same number of poles as a good alternator, that is, low- frequency machines of large output and relatively high speed; while high-frequency low-speed double-current generators are undesirable. The essential difference between double-current generator and converter is, however, that in the former ...", "... ed to those sizes and speeds at which a good direct-current generator can be built with the same number of poles as a good alternator, that is, low- frequency machines of large output and relatively high speed; while high-frequency low-speed double-current generators are undesirable. The essential difference between double-current generator and converter is, however, that in the former the direct current and the alternating current are not in opposition a ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-04", "section_label": "Chapter 4: Vector Representation", "section_title": "Vector Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2149-2759", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-04/", "snippets": [ "... . This makes us inde- pendent of the ratio of transformation. Ei-^ From the secondary e.m.f., Ei, we get the flux, , required to induce this e.m.f., from the equation El = ^/2 7^/^l/$ 10-8; where El = secondary e.m.f., in effective volts, / = frequency, in cycles per second, Wi = number of secondary turns, $ = maximum value of magnetic flux, in lines of magnetic force. The derivation of this equation has been given in a preceding chapter. This magnetic flux, $, is represented by a vector, 0^, QO'' ...", "... s inde- pendent of the ratio of transformation. Ei-^ From the secondary e.m.f., Ei, we get the flux, , required to induce this e.m.f., from the equation El = ^/2 7^/^l/$ 10-8; where El = secondary e.m.f., in effective volts, / = frequency, in cycles per second, Wi = number of secondary turns, $ = maximum value of magnetic flux, in lines of magnetic force. The derivation of this equation has been given in a preceding chapter. This magnetic flux, $, is represented by a vector, 0^, QO'' in phase, and to prod ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-05", "section_label": "Chapter 5: Symbolic Method", "section_title": "Symbolic Method", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2760-3266", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-05/", "snippets": [ "... components, in any direction, of all the currents at a distributing point equals zero. Joule's law and the power equation do not give a simple expression in complex quantities, since the effect or power is SYMBOLIC METHOD 37 a quantity of double the frequency of the current or e.m.f. wave, and therefore requires for its representation as a vector a transition from single to double frequency, as will be shown in Chapter XVI. In what follows, complex vector quantities will always be denoted by dotted capitals ...", "... e a simple expression in complex quantities, since the effect or power is SYMBOLIC METHOD 37 a quantity of double the frequency of the current or e.m.f. wave, and therefore requires for its representation as a vector a transition from single to double frequency, as will be shown in Chapter XVI. In what follows, complex vector quantities will always be denoted by dotted capitals when not written out in full; abso- lute quantities and real quantities by undotted letters. 34. Referring to the example given in th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-28", "section_label": "Chapter 28: General Polyphase Systems", "section_title": "General Polyphase Systems", "kind": "chapter", "sequence": 28, "number": 28, "location": "lines 34777-34928", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-28/", "snippets": [ "CHAPTER XXVIII GENERAL POLYPHASE SYSTEMS 266. A polyphase system is an alternating-current system in which several e.m.fs. of the same frequency, but displaced in phase from each other, produce several currents of equal fre- quency, but displaced phases. Thus any polyphase system can be considered as consisting of a number of single circuits, or branches of the polyphase sys- tem, which may be m ...", "... em. The quarter-phase system, consisting of two equal e.m.fs. displaced by 90°, or one-quarter of a period, is an unsymmetrical system.- 267. The power in a single-phase system is pulsating; that is, the watt curve of the circuit is a sine wave of double frequency, alternating between a maximum value and zero, or a negative maximum value. In a polyphase system the watt curves of the different branches of the system are pulsating also. Their sum, however, or the total power of the system, may be either con- 396 ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-09", "section_label": "Chapter 10: Hysteresis Motor", "section_title": "Hysteresis Motor", "kind": "chapter", "sequence": 9, "number": 10, "location": "lines 14551-14761", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-09/", "snippets": [ "... ed m.m.f. independent of the speed also. If, now: V = volume of iron of the movable part, (B = magnetic density, and rj = coefficient of hysteresis, the energy expended by hysteresis in the movable disk, 7, is per cycle: Wo = VV®1\\ hence, if / = frequency, the power supplied by the m.m.f. to the rotating iron disk in the hysteretic loop of the m.m.f. is: p0 =/Fi?(B,-e. At the slip, sfj that is, the speed (1 — s) f, the power expended by hysteresis in the rotating disk is, however: Pi = s/FtjCB1-6. 1 ...", "... under \"Reaction Machine\" in Chapter XVI. 100. In the hysteresis motor, consisting of an iron disk of uniform magnetic reluctance, which revolves in a uniformly rotating magnetic field, below synchronism, the magnetic mix rotates in the armature with the frequency of slip, and the resultant line of magnetic induction in the disk thus lags, in space, behind the synchronously rotating line of resultant m.m.f HYSTERESIS MOTOR 171 of the exciting coils, by the angle of hysteretic lead, or, which is constant, and so ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-06", "section_label": "Chapter 2: Long Distance Transmission Line. 279", "section_title": "Long Distance Transmission Line. 279", "kind": "chapter", "sequence": 6, "number": 2, "location": "lines 755-835", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-06/", "snippets": [ "CHAPTER II. LONG DISTANCE TRANSMISSION LINE. 279 3. Relation of wave length of impressed frequency to natural frequency of line, and limits of approximate line cal- culations. 279 4. Electrical and magnetic phenomena in transmission line. 281 5. The four constants of the transmission line : r, L, g, C. 282 6. The problem of the transmission line. ...", "CHAPTER II. LONG DISTANCE TRANSMISSION LINE. 279 3. Relation of wave length of impressed frequency to natural frequency of line, and limits of approximate line cal- culations. 279 4. Electrical and magnetic phenomena in transmission line. 281 5. The four constants of the transmission line : r, L, g, C. 282 6. The problem of the transmission line. 283 7. The differenti ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-07", "section_label": "Chapter 3: The Natural Period Of The Transmission Line. 320", "section_title": "The Natural Period Of The Transmission Line. 320", "kind": "chapter", "sequence": 7, "number": 3, "location": "lines 836-874", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-07/", "snippets": [ "... THE TRANSMISSION LINE. 320 27. The oscillation of the transmission line as condenser. 320 28. The conditions of free oscillation. 321 29. Circuit open at one end, grounded at other end. 322 30. Quarter-wave oscillation of transmission line. 323 31. Frequencies of line discharges, and complex discharge wave. 327 32. Example of discharge of line of constant voltage and zero current. 329 33. Example of short-circuit oscillation of line. 331 34. Circuit grounded at both ends : Half-wave oscillation. 333 35. ...", "... ion of line. 331 34. Circuit grounded at both ends : Half-wave oscillation. 333 35. The even harmonics of the half-wave oscillation. 334 36. Circuit open at both ends. 335 37. Circuit closed upon itself: Full-wave oscillation. 336 38. Wave shape and frequency of oscillation. 338 39. Time decrement of oscillation, and energy transfer be- tween sections of complex oscillating circuit. 339 xx CONTENTS. PAGE" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-24", "section_label": "Chapter 2: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 24, "number": 2, "location": "lines 1993-2658", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "snippets": [ "... soon as the condenser charge has reached a certain value, and so starts a transient term; the condenser charges again, and discharges, and so by the successive charges and discharges of the condenser a series of transient terms is produced, recurring at a frequency depending upon the circuit constants and upon the ratio of the disruptive voltage of the spark gap to the impressed e.m.f. INTRODUCTION 23 >uch a phenomenon for instance occurs when on a high- potential alternating-current system a weak spot appea ...", "... ial surges, etc., are in their nature essentially transient phenomena, usually of oscillating character. (c) The periodical production of transient terms of oscillating character is one of the foremost means of generating electric cur- rents of very high frequency as used in wireless telegraphy, etc. (d) In alternating-current rectifying apparatus, by which the direction of current in a part of the circuit is reversed every half wave, and the current so made unidirectional, the stationary condition of the current ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-33", "section_label": "Chapter 40: General System Of Circuits", "section_title": "General System Of Circuits", "kind": "chapter", "sequence": 33, "number": 40, "location": "lines 12217-12884", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-33/", "snippets": [ "... e and inductance only. 95. Let, upon a general system or network of circuits con- nected with each other directly or inductively, and containing resistance and inductance, but no capacity, a system of e.m.fs., ey be impressed. These e.m.fs. may be of any frequency or wave shape, or may be continuous or anything else, but are supposed to be given by their equations. They may be free of transient terms, or may contain transient terms depending upon the currents in the system. In the latter case, the dependency of th ...", "... l method of the determination of the transient phenomena occurring in any system or net work of circuits containing resistances, self-indue- 178 TRANSIENT PHENOMENA tances and mutual inductances and capacities, and impressed and counter e.m.fs. of any frequency or wave shape, alternating or con- tinuous. It presupposes, however, (1) That the solution of the system for the permanent terms of currents and e.m.fs. is given. (2) That, if the impressed e.m.fs. contain transient terms depending upon the currents ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-41", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 41, "number": 1, "location": "lines 19260-19338", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "snippets": [ "... ution of the electric field of a conductor through space, resulting from the finite velocity of propagation of the electric field, and the variation of self-inductance and mutual inductance and of capacity of a conductor without return, as function of the frequency, in its effect on wireless telegraphy. (e) Conductors conveying very high frequency currents, as lightning discharges.", "... locity of propagation of the electric field, and the variation of self-inductance and mutual inductance and of capacity of a conductor without return, as function of the frequency, in its effect on wireless telegraphy. (e) Conductors conveying very high frequency currents, as lightning discharges." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-01-recommendations", "section_label": "Report Section 2: Recommendations", "section_title": "Recommendations", "kind": "report-section", "sequence": 2, "number": 2, "location": "PDF pages 7-12, lines 145-720", "status": "pdf-text-extracted-candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "snippets": [ "... rouble is perfectly cleared. 6.) Install in each station section, as permanent busbar instruments, as many suitable synchronoscopes as there are other station sections (three at present) , for the purpose of continually indicating the phase difference and the frequency difference of the station section from all other station sections. If by some trouble a station section has broken out of synchronism with the rest of the system, it appears practically impossible without the assistance of a synchronoscope, to control the ste ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 6125-6803", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-09/", "snippets": [ "... formly distributed throughout the entire circuit, and if it is not so in the beginning of the transient, local traveling waves redistribute the energy throughout the oscillat- ing circuit, as stated before. Such local oscillations are usually of very high frequency, but sometimes come within the range of the oscillograph, as in Fig. 47. During the oscillation of the complex circuit, every circuit element d\\ (in velocity measure), or every wave length or equal part of the wave length, therefore contains the same amo ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 5521-6088", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "snippets": [ "... formly distributed throughout the entire circuit, and if it is not so in the beginning of the transient, local traveling waves redistribute the energy throughout the oscillat- ing circuit, as stated before. Such local oscillations are usually of very high frequency, but sometimes come within the range of the oscillograph, as in Fig. 47. During the oscillation of the complex circuit, every circuit element d\\ (in velocity measure), or every wave length or equal part of the wave length, therefore contains the same amo ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-09", "section_label": "Lecture 9: Measurement Of Light And Radiation", "section_title": "Measurement Of Light And Radiation", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 8511-9388", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-09/", "snippets": [ "... garding particular features of the quantities which they have in common. Thus a piece of stone and a piece of ice can be compared regarding their weight, or their density, etc. In the same manner, two different colors of light, or in general two different frequencies of radiation, can be compared by any feature which they have in common. Thus, for instance, the photographic plate compares them in their chemical activity, the bolometer by their physical energy. Light is used for seeing things by, that is, distinguishi ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-07", "section_label": "Theory Section 7: Inductance in Alternating-current Circuits", "section_title": "Inductance in Alternating-current Circuits", "kind": "theory-section", "sequence": 7, "number": 7, "location": "lines 2250-2717", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-07/", "snippets": [ "... the current. Their effective values are E, E cos 00) E sin 00. EXAMPLES 37. (1) What is the reactance per wire of a transmission line of length Z, if ld = diameter of the wire, 18 = spacing of the wires, and/ = frequency? If / = current, in absolute units, in one wire of the trans- mission line, the m.m.f. is I; thus the magnetizing force in a zone dlx at distance lx from center of wire (Fig. 12) is / = 0 7 Z TTlx and the fie ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-111", "section_label": "Apparatus Section 5: Induction Machines: Induction Booster", "section_title": "Induction Machines: Induction Booster", "kind": "apparatus-section", "sequence": 111, "number": 5, "location": "lines 21589-21646", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-111/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-111/", "snippets": [ "... apparent resistance, thereby lowering the effi- ciency of the apparatus, but at the same time making it less de- pendent upon minor variations of speed ; that is, requires a lesser constancy of slip, and thus of speed and frequency, to give a steady boosting effect." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-53", "section_label": "Apparatus Subsection 53: Direct-current Commutating Machines: C. Commutating Machines 185", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 185", "kind": "apparatus-subsection", "sequence": 53, "number": null, "location": "lines 11132-11213", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-53/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-53/", "snippets": [ "... short-circuited armature coil under the brush, and thus impairs commutation. If therefore the commutation constants of the machines are not abnormally good — high field strength, low armature reaction, low self-in- ductance and frequency of commutation — the machine does not commutate satisfactorily under load, with the brushes midway between the field poles, and the brushes have to be shifted to the edge of the next field poles, as shown in Fig. 95, unti ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-56", "section_label": "Apparatus Section 7: Direct-current Commutating Machines: Effect of Slots on Magnetic Flux", "section_title": "Direct-current Commutating Machines: Effect of Slots on Magnetic Flux", "kind": "apparatus-section", "sequence": 56, "number": 7, "location": "lines 11387-11400", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-56/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-56/", "snippets": [ "... age of the armature slots across the field pole a local pulsation of the magnetic flux in the pole face is produced, which, while harmless with laminated field pole faces, generates eddy currents in solid pole pieces. The frequency of this pul- sation is extremely high, and thus the energy loss due to eddy currents in the 'pole faces may be considerable, even with pul- sations of small amplitude. If S = peripheral speed of the arma-" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-82", "section_label": "Apparatus Section 3: Synchronous Converters: Variation of the Ratio of Electromotive Forces", "section_title": "Synchronous Converters: Variation of the Ratio of Electromotive Forces", "kind": "apparatus-section", "sequence": 82, "number": 3, "location": "lines 13796-13888", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-82/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-82/", "snippets": [ "... maximum to effective of the sine wave on which the ratios in Section II were based), that is, by a \"form factor\" of the e.m.f. wave. With an impressed wave differing from the sine shape, there is a current of higher frequency, but generally of negligible mag- nitude, through the converter armature, due to the difference between impressed and counter e.m.f. wave." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-91", "section_label": "Apparatus Section 13: Synchronous Converters: Direct-current Converter", "section_title": "Synchronous Converters: Direct-current Converter", "kind": "apparatus-section", "sequence": 91, "number": 13, "location": "lines 16065-16540", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-91/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-91/", "snippets": [ "... rsed currents in the direct-current generator or motor, and distorted triple-fre- quency currents in the synchronous converter, the currents in the armature coils of the direct-current converter are approximately triangular double-frequency waves. Let Fig. 142 represent a development of a direct-current con- verter with brushes BI and B2, and C one autotransformer re- ceiving current 2 i from the neutral. Consider first an armature coil ai adjacent and behind ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-11", "section_label": "Chapter 11: Phase Control", "section_title": "Phase Control", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 9767-10717", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-11/", "snippets": [ "... motor speed increases, as the armature has to revolve faster to consume the impressed e.m.f., and if the field excitation is increased, the motor slows down. A synchronous motor, however, cannot vary in speed, since it must keep in step with the impressed frequency, and if, therefore, at constant impressed voltage the field excitation is decreased below that which gives a field magnetism, that at the synchronous speed consumes the impressed voltage, the field magnetism still must remain the same, and the armature cu ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-20", "section_label": "Chapter 20: Single-Phase Induction Motors", "section_title": "Single-Phase Induction Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 21538-22301", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-20/", "snippets": [ "... relatively small. The use of shunted capacity, however, has the dis- advantage of requiring a wave of impressed e.m.f. very close to sine shape, since even with a moderate variation from sine shape the wattless charging current of the condenser of higher frequency may lower the power-factor more than the compen- sation for the wattless component of the fundamental wave raises it, as will be seen in the chapter on General Alternating- current Waves. Thus the most satisfactory application of the condenser in the si ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-21", "section_label": "Chapter 21: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 22302-23970", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-21/", "snippets": [ "... t in the field- spools, or the open-circuit voltage, more properly called the \"nominal generated e.m.f.,\" since in reality it does not exist as before stated. Then Eo = V2 7r/j/4> 10-8; where n = total number of turns in series on the armature, / = frequency, $ = total magnetic flux per field-pole. Let Xo = synchronous reactance, ro = internal resistance of the alternator; then Zo ^ To -{- jxo = internal impedance. If the circuit of the alternator is closed by the external im- pedance, Z = r + jx, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-29", "section_label": "Chapter 29: Symmetrical Polyphase Systems", "section_title": "Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 29, "number": 29, "location": "lines 34929-35255", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-29/", "snippets": [ "... hase of the resultant m.m.f. at the time represented by the angle /3 is tan d ^ — cot jS; hence d = ~ ^ o' That is, the m.m.f. produced by a symmetrical ?i-phase system revolves with constant intensity, V2 and constant speed, in synchronism with the frequency of the system; and, if the reluctance of the magnetic circuit is constant, the magnetism revolves with constant intensity and constant speed also, at the point acted upon symmetrically by the n m.m.fs. of the n-phase system. This is a characteristic fea ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-05", "section_label": "Chapter 5: Symbouc Mbthod", "section_title": "Symbouc Mbthod", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2744-3229", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "snippets": [ "... of the components, in any direction, of all the currents flowing towards a distributing point, equals zero. Joule's Law and the energy equation do not give a simple expression in complex quantities, since the effect or power is a quantity of double the frequency of the current or E.M.F. wave, and therefore cannot be represented as a vector in the diagram. In what follows, complex quantities will always be de- noted by capitals, absolute quantities and real quantities by small letters. 32. Referring to the ins ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-16", "section_label": "Chapter 16: Aiitebnatingh-Current Osnebator", "section_title": "Aiitebnatingh-Current Osnebator", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 17025-18828", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "snippets": [ "... magnetic field produced by the cur- rent in the field spools, or the open circuit voltage of the alternator. § 164 J AL TERN A TING-CUKREXT GENERA TOR. 239 Then e^ = -s/^icnN Ml^'^-, where // = total number of turns in series on the armature, N = frequency, J/ = total magnetic ffux per field pole. Let Xo = synchronous reactance, To = internal resistance of alternator ; then Zo = ^o — j x^ = internal impedance. If the circuit of the alternator is closed by the external impedance, and cinrcnt 7 = ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-24", "section_label": "Chapter 24: Symmetbicaii Polyphase Ststems", "section_title": "Symmetbicaii Polyphase Ststems", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 25271-25604", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-24/", "snippets": [ "... se of the resultant M.M.F. at the time repre- sented by the angle /3 is : tan a> = cot P ; That is, the M.M.F. produced by a symmetrical «-phase system revolves with constant intensity : F = ,— » V2 and constant speed, in synchronism with the frequency of the system ; and, if the reluctance of the magnetic circuit §238] SYMMETRICAL POLYPHASE SYSTEMS. 355 is constant, the magnetism revolves with constant intensity and constant speed also, at the point acted upon symmetri- cally by the ;/ M.M.Fs. of t ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-05", "section_label": "Chapter 5: Symbolic Method", "section_title": "Symbolic Method", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2322-2773", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-05/", "snippets": [ "... he sum of the components, in any direction, of all the currents flowing to a distributing point, equals zero. Joule's Law and the energy equation do not give a simple expression in complex quantities, since the effect or power is a quantity of double the frequency of the current or E.M.F. wave, and therefore requires for its representa- tion as a vector, a transition from single to double fre- quency, as will be shown in chapter XII. In what follows, complex vector quantities will always be denoted by dotted capi ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-17", "section_label": "Chapter 17: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16362-17596", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "snippets": [ "... ced by the cur- rent in the field spools, or the open circuit voltage, more properly called the \"nominal induced E.M.F.,\" since in reality it does not exist, as before stated. Then E0 where n = total number of turns in series on the armature, JV = frequency, M = total magnetic flux per field pole. Let x0 = synchronous reactance, r0 = internal resistance of alternator ; then Z0 — r0 — j x0 = internal impedance. If the circuit of the alternator is closed by the external impedance, Z = r-jx, the curren ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-26", "section_label": "Chapter 26: Symmetrical Polyphase Systems", "section_title": "Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 23781-24053", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-26/", "snippets": [ "... ed by the angle ft is : tan w = — cot /8 ; hence w = /? — ^ That is, the M.M.F. produced by a symmetrical «-phase system revolves with constant intensity : SYMMETRICAL POLYPHASE SYSTEMS. 439 F= — • V25 and constant speed, in synchronism with the frequency of the system ; and, if the reluctance of the magnetic circuit is constant, the magnetism revolves with constant intensity and constant speed also, at the point acted upon symmetri- cally by the n M.M.Fs. of the w-phase system. This is a characteristic ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-04", "section_label": "Chapter 5: Single-Phase Induction Motor", "section_title": "Single-Phase Induction Motor", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 8555-10582", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-04/", "snippets": [ "... ery small motors which require little starting torque, such as fan motors, and thus industrially constitutes the most important single- phase induction motor-starting device. 73. Let, all the quantities being reduced to the primary num- ber of turns and frequency, as customary in induction machines: Z0 = r<> + jxo = primary self-inductive impedance, y = g — jb = primary exciting admittance of unshaded poles (assuming total pole unshaded), SINGLE-PHASE INDUCTION MOTOR 113 Y' = g' — jb' = primary exciting admi ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-10", "section_label": "Chapter 11: Rotary Terminal Single-Phase Induction Motor", "section_title": "Rotary Terminal Single-Phase Induction Motor", "kind": "chapter", "sequence": 10, "number": 11, "location": "lines 14762-14896", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-10/", "snippets": [ "... oversynchronous speed: /i>/, the motor torque is reversed, and the rotor turns in the same direction as the brushes. In general, it is: /i+/2 + s=/, where /i = brush speed, /2 = motor speed, s = slip required to give the desired torque, / = supply frequency. 102. An application of this type of motor for starting larger motors under power, by means of a small auxiliary motor, is shown diagrammatically, in section, in Fig. 61. Po is the stationary primary or stator, So the revolving squirrel- cage secondary ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-20", "section_label": "Chapter 22: Unipolar Machines", "section_title": "Unipolar Machines", "kind": "chapter", "sequence": 20, "number": 22, "location": "lines 31716-32137", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-20/", "snippets": [ "... ,* signifying uniformity of polarity, or acyclic machine, signifying absence of any cyclic change: in all other electromagnetic machines, the voltage induced in a con- ductor changes cyclically, and the voltage in each turn is alter- nating, thus having a frequency, even if the terminal voltage and current at the corjimutator are continuous. 450 UNIPOLAR MACHINES 451 By bringing the conductor, C, over the end of the magnet close to the shaft, as shown in Fig. 216, the peripheral speed of motion of brush, J32, ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-17", "section_label": "Chapter 17: Circuits With Distributed Leakage", "section_title": "Circuits With Distributed Leakage", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 30429-31656", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-17/", "snippets": [ "... ctance. Inductance also is absent with the current induced in the cable armor by an alternating current traversing the cable conductor, 330 CIRCUITS WITH DISTRIBUTED LEAKAGE 331 and with all low- and medium-voltage conductors, with the com- mercial frequencies of alternating currents, the capacity effects are so small as to be negligible. In high-voltage conductors, such as transmission lines, etc., in general, capacity and inductance require consideration as well as resistance and shunted conductance. This ge ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-01", "section_label": "Chapter 1: Introduction. 217", "section_title": "Introduction. 217", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 659-674", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-01/", "snippets": [ "... racter of periodically recurring transient phenomena in time. 217 2. Periodic transient phenomena with single cycle. 218 3. Multi-cycle periodic transient phenomena. 218 4. Industrial importance of periodic transient phenomena: circuit control, high frequency generation, rectification. 220 5. Types of rectifiers. Arc machines. 221" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-11", "section_label": "Chapter 7: Distribution Of Alternating-Current Density", "section_title": "Distribution Of Alternating-Current Density", "kind": "chapter", "sequence": 11, "number": 7, "location": "lines 938-971", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-11/", "snippets": [ "... uations. 375 63. Mean value of current, and effective resistance. 376 64. Equations for large conductors. 377 65. Effective resistance and depth of penetration. 379 66. Depth of penetration, or conducting layer, for different materials and different frequencies, and maximum economical conductor diameter. 384" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-12", "section_label": "Chapter 8: Velocity Of Propagation Op Electric Field. 387", "section_title": "Velocity Of Propagation Op Electric Field. 387", "kind": "chapter", "sequence": 12, "number": 8, "location": "lines 972-1013", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-12/", "snippets": [ "... effective resistance of radia- tion, inductance and impedance. 391 72. Evaluation of functions sil al and col al. 394 73. Self-inductive impedance, and numerical example. 395 74. Discussion of effective resistance and radiated power, as function of frequency. 396 75. Mutual inductance of two distant conductors of finite length. 398 76. Example. 399 77. Capacity of a sphere in space. 400 78. Example. 401 79. Sphere at a distance from ground. 402" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-15", "section_label": "Chapter 2: Discussion Of General Equations. 431", "section_title": "Discussion Of General Equations. 431", "kind": "chapter", "sequence": 15, "number": 2, "location": "lines 1063-1086", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-15/", "snippets": [ "CHAPTER II. DISCUSSION OF GENERAL EQUATIONS. 431 7. The two component waves and their reflected waves. Attenuation in time and in space. 431 8. Period, wave length, time and distance attenuation constants. 433 9. Simplification of equations at high frequency, and the velocity unit of distance. 434 10. Decrement of traveling wave. 436 11. Physical meaning of the two component waves. 437 12. Stationary or standing wave. Trigonometric arid logarith- mic waves. 438 13. Propagation constant of wave. 440" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-19", "section_label": "Chapter 6: Transition Points And The Complex Circuit. 498", "section_title": "Transition Points And The Complex Circuit. 498", "kind": "chapter", "sequence": 19, "number": 6, "location": "lines 1187-1227", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-19/", "snippets": [ "... The energy transfer constant of the circuit section, and the transfer of power between the sections. 507 47. The final form of the general equations of the complex circuit, . 508 48. Full-wave, half-wave, quarter-wave oscillation, and gen- eral high-frequency oscillation. 509 49. Determination of the resultant time decrement of the cir- cuit. 510" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-22", "section_label": "Chapter 9: Inductive Discharges. 535", "section_title": "Inductive Discharges. 535", "kind": "chapter", "sequence": 22, "number": 9, "location": "lines 1286-1316", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-22/", "snippets": [ "... 5 64. Massed inductance discharging into distributed circuit. Combination of generating station and transmission line. 535 65. Equations of inductance, and change of constants at transition point. 536 66. Line open or grounded at end. Evaluation of frequency constant and resultant decrement. 538 67. The final equations, and their discussion. 540 68. Numerical example. Calculation of the first six har- monics. 542 APPENDIX: VELOCITY FUNCTIONS OF THE ELECTRIC FIELD. 545 SECTION I TRANSIENTS IN TIME ..." ] } ] }, { "id": "reactance", "label": "Reactance", "aliases": [ "condensive reactance", "inductive reactance", "reactance", "reactive" ], "total_occurrences": 2490, "matching_section_count": 188, "matching_source_count": 13, "source_totals": [ { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 502, "section_count": 26 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 442, "section_count": 14 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 285, "section_count": 22 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 272, "section_count": 38 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 253, "section_count": 21 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 226, "section_count": 25 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 218, "section_count": 15 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 80, "section_count": 9 }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 80, "section_count": 3 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 49, "section_count": 5 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 32, "section_count": 4 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 30, "section_count": 4 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 21, "section_count": 2 } ], "section_hits": [ { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-14", "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "section_title": "Constant-Potential Constant-Current Trans Formation", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 180, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "... stant-voltage supply source, are Huch as U) approach constant-voltage constant-current tran.sfonnation, as in for instance the case in very long transmission line«, or>^;n-<:ircuit- ing may lead to dangeroiLs or even destructive voltage rh¥% 128. With an inductive reactance inserted in series to an alt^^r- 245 246 ELECTRIC CIRCUITS nating-current non-inductive circuit, at constant-supply voltage, the current in this circuit is approximately constant, as long as the resistance of the circuit is small compared with the se ...", "... rted in series to an alt^^r- 245 246 ELECTRIC CIRCUITS nating-current non-inductive circuit, at constant-supply voltage, the current in this circuit is approximately constant, as long as the resistance of the circuit is small compared with the series inductive reactance. Let ^0 = Co = constant impressed alternating voltage; r = resistance of non-inductive receiver circuit; Xo = inductive reactance inserted in series with this circuit. The impedance of this circuit then is Z = r + jxof and, absolute, and thus th ...", "... t in this circuit is approximately constant, as long as the resistance of the circuit is small compared with the series inductive reactance. Let ^0 = Co = constant impressed alternating voltage; r = resistance of non-inductive receiver circuit; Xo = inductive reactance inserted in series with this circuit. The impedance of this circuit then is Z = r + jxof and, absolute, and thus the current, / = ^* = -^ (1) ^ r + jxo and the absolute value is eo Co the phase angle of the supply circuit is given by (2) ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-12", "section_label": "Chapter 12: Reactance Of Induction Apparatus", "section_title": "Reactance Of Induction Apparatus", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 22634-23465", "status": "candidate", "occurrence_count": 62, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-12/", "snippets": [ "CHAPTER XII REACTANCE OF INDUCTION APPARATUS 109. An electric current passing through a conductor is ac- companied by a magnetic field surrounding this conductor, and this magnetic field is as integral a part of the phenomenon, as is the energy dissipation by the resistance o ...", "... d \"non-inductive\" circuit. With continuous current in stationary conditions, the inductance, L, has no effect on the energy flow; with alternating current of frequency, /, the inductance, L, consumes a voltage 2 x/Li, and is, therefore, represented by the reactance, x = 2x/L, which is measured in ohms, and differs from the ohmic resistance, r, merely by being wattless or reactive, that is, representing not dissipation of energy, but surging of energy. Every alternating-current circuit thus has a resistance and a r ...", "... nergy flow; with alternating current of frequency, /, the inductance, L, consumes a voltage 2 x/Li, and is, therefore, represented by the reactance, x = 2x/L, which is measured in ohms, and differs from the ohmic resistance, r, merely by being wattless or reactive, that is, representing not dissipation of energy, but surging of energy. Every alternating-current circuit thus has a resistance and a reactance, the latter representing the effect of the magnetic field of the current in the conductor. When dealing wit ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-09", "section_label": "Chapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "section_title": "Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 4674-6992", "status": "candidate", "occurrence_count": 59, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-09/", "snippets": [ "CHAPTER IX CIRCUITS CONTAINING RESISTANCE, INDUCTIVE REACTANCE, AND CONDENSIVE REACTANCE 53. Having, in the foregoing, re-established Ohm's law and Kirchhoff 's laws as being also the fundamental laws of alternating- current circuits, when expressed in their complex form, E = ZI, or, 7 = YE, and \"EE = 0 in a cl ...", "CHAPTER IX CIRCUITS CONTAINING RESISTANCE, INDUCTIVE REACTANCE, AND CONDENSIVE REACTANCE 53. Having, in the foregoing, re-established Ohm's law and Kirchhoff 's laws as being also the fundamental laws of alternating- current circuits, when expressed in their complex form, E = ZI, or, 7 = YE, and \"EE = 0 in a closed circuit, S/ = 0 at ...", "... can now — by application of these laws, and in the same manner as with continuous-current circuits, keeping in mind, however, that E, I, Z, Y, are complex quanti- ties— calculate alternating-current circuits and networks of circuits containing resistance, inductive reactance, and conden- sive reactance in any combination, without meeting with greater difficulties than when dealing with continuous-current circuits. It is obviously not possible to discuss with any completeness all the infinite varieties of combinations of resis ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-appendix-01-synchronous-operation", "section_label": "Mathematical Appendix 5: Appendix: Synchronous Operation", "section_title": "Appendix: Synchronous Operation", "kind": "mathematical-appendix", "sequence": 5, "number": 5, "location": "PDF pages 27-68, lines 2165-5013", "status": "pdf-text-extracted-candidate", "occurrence_count": 58, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "snippets": [ "... ngle 2w. That is, the one alternator has the voltage phase ( to), the other the voltage phase (0+w). We may assume the alternators as of equal voltage, since a voltage difference superposes on the synchronizing energy current due to the phase difference, a reactive magnetizing current due to the voltage difference without materially changing the energy relations. The EMFs of the two alternators then may be represented by: ei = E cos (0 co) 1 e2 = Ecos (0+co) / (1) and the resultant voltage in the circuit between the alt ...", "... [ = 2E sin co sin (2) and the interchange currentwbeteen the alternators is: 2E . i = sin co sin ( a) (3) where: z = r2+x 2 is the impedance of the circuit between the two alternators, and the phase angle a is given by: x tan a = - r and: r= resistance x = reactance of the circuit between the alternators (including their internal resistances and reactances). [[END_PDF_PAGE:28]] [[PDF_PAGE:29]] Report of Charles P. Steinmetz 23 The power of one of the two alternators then is given by: 2E 2 = sin co sin (d> a) cos ( co ...", "... t in synchronism, thus is given by the expression: E 2 P=- sin a sin 2co (6) Thus, the synchronizing power p, is a maximum, and is : _E 2 . for a = 90 degrees, that is, if the resistance r of the circuit between the alternators is negligible compared with the reactance. The synchronizing power p = for a = 0, that is, in the (theoretical) case, when the circuit between the alternators contains no reactance, but only resistance. For phase angles w up to 45 degrees, that is, phase displacements between the two alternators up t ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-22", "section_label": "Chapter 22: Armature Reactions Of Alternators", "section_title": "Armature Reactions Of Alternators", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 23971-25134", "status": "candidate", "occurrence_count": 52, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-22/", "snippets": [ "... ective self-induction, that is, instead of the counter m.m.f. of the armature reaction, the e.m.f. considered, which would be generated by the magnetic flux, which the arma- ture reaction would produce. That is, both effects are com- bined in an effective reactance, the \"synchronous reactance.\" While armature reaction and self-inductance are similar in ARMATURE REACTIONS OF ALTERNATORS 273 effect, in some cases they differ in their action; the e.m.f. of self-inductance is instantaneous, that is, appears and disa ...", "... is, instead of the counter m.m.f. of the armature reaction, the e.m.f. considered, which would be generated by the magnetic flux, which the arma- ture reaction would produce. That is, both effects are com- bined in an effective reactance, the \"synchronous reactance.\" While armature reaction and self-inductance are similar in ARMATURE REACTIONS OF ALTERNATORS 273 effect, in some cases they differ in their action; the e.m.f. of self-inductance is instantaneous, that is, appears and disappears with the current to ...", "... 2 = a $ (8) and since the generated e.m.f. is 90° behind the generating flux, in symbolic expression, E2= - ja^; (9) hence, substituting (5) in (9), E2 = a(P{fo - ni2) - jaiPnii, . (10) the virtual generated e.m.f. The e.m.f. consumed by the self-inductive reactance of the armature circuit is, E3 = jxl = jxii + xi2; (11) and therefore, the actual generated e.m.f. El = E2 — Es = {a(P/o - {a(Pn -{- x)i2} - jii{a(?n + x). (12) 276 ALTERNATING-CURRENT PHENOMENA The e.m.f. consumed by the armature resistance, r, ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-13", "section_label": "Chapter 13: Reactance Of Synchronous Machines", "section_title": "Reactance Of Synchronous Machines", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 23466-24022", "status": "candidate", "occurrence_count": 43, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-13/", "snippets": [ "CHAPTER XIII REACTANCE OF SYNCHRONOUS MACHINES 119. The synchronous machine — ^alternating-current generator, synchronous motor or synchronous condenser — consists of an armature containing one or more electric circuits traversed by alternating currents and synchronously revo ...", "... ts and synchronously revolving relative to a unidirectional magnetic field, excited by direct current. The armature circuit, like every electric circuit, has a resistance, r, in which power is being dissipated by the current, /, and an in- ductance, L, or reactance, a; = 2 irfL^ which represents the mag- netic flux produced by the current in the armature circuit, and interlinked with this circuit. Thus, if ^^ = voltage induced in the armature circuit by its rotation through the magnetic field — or, as now more usual ...", "... ally the path of the field flux, in two different positions, A with an armature slot standing mid- way between two field poles, B with an armature slot standing opposite the field pole. In Fig. Ill is shown diagrammatically the magnetic flux of armature reactance, that is, the magnetic flux produced by the current in the armature circuit, and interlinked with this circuit, which is represented by the reactance x, for the same two relative positions of field and armature. As seen, field flux and armature flux pass ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-15", "section_label": "Chapter 15: Constant-Voltage Series Operation", "section_title": "Constant-Voltage Series Operation", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 27996-29301", "status": "candidate", "occurrence_count": 42, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-15/", "snippets": [ "... he second lamp in circuit. However, in general such arrange- ment is too complicated for use. As practically all such circuits would be alternating-current circuits, and thus alternating currents only need to be considered, the question arises, whether a reactance shunting each lamp would not give the desired effect. Suppose each lamp, of resist- ance, r, is shunted by a reactance, x, which is sufficiently large not to withdraw too much current from the lamp: assuming the cur- rent shunted by x is 20 per cent, of t ...", "... circuits would be alternating-current circuits, and thus alternating currents only need to be considered, the question arises, whether a reactance shunting each lamp would not give the desired effect. Suppose each lamp, of resist- ance, r, is shunted by a reactance, x, which is sufficiently large not to withdraw too much current from the lamp: assuming the cur- rent shunted by x is 20 per cent, of the current in the lamp, or x = 5 r. With 6.6 amp. in r, x thus would take 1.32 amp., and the total, or line current wou ...", "... s voltage, however, is in quadrature with the current, thus combines vectorially with the voltages of the other consuming devices, which are practically in phase with the cur- rent, and the question then arises, whether, and under what con- ditions such a reactance shunt would maintain constant voltage on the other consuming devices, or, what amounts to the same, constant current in the series circuit. Such a reactance shunting the consuming device could at the same time be used as autotransformer (compensator), to ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 39, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "... characteristic of the induction machine is, that the magnetic field is excited by an alternating current derived from the alter- nating supply voltage, just as in the alternating-current trans- former. As the alternating magnetizing current is a wattless reactive current, the result is, that the alternating-current input into the induction motor is always lagging, the more so, the larger a part of the total current is given by the magnetizing current. To secure good power-factor in an induction motor, the magnetiz ...", "... he latter may be. That is, the induction motor remains asynchronous, increases in slip with increase of load. 5. Excitation by a condenser in the secondary circuit of the induction motor. As the magnetizing current required by the induction motor is a reactive, that is, wattless lagging current, it does not require a generator for its production, but any apparatus consuming lead- ing, that is, generating lagging currents, such as a condenser, can be used to supply the magnetizing current. 40, However, condense ...", "... a, acts magnetizing or demagnetizing, the other com- ponent: cos a, acts increasing or decreasing the speed, and thus various efferts can be produced. As the current consumed by a condenser is proportional to the frequency, while that passing through an inductive reactance is inverse proportional to the frequency, when using a condenser in the secondary circuit of the induction motor, its effective im- pedance at the varying frequency of slip is: Z,' = n+j («i- 7)' where xt is the capacity reactance at full frequency. ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-11", "section_label": "Chapter 11: Phase Control", "section_title": "Phase Control", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 9767-10717", "status": "candidate", "occurrence_count": 38, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-11/", "snippets": [ "... ng circuit, causes the voltage, e, at the receiver circuit to decrease with increasing current, /, through the resistance. The decrease of the voltage, e, is greatest if the current, /, is in phase with the voltage, e — less if the current is not in phase. Inductive reactance in series with the receiving circuit, e, at constant impressed e.m.f., eo, causes the voltage, e, to drop less with a unity power-factor current, 7, but far more with a lagging current, and causes the voltage, e, to rise with a leading current. While se ...", "... pressed e.m.f., eo, causes the voltage, e, to drop less with a unity power-factor current, 7, but far more with a lagging current, and causes the voltage, e, to rise with a leading current. While series resistance always causes a drop of voltage, series inductive reactance, x, may cause a drop of voltage or a rise of voltage, depending on whether the current is lagging or leading. If the supply line contains resistance, r, as well as reactance, x, and the phase of the current, I, can be varied at will, by producing in the r ...", "... rent. While series resistance always causes a drop of voltage, series inductive reactance, x, may cause a drop of voltage or a rise of voltage, depending on whether the current is lagging or leading. If the supply line contains resistance, r, as well as reactance, x, and the phase of the current, I, can be varied at will, by producing in the receiver circuit lagging or leading currents, the change of voltage, e, with a change of load in the circuit can be controlled. For instance, by changing the current from lagg ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 34, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... starting-point of calculation of the phase of alternating currents. For instance, if a is the phase angle of a vector 98 ENGINEERING MATHEMATICS. quantity, tan a is given as the ratio of the vertical component over the horizontal component, or of the reactive component over the power component. In this case, if m . ,. . tan ex = a sin a = a and cos « = Va^ + h^ cot a = c \"d' sin a = d and COS a = or, if Vc^+d^' Vc^+d^' (5c) The secant functions, and versed sine functi ...", "... : e = eo{sin ^-0.12 sin (3<9- 2. 3°) -0.23 sin (5^-1.5°) +0.13 sin (7^-6. 2°)1. . (1) In first approximation, the line capacity may be considered as a condenser shunted across the middle of the line; that is, half the line resistance and half the line reactance is in series with the line capacity. As the receiving apparatus do not utilize the higher har- monics of the generator wave, when using the old generators, their voltage has to be transformed up so as to give the first harmonic or fundamental of 44,000 ...", "... by the formula : Lo = 0.7415 log ^+0.0805mh, .... (3) where h is the distance between the wires, and Z^ the radius of the wire. In the present case, this gives Z^ = 5 ft. = 60 in. Z^ = 0 . 1625 in. L() = l .9655 mh., and, herefrom it follows that the reactance, at /= 60 cycles is Xo = 27r/Lo = 0 . 75 ohms per mile (4) The capacity per mile of wire is given by the formula : r 0-0408 , ... logf hence, in the present case, Co = 0.0159 mf., and the condensive reactance is derived herefrom as : ^co==?rr^7r ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-08", "section_label": "Chapter 8: Circuits Containing Resistance, Inductance, And Capacity", "section_title": "Circuits Containing Resistance, Inductance, And Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3577-5333", "status": "candidate", "occurrence_count": 34, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "snippets": [ "... difference of phase in the receiver circuit. As an instance, in Fig. 37 is shown the E.M.F., E, at the receiver circuit, for E0 = const. = 100 volts, s = 1 ohm ; hence / = E, and — a.) r0 = .2 ohm (Curve I.) b.) r0 = .8 ohm (Curve II.) with values of reactance, x = V^2 — r2, for abscissae, from x = + 1.0 to x = — 1.0 ohm. As shown, / and E are smallest for x = 0, r = 1.0, or for the non-inductive receiver circuit, and largest for x = ± 1.0, r = 0, or for the wattless circuit, in which latter a series resistan ...", "... ial. Hence the control of a circuit by series resistance de- pends upon the difference of phase in the circuit. For r0 = .8, and x = 0, x = + .8, x = — .8, the polar diagrams are shown in Figs. 38 to 40. RESISTANCE, INDUCTANCE, CAPACITY. 61 2.) Reactance in series witJi a circuit. 45. In a constant potential system of impressed E.M.F., let a reactance, x0 , be connected in series in a receiver cir- cuit of impedance Z = r — jx, z = -\\/r2 -|- x'2. IMPRESSED E.M.F. CONSTANT, E0=IOO IMPEDANCE OF RECEI ...", "... he circuit. For r0 = .8, and x = 0, x = + .8, x = — .8, the polar diagrams are shown in Figs. 38 to 40. RESISTANCE, INDUCTANCE, CAPACITY. 61 2.) Reactance in series witJi a circuit. 45. In a constant potential system of impressed E.M.F., let a reactance, x0 , be connected in series in a receiver cir- cuit of impedance Z = r — jx, z = -\\/r2 -|- x'2. IMPRESSED E.M.F. CONSTANT, E0=IOO IMPEDANCE OF RECEIVER CIRCUIT CONSTANT, Z - 1.0 LINE RESISTANCE CONSTANT n =.2 3 - -.4 T-5 ' '.6 T.7 r-8 Fig. 37 ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-14", "section_label": "Chapter 16: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 14, "number": 16, "location": "lines 19374-20293", "status": "candidate", "occurrence_count": 33, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-14/", "snippets": [ "CHAPTER XVI REACTION MACHINES 147. In the usual treatment of synchronous machines and induction machines, the assumption is made that the reactance, x, of the machine is a constant. While this is more or less approximately the case in many alternators, in others, especially in machines of large armature reaction, the reactance, x, is variable, and is different in the different positions of the armatu ...", "... nchronous machines and induction machines, the assumption is made that the reactance, x, of the machine is a constant. While this is more or less approximately the case in many alternators, in others, especially in machines of large armature reaction, the reactance, x, is variable, and is different in the different positions of the armature coils in the magnetic circuit. This variation of the reactance causes phenomena which do not find their explanation by the theoretical calculations made under the assumption of c ...", "... less approximately the case in many alternators, in others, especially in machines of large armature reaction, the reactance, x, is variable, and is different in the different positions of the armature coils in the magnetic circuit. This variation of the reactance causes phenomena which do not find their explanation by the theoretical calculations made under the assumption of constant reactance. It is known that synchronous motors or converters of large and variable reactance keep in synchronism, and are able to ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-18", "section_label": "Chapter 20: Single-Phase Commutator Motors", "section_title": "Single-Phase Commutator Motors", "kind": "chapter", "sequence": 18, "number": 20, "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 33, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "... by the counter e.m.f. of rotation, which represents the power output of the motor, and by the resistance, which represents the power loss. In addition thereto, in the alternating-cur rent motor voltage is consumed by the inductance, which is wattless or reactive and therefore causes a lag of current behind the vol- tage, that is, a lowering of the power-factor. While in the direct- current motor good design requires the combination of a strong field and a relatively weak armature, so as to reduce the armature rea ...", "... ction beyond the limits of good motor design, the power-factor is still too low for use. The armature, however, also has a self -inductance; that is, the magnetic flux produced by the armature cur- rent as shown diagrammatically in Fig. 155 generates a reactive e.m.f. in the armature conductors, which again lowers the power-factor. While this armature self-inductance is low with small number of armature turns, it becomes considerable when the num- ber of armature turns, rti, is large compared with the field t ...", "... n Fig. 159. This, how- ever, results in bringing the field coils further away from the armature surface, aftd so increases the magnetic stray flux of the field winding, that is, the magnetic flux, which passes through the field coils, and there produces a reactive voltage of self-in- 340 ELECTRICAL APPARATUS ductance, but does not pass through the armature conductor? and so does no work; that is, it lowers the power factor, just overcompensation would do. The distribution curve of the armature winding can, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-10", "section_label": "Chapter 10: Resistance And Reactance Of Transmission", "section_title": "Resistance And Reactance Of Transmission", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6993-9766", "status": "candidate", "occurrence_count": 32, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-10/", "snippets": [ "CHAPTER X RESISTANCE AND REACTANCE OF TRANSMISSION LINES 65. In alternating-current circuits, voltage is consumed in the feeders of distributing networks, and in the lines of long- distance transmissions, not only by the resistance, but also by the reactance, of the line. The voltage co ...", "CHAPTER X RESISTANCE AND REACTANCE OF TRANSMISSION LINES 65. In alternating-current circuits, voltage is consumed in the feeders of distributing networks, and in the lines of long- distance transmissions, not only by the resistance, but also by the reactance, of the line. The voltage consumed by the resistance is in phase, while the voltage consumed by the react- ance is in quadrature, with the current. Hence their in- fluence upon the voltage at the receiver circuit depends upon the difference of phase betwe ...", "... tween the current and the voltage in that circuit. As discussed before, the drop of potential due to the resistance is a maximum when the receiver current is in phase, a minimum when it is in quadrature, with the voltage. The change of voltage due to line reactance is small if the current is in phase with the voltage, while a drop of potential is produced with a lagging, and a rise of potential with a leading, current in the receiver circuit. Thus the change of voltage due to a line of given resistance and reactan ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-21", "section_label": "Chapter 21: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 22302-23970", "status": "candidate", "occurrence_count": 32, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-21/", "snippets": [ "... he resultant e.m.f., will take place in this case only when the magnetic densities are so near to saturation that the rise of density at the leading pole corner will be less than the decrease of density at the trailing pole corner. Since the internal self-inductive reactance of the alternator itself causes a certain lag of the current behind the generated e.m.f., this condition of no displacement can exist only in a circuit with external negative reactance, as capacity, etc. ALTERNATING-CURRENT GENERATOR 2G1 If the armatu ...", "... density at the trailing pole corner. Since the internal self-inductive reactance of the alternator itself causes a certain lag of the current behind the generated e.m.f., this condition of no displacement can exist only in a circuit with external negative reactance, as capacity, etc. ALTERNATING-CURRENT GENERATOR 2G1 If the armature current lags, it reaches the maximum later than the e.m.f.; that is, in a position where the armature-coil partly faces the field-pole which it approaches, as shown in dia- gram in F ...", "... generated in the armature by the resultant magnetic flux, produced by the resultant m.m.f. of the field and of the armature, is not the terminal voltage of the machine; the terminal voltage is the resultant of this generated e.m.f. and the e.m.f. of self-inductive reactance and the e.m.f. representing the power loss by resistance in the alternator armature. That is, in other words, the armature current not only opposes or assists the field m.m.f. in creating the resultant magnetic flux, but sends a second magnetic flux in a ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-40", "section_label": "Chapter 4: Arc Rectification", "section_title": "Arc Rectification", "kind": "chapter", "sequence": 40, "number": 4, "location": "lines 17755-19259", "status": "candidate", "occurrence_count": 31, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "snippets": [ "... Fig. 61. Constant-potential mercury arc rectifier. current transformer is replaced by a constant-potential trans- former or compensator (auto-transformer) having considerable inductance between the two half coils II and III, as shown in Fig. 61. Two reactive coils are inserted between the outside terminals of the transformer and rectifier tube respectively, for the purpose of producing an overlap between the two rectifying arcs, ca and cb, and thereby the required continuity of the arc stream at c. Or instead ...", "... ier tube respectively, for the purpose of producing an overlap between the two rectifying arcs, ca and cb, and thereby the required continuity of the arc stream at c. Or instead of separate reactances, the two half coils II and III may be given sufficient reactance, as in Fig. 61. A reactive coil is inserted into the rectified or arc circuit, which connects between transformer neutral C and rectifier neutral c, for the purpose of reducing the fluctuation of the rectified current to the desired amount. In the const ...", "... he purpose of producing an overlap between the two rectifying arcs, ca and cb, and thereby the required continuity of the arc stream at c. Or instead of separate reactances, the two half coils II and III may be given sufficient reactance, as in Fig. 61. A reactive coil is inserted into the rectified or arc circuit, which connects between transformer neutral C and rectifier neutral c, for the purpose of reducing the fluctuation of the rectified current to the desired amount. In the constant-potential rectifier, ins ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-25", "section_label": "Chapter 25: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 29375-32539", "status": "candidate", "occurrence_count": 30, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-25/", "snippets": [ "... ircuit, a dis- torting effect will cause higher harmonics of e.m.f. 233. In a conductor revolving with uniform velocity through a uniform and constant magnetic field, a sine wave of e.m.f. is generated. In a circuit with constant resistance and constant reactance, this sine wave of e.m.f. produces a sine wave of current. Thus distortion of the wave-shape or higher har- monics may be due to lack of uniformity of the velocity of the revolving conductor; lack of uniformity or pulsation of the magnetic field; pulsatio ...", "... e wave of current. Thus distortion of the wave-shape or higher har- monics may be due to lack of uniformity of the velocity of the revolving conductor; lack of uniformity or pulsation of the magnetic field; pulsation of the resistance or pulsation of the reactance. 341 342 ALTERNATING-CURRENT PHENOMENA The first two cases, lack of uniformity of the rotation or of the magnetic field, cause higher harmonics of e.m.f. at open circuit. The last, pulsation of resistance and reactance, causes higher har- monics onl ...", "... resistance or pulsation of the reactance. 341 342 ALTERNATING-CURRENT PHENOMENA The first two cases, lack of uniformity of the rotation or of the magnetic field, cause higher harmonics of e.m.f. at open circuit. The last, pulsation of resistance and reactance, causes higher har- monics only when there is current in the circuit, that is, underload. Lack of uniformity of the rotation is hardly ever of practical interest as a cause of distortion, since in alternators, due to mechanical momentum, the speed is alw ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-49", "section_label": "Chapter 9: High-Frequency Conductors", "section_title": "High-Frequency Conductors", "kind": "chapter", "sequence": 49, "number": 9, "location": "lines 27003-27760", "status": "candidate", "occurrence_count": 30, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "snippets": [ "... conductor, X = the conductivity of conductor material, fi. = the permeability of conductor material, / = the frequency, S = the speed of light = 3 X 1010 cm., and (1) a = — — = the wave length constant, o the true ohmic resistance is the ohmic reactance, low frequency value is *o = 2 7r/70 1 2 loge f + ^l 10~9 ohms; (3) or, reduced to common logarithms by dividing by log e, x0 = 2 TT/Z f4.6 log^ + |) 10~9 ohms. (4) \\ l>r ** The equivalent depth of penetration of the current into the con- ductor, f ...", "... the current into the con- ductor, from Chapter VII, (40), is 104 5030 (5) 406 TRANSIENT PHENOMENA hence, the effective resistance of unequal current distribution, or thermal resistance of the conductor, is, approximately, (6) and the effective reactance of the internal flux is 10- ohms. (7) The effective resistance resulting from the finite velocity of the electric field, or radiation resistance, by assuming the conductor as a section of an infinitely long conductor without return con- ductor, from Ch ...", "... the finite velocity of the electric field, or radiation resistance, by assuming the conductor as a section of an infinitely long conductor without return con- ductor, from Chapter VIII, (25), is r2 = 2 l^flO-* « 1.97 IJ1Q-* ohms, (8) and the effective reactance of the external field of finite section of an infinitely long round conductor without return conductor, from Chapter VIII, (25), is z2 = 4 7r/Z0 flog. 4- - 0.5772) 10-9. (9) \\ aL I Assuming now that the external magnetic field of a conductor of any ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-08", "section_label": "Chapter 8: Shaping Of Waves By Magnetic Saturation", "section_title": "Shaping Of Waves By Magnetic Saturation", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 12962-16963", "status": "candidate", "occurrence_count": 29, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-08/", "snippets": [ "... ne wave of the same effective value, ei, that is, more than five times as high, as would be expected from the voltmeter reading, and it is 18.6 times as high as it would be with a sine wave of magnetic flux. Thus, an oversaturated closed magnetic circuit reactance, which consumes e© = 50 volts with a sine wave of voltage, e©, and thus of magnetic density, B, would, at the same maximum mag- netic density, that is, the same saturation, with a sine wave of current — as would be the case if the reactance is connected i ...", "... gnetic circuit reactance, which consumes e© = 50 volts with a sine wave of voltage, e©, and thus of magnetic density, B, would, at the same maximum mag- netic density, that is, the same saturation, with a sine wave of current — as would be the case if the reactance is connected in ser- ies in a constant-current circuit — give an effective value of ter- minal voltage of ei = 3.5 X 50 = 175 volts, and a maximmn peak voltage of 6 = 18.8 X 50 X y/2 = 1330 volts. Thus, while supposed to be a low-voltage reactance, eo = ...", "... if the reactance is connected in ser- ies in a constant-current circuit — give an effective value of ter- minal voltage of ei = 3.5 X 50 = 175 volts, and a maximmn peak voltage of 6 = 18.8 X 50 X y/2 = 1330 volts. Thus, while supposed to be a low-voltage reactance, eo = 50 volts, and even the voltmeter shows a voltage of only Ci = 175, which, while much higher, is still within the limit that does not endanger life, the actual peak voltage e = 1330 is beyond the danger limit. Thus, magnetic saturation may in suppo ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-05", "section_label": "Lecture 5: Long Distance Transmission", "section_title": "Long Distance Transmission", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2562-3132", "status": "candidate", "occurrence_count": 28, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-05/", "snippets": [ "... tirely independent of the generator, or of a frequency which originates in the circuit, that is, high frequency oscillations as arcing grounds, etc. If a capacity is in series with an inductance, as the line capacity and the line inductance, the capacity reactance and the inductive reactance are opposed to each other ; if they hap- pened to be equal they would neutralize each other, the current would depend on the resistance only and therefore be very large, and with this very large current passing through the ind ...", "... of the generator, or of a frequency which originates in the circuit, that is, high frequency oscillations as arcing grounds, etc. If a capacity is in series with an inductance, as the line capacity and the line inductance, the capacity reactance and the inductive reactance are opposed to each other ; if they hap- pened to be equal they would neutralize each other, the current would depend on the resistance only and therefore be very large, and with this very large current passing through the inductance and capacity, the vol ...", "... and with this very large current passing through the inductance and capacity, the voltage at the inductance and at the capacity would be very high. For instance, if we have 20,000 volts supplied to a circuit having a resistance of 10 ohms and a capacity reactance of 1000 ohms, then the total impedance of the circuit is V^io* + 1000' = 1000 and the current in the circuit 20,000 — = 20 amperes. 1000 If now in addition to the 10 ohms resistance and 1000 ohms capacity reactance, the circuit contains 1000 ohm ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1120-1683", "status": "candidate", "occurrence_count": 28, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-01/", "snippets": [ "... ing iron, etc., also upon the e.m.f. Impedance, z, is, in the system of absolute units, of the same dimension as resistance (that is, of the dimension lt~^ = velocity), and is expressed in ohms. It consists of two components, the resistance, r, and the reactance, x, or z — \\/r\" + X\". The resistance, r, in circuits where energy is expended only in heating the conductor, is the same as the ohmic resistance of continuous-current circuits. In circuits, however, where energy is also expended outside of the conducto ...", "... inductance, dielectric hysteresis, etc., r is larger than the true ohmic resistance of the conductor, since it refers to the total expenditure of energy. It may be called then the effective re- sistance. It may no longer be a constant of the circuit. The reactance, x, does not represent the expenditure of energy as does the effective resistance, r, but merelj^ the surging to and fro of energy. It is not a constant of the circuit, but depends upon the frequency, and frequently, as in circuits containing iron, or in ...", "... rcuits containing iron, or in electrolytic conductors, upon the e.m.f. also. Hence while the effective resistance, r, refers to the power or active component of e.m.f., or the e.m.f. in phase with the current, the re- actance, X, refers to the wattless or reactive component of e.m.f., or the e.m.f. in quadrature with the current. 3. The principal sources of reactance are electromagnetism and capacity. Electromagnetism An electric current, i, in a circuit produces a magnetic flux surrounding the conductor in li ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-08", "section_label": "Chapter 8: Capacity", "section_title": "Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3872-6370", "status": "candidate", "occurrence_count": 28, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "snippets": [ "... receiver circuit. As an instance, in Fig. 37 are shown in dotted lines the current, /, and the E.M.F., E^ at the receiver circuit, for E^ = const. = 100 volts, -cr = 1 ohm, and — ^.) r^ = .2 ohm (Curve I.) d.) r, = .8 ohm (Curve II.) with values of reactance, x= y/a^ — r^, for abscissae, from X = + 1.0 to ;r = + 1.0 ohm. As shown, / and E are smallest for ;r = 0, r = 1.0, or for the non-inductive receiver circuit, and largest for X = ± 1.0, r = 0, or for the wattless circuit, in which latter a series resist ...", "... . Hence the control of a circuit by series resistance de- pends upon the difference of phase in the circuit. For r^ = .8 and x = 0,x = + .8, and x = — .8, the polar diagrams are shown in Figs. 37, 38, 39. 1451 RESISTANCE, INDUCTANCE, CAPACITY. 2.) Reactance in series with a circuit. 4p. In a constant potential system of impressed E.M.F., let a reactance, x^ , be connected in series in a receiver cir- cuit of impedance Z=r—jx, s = Vr*^fx*. >u fM aat E. CO sr NT E. 100 \" ■'^ ...", "... circuit. For r^ = .8 and x = 0,x = + .8, and x = — .8, the polar diagrams are shown in Figs. 37, 38, 39. 1451 RESISTANCE, INDUCTANCE, CAPACITY. 2.) Reactance in series with a circuit. 4p. In a constant potential system of impressed E.M.F., let a reactance, x^ , be connected in series in a receiver cir- cuit of impedance Z=r—jx, s = Vr*^fx*. >u fM aat E. CO sr NT E. 100 \" ■'^ ^ 1 r. 2 _ ' c \" ■: _^ -J s — 1 — ' ' e s\" r ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-11", "section_label": "Chapter 12: Frequency Converter Or General Alternating Current Transformer", "section_title": "Frequency Converter Or General Alternating Current Transformer", "kind": "chapter", "sequence": 11, "number": 12, "location": "lines 14897-17124", "status": "candidate", "occurrence_count": 28, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-11/", "snippets": [ "... osing the magnetic circuit, and by the magnetic induction. At open secondary circuit, this m.m.f. is the m.m.f. of the primary current, which in this case is called the exciting current, and consists of a power component, the magnetic power current, and a reactive component, the magnetizing current. In the general alternating-current transformer, where the secondary is movable with regard to the primary, the rate of cutting of the secondary electric circuit with the mutual mag- netic flux is different from that o ...", "... Til Y = g — jb = primary exciting admittance per circuit; where: g = effective conductance; b = susceptance; Zq = r0 + jxo = internal primary self-inductive impedance per circuit, where: r0 = effective resistance of primary circuit; Xq = self-inductive reactance of primary circuit; Zn = n + jx\\ = internal secondary self-inductive im- pedance per circuit at standstill, or for « = 1, where: rx = effective resistance of secondary coil; Xi = self-inductive reactance of secondary coil at stand- still, or full freq ...", "... ective resistance of primary circuit; Xq = self-inductive reactance of primary circuit; Zn = n + jx\\ = internal secondary self-inductive im- pedance per circuit at standstill, or for « = 1, where: rx = effective resistance of secondary coil; Xi = self-inductive reactance of secondary coil at stand- still, or full frequency, s = 1. FREQUENCY CONVERTER 179 Since the reactance is proportional to the frequency, at the slip, 8, or the secondary frequency, sf, the secondary impedance is: Zi = ri + jsxi. Let the secondar ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-12", "section_label": "Theory Section 12: Impedance of Transmission Lines", "section_title": "Impedance of Transmission Lines", "kind": "theory-section", "sequence": 12, "number": 12, "location": "lines 3761-4464", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-12/", "snippets": [ "12. IMPEDANCE OF TRANSMISSION LINES 54. Let r = resistance; x = 2 irfL = the reactance of a trans- mission line; E0 = the alternating e.m.f. impressed upon the line; I = the line current; E = the e.m.f. at receiving end of the line, and 6 = the angle of lag of current 7 behind e.m.f. E. B < 0 thus ...", "... polar diagram, zero capacity. Fig. 27, the e.m.f. E is represented by vector OE, ahead of 07 by angle 0. The e.m.f. consumed by re- sistance r is OEi = Ei = Ir in phase with the current, and the e.m.f. consumed by reactance x is OE% = Ez = Ix, 90 time de- grees ahead of the current; thus the total e.m.f. consumed by the line, or e.m.f. consumed by impedance, is the resultant OES of and O#2, jind is E3 = Iz. Combining OEz and OE gives ...", "... -^—= — , and the drop of voltage in the line, EQ - E = \\ (E + Iz}2 - 4 EIz sin2 -^ E. IMPEDANCE OF TRANSMISSION LINES 59 65. That is, the voltage EQ required at the sending end of a line of resistance r and reactance x, delivering current / at vol- tage E} and the voltage drop in the line, do not depend upon current and line constants only, but depend also upon the angle of phase displacement of the current delivered over the line. ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-24", "section_label": "Chapter 24: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 25682-29374", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-24/", "snippets": [ "... . Since in this case several e.m.fs. are acting in circuit with the same current, it is convenient to use the current, /, as zero line 01 of the polar diagram. (Fig. 145.) Ji I = i = current, and Z = impedance, r = effective resist- ance, X = effective reactance, and z = \\/r^ -{- x^ = absolute value of impedance, then the e.m.f. consumed by the resistance is £'11 = ri, and is in phase with the current; hence represented by vector OEn] and the e.m.f. consumed by the reactance is E2 = xi, and 90° ahead of the curre ...", "... effective resist- ance, X = effective reactance, and z = \\/r^ -{- x^ = absolute value of impedance, then the e.m.f. consumed by the resistance is £'11 = ri, and is in phase with the current; hence represented by vector OEn] and the e.m.f. consumed by the reactance is E2 = xi, and 90° ahead of the current; hence the e.m.f. consumed 301 302 ALTERNATING-CURRENT PHENOMENA by the impedance hE = ViEuY\" + (£'2)^ or = i -s/r\"^ -\\- x- = iz, X and ahead of the current by the angle 8, where tan 8 = ~. We have now ac ...", "... , into a non-inductive circuit. In this case, 7-1 ■> ^ -^0 ^ \"^/^e) In general, it is, taken from the diagram, at the condition of maximum efficiency, El = V{Eo - Iry-\\- Px^- Comparing these results with those in Chapter XI on Induct- ive and Condensive Reactance, we see that the condition of maximum efficiency of the synchronous motor system is the same as in a system containing resistance and condensive reactance, fed over an inductive line, the lead of the current against the generated e.m.f., Ei, here acting i ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-21", "section_label": "Chapter 21: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 20502-21189", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-21/", "snippets": [ "CHAPTER XXI. REACTION MACHINES. 225. In the chapters on Alternating-Current Genera- tors and on Induction Motors, the assumption has been made that the reactance x of the machine is a constant. While this is more or less approximately the case in many alternators, in others, especially in machines of large arma- ture reaction, the reactance x is variable, and is different in the different positions of the armature ...", "... nera- tors and on Induction Motors, the assumption has been made that the reactance x of the machine is a constant. While this is more or less approximately the case in many alternators, in others, especially in machines of large arma- ture reaction, the reactance x is variable, and is different in the different positions of the armature coils in the magnetic circuit. This variation of the reactance causes phenomena which do not find their explanation by the theoretical cal- culations made under the assumption of c ...", "... less approximately the case in many alternators, in others, especially in machines of large arma- ture reaction, the reactance x is variable, and is different in the different positions of the armature coils in the magnetic circuit. This variation of the reactance causes phenomena which do not find their explanation by the theoretical cal- culations made under the assumption of constant reactance. It is known that synchronous motors of large and variable reactance keep in synchronism, and are able to do a conside ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-16", "section_label": "Chapter 16: Load Balance Of Polyphase Systems", "section_title": "Load Balance Of Polyphase Systems", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 29302-30428", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-16/", "snippets": [ "... stem can be expressed, p = P H- Q cos (2 - a) (18) where P is the constant component of power, and Q the amplitude of the double-frequency alternating component of power, and Q may be larger or smaller than P. It must be noted, that Q is not the total reactive power of the system — which would have to be considered, for instance, in power-factor compensation etc. — but Q is the vector resultant of the reactive powers of the individual circuits, while the total reactive power of the system is the algebraic sum o ...", "... component of power, and Q may be larger or smaller than P. It must be noted, that Q is not the total reactive power of the system — which would have to be considered, for instance, in power-factor compensation etc. — but Q is the vector resultant of the reactive powers of the individual circuits, while the total reactive power of the system is the algebraic sum of the individual reactive powers (see \"Theory and Calculation of Alternating- current Phenomena,\" Chapter XVI). Thus, for instance, in a system of balan ...", "... It must be noted, that Q is not the total reactive power of the system — which would have to be considered, for instance, in power-factor compensation etc. — but Q is the vector resultant of the reactive powers of the individual circuits, while the total reactive power of the system is the algebraic sum of the individual reactive powers (see \"Theory and Calculation of Alternating- current Phenomena,\" Chapter XVI). Thus, for instance, in a system of balanced load, even if the load is reactive, Q = 0. Thus, Q is th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-27", "section_label": "Chapter 27: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 33011-34776", "status": "candidate", "occurrence_count": 25, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-27/", "snippets": [ "... effective intensity and equal power, while sufficiently accurate in many cases, completely fails in other cases, especially in circuits con- taining capacity, or in circuits containing periodically (and in synchronism with the wave) varying resistance or reactance (as alternating arcs, reaction machines, synchronous induction motors, oversaturated magnetic circuits, etc.). Since, however, the individual harmonics of the general alter- nating wave are independent of each other, that is, all products of different h ...", "... thus cannot be combined. The general wave of e.m.f. is thus represented by E = 2:2n-i(e„i4-j„e„ii), 1 the general wave of current by 1 If Zi = r -^ j (x„, -{- xo -\\- Xc) is the impedance of the fundamental harmonic, where Xm is that part of the reactance which is proportional to the frequency (inductance, etc.), ^ Xo is that part of the reactance which is independent of the frequency (mutual inductance, synchronous motion, etc.). Xc is that part of the reactance which is inversely propor- tional to the ...", "... „ii), 1 the general wave of current by 1 If Zi = r -^ j (x„, -{- xo -\\- Xc) is the impedance of the fundamental harmonic, where Xm is that part of the reactance which is proportional to the frequency (inductance, etc.), ^ Xo is that part of the reactance which is independent of the frequency (mutual inductance, synchronous motion, etc.). Xc is that part of the reactance which is inversely propor- tional to the frequency (capacity, etc.). The impedance for the nth harmonic is + jn (nxr^ + a^o + -^ ) ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-101", "section_label": "Apparatus Section 4: Alternating-current Transformer: Regulation", "section_title": "Alternating-current Transformer: Regulation", "kind": "apparatus-section", "sequence": 101, "number": 4, "location": "lines 17538-18397", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-101/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-101/", "snippets": [ "... i- mary and secondary winding through which the self-inductive or leakage flux passes, that is, the flux interlinked with one wind- ing only, but not the other one. The latter flux thus does not transmit power, but consumes reactive voltage and thereby pro- duces a voltage drop and a lag of the current behind the voltage, that is, is in general objectionable. The mutual magnetic flux passes through a closed magnetic circuit, with the (vector) differen ...", "... ry or secondary current and, therefore, in spite of the high reluctance of the leakage flux path due to the high m.m.f. (20 times as great as that of the mutual flux at 5 per cent, exciting current), this flux and the reactance voltages caused by it are appreci- 286 ELEMENTS OF ELECTRICAL ENGINEERING able, usually between 2 per cent, and 8 per cent, in modern transformers. The distribution of the leakage flux between primary and secondary w ...", "... ci- 286 ELEMENTS OF ELECTRICAL ENGINEERING able, usually between 2 per cent, and 8 per cent, in modern transformers. The distribution of the leakage flux between primary and secondary winding, that is, between primary reactance x\\ and secondary Xz, is to some extent arbitrary (see discussion in \"Theory and Calculation of Electric Circuits'')) and the methods of test give only the sum of the primary and the secondary re- actance, the latter reduce ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-20", "section_label": "Chapter 20: Beactiox Machines", "section_title": "Beactiox Machines", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 22388-23273", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "snippets": [ "CHAPTER XX. BEACTIOX MACHINES. 204. In the chapters on Alternating-Current Genera- tors and on Induction Motors, the assumption has been made that the reactance x of the machine is a constant. While this is more or less approximately thd case in many alternators, in others, especially in machines of large arma- ture reaction, the reactance x is variable, and is different in the different positions of the armature ...", "... nera- tors and on Induction Motors, the assumption has been made that the reactance x of the machine is a constant. While this is more or less approximately thd case in many alternators, in others, especially in machines of large arma- ture reaction, the reactance x is variable, and is different in the different positions of the armature coils in the magnetic circuit. This variation of the reactance causes phenomena which do not find their explanation by the theoretical cal- culations made under the assumption of c ...", "... less approximately thd case in many alternators, in others, especially in machines of large arma- ture reaction, the reactance x is variable, and is different in the different positions of the armature coils in the magnetic circuit. This variation of the reactance causes phenomena which do not find their explanation by the theoretical cal- culations made under the assumption of constant reactance. It is known that synchronous motors of large and variable reactance keep in synchronism, and are able to do a conside ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-02", "section_label": "Chapter 2: Multiple Squirrel-Cage Induction Motor", "section_title": "Multiple Squirrel-Cage Induction Motor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3543-5554", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-02/", "snippets": [ "CHAPTER II MULTIPLE SQUIRREL-CAGE INDUCTION MOTOR 18. In an induction motor, a high-resistance low-reactance secondary is produced by the use of an external non-inductive resistance in the secondary, or in a motor with squirrel-cage secondary, by small bars of high-resistance material located clow* to the periphery of the rotor. Such a motor has a great slip of ...", "... ed clow* to the periphery of the rotor. Such a motor has a great slip of speed under load, therefore poor efficiency and poor speed regu- lation, but it has a high starting torque and torque at low and intermediate speed. With a low resistance fairly high-reactance secondary, the slip of speed under load is small, therefore effi- ciency and speed regulation good, but the starting torque arid torque at low and intermediate speeds is low, and the current in starting and at low speed is large. To combine good start- i ...", "... inductive resistance is used in the secondary, which is cut out during acceleration. This, however, involves a complication, which is undesirable in many cases, such as in ship propulsion, etc. By arranging then two squirrel cages, one high-resistance low-reactance one, consisting of high-resistance bars clow* to the rotor surface, and one of low-resistance bars, located deeper in the armature iron, that is, inside of the first squirrel cage, and thus of higher reactance, a \"double squirrel-cage induction motor\" in ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 23, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... JjJ = e(cos 6 — j sin 0) dec a = (ei — je2) dec a, where a = tan a is the exponential decrement, a the angular decrement, e\"^'** the numerical decrement. OSCILLATING CURRENTS 347 Inductance 186. Let r = resistance, L = inductance, and x = 27r/L = reactance, in a circuit excited by the oscillating current, I = fc\"\"** cos (0 — ^) = i{cos d + j sin 6) dec a = (ii + jii) dec a, where ii = i cos ^, 12 = i sin 6j a = tan a. We have then, the e.m.f. consumed by the resistance, r, of the circuit, Er = rl de ...", "... a;i€-\"*{sin (0 — ^) + a cos (0 — ^)} = sm (0 — ^ + a). cos a Thus, in symbolic expression, jFx = I — sin {B — a) — j cos (^ — a) } dec a cos a / ^ \\ /I = — xtXa — j) (cos ^ — j sin ^) dec a; that is, jFx = — x7 (a — j) dec a. Hence the apparent reactance of the oscillating-current cir- cuit is, in symbolic expression, X = x{a — j) dec a. Hence it contains a power component, ax, and the impedance is Z = (r—X) dec a= {r—x{a—j)] dec a = {r —ax +jx) dec a. Capacity 186. Let r = resistance, C = capacity ...", "... in symbolic expression, X = x{a — j) dec a. Hence it contains a power component, ax, and the impedance is Z = (r—X) dec a= {r—x{a—j)] dec a = {r —ax +jx) dec a. Capacity 186. Let r = resistance, C = capacity, and Xc = o~~7?t = con- ZtJkj densive reactance. In a circuit excited by the oscillating current, 7, the e.m.f. consumed due to the capacity, C, is Ere = ^(idt = 2^ J /d« = fc fld4>; 348 ELECTRIC CIRCUITS or, by substitution, Es^ = xl i€-*»* cos (0 — e) d4> X i€\"\"<** {sin (0 — «) — a cos (0 — ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-31", "section_label": "Chapter 9: Divided Circuit", "section_title": "Divided Circuit", "kind": "chapter", "sequence": 31, "number": 9, "location": "lines 9228-10474", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "snippets": [ "... of circuit 2 is e = di 121 (2) (3) 122 TRANSIENT PHENOMENA and of circuit 3 is (4) Instead of the inductances, L, and capacities, C, it is usually preferable, even in direct-current circuits, to introduce the reactances, x = 2 nfL = inductive reactance, xc = = con- 2 7T/G densive reactance, referred to a standard frequency, such as / = 60 cycles per second. Instead of the time t, then, an angle 0 = 2 nft (5) is introduced, and then we have di x di dd di ^ * (6) i/iift - 2 Kfo f Id0 - Xc/i dd ...", "... 122 TRANSIENT PHENOMENA and of circuit 3 is (4) Instead of the inductances, L, and capacities, C, it is usually preferable, even in direct-current circuits, to introduce the reactances, x = 2 nfL = inductive reactance, xc = = con- 2 7T/G densive reactance, referred to a standard frequency, such as / = 60 cycles per second. Instead of the time t, then, an angle 0 = 2 nft (5) is introduced, and then we have di x di dd di ^ * (6) i/iift - 2 Kfo f Id0 - Xc/i dd, t since Hereby resistance, induct ...", "... rable with the phenomena on a 60-cycle circuit. A better conception of the size or magnitude of inductance and capacity is secured. Since inductance and capacity are mostly observed and of importance in alternating-current cir- cuits, a reactor having an inductive reactance of x ohms and i amperes conveys to the engineer a more definite meaning as regards size: it has a volt-ampere capacity of tfx, that is, the approximate size of a transformer of half this capacity, or of a ^2x — -watt transformer. A reactor having an in ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-32", "section_label": "Chapter 10: Mutual Inductance", "section_title": "Mutual Inductance", "kind": "chapter", "sequence": 32, "number": 10, "location": "lines 10475-12216", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "snippets": [ "... ve di L{j± = e.m.f. consumed by the inductance, ctt where, t = time. If instead of time t an angle 6 = 2 nft is introduced, where / is some standard frequency, as 60 cycles, di x. 3^ = e.m.f. consumed by the inductance, au where x1 = 2 nfL^ = inductive reactance. If now M = mutual inductance between the circuit and another circuit, that is, number of interlinkages of the circuit with the magnetic flux produced by unit current in the second circuit, and i2 = the current in the second circuit, then M—~= e.m.f. c ...", "... rrent in the second circuit, and i2 = the current in the second circuit, then M—~= e.m.f. consumed by mutual inductance in the first at circuit, M— - = e.m.f. consumed by mutual inductance in the second at circuit. Introducing xm = 2 nfM = mutual reactance between the two circuits, we have di xm-^= e.m.f. consumed by mutual inductance in the first do circuit, di xm—±= e.m.f. consumed by mutual inductance in the second au circuit. MUTUAL INDUCTANCE 143 If now e^ = the e.m.f. impressed upon th ...", "... = the e.m.f. impressed upon the second circuit, the equations of the circuits are dL di7 e, = r^ + x^-± + xm ^ + xci and r J il dO (1) -*2^+^^+*C2/V^, (2) where r1 = the resistance, xl = 2 7r/L1 = the inductive re- actance, and xci = = the condensive reactance of the first circuit; r2 = the resistance, x2 = 2 rfL2 = the inductive reactance, xca = = the condensive reactance of the second circuit, and xm = 2 nfM = mutual inductive reactance between the two circuits. 83. In these equations, xl and x2 are the to ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-16", "section_label": "Theory Section 16: Phase Control of Transmission Lines", "section_title": "Phase Control of Transmission Lines", "kind": "theory-section", "sequence": 16, "number": 16, "location": "lines 6222-6813", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-16/", "snippets": [ "... e transmission can be compounded for constant voltage at the receiving end, or even over-compounded for a voltage increasing with the load. 1. Compounding of Transmission Lines for Constant Voltage Let r = resistance, x = reactance of the transmission line, CQ = voltage impressed upon the beginning of the line, e = vol- tage received at the end of end line. PHASE CONTROL OF TRANSMISSION LINES 91 Let i = power current in the receiving circuit; ...", "... upon the beginning of the line, e = vol- tage received at the end of end line. PHASE CONTROL OF TRANSMISSION LINES 91 Let i = power current in the receiving circuit; that is, P — ei = transmitted power, and ii = reactive current produced in the system for controlling the voltage. i\\ shall be considered positive as lagging, negative as leading current. Then the total current, in symbolic representation, is / = i - jii; the line impedance ...", "... . Hence the voltage impressed upon the line Eo = e 4- Ei = (e + ri + xii) - j (rii - xi) ; (1) or, reduced, _ eo = V(e + ri + xii)* + (n\\ - xi)*. (2) If in this equation e and eQ are constant, ii, the reactive com- ponent of the current, is given as a function of the power com- ponent current i and thus of the load ei. Hence either eQ and e can be chosen, or one of the e.m.fs. eQ or e and the reactive current ii correspon ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "... -current circuit have been discussed; and it has been shown that the mutual relation between current and e.m.f. can be expressed by two of the four constants: power component of e.m.f., in phase with current, and = current X effective resistance, or r; reactive component of e.m.f., in quadrature with current, and = current X effective reactance, or x; power component of current, in phase with e.m.f., and = e.m.f. X effective conductance, or g; reactive component of current, in quadrature with e.m.f., and = e ...", "... between current and e.m.f. can be expressed by two of the four constants: power component of e.m.f., in phase with current, and = current X effective resistance, or r; reactive component of e.m.f., in quadrature with current, and = current X effective reactance, or x; power component of current, in phase with e.m.f., and = e.m.f. X effective conductance, or g; reactive component of current, in quadrature with e.m.f., and = e.m.f. X effective susceptance, or b. In many cases the exact calculation of the quant ...", "... th current, and = current X effective resistance, or r; reactive component of e.m.f., in quadrature with current, and = current X effective reactance, or x; power component of current, in phase with e.m.f., and = e.m.f. X effective conductance, or g; reactive component of current, in quadrature with e.m.f., and = e.m.f. X effective susceptance, or b. In many cases the exact calculation of the quantities, r, x, g, h, is not possible in the present state of the art. In general, r, x, g, b, are not constants o ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-17", "section_label": "Chapter 19: Alternating- Current Motors In General", "section_title": "Alternating- Current Motors In General", "kind": "chapter", "sequence": 17, "number": 19, "location": "lines 21713-23905", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-17/", "snippets": [ "... plied. The appearance of such \"dead points\" in the speed curve is due to a mechanical defect — as eccentricity of the rotor — or faulty electrical design: an improper distribution of primary and secondary windings causes a periodic variation of the mutual inductive reactance and so of the effective primary inductive reactance, (2) or the use of sharply defined and im- properly arranged teeth in both elements causes a periodic magnetic lock (opening and closing of the magnetic circuit, (3) and so a tendency to synchronize at t ...", "... eed curve is due to a mechanical defect — as eccentricity of the rotor — or faulty electrical design: an improper distribution of primary and secondary windings causes a periodic variation of the mutual inductive reactance and so of the effective primary inductive reactance, (2) or the use of sharply defined and im- properly arranged teeth in both elements causes a periodic magnetic lock (opening and closing of the magnetic circuit, (3) and so a tendency to synchronize at the speed corresponding to this cycle. Synchronous ...", "... erates an e.m.f., 5 = 2 tt/;i, where / = frequency, n = number of turns of electric circuit. This generated e.m.f., E, lags 90° behind the magnetic flux, *, hence consumes an e.m.f. 90° ahead of ♦, or 90—ci degrees ahead of /. This may be resolved in a reactive component: E = 2x/ft* eos a = 2 t/LI = xl, the o.m.f, con- sumed by self-induction, and power component: E\" = 2r/n* sin a = 2irfHI = r\"I = e.m.f. consumed by hysteresis (eddj currents, etc.), and is, therefore, in vector representation denoted by: E' = ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2485-3386", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-04/", "snippets": [ "... ar, similar as in starting transformers of high magnetic density. In polyphase rotary SINGLE-ENERGY TRANSIENTS. 37 apparatus, however, these momentary starting currents usually are far more limited than in transformers, by the higher stray field (self-inductive reactance), etc., of the apparatus, resulting from the air gap in the magnetic circuit. 19. As instance of the use of the single-energy transient in engineering calculations may be considered the investigation of the momentary short-circuit phenomena of synchronou ...", "... f-induction. Under permanent condi- tion, both usually act in the same way, reducing the voltage at noninductive and still much more at inductive load, and increasing it at antiinductive load; and both are usually combined in one quantity, the synchronous reactance Xq. In the transients result- ing from circuit changes, as short circuits, the self-inductive armature reactance and the magnetic armature reaction act very differently:* the former is instantaneous in its effect, while the latter requires time. The self- ...", "... and still much more at inductive load, and increasing it at antiinductive load; and both are usually combined in one quantity, the synchronous reactance Xq. In the transients result- ing from circuit changes, as short circuits, the self-inductive armature reactance and the magnetic armature reaction act very differently:* the former is instantaneous in its effect, while the latter requires time. The self-inductive armature reactance Xi con- sumes a voltage Xii by the magnetic flux surrounding the armature conductors ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-12", "section_label": "Chapter 12: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 10718-13483", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-12/", "snippets": [ "CHAPTER XII EFFECTIVE RESISTANCE AND REACTANCE 89. The resistance of an electric circuit is determined : 1. By direct comparison with a known resistance (Wheat- stone bridge method, etc.). This method gives what may be called the true ohmic resist- ance of the circuit. 2. By the ratio: Volts c ...", "... current, Power component of current ^ \" Total e.m.f. ' is called the effective conductance of the circuit. Ill 112 ALTERNATING-CURRENT PHENOMENA In the same way, the value, Wattless component of e.m.f. X = Total current is the effective reactance, and Wattless component of current Total e.m.f. is the effective suscepta7ice of the circuit. While the true ohmic resistance represents the expenditure of power as heat inside of the electric conductor b}^ a current of uniform density, the effective ...", "... equently differs from the true ohmic resistance in such way as to represent a larger expenditure of power. In dealing with alternating-current circuits, it is necessarj-, therefore, to substitute everywhere the values \"effective re- sistance,\" \"effective reactance,\" \"effective conductance,\" and \"effective susceptance,\" to make the calculation applicable to general alternating-current circuits, such as inductive reactances containing iron, etc. While the true ohmic resistance is a constant of the circuit, dependin ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-16", "section_label": "Chapter 16: Aiitebnatingh-Current Osnebator", "section_title": "Aiitebnatingh-Current Osnebator", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 17025-18828", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "snippets": [ "... § 160 density at the trailing-pole corner. Since the internal self- inductance of the alternator alone causes a certain lag of the current behind the induced E.M.F., this condition of no displacement can exist only in a circuit with external nega- tive reactance, as capacity, etc. If the armature current lags, it reaches the maximum later than the E.M.F. ; that is, in a position where the armature coil partly faces the following-field pole, as shown in diagram in Fig. 111. Since the armature current flows Fiq ...", "... or the magnetizing action of. the arma- ture upon the field, and armature self-inductance, or the E.M.F. induced in the armature conductors by the current flowing therein. This E.M.F. of self-inductance is (if the magnetic reluctance, and consequently the reactance, of the armature circuit is assumed as constant) in quadrature behind the armature current, and will thus combine with the induced E.M.F. in the proper phase relation. This means that, if the armature current lags, the E.M.F. of self-inductance will be m ...", "... the ter- minal voltage with a leading, and decreases it with a lagging current, or, in other words, acts in the same manner as the armature reaction. For this reason both actions can be combined in one, and represented by what is called the synchronous reactance of the alternator. In the following, we shall represent the total reaction of the armature of the alternator by the one term, synchronous reactance. While this is not exact, as stated above, since the reactance should be resolved into the magnetic react ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-09", "section_label": "Chapter 9: Resistance And Reactance Of Transmission Lines", "section_title": "Resistance And Reactance Of Transmission Lines", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 5334-6956", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "snippets": [ "CHAPTER IX. RESISTANCE AND REACTANCE OF TRANSMISSION LINES. 57. In alternating-current circuits, E.M.F. is consumed in the feeders of distributing networks, and in the lines of long-distance transmissions, not only by the resistance, but also by the reactance, of the line. The E.M.F. consum ...", "CHAPTER IX. RESISTANCE AND REACTANCE OF TRANSMISSION LINES. 57. In alternating-current circuits, E.M.F. is consumed in the feeders of distributing networks, and in the lines of long-distance transmissions, not only by the resistance, but also by the reactance, of the line. The E.M.F. consumed by the resistance is in phase, while the E.M.F. consumed by the reactance is in quadrature, with the current. Hence their influence upon the E.M.F. at the receiver circuit depends upon the difference of phase between the ...", "... is consumed in the feeders of distributing networks, and in the lines of long-distance transmissions, not only by the resistance, but also by the reactance, of the line. The E.M.F. consumed by the resistance is in phase, while the E.M.F. consumed by the reactance is in quadrature, with the current. Hence their influence upon the E.M.F. at the receiver circuit depends upon the difference of phase between the current and the E.M.F. in that circuit. As discussed before, the drop of potential due to the resistance is ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-17", "section_label": "Chapter 17: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16362-17596", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "snippets": [ "... 299 density at the trailing-pole corner. Since the internal self- inductance of the alternator itself causes a certain lag of the current behind the induced E.M.F., this condition of no displacement can exist only in a circuit with external nega- tive reactance, as capacity, etc. If the armature current lags, it reaches the maximum later than the E.M.F. ; that is, in a position where the armature coil partly faces the following-field pole, as shown in diagram in Fig. 127. Since the armature current flows Fig ...", "... or the magnetizing action of the arma- ture upon the field, and armature self-inductance, or the E.M.F. induced in the armature conductors by the current flowing therein. This E.M.F. of self-inductance is (if the magnetic reluctance, and consequently the reactance, of the armature circuit is assumed as constant) in quadrature behind the armature current, and will thus combine with the induced E.M.F. in the proper phase relation. Obvi- ously the E.M.F. of self-inductance and the induced E.M.F. do not in reality com ...", "... he ter- minal voltage with a leading, and decreases it with a lagging current, or, in other words, acts in the same manner as the armature reaction. For this reason both actions can be combined in one, and represented by what is called the syn- cJironous reactance of the alternator. In the following, we shall represent the total reaction of the armature of the alternator by the one term, synchronous reactance. While this is not exact, as stated above, since the reactance should be resolved into the magnetic reactio ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-36", "section_label": "Chapter 14: Short-Circuit Currents Of Alternators", "section_title": "Short-Circuit Currents Of Alternators", "kind": "chapter", "sequence": 36, "number": 14, "location": "lines 14549-15353", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "snippets": [ "... m.f., eOJ to the virtual generated e.m.f., er The armature current also produces a local magnetic flux in the armature iron and pole- faces which does not interlink with the field coils, but is a true self-inductive flux, and therefore is represented by a reactance xr Combined with the effective resistance, rv of the armature winding, this gives the self-inductive impedance Zl = rl — or zt = Vr* + x*. Vectorially subtracted from the virtual generated e.m.f., ev the voltage consumed by the armature current in the ...", "... self-inductive impedance Zl then gives the ter- minal voltage, e. At short circuit, the virtual generated e.m.f., ev is consumed by the armature self-inductive impedance, zr As the effective armature resistance, rv is very small compared with its self- inductive reactance, xv it can be neglected compared thereto, and the short-circuit current of the alternator, in permanent condition, thus is As shown in Chapter XXII, \"Theory and Calculation of Alternating Current Phenomena,\" the armature reaction can be represented by ...", "... pared thereto, and the short-circuit current of the alternator, in permanent condition, thus is As shown in Chapter XXII, \"Theory and Calculation of Alternating Current Phenomena,\" the armature reaction can be represented by an equivalent, or effective reactance, z2, and the self-inductive reactance, xv and the effective reactance of 199 200 TRANSIENT PHENOMENA armature reaction, x2J combine to form the synchronous react- ance, XQ = xl + x2, and the short-circuit current of the alterna- tor, in permanent co ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-08", "section_label": "Lecture 8: Arc Lamps And Arc Lighting", "section_title": "Arc Lamps And Arc Lighting", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 7141-8510", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-08/", "snippets": [ "... teadying device increases with increase of current, and pulsations of current thus limit themselves. All arc lamps for use on constant voltage supply thus contain a sufficiently high steadying resistance, or, in alternating-current circuits, a steadying reactance. Arc lamps for use on constant-current circuits, that is, cir- cuits in which the current is kept constant by the source of power supply, as the constant-current transformer or the arc machine, require no steadying resistance or reactance. 152 RADIATI ...", "... ts, a steadying reactance. Arc lamps for use on constant-current circuits, that is, cir- cuits in which the current is kept constant by the source of power supply, as the constant-current transformer or the arc machine, require no steadying resistance or reactance. 152 RADIATION, LIGHT, AND ILLUMINATION. Where several lamps are operated in series on constant poten- tial mains, as two flame-carbon arcs in series in a 110-volt cir- cuit, or five enclosed arc lamps in a 550-volt railway circuit, either each lamp m ...", "... ated in series on constant poten- tial mains, as two flame-carbon arcs in series in a 110-volt cir- cuit, or five enclosed arc lamps in a 550-volt railway circuit, either each lamp may have its own steadying resistance, or a single steadying resistance or reactance of sufficient size may be used for all lamps which are in series on the constant poten- tial mains. (2) Since the arc does not start itself, but has to be started by forming the conducting vapor bridge between the terminals, all arc lamps must have a st ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-17", "section_label": "Theory Section 17: Impedance and Admittance", "section_title": "Impedance and Admittance", "kind": "theory-section", "sequence": 17, "number": 17, "location": "lines 6814-7380", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-17/", "snippets": [ "... ization, etc. The counter e.m.f. of self-induction, or e.m.f. generated by the magnetic field produced by the alternating current i, is repre- sented by a quantity of the same dimensions as resistance, and measured in ohms: reactance x. The e.m.f. consumed by reactance x is in quadrature with the current, that consumed by resistance r in phase with the current. Reactance and resistance combined give the impedance, + x2; or, in symbolic or vector r ...", "... self-induction, or e.m.f. generated by the magnetic field produced by the alternating current i, is repre- sented by a quantity of the same dimensions as resistance, and measured in ohms: reactance x. The e.m.f. consumed by reactance x is in quadrature with the current, that consumed by resistance r in phase with the current. Reactance and resistance combined give the impedance, + x2; or, in symbolic or vector representation, Z = r + jx. In gene ...", "... sented by a quantity of the same dimensions as resistance, and measured in ohms: reactance x. The e.m.f. consumed by reactance x is in quadrature with the current, that consumed by resistance r in phase with the current. Reactance and resistance combined give the impedance, + x2; or, in symbolic or vector representation, Z = r + jx. In general in an alternating-current circuit of current i, the e.m.f. e can be resolved in two components, a pow ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-17", "section_label": "Chapter 17: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16521-17716", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-17/", "snippets": [ "... h the other. This magnetic cross-flux is proportional to the current in the electric circuit, or rather, the ampere-turns or m.m.f., and so increases with the increasing load on the transformer, and constitutes what is called the self-inductive or leakage reactance of the trans- former; while the flux surrounding both coils may be con- sidered as mutual inductive reactance. This cross-flux of self-induction does not generate e.m.f. in the secondary circuit, 187 188 ALTERNATING-CURRENT PHENOMENA and is thus, in ...", "... her, the ampere-turns or m.m.f., and so increases with the increasing load on the transformer, and constitutes what is called the self-inductive or leakage reactance of the trans- former; while the flux surrounding both coils may be con- sidered as mutual inductive reactance. This cross-flux of self-induction does not generate e.m.f. in the secondary circuit, 187 188 ALTERNATING-CURRENT PHENOMENA and is thus, in general, objectionable, by causing a drop of voltage and a decrease of output. It is this cross-flux, how- ev ...", "... self-induction does not generate e.m.f. in the secondary circuit, 187 188 ALTERNATING-CURRENT PHENOMENA and is thus, in general, objectionable, by causing a drop of voltage and a decrease of output. It is this cross-flux, how- ever, or flux of self-inductive reactance, which is utilized in special transformers, to secure automatic regulation, for con- stant power, or for constant current, and in this case is exagger- ated by separating primary and secondary coils. In the con- stant potential transformer, however, the p ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-09", "section_label": "Chapter 9: Kbsistanci: And Kbactance Of Transmission Iine8", "section_title": "Kbsistanci: And Kbactance Of Transmission Iine8", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 6371-8268", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "snippets": [ "CHAPTER IX. KBSISTANCi: AND KBACTANCE OF TRANSMISSION IINE8. 57. In alternating-current circuits, E.M.F. is consumed in the feeders of distributing networks, and in the lines of long-distance transmissions, not only by the resistance, but also by the reactance, of the line. The E.M.F. consumed by the resistance is in phase, while the E.M.F. consumed by the reactance is in quadrature, with the current. Hence their influence upon the E.M.F. at the receiver circuit depends upon the difference of phase between the ...", "... is consumed in the feeders of distributing networks, and in the lines of long-distance transmissions, not only by the resistance, but also by the reactance, of the line. The E.M.F. consumed by the resistance is in phase, while the E.M.F. consumed by the reactance is in quadrature, with the current. Hence their influence upon the E.M.F. at the receiver circuit depends upon the difference of phase between the current and the E.M.F. in that circuit. As discussed before, the drop of potential due to the resistance is ...", "... tween the current and the E.M.F. in that circuit. As discussed before, the drop of potential due to the resistance is a maximum when the receiver current is in phase, a minimum when it is in quadrature, with the E.M.F. The change of potential due to line reactance is small if the current is in phase with the E.M.F., while a drop of potential is produced with a lagging, and a rise of potential with a leading, current in the receiver circuit. Thus the change of potential due to a line of given re- sistance and indu ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "section_label": "Chapter 30: Quartbr-Fhase System", "section_title": "Quartbr-Fhase System", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... (cos a> +y sin ui) dec a = {e^ +jc^ dec a, where a = tan a is the exponential decrement, a the angular decrement, t~^^** the numerical decrement. 414 APPENDIX //. [§§ 284, 286 Inductance. 284. Let r = resistance, L = inductance, and x = 2 IT N L = reactance. In a circuit excited by the oscillating current, /= /c\"^*^ cos ( — co) = /(cos tu +/ sin o>) dec a = {h +Jh) dec a, where t\\ == / cos oj, /j = / sin o>, a = tan a. We have then. The electromotive force consumed by the resistance r of the circui ...", "... sin ( — w) + ^ cos ( — w)} = -— — - -- sin ( — (u + «)• cos tt Thus, in symbolic expression, ^x = — {— sin (w — a) +ycos (w — a)} dec a COS a = — xi {a -\\- J) (cos « + y sin w) dec a ; that is, E^ = — X I{a +j) dec a. Hence the apparent reactance of the oscillating current circuit is, in symbolic expression, X == X (a +y) dec a. Hence it contains an energy component ax, and the impedance is Z ={r — X) dec a = {r — x (a +j)) dec a = {r—ax —jx) dec a. Capacity, 285. Let r = resistance, C= ca ...", "... , in symbolic expression, X == X (a +y) dec a. Hence it contains an energy component ax, and the impedance is Z ={r — X) dec a = {r — x (a +j)) dec a = {r—ax —jx) dec a. Capacity, 285. Let r = resistance, C= capacity, and x^ = 1/ 2 «• C = capacity reactance. In a circuit excited by the oscillating §286] OSCILLATING CURRENTS. 415 current /, the electromotive force consumed by the capacity C is or, by substitution, Ej,^x Cu-^* cos (<^ — «) // — w)} (1 + f^ ) cos ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-32", "section_label": "Chapter 32: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 25904-27405", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "snippets": [ "... ol E = e (cos w -\\-j sin w) dec a = (e± -\\-j'e^) dec a, where a = tan a is the exponential decrement, a the angular decrement, e~27ra the numerical decrement. 502 APPENDIX II. Inductance. 313. Let r = resistance, L = inductance, and x = 2 IT N L = reactance. In a circuit excited by the oscillating current, /= /£-«* cos (<£ — w) = /(cos to +y sin w) dec a = (*i -\\-J*z) dec a, where /i = / cos w, /2 = / sin £>, a = tan a. We have then, The electromotive force consumed by the resistance r of the circuit ...", "... s (<£ — w)} xi(.~a^ . ,. „ , N = sin (^> — w -f- a). COS a Thus, in symbolic expression, £x = - °^—{— sin (w — a) +/ cos (w — a)} dec a COS a = — x i (a -f y ) (cos w + 7 sin a>) dec a ; that is, Ex = — x I (a +/') dec a . Hence the apparent reactance of the oscillating current circuit is, in symbolic expression, X = x (a +y') dec a. Hence it contains an energy component ax, and the impedance is Z = (r — X) dec a = {r — x (a +/')} dec a = (r — ax —jx) dec a. Capacity. 314. Let r = resistance, C ...", "... ymbolic expression, X = x (a +y') dec a. Hence it contains an energy component ax, and the impedance is Z = (r — X) dec a = {r — x (a +/')} dec a = (r — ax —jx) dec a. Capacity. 314. Let r = resistance, C = capacity, and xc = 1 /2-n-JVC = capacity reactance. In a circuit excited by the oscillating OSCILLATING CURRENTS. 503 current /, the electromotive force consumed by the capacity Cis or, by substitution, Ex = x I * e~a* cos (<£ {sin (<£ — w) — a COS (<£ — oi 2 (1 + 02) COS a hence, in symb ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2162-2971", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "snippets": [ "... ar, similar as in starting transformers of high magnetic density. In polyphase rotary SINGLE-ENERGY TRANSIENTS. 37 apparatus, however, these momentary starting currents usually are far more limited than in transformers, by the higher stray field (self-inductive reactance), etc., of the apparatus, resulting from the air gap in the magnetic circuit. 19. As instance of the use of the single-energy transient in engineering calculations may be considered the investigation of the momentary short-circuit phenomena of synchronou ...", "... -induction. Under permanent condi- tion, both usually act\" in the same way, reducing the voltage at noninductive and still much more at inductive load, and increasing it at antiinductive load; and both are usually combined in one quantity, the synchronous reactance XQ. In the transients result- ing from circuit changes, as short circuits, the self-inductive armature reactance and the magnetic armature reaction act very differently:* the former is instantaneous in its effect, while the latter requires time. The self- ...", "... and still much more at inductive load, and increasing it at antiinductive load; and both are usually combined in one quantity, the synchronous reactance XQ. In the transients result- ing from circuit changes, as short circuits, the self-inductive armature reactance and the magnetic armature reaction act very differently:* the former is instantaneous in its effect, while the latter requires time. The self-inductive armature reactance Xi consumes a voltage x\\i by the magnetic flux surrounding the armature conductors, ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-07", "section_label": "Theory Section 7: Inductance in Alternating-current Circuits", "section_title": "Inductance in Alternating-current Circuits", "kind": "theory-section", "sequence": 7, "number": 7, "location": "lines 2250-2717", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-07/", "snippets": [ "... ve of current. This e.m.f. is called the counter e.m.f. of inductance. It is .'•'• '•••• e'*=-Ljt = - 2 TT/L/O cos 2 irft. It is shown in dotted line in Fig. 11 as e'2. The quantity 2 irfL is called the inductive reactance of the circuit, and denoted by x. It is of the nature of a resistance, and expressed in ohms. If L is given in 109 absolute units or henrys, x appears in ohms. The counter e.m.f. of inductance of the current, i = / ...", "... irft = — xIQ cos 6, having a maximum value of X!Q and an effective value of xh T E, = -- = xl; ALTERNATING-CURRENT CIRCUITS 33 that is, the effective value of the counter e.m.f. of inductance equals the reactance, x, times the effective value of the current, /, and lags 90 time degrees, or a quarter period, behind the current. 35. By the counter e.m.f. of inductance, e'z = — xIQ cos 0, which is generated by the change in fl ...", "... or a quarter period, behind the current. 35. By the counter e.m.f. of inductance, e'z = — xIQ cos 0, which is generated by the change in flux due to the passage of the current i — IQ sin 0 through the circuit of reactance x, an equal but opposite e.m.f. ez = xIQ cos 0 is consumed, and thus has to be impressed upon the circuit. This e.m.f. is called the e.m.f. consumed by inductance. It is 90 time degrees, or a quarter period, ahead o ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-26", "section_label": "Apparatus Section 5: Synchronous Machines: Synchronous Reactance", "section_title": "Synchronous Machines: Synchronous Reactance", "kind": "apparatus-section", "sequence": 26, "number": 5, "location": "lines 9035-9169", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-26/", "snippets": [ "V. Synchronous Reactance 14. In general, both effects, armature self-inductance and armature reaction, can be combined by the term \" synchronous reactance.\" FIG. 55. — Diagram showing effect of synchronous reactance. FIG. 56. — Diagram of generato ...", "V. Synchronous Reactance 14. In general, both effects, armature self-inductance and armature reaction, can be combined by the term \" synchronous reactance.\" FIG. 55. — Diagram showing effect of synchronous reactance. FIG. 56. — Diagram of generator e.m.f s. showing affect of synchronous reactance with non-reactive load. In a polyphase machine, the synchronous reactance is d ...", "V. Synchronous Reactance 14. In general, both effects, armature self-inductance and armature reaction, can be combined by the term \" synchronous reactance.\" FIG. 55. — Diagram showing effect of synchronous reactance. FIG. 56. — Diagram of generator e.m.f s. showing affect of synchronous reactance with non-reactive load. In a polyphase machine, the synchronous reactance is different, and lower, with one phase only loaded, as \" single-p ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-08", "section_label": "Chapter 8: Admittance, Conductance, Susceptance", "section_title": "Admittance, Conductance, Susceptance", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 4088-4673", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-08/", "snippets": [ "... to the sum of the individual conductances. 64 ADMITTANCE, CONDUCTANCE, SUSCEPTANCE 55 49. In alternating-current circuits, instead of the term resist- ance we have the term impedance, Z = r -\\- jx, with its two components, the resistance, r, and the reactance, x, in the formula of Ohm's law, E = IZ. The resistance, r, gives the component of e.m.f. in phase with the current, or the power component of the e.m.f., Ir; the reactance, x, gives the component of the e.m.f. in quadrature with the current, or the wattl ...", "... term impedance, Z = r -\\- jx, with its two components, the resistance, r, and the reactance, x, in the formula of Ohm's law, E = IZ. The resistance, r, gives the component of e.m.f. in phase with the current, or the power component of the e.m.f., Ir; the reactance, x, gives the component of the e.m.f. in quadrature with the current, or the wattless component of e.m.f., Ix; both combined give the total e.m.f., Iz = iVr^ + x^. Since e.m.fs. are combined by adding their complex expressions, we have: The joint impe ...", "... of current in phase with the e.m.f., or the power or active com- ponent, gE, of the current, in the equation of Ohm's law, I =YE ={g- jh)E, and the component, h, which represents the coefficient of current in quadrature with the e.m.f., or wattless or reactive component, hE, of the current. g is called the conductance, and h the susceptance, of the cir- cuit. Hence the conductance, g, is the power component, and 56 ALTERNATING-CURRENT PHENOMENA the susceptance, h, the wattless component, of the admittance, ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-06", "section_label": "Chapter 6: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 11051-12221", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-06/", "snippets": [ "... pull or force of the electromagnet pulsates with double frequency between and 2F. 63. In the alternating-current electromagnet usually the vol- tage consumed by the resistance of the winding, tV, can be neglected compared with the voltage consumed by the reactance of the winding, ioXy and the latter, therefore, is practically equal to the terminal voltage, e, of the electromagnet. We have then, by the general equation of self-induction, e = 27r fLio (20) 96 ELECTRIC CIRCUITS where / = frequency, in cycles per ...", "... s. 98 ELECTRIC CIRCUITS 3. The Constant-potential Alternating Electromagnet 64. If a constant alternating potential, eo, is impressed upon an electromagnet, and the voltage consumed by the resistance, ir, can be neglected, the voltage consumed by the reactance, x, is constant and is the terminal voltage, eo, thus the magnetic flux, $, also is constant during the motion of the armature of the electromagnet. The current, i, however, varies, and decreases from a maximiun, ^l, in the initial position, to a minimum, ...", "... f the transformer even at short-circuit, full magnetic flux passes through the primary coils. ^ In this case the total magnetic flux passes between primary coils and secondary coils, as self-inductive or leakage flux. If then x = self-inductive or leakage reactance, eo = im- pressed e.m.f., io = — is the short-circuit current of the trans- former. Or, if as usual the reactance is given in per cent., that is, the ix (where i = full-load current of the transformer) given in per cent, of e, the short-circuit current is ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-04", "section_label": "Chapter 4: Vector Representation", "section_title": "Vector Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2149-2759", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-04/", "snippets": [ "... the polygon of sine waves. Kirchhofif's laws now assume, for alternating sine waves, the form : (a) The resultant of all the e.m.fs. in a closed circuit, as found by the parallelogram of sine waves, is zero if the counter e.m.fs. of resistance and of reactance are included. (6) The resultant of all the currents toward a distributing point, as found by the parallelogram of sine waves, is zero. The power equation expressed graphically is as follows: The power of an alternating-current circuit is represented i ...", "... t, or by the e.m.f., E, into the projection of the current, I, £3 Eo upon the e.m.f., or by IE cos d, where A ^,--^^'' ^ ~ angle of phase displacement. ^J,.^--^ / 19. Suppose, as an example, that in ^^ *E ^' a line having the resistance, r, and the reactance, x = 2 irfL — where / = fre- quency and L = inductance — there p, ,r> exists a current of / amp., the line being connected to a non-inductive circuit operating at a voltage of E volts. What will be the voltage required at the generator end of the line? ...", "... the end of the line, impressed upon the receiving circuit, is represented by a vector, OE. To overcome VECTOR REPRESENTATION 23 the resistance, r, of the hne, a voltage, Ir, is required in phase with the current, represented by OEi in the diagram. The inductive reactance of the hne generates an e.m.f. which is pro- portional to the current, /, and the reactance, x, and lags a quarter of a period, or 90°, behind the current. To overcome this counter e.m.f. of inductive reactance, a voltage of the value Ix is required, in p ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "... ffective intensity and equal power, while sufficiently accu- rate in many cases, completely fails in other cases, espe- cially in circuits containing capacity, or in circuits containing periodically (and in synchronism with the wave) varying resistance or reactance (as alternating arcs, reaction ma- chines, synchronous induction motors, oversaturated mag- netic circuits, etc.). Since, however, the individual harmonics of the general alternating wave are independent of each other, that is, all products of different ...", "... ntical, physically rep- resent different frequencies, and thus cannot be combined. The general wave of E.M.F. is thus represented by, the general wave of current by, if, is the impedance of the fundamental harmonic, where xm is that part of the reactance which is proportional to the frequency (inductance, etc.). x0 is that part of the reactance which is independent of the frequency (mutual induction, synchronous motion, etc.). xc is that part of the reactance which is inversely pro- portional to the ...", "... al wave of E.M.F. is thus represented by, the general wave of current by, if, is the impedance of the fundamental harmonic, where xm is that part of the reactance which is proportional to the frequency (inductance, etc.). x0 is that part of the reactance which is independent of the frequency (mutual induction, synchronous motion, etc.). xc is that part of the reactance which is inversely pro- portional to the frequency (capacity, etc.). The impedance for the nth harmonic is, r —Jnn xm This term c ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-29", "section_label": "Chapter 7: Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "section_title": "Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "kind": "chapter", "sequence": 29, "number": 7, "location": "lines 6798-7825", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "snippets": [ "... , INDUCTANCE, AND CAPACITY IN SERIES IN ALTERNATING-CURRENT CIRCUIT. 65. Let, at time t = 0 or 0 = 0, the e.m.f., e = E cos (0 - 00), (1) be impressed upon a circuit containing in series the resistance, r, the inductance, L, and the capacity, C. The inductive reactance is x = 2 TT/L 1 and the condensive reactance is xc = > 2 7T/C J where/ = frequency and 6 = 2 nft. (3) Then the e.m.f. consumed by resistance is ri\\ the e.m.f. consumed by inductance, is di di Ldt = xJe' and the e.m.f. consumed by capacity is , ...", "... RNATING-CURRENT CIRCUIT. 65. Let, at time t = 0 or 0 = 0, the e.m.f., e = E cos (0 - 00), (1) be impressed upon a circuit containing in series the resistance, r, the inductance, L, and the capacity, C. The inductive reactance is x = 2 TT/L 1 and the condensive reactance is xc = > 2 7T/C J where/ = frequency and 6 = 2 nft. (3) Then the e.m.f. consumed by resistance is ri\\ the e.m.f. consumed by inductance, is di di Ldt = xJe' and the e.m.f. consumed by capacity is , (4) where i = instantaneous value of the c ...", "... e shown in Figs. 20 and 21, the starting of the current i, its permanent term i1 ', and the two transient terms i1 and iv and their difference, for the constants E = 1000 volts = maximum value of impressed e.m.f.; r = 200 ohms = resistance ; x = 75 ohms = inductive reactance, and xc = 75 ohms = condensive reactance. We have 4 x xc = 22,500 and r2 = 40,000; therefore r2 > 4 x xc, RESISTANCE, INDUCTANCE, AND CAPACITY 95 that is, the start is logarithmic, and z0 = 200, s = 132, and 7 = 0. 20 60 80 100 120 14 ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-06", "section_label": "Lecture 6: Higher Harmonics Of The Generator Wave", "section_title": "Higher Harmonics Of The Generator Wave", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3133-3507", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-06/", "snippets": [ "SIXTH LECTURE HIGHER HARMONICS OF THE GENERATOR WAVE mHE open circuit reactance of the transformer is the only reactance high enough to give resonance with the line capacity at fundamental frequency. All other reactances are too low for this. Since, however, the inductive reactance increases and the capacity reactance decreases prop ...", "SIXTH LECTURE HIGHER HARMONICS OF THE GENERATOR WAVE mHE open circuit reactance of the transformer is the only reactance high enough to give resonance with the line capacity at fundamental frequency. All other reactances are too low for this. Since, however, the inductive reactance increases and the capacity reactance decreases proportionally to the frequency, the two reac ...", "... HIGHER HARMONICS OF THE GENERATOR WAVE mHE open circuit reactance of the transformer is the only reactance high enough to give resonance with the line capacity at fundamental frequency. All other reactances are too low for this. Since, however, the inductive reactance increases and the capacity reactance decreases proportionally to the frequency, the two reactances come nearer together for higher frequency; that is, for the higher harmonics of the generator wave, and for some of the higher harmonics of the generator wa ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-10", "section_label": "Theory Section 10: Hysteresis and Effective Resistance", "section_title": "Hysteresis and Effective Resistance", "kind": "theory-section", "sequence": 10, "number": 10, "location": "lines 3234-3585", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-10/", "snippets": [ "10. HYSTERESIS AND EFFECTIVE RESISTANCE 46. If an alternating current 01 = I, in Fig. 21, exists in a circuit of reactance x = 2 irfL and of negligible resistance, the HYSTERESIS AND EFFECTIVE RESISTANCE 49 magnetic flux produced by the current, 0$ = $, is in phase with the current, and the e.m.f. generated by this flux, or counter e ...", "... lags 90 degrees be- hind the current. The e.m.f. consumed by self-inductance or impressed e.m.f. OE\" = E\" = xl is thus 90 degrees ahead of the current. Inversely, if the e.m.f. OE\" = E\" is impressed upon a circuit of reactance x = 2 irfL and of negligible resistance, the current E\" 01 = I = - - lags 90 degrees behind the impressed e.m.f. x This current' is called the exciting or magnetizing current of the magnetic circuit, and is wattless ...", "... re the two com- ponents of the exciting current. FIG. 22. — Angle of hysteretic lead. FIG. 23. — Effect of resistance on phase relation of impressed e.m.f. in a hysteresisless circuit. If the circuit contains besides the reactance x = 2 wfL, a re- sistance r, the e.m.f. OE\" = E\" in the preceding Figs. 21 and 22 is not the impressed e.m.f., but the e.m.f. consumed by self- inductance or reactance, and has to be combined, Figs. 23 and 24, with ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-10", "section_label": "Chapter 10: F", "section_title": "F", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 8269-10499", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "snippets": [ "... e of the circuit, since it represents the effect, or power, expended by the circuit. The energy coefficient of current, _ Energy component of current ^ Total E.M.F. is called the effective conductance of the circuit. § 733 EFFECTIVE RESISTANCE AND REACTANCE. 105 In the same way, the value, _ Wattless component of E.M.F. Total current is the effective reactance, and , _ Wattless compo nent of current ■\" Total E.M.F. is the effective susceptance of the circuit. While the true ohmic resistance represe ...", "... of current, _ Energy component of current ^ Total E.M.F. is called the effective conductance of the circuit. § 733 EFFECTIVE RESISTANCE AND REACTANCE. 105 In the same way, the value, _ Wattless component of E.M.F. Total current is the effective reactance, and , _ Wattless compo nent of current ■\" Total E.M.F. is the effective susceptance of the circuit. While the true ohmic resistance represents the expendi- ture of energy as heat inside of the electric conductor by a current of uniform density, the ...", "... equently differs from the true ohmic resistance in such way as to represent a larger expenditure of energy. In dealing with alternating-current circuits, it is necessary, therefore, to substitute everywhere the values \"effective re- sistance,\" \"effective reactance,\" \"effective conductance,'* and \" effective susceptance,\" to make the calculation appli- cable to general alternating-current circuits, such as ferric inductances, etc. While the true ohmic resistance is a constant of the circuit, depending only upon th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-21", "section_label": "Chapter 21: Dibtobtiox Of Wavs-Shafe And Its Causes", "section_title": "Dibtobtiox Of Wavs-Shafe And Its Causes", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 23274-24559", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "snippets": [ "... he circuit, a distorting effect will cause higher harmonics of E.M.F. 213. In a conductor revolving with uniform velocity through a uniform and constant magnetic field, a sine wave of E.M.F. is induced. In a circuit with constant resistance and constant reactance, this sine wave of E.M.F. produces 1214] DISTORTION OF WAVE-SHAPE. 321 a sine wave of current. Thus distortion of the wave-shape or higher harmonics may be due to : lack of uniformity of the velocity of the revolving conductor ; lack of uniformity or ...", "... e of current. Thus distortion of the wave-shape or higher harmonics may be due to : lack of uniformity of the velocity of the revolving conductor ; lack of uniformity or pulsation of the magnetic field ; pulsation of the resis- tance ; or pulsation of the reactance. The first two cases, lack of uniformity of the rotation or of the magnetic field, cause higher harmonics of E.M.F. at open circuit. The last, pulsation of resistance and reac- tance, causes higher harmonics only with a current flowing in the circuit, t ...", "... , the speed is always very nearly uniform. Thus as causes of higher harmonics remain : 1st. Lack of uniformity and pulsation of the magnetic field, causing a distortion of the induced E.M.F. at open circuit as well as under load. 2d. Pulsation of the reactance, causing higher harmonics under load. 3d. Pulsation of the resistance, causing higher harmonics under load also. Taking up the different causes of higher harmonics we have : — Lack of Uniformity and Pulsation of the Magnetic Field, 214. Since most ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 963-1366", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "snippets": [ "... iron, etc., also upon the E.M.F. Impedance, z, is, in the system of absolute units, of the same dimensions as resistance (that is, of the dimension LT~l = velocity), and is expressed in ohms. It consists of two components, the resistance, r, and the reactance, x, or — , 0= Vr2 + Ar2. The resistance, r, in circuits where energy is expended only in heating the conductor, is the same as the ohmic resistance of continuous-current circuits. In circuits, how- ever, where energy is also expended outside of the con ...", "... tual inductance, dielectric hysteresis, etc., r is larger than the true ohmic resistance of the conductor, since it refers to the total expenditure of energy. It may be called then the effective resistance. It is no longer a constant of the circuit. The reactance, x, does not represent the expenditure of power, as does the effective resistance, r, but merely the surging to and fro of energy. It is not a constant of the INTRODUCTION. 3 circuit, but depends upon the frequency, and frequently, as in circuits cont ...", "... nds upon the frequency, and frequently, as in circuits containing iron, or in electrolytic conductors, upon the E.M.F. also. Hence, while the effective resist- ance, r, refers to the energy component of E.M.F., or the E.M.F. in phase with the current, the reactance, x, refers to the wattless component of E.M.F., or the E.M.F. in quadrature with the current. 3. The principal sources of reactance are electro-mag- netism and capacity. ELECTRO— MAGNETISM. An electric current, i, flowing through a circuit, produces ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "section_label": "Chapter 10: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "CHAPTER X. EFFECTIVE RESISTANCE AND REACTANCE. 72. The resistance of an electric circuit is determined : — 1.) By direct comparison with a known resistance (Wheat- stone bridge method, etc.). This method gives what may be called the true ohmic resistance of the circuit. 2.) By the ratio : Vol ...", "... esistance of the circuit, since it represents the effect, or power, expended by the circuit. The energy coefficient of current, a._ Energy component of current Total E.M.F. is called the effective conductance of the circuit. EFFECTIVE RESISTANCE AND REACTANCE. 105 In the same way, the value, _ Wattless component of E.M.F. Total current is the effective reactance, and , _ Wattless component of current TotafE.M.F. is the effective susceptance of the circuit. While the true ohmic resistance represents t ...", "... cient of current, a._ Energy component of current Total E.M.F. is called the effective conductance of the circuit. EFFECTIVE RESISTANCE AND REACTANCE. 105 In the same way, the value, _ Wattless component of E.M.F. Total current is the effective reactance, and , _ Wattless component of current TotafE.M.F. is the effective susceptance of the circuit. While the true ohmic resistance represents the expendi- ture of energy as heat inside of the electric conductor by a current of uniform density, the effec ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-22", "section_label": "Chapter 22: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 21190-21982", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "snippets": [ "... he circuit, a distorting effect will cause higher harmonics of E.M.F. 234. In a conductor revolving with uniform velocity through a uniform and constant magnetic field, a sine wave of E.M.F. is induced. In a circuit with constant resistance and constant reactance, this sine wave of E.M.F. produces 384 ALTERNATING-CURRENT PHENOMENA. a sine wave of current. Thus distortion of the wave-shape or higher harmonics may be due to : lack of uniformity of the velocity of the revolving conductor ; lack of uniformity or p ...", "... e of current. Thus distortion of the wave-shape or higher harmonics may be due to : lack of uniformity of the velocity of the revolving conductor ; lack of uniformity or pulsation of the magnetic field ; pulsation of the resis- tance ; or pulsation of the reactance. The first two cases, lack of uniformity of the rotation or of the magnetic field, cause higher harmonics of E.M.F. at open circuit. The last, pulsation of resistance and reac- tance, causes higher harmonics only with a current flowing in the circuit, t ...", "... ays very nearly uniform during the period. Thus as causes of higher harmonics remain : 1st. Lack of uniformity and pulsation of the magnetic field, causing a distortion of the induced E.M.F. at open circuit as well as under load. 2d. Pulsation of the reactance, causing higher harmonics under load. 3d. Pulsation of the resistance, causing higher harmonics under load also. Taking up the different causes of higher harmonics we have : — Lack of Uniformity and Pulsation of tJie Magnetic Field. 235. Since most ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-03-record", "section_label": "Report Record 4: Record of Four Troubles", "section_title": "Record of Four Troubles", "kind": "report-record", "sequence": 4, "number": 4, "location": "PDF pages 16-27, lines 1139-2164", "status": "pdf-text-extracted-candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-03-record/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-03-record/", "snippets": [ "... , with the A section of Fisk Street, and the Northwest Station as the two ends of the chain, and with power limiting reactors stated to be 1.75 ohms each, between Fisk A and Quarry Street, and between Quarry Street and Fisk B, and six tie cables of negligible reactance and about .3 ohms joint resistance between Fisk B and the Northwest Station. 1.) Sept. 18th, 19193:47 P. M. a) A short circuit close to the busbars of B section of Fisk Street held on for several seconds, before it was opened. As there are no power limiting r ...", "... affects too large a part of the entire system. It is dangerous, as Fisk B and Northwest combined give too large a power for safe handling under all emergencies. Furthermore, due to the connection between these stations being practically all resistance and no reactance, the synchronizing power between Fisk B and Northwest must be small, and when synchronism is once lost under short circuit, etc., trouble must be anticipated in these stations pulling into synchronism with each other. The interference between Fisk A, Quarry S ...", "... fed from the troubled station A, dropped out, those which receive power from the other stations should hold on to carry the load. 4.) May 19th, 1919 7:25 A. M. a) A generator in Fisk Street A burned out, short circuiting with only the generator power limiting reactance, of about .4 ohms, between the short and the busbars. b) The voltage dropped about 1,000 volts in all four station sec- tions a little more in Fisk A, where the trouble occurred, a little less in Fisk B and Northwest, the stations most remote from the trouble ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-106", "section_label": "Apparatus Section 9: Alternating-current Transformer: Reactors", "section_title": "Alternating-current Transformer: Reactors", "kind": "apparatus-section", "sequence": 106, "number": 9, "location": "lines 18813-18948", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-106/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-106/", "snippets": [ "IX. Reactors (Reactive Coils, Reactances) 129. The reactor consists of one electric circuit interlinked with a magnetic circuit, and its purpose is, not to transform power, but to produce wattless or reactive power, that is, lagging current, or ...", "IX. Reactors (Reactive Coils, Reactances) 129. The reactor consists of one electric circuit interlinked with a magnetic circuit, and its purpose is, not to transform power, but to produce wattless or reactive power, that is, lagging current, or what amounts to the same, leading voltage. While therefore theoretically we cannot speak of an ''efficiency\" of a reactor, since there is no power output, nevertheless in the in- dustry t ...", "... , or what amounts to the same, leading voltage. While therefore theoretically we cannot speak of an ''efficiency\" of a reactor, since there is no power output, nevertheless in the in- dustry the expression \" efficiency of a reactive coil\" is gener- ally used, and generally understood, in the conventional definition : T^C • 1°SS Efficiency = 1 — -. — input and the input is given in total volt-amperes, the loss in energy volt-amperes, that is, wat ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-14", "section_label": "Theory Section 14: Rectangular Coordinates", "section_title": "Rectangular Coordinates", "kind": "theory-section", "sequence": 14, "number": 14, "location": "lines 5264-5831", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-14/", "snippets": [ "... sin 0i, (6) and the primary load current corresponding thereto is I' = - aii = aii - jaiz. (7) The primary exciting current, Joo = h - jg, (8) where h = J0o sin a is the hysteresis current, g = I0o cos a the reactive magnetizing current. Thus the total primary current is J0 = I' + J00 = (aii + h) -j (aiz + g). (9) The e.m.f. consumed by primary resistance rQ is r0Jo = TQ (aii + h) - jr0 (aiz + 0). (10) The horizontal compon ...", "... I' + J00 = (aii + h) -j (aiz + g). (9) The e.m.f. consumed by primary resistance rQ is r0Jo = TQ (aii + h) - jr0 (aiz + 0). (10) The horizontal component of primary current (aii + h) gives as e.m.f. consumed by reactance XQ a negative vertical com- ponent, denoted by JXQ (aii + h). The vertical component of primary current j (aiz + g) gives as e.m.f. consumed by react- ance XQ a positive horizontal component, denoted by XQ (aiz + (/)• T ...", "... ed by JXQ (aii + h). The vertical component of primary current j (aiz + g) gives as e.m.f. consumed by react- ance XQ a positive horizontal component, denoted by XQ (aiz + (/)• Thus the total e.m.f. consumed by primary reactance XQ is XQ (aiz + g) + jxQ (aii + h), (11) and the total e.m.f. consumed by primary impedance is r0 (aii + A) + x0 (aiz + g) - j[rQ (aiz + g) - XQ (aii + h)]. (12) RECTANGULAR COORDINATES 79 Thus, to get from ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-05", "section_label": "Chapter 5: Symbolic Method", "section_title": "Symbolic Method", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2760-3266", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-05/", "snippets": [ "... or instance, in the trans- former diagrams (c/. Figs. 18-20), the different magnitudes have numerical values in practice somewhat like the following: Ei = 100 volts, and 7i = 75 amp. For a non-inductive second- ary load, as of incandescent lamps, the only reactance of the secondaiy circuit thus is that of the secondary coil, or Xi = 0.08 ohms, giving a lag of ^i = 3.6°. We have also, rii = 30 turns. rio = 300 turns. Fi = 2250 ampere-turns. F =100 ampere-turns. Er = 10 volts. E:, = 60 volts. Ei = 1000 vol ...", "... the resistance, the voltage consumed by the resistance is in phase with the current, and equal to the product of the current and resistance. Or rl = ri -\\- jri'. If L is the inductance, and x = 2x/L the inductive react- ance, the e.m.f. produced by the reactance, or the counter e.m.f. 1 In this representation of the sine wave by the exponential expression of the complex quantity, the angle 0 necessarily must be expressed in radians, and not in degrees, that is, with one complete revolution or cycle as 2 tt. or ...", "... complex quantity, the angle 0 necessarily must be expressed in radians, and not in degrees, that is, with one complete revolution or cycle as 2 tt. or 180 with — = 57.3° as unit. SYMBOLIC METHOD 35 of self-induction, is the product of the current and reactance, and lags in phase 90° behind the current; it is, therefore, repre- sented by the expression — jxl = — jxi -\\- xi'. The voltage required to overcome the reactance is consequently 90° ahead of the current (or, as usually expressed, the current lags 90° ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... dielectric and dynamic, 159 factor of general wave, 383 Coefficient of eddy currents, 138 of hysteresis, 123 Combination of sine waves, 31 Compensation for lagging currents by condensance, 72 Condensance in symbolic expression, 36 Condenser as reactance and suscep- tance, 96 with distorted wave, 384 motor on distorted wave, 392 motor, single-phase induction, 249, 257 synchronous, 339 Conductance of circuit with induc- tive line, 84 direct current, 55 due to eddy currents, 137 effective, 111 due ...", "... formers, six -phase, 429 Dielectric circuit, 159 density, 152 field, 1.50 hysteresis, 112, 1.50 strength. 161 Direct-current system, erhciency, 441 Displacement current. 152 Disruptive gradient. 165 Distortion by magnetic field, resist- ance and reactance pulsa- tion. a42 of magnetizing current. 117 of wave, see Harmonics by hysteresis, 116 Distributed capacity. 168 Double delta connections of trans- formers to sis-phase. 428 frequency power and torque with distorted wave, 381 quantities, 180 peak w ...", "... - formers, six-phase, 429 Dielectric circuit, 159 density, 152 field, 150 hysteresis, 112, 150 strength, 161 Direct-current system, efficiency, 441 Displacement current, 152 Disruptive gradient, 165 Distortion by magnetic field, resist- ance and reactance pulsa- tion, 342 of magnetizing current, 117 of wave, see Harmonics by hysteresis, 116 Distributed capacity, 168 Double delta connections of trans- formers to six-phase, 428 frequency power and torque with distorted wave, 381 quantities, 180 peak w ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1224-1727", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "snippets": [ "... iron, etc., also upon the E.M.F. Impedance, ^, is, in the system of absolute units, of the same dimensions as resistance (that is, of the dimension L T~ * = velocity), and is expressed in ohms. It consists of two components, the resistance, r, and the reactance, x, or — , The resistance, r, in circuits where energy is expended only in heating the conductor, is the same as the ohmic resistance of continuous-current circuits. In circuits, how- ever, where energy is also expended outside of the con- ductor by mag ...", "... tual inductance, dielectric hysteresis, etc., r is larger than the true ohmic resistance of the conductor, since it refers to the total expenditure of energy. It may be called then the effective resistance. It is no longer a constant of the circuit. The reactance, ;r, does not represent the expenditure of power, as does the effective resistance, r, but merely the surging to and fro of energy. It is not a constant of the §3] I.XTRODUCriO.V, 3 circuit, but depends upon the frequency, and frequently, as in circui ...", "... ds upon the frequency, and frequently, as in circuits containing iron, or in electrolytic conductors, upon the E.M.F. also. Hence, while the effective resist- ance, /', refers to the energy component of E.M.F., or the E.M.F. in phase with the current, the reactance, ;r, refers to the wattless component of E.M.F., or the E.M.F. in quadrature with the current. 3. The principal sources of reactance are electro-mag- netism and capacity. ELECTRO-MAGNETISM, An electric current, /, flowing through a circuit, produces ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-14", "section_label": "Chapter 14: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 11605-12682", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "snippets": [ "... by the angle &O® = a. The induced E.M.Fs. have the phase 180°, that is, are plotted towards the left, and represented by the vectors OZT; and OE±. If, now, ft' = angle of lag in the secondary circuit, due to the total (internal and external) secondary reactance, the secondary current II , and hence the secondary M.M.F., JF1= «j /L, will lag behind £•[ by an angle ft1, and have the phase, 180° + ft', represented by the vector O^1. Con- structing a parallelogram of M.M.Fs., with Off as a diag- onal and Oif1 as on ...", "... mber of primary turns, n0, the primary current is /.-*./*.. To complete the diagram of E M.Fs. , we have now, — In the primary circuit : E.M.F. consumed by resistance is 70r0, in phase with fot and represented by the vector OEr0 • E.M.F. consumed by reactance is IoX0, 90° ahead of I0, and represented by the vector OEx0 ; E.M.F. consumed by induced E.M.F. is E', equal and oppo- site to E'o, and represented by the vector Off. Hence, the total primary impressed E.M.F. by combina- tion of OEr0, OEx0, and OE' by ...", "... M.F. and the primary current is ft0 = E0O50. In the secondary circuit : Counter E.M.F. of resistance is 1^ in opposition with Iv and represented by the vector OJS'r^ ; 198 AL TERNA TING-CURRENT PHENOMENA, 90° behind 7X, and Counter E.M.F. of reactance is represented by the vector OE^x^ Induced E.M.Fs., E( represented by the vector OE-[. Hence, the secondary terminal voltage, by combination of OEr^ OEx{ and OE^ by means of the parallelogram of E.M.Fs. is -==• A = M»II and the difference of phase ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... a potential of 10,000 volts, is far larger than a 200-volt condenser of 100 mf. capacity. The energy which the former is able to Ce2 store is -77-= 50 joules, while the latter stores only 2 joules, 2 and therefore the former is 25 times as large. A reactive coil of 0.1 henry inductance, designed to carry continuously 100 amperes, stores— = 500 joules; a reactive coil of 1000 times the inductance, 100 henrys, but of a current- carrying capacity of 1 ampere, stores 5 joules only, therefore is only about one- ...", "... the former is able to Ce2 store is -77-= 50 joules, while the latter stores only 2 joules, 2 and therefore the former is 25 times as large. A reactive coil of 0.1 henry inductance, designed to carry continuously 100 amperes, stores— = 500 joules; a reactive coil of 1000 times the inductance, 100 henrys, but of a current- carrying capacity of 1 ampere, stores 5 joules only, therefore is only about one-hundredth the size of the former. A resistor of 1 ohm, carrying continuously 1000 amperes, is a ponderous ...", "... former of 1000 volts. \" A bulk of 1 cu. ft. in condenser can give about 5 to 10 kv-amp. at 60 cycles. Hence, 100 kv-amp. constitutes a very large size of condenser. In the oscillating condenser discharge, the frequency of oscil- lation is such that the inductive reactance equals the condensive reactance. The same current is in both at the same terminal voltage. That means that the volt-amperes consumed by the inductance equal the volt-amperes consumed by the capacity. The kilovolt-amperes of a condenser as well as of a re ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... d so limits itself. While therefore arcs can be operated on a constant cur- rent system, to run arc lamps on constant potential, some cur- rent limiting device is necessary in series with the arc, as a resistance; or, in an alternating current circuit, a reactance. The voltage consumed by the resistance is proportional to the current, and a resistance of 8 ohms inserted in series to the arc would thus consume the voltage shown in straight line II in Fig. 47. The voltage consumed by the arc plus the resistance then ...", "... and for supply voltages higher than 104, the arc is stable, the more so, the higher the supply voltage is above 104. The difference in voltage between the supply voltage and the arc voltage thus is consumed by the \"steadying resistance\" of the arc. High reactance in series with the direct current arc retards the current fluctuations and so reduces them ; so that with reactance in series to the direct current arc, the arc can be operated by a supply voltage closer to the stability curve IV than without reactance ; ...", "... The difference in voltage between the supply voltage and the arc voltage thus is consumed by the \"steadying resistance\" of the arc. High reactance in series with the direct current arc retards the current fluctuations and so reduces them ; so that with reactance in series to the direct current arc, the arc can be operated by a supply voltage closer to the stability curve IV than without reactance ; reactance therefore is very essential in the steadying resistance of a direct current arc. Obviously, no series reac ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-13", "section_label": "Chapter 13: Ths Alternating^Cnrrent Traxsfobmer", "section_title": "Ths Alternating^Cnrrent Traxsfobmer", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 12673-14088", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "snippets": [ "... the angle ^(7* = ea. The induced E.M.Fs. have the phase 180\"^, that is, are plotted towards the left, and represented by the vectors OE;, and 0E{. If, now, Wj' = angle of lag in the secondary circuit, due to the total (internal and ewXternal) secondary reactance, the secondary current Z^, and hence the secondary M.M.F., (Fi= ;/i /p will lag behind E^ by an angle ^\\ and have the phase, 180° + )S', represented by the vector O'S^, Con- structing a parallelogram of M.M.Fs., with C^$F as a diag- onal and C^tFj as one ...", "... by the number of primary turns, ;/^, the primary current is To complete the diagram of E.M.Fs., we have now, — In the primary circuit : E.M.F. consumed by resistance is lo^o^ in phase with /<,, and represented by the vector OEor ; E.M.F. consumed by reactance is IqXo^ 90° ahead of /«,, and represented by the vector OEo x \\ E.M.F. consumed by induced E.M.F. is Eo^ equal and oppo- site thereto, and represented by the vector OEo . Hence, the total primary impressed E.M.F. by combina- tion of OE^f.^ OEo^t and O ...", "... ssed E.M.F. and the primary current is /8o = Eo 0^0. ^ In the secondary circuit : Counter E.M.F. of resistance is /i^i in opposition with/i, and represented by the vector OEi / ; / 172 ALTERNATING-CURRENT PHENOMENA, [§121 Counter E.M.F. of reactance is I\\Xxy 90° behind /i, and represented by the vector OEu ; Induced E.M.Fs., E{ represented by the vector 0E(. Hence, the secondary terminal voltage, by combination of OEy^, OEi^ and 0E{ by means of the parallelogram of E.M.Fs. is E^ = OE^, and the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-05", "section_label": "Chapter 5: Symbolic Method", "section_title": "Symbolic Method", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2322-2773", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-05/", "snippets": [ "... e wave of alternating current, and r is the resistance, the E.M.F. consumed by the re- sistance is in phase with the current, and equal to the prod- uct of the current and resistance. Or — rl ' — ri -\\- jri' . If L is the inductance, and x = 2 TT NL the reactance, the E.M.F. produced by the reactance, or the counter SYMBOLIC METHOD. 39 E.M.F. of self-induction, is the product of the current and reactance, and lags 90° behind the current ; it is, therefore, represented by the expression — The E.M.F. required ...", "... s the resistance, the E.M.F. consumed by the re- sistance is in phase with the current, and equal to the prod- uct of the current and resistance. Or — rl ' — ri -\\- jri' . If L is the inductance, and x = 2 TT NL the reactance, the E.M.F. produced by the reactance, or the counter SYMBOLIC METHOD. 39 E.M.F. of self-induction, is the product of the current and reactance, and lags 90° behind the current ; it is, therefore, represented by the expression — The E.M.F. required to overcome the reactance is con- , s ...", "... uct of the current and resistance. Or — rl ' — ri -\\- jri' . If L is the inductance, and x = 2 TT NL the reactance, the E.M.F. produced by the reactance, or the counter SYMBOLIC METHOD. 39 E.M.F. of self-induction, is the product of the current and reactance, and lags 90° behind the current ; it is, therefore, represented by the expression — The E.M.F. required to overcome the reactance is con- , sequently 90° ahead of the current (or, as usually expressed,-** the current lags 90° behind the E.M.F.), and re ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-08", "section_label": "Theory Section 8: Power in Alternating-current Circuits", "section_title": "Power in Alternating-current Circuits", "kind": "theory-section", "sequence": 8, "number": 8, "location": "lines 2718-2864", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-08/", "snippets": [ "... tance x = 2 nfL, is p = ei, where e = z!Q sin (0 + 00) is the impressed e.m.f., consisting of the components ei = r/0 sin 0, the e.m.f. consumed by resistance and 62 = x!Q cos 0, the e.m.f. consumed by reactance. z = \\/r2 + x2 is the impedance and tan 00 = — the phase angle of the circuit; thus the power is p = z/o2 sin 0 sin (0 + 00) = ^- (€OS 00 - COS (20+ 00)) = zP (cos 00 - cos (20 + 00)). Since the avera ...", "... zP (cos 00 - cos (20 + 00)). Since the average cos (20 + 00) = zero, the average power is P = zP cos 00 = rP = EJ-, that is, the power in the circuit is that consumed by the resistance, and independent of the reactance. Reactance or self-inductance consumes no power, and the e.m.f. of self-inductance is a wattless or reactive e.m.f., while the e.m.f. of resistance is a power or active e.m.f. The wattless e.m.f. is in quadrature, the pow ...", "... 0 - cos (20 + 00)). Since the average cos (20 + 00) = zero, the average power is P = zP cos 00 = rP = EJ-, that is, the power in the circuit is that consumed by the resistance, and independent of the reactance. Reactance or self-inductance consumes no power, and the e.m.f. of self-inductance is a wattless or reactive e.m.f., while the e.m.f. of resistance is a power or active e.m.f. The wattless e.m.f. is in quadrature, the power e.m.f. i ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-05", "section_label": "Chapter 5: Symbouc Mbthod", "section_title": "Symbouc Mbthod", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2744-3229", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "snippets": [ "... sine wave of alternating current, and r is the resistance, the E.M.F. consumed by the re- sistance is in phase with the current, and equal to the prod- uct of the current and resistance. Or — r/= ri '\\' jri\\ If L is the inductance, and j: = 2 tt NL the reactance, the E.M.F. produced by the reactance, or the counter §20] SYMBOLIC METHOD. 39' E.M.F. of self-inductance, is the product of the current and reactance, and lags 90° behind the current; it is, therefore, represented by the expression — jxl =jxi — xi\\ ...", "... r is the resistance, the E.M.F. consumed by the re- sistance is in phase with the current, and equal to the prod- uct of the current and resistance. Or — r/= ri '\\' jri\\ If L is the inductance, and j: = 2 tt NL the reactance, the E.M.F. produced by the reactance, or the counter §20] SYMBOLIC METHOD. 39' E.M.F. of self-inductance, is the product of the current and reactance, and lags 90° behind the current; it is, therefore, represented by the expression — jxl =jxi — xi\\ The E.M.F. required to overcome the ...", "... of the current and resistance. Or — r/= ri '\\' jri\\ If L is the inductance, and j: = 2 tt NL the reactance, the E.M.F. produced by the reactance, or the counter §20] SYMBOLIC METHOD. 39' E.M.F. of self-inductance, is the product of the current and reactance, and lags 90° behind the current; it is, therefore, represented by the expression — jxl =jxi — xi\\ The E.M.F. required to overcome the reactance is con- sequently 90° ahead of the current (or, as usually expressed, the current lags 90° behind the E.M.F ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-07", "section_label": "Chapter 7: Admittance, Conductance, Susceftance", "section_title": "Admittance, Conductance, Susceftance", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 3546-3871", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-07/", "snippets": [ "... umber of parallel-connected conduc- tances is equal to the sum of the individual conductances, 39. In alternating-current circuits, instead of the term resistance we have the term impedance , Z = r —jx, with its two components, the resistance^ r, and the reactance^ x, in the formula of Ohm's law, E = IZ, The resistance, r, gives the component of E.M.F. in phase with the current, or the energy component of the E.M.F., Ir\\ the reactance, Xy gives the component of the E.M.F. in quadrature with the current, or the wat ...", "... e term impedance , Z = r —jx, with its two components, the resistance^ r, and the reactance^ x, in the formula of Ohm's law, E = IZ, The resistance, r, gives the component of E.M.F. in phase with the current, or the energy component of the E.M.F., Ir\\ the reactance, Xy gives the component of the E.M.F. in quadrature with the current, or the wattless component of E.M.F., Ix\\ both combined give the total E.M.F., — Iz = lWr' + x\\ Since E.M.Fs. are combined by adding their complex ex- pressions, we have : The joi ...", "... ceptanccy of the circuit. Hence the conductance, g^ is the energy component, and the susceptance, by the wattless component, of the admittance, Y = g -\\-jby while the numerical value of admittance is — the resistance, r, is the energy component, and the reactance^ Xy the wattless component, of the impedance, Z = r — jx\\ the numerical value of impedance being — 40. As shown, the term admittance implies resolving the current into two components, in phase and in quadra- ture with the E.M.F., or the energy current ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-07", "section_label": "Chapter 7: Admittance, Conductance, Susceptance", "section_title": "Admittance, Conductance, Susceptance", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 3132-3576", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-07/", "snippets": [ "... number of parallel-connected conduc~ tances is equal to the sum of the individual conductances. 39. In alternating-current circuits, instead of the term resistance we have the term impedance, Z = r —Jx, with its two components, the resistance, r, and the reactance, x, in the formula of Ohm's law, E = IZ. The resistance, r, gives the component of E.M.F. in phase with the current, or the energy component of the E.M.F., Ir; the reactance, x, gives the component of the E.M.F. in quadrature with the current, or the wat ...", "... he term impedance, Z = r —Jx, with its two components, the resistance, r, and the reactance, x, in the formula of Ohm's law, E = IZ. The resistance, r, gives the component of E.M.F. in phase with the current, or the energy component of the E.M.F., Ir; the reactance, x, gives the component of the E.M.F. in quadrature with the current, or the wattless component of E.M.F., Ix ; both combined give the total E.M.F., — Since E.M.Fs. are combined by adding their complex ex- pressions, we have : The joint impedance of ...", "... ircuit. Hence the conductance, g, is the energy com- ponent, and the susceptance, b, the wattless component, of the admittance, Y = g -f jb, while the numerical value of admittance is — y = Vr1 + P ; the resistance, r, is the energy component, and the reactance, x, the wattless component, of the impedance, Z — r — jx, the numerical value of impedance being — z = VV' + x\\ 40. As shown, the term admittance implies resolving the current into two components, in phase and in quadra- ture with the E.M.F., or the e ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-04", "section_label": "Chapter 5: Methods Of Approximation", "section_title": "Methods Of Approximation", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 15156-16482", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-04/", "snippets": [ "... ith secondary circuit, in the primary circuit. Since the fre- quency of the secondary circuit is the fraction 8 of the frequency 192 ENGINEERING MATHEMATICS. of the primary circuit, the generated e.m.f. of the secondary circuit is sE. Since x\\ is the reactance of the secondary circuit at full frequency, at the fraction s of full frequency the reactance of the secondary circuit is sxi, and the impedance of the sec- ondary circuit at slip s, therefore, is ri — jsx\\] hence the secondary current is, • ri-]sxi I ...", "... is the fraction 8 of the frequency 192 ENGINEERING MATHEMATICS. of the primary circuit, the generated e.m.f. of the secondary circuit is sE. Since x\\ is the reactance of the secondary circuit at full frequency, at the fraction s of full frequency the reactance of the secondary circuit is sxi, and the impedance of the sec- ondary circuit at slip s, therefore, is ri — jsx\\] hence the secondary current is, • ri-]sxi If the exciting current is neglected, the primary current equals the secondary current (assumin ...", "... +-J-J = 40,000(1 +j-y =40,400; 29.92 = 302(l-3i3)^900(l-j^^)=000-6 = 894; vmS = 10\\/l-0.02 = 10(1 -0.02)2 =10(1-0.01) = 9.99; 1 1 1 XOS (1+0.03)1/2 1.015 = 0.985; etc. METHODS OF APPROXIMATION. 195 130. Example i. If r is the resistance, x the reactance of an alternating-current circuit with impressed voltage e, the current is 1 = r2+x2 If the reactance x is small compared with the resistance r, as is the case in an incandescent lamp circuit, then, ._ _ _ _ef /xV] ~2 m i^' e r If t ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-16", "section_label": "Chapter 16: Power, And Double-Frequency Quantities In", "section_title": "Power, And Double-Frequency Quantities In", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 16077-16520", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-16/", "snippets": [ "... giizii); and the imaginary component, jpi ^ j[Eiy = j(e'H' - elf 11). The component, pi ^ [Ely ^ (giji + giiiii), is the true or \"effective\" power of the circuit, = EI cos (EI). The component, pi = [Ely = (giir - eifii), is what may be called Che \"reactive power,\" or the wattless or quadrature volt-amperes of the circuit, = EI sin (£\"7). DOUBLE-FREQUENCY QUANTITIES 181 The real component will be distinguished by the index 1; the imaginary or reactive component by the index, j. By introducing this symbo ...", "... i = [Ely = (giir - eifii), is what may be called Che \"reactive power,\" or the wattless or quadrature volt-amperes of the circuit, = EI sin (£\"7). DOUBLE-FREQUENCY QUANTITIES 181 The real component will be distinguished by the index 1; the imaginary or reactive component by the index, j. By introducing this symbolism, the power of an alternatmg circuit can be represented in the same way as in the direct-cur- rent circuit, as the symbolic product of current and voltage. Just as the symbolic expression of curren ...", "... ^ = \\e' + ell' tan 6 = —r, so the double-frequency vector product P = [EI] denotes more than the mere power, by giving with its two components, P^ = [Eiy and P' = [EIY, the true power volt-ampere, or \"effective power,\" and the wattless volt-amperes, or \"reactive power.\" If E = el + jell, / = i^ + ji^\\ then ^ = Ve'' + el / = ^/^ ' + ^•ll and or pi := [Ely = (eH'i + eiizii), pi = [EI]i = (giH-i _ gi^-ii)^ pi' J^ pr-=. e^\\i' + gii\\-u= _^ gii\\-i' _^ f,v^n' = (gi' + eii')(ii' + z'li') = (Ely = ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-14", "section_label": "Chapter 14: The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "section_title": "The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14089-14918", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "snippets": [ "... n- clad construction again greatly increases the self-induction of primary and secondary circuit. Thus the induction motor is a transformer of large magnetizing current and large self-induction ; that is, comparatively large primary susceptance and large reactance. The general alternating-current transformer transforms between electrical and mechanical power, and changes not only E.M.Fs. and currents, but frequencies also. 132. Besides the magnetic flux interlinked with both primary and secondary electric circui ...", "... g the magnetic circuit, and by the magnetic induction. At open secondary circuit, this M.M.F. is the M.M.F. of the primary current, which in this case is called the exciting current, and consists of an energy component, the magnetic energy current, and a reactive component, the magnetizing current. 134. In the general alternating-current transformer, where the secondary is movable with regard to the primary, the rate of cutting of the secondary electric circuit with the mutual magnetic flux is different from that ...", "... a = — = ratio of turns ; Vq = go +y^o = primary admittance per circuit ; where go '= effective conductance ; do = susceptance ; Zq == Tq — jXo = internal primary impedance per circuit, where To = effective resistance of primary circuit ; Xo = reactance of primary circuit ; Zii = ri — jxi = internal secondary impedance per circuit at standstill, or for x = 1, where ri = effective resistance of secondary coil ; ^1 = reactance of secondary coil at standstill, or full fre- quency, s = 1, Since the rea ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-15", "section_label": "Chapter 15: The General Alternating-Current Transformer Or Frequency Converter", "section_title": "The General Alternating-Current Transformer Or Frequency Converter", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 12683-13648", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "snippets": [ "... construction again greatly increases the self-induction of primary and secondary circuit. Thus the induction motor is a transformer of large magnetizing current and large self-induction; that is, comparatively large primary exciting susceptance and large reactance. The general alternating-current transformer transforms between electrical and mechanical power, and changes not only E.M.Fs. and currents, but frequencies also, and may therefore be called a \"frequency converter.\" Obviously, it also may change the numb ...", "... g the magnetic circuit, and by the magnetic induction. At open secondary circuit, this M.M.F. is the M.M.F. of the primary current, which in this case is called the exciting current, and consists of an energy component, the magnetic energy current, and a reactive component, the magnetizing current. 144. In the general alternating-current transformer, where the secondary is movable with regard to the primary, the rate of cutting of the secondary electric circuit with the mutual magnetic flux is different from that ...", "... i Y0 =£\"0 H~./A) = primary exciting admittance per circuit; where gQ = effective conductance ; b0 = susceptance ; Z0 = r0 —jx0 = internal primary self-inductive impedance per circuit, where r0 = effective resistance of primary circuit ; jr0 = reactance of primary circuit ; Zu = TI — jxv = internal secondary self -inductive impedance per circuit at standstill, or for s = 1, where rj = effective resistance of secondary coil ; Xl — reactance of secondary coil at standstill, or full fre- quency, s = 1. ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-04", "section_label": "Chapter 5: Single-Phase Induction Motor", "section_title": "Single-Phase Induction Motor", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 8555-10582", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-04/", "snippets": [ "... ther so as to produce a phase displacement. 98 ELECTRICAL APPARATUS This inductive relation may be established outside of the motor by an external phase-splitting device, or may take place in the motor proper. C. Monocyclic Devices. — An essentially reactive quadrature voltage is produced outside of the motor, and used to energize a cross-magnetic circuit in the motor, either directly through a separate motor coil, or after combination with the main voltage to a system of voltages of approximate three-phase o ...", "... secondary, the starting torque per volt-ampere input is low. With a high-resistance motor armature, which on polyphase supply gives a good apparent starting-torque efficiency, v would be much lower, due to the lower angle, . In this case, however, a reactance, +ja, would give fairly good starting-torque efficiency . In the same manner the effect of reactance or capacity inserted into one of the two motor coils can be calculated. As instances are given, in Fig. 37, the apparent torque efficiency, v, of the si ...", "... which on polyphase supply gives a good apparent starting-torque efficiency, v would be much lower, due to the lower angle, . In this case, however, a reactance, +ja, would give fairly good starting-torque efficiency . In the same manner the effect of reactance or capacity inserted into one of the two motor coils can be calculated. As instances are given, in Fig. 37, the apparent torque efficiency, v, of the single-phase induction-motor starting device consisting of the insertion, in one of the two parallel mot ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-21", "section_label": "Chapter 23: Review", "section_title": "Review", "kind": "chapter", "sequence": 21, "number": 23, "location": "lines 32138-32819", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-21/", "snippets": [ "... as the armature reaction of non-inductive load is absent. 3. A Synchronous Commutating Machine. — 112. The couple is synchronous, and called motor converter. It has the advantage of lower frequency commutation, and permits phase control by the internal reactance of the induction machine. It has higher efficiency and smaller size than a motor-generator set, but is larger and less efficient than the synchronous converter, and therefore has not been able to compete with the latter. 4. A direct-current commutating m ...", "... the secondary resistance thus is low. At high slips, u ing, unequal current distribution in the rotor bars concentrates the current in the top of the bars, thus gives a greatly increased effective resistance, and thereby higher torque. However, the high reactance of the deep bar somewhat impairs the power- factor. The effect is very closely the same as in the double squirrel cage. (See \"Double Squirrel-cage Induction Motor. \"I Double Squirrel-cage Induction Motor.— II, 18. Induction motor having a high-resistance ...", "... he deep bar somewhat impairs the power- factor. The effect is very closely the same as in the double squirrel cage. (See \"Double Squirrel-cage Induction Motor. \"I Double Squirrel-cage Induction Motor.— II, 18. Induction motor having a high-resistance low-reactance squirrel cage, plan to the rotor surface, and a low-resistance high-reactance squirrel cage, embedded in the core. The latter gives torque at good speed regulation near synchronism, but carries little current at lower speeds, due to itst high reactance. T ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-09", "section_label": "Chapter 9: Wave Screens. Even Harmonics", "section_title": "Wave Screens. Even Harmonics", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 16964-17631", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-09/", "snippets": [ "... 76. The elimination of voltage and current distortion, and production of sine waves from any kind of supply wave, that is, the reverse procedure from that discussed in the preceding chapter, is accomplished by what has been called ''wave screens.\" Series reactance alone acts to a considerable extent as wave screen, by consuming voltage proportional to the frequency and the current, and thereby reducing the harmonics of voltage in the rest of the circuit the more, the higher their order. Let the voltage impressed u ...", "... the circuit the more, the higher their order. Let the voltage impressed upon the circuit be denoted sym- bolically by e = €i + 63 + es + ej + . . . =^i:en (29) where n denotes the order of the harmonic of absolute numerical value 6n. If, then, the reactance x (at fundamental frequency) is inserted into the circuit of resistance, r, the impedance is 2i = -y/r^ + x^ for the fundamental frequency, and Zn = y/r^ + n^^ for the nth harmonic, (30) and the current thus is e or, denoting f = ? = y , ^ (31) ...", "... harmonics of the supply voltage, e, reduced in propor- tion to their order, n. Even if r is large compared with x, and thus c^>lj iSnally c^ becomes negligible with n^, and the harmonics decrease with their order. 77. The screening effect of the series reactance is increased by shunting a capacity, C, beyond the inductance, L, that is, across the resistance, r, as shown in Fig. 73. By consuming current jTRRRRRTl e 1 rmmM Fig. 73. r e Fig. 74. proportional to frequency and voltage, the conden ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-55", "section_label": "Chapter 6: Transition Points And The Complex Circuit", "section_title": "Transition Points And The Complex Circuit", "kind": "chapter", "sequence": 55, "number": 6, "location": "lines 32709-33527", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "snippets": [ "... ion of a complex circuit, connecting to other sections of 'very different constants, so that the ends of the circuit can, approximately, be considered as reflection points. For instance, an underground cable of low L and high (7, when connected to a large reactive coil of high L and low C, may, approximately, at its ends be considered as having reflection points i = 0. A high-potential transformer coil of high L and low C, when connected to a cable of low L and high (7, may at its ends be considered as having refle ...", "... be considered as having reflection points i = 0. A high-potential transformer coil of high L and low C, when connected to a cable of low L and high (7, may at its ends be considered as having reflection points e = 0. In other words, in the first case the reactive coil may be considered as stopping the current, in the latter case the cable considered as short-circuiting the transformer. This approximation, however, while frequently relied upon in engi- neering practice, and often permissible for the circuit section ...", "... he transient phenomenon originates, is not permissible in considering the effect of the phenomenon on the adjacent sections of the circuit. For instance, in the first case above mentioned, a transient phenomenon in an underground cable connected to a high reactance, the current and e.m.f. in the cable may approx- imately be represented by considering the reactive coil as a reflection point, that is, an open circuit, since only a small current 498 TRANSITION POINTS AND THE COMPLEX CIRCUIT 499 exists in the react ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-04", "section_label": "Chapter 4: Graphic Befrisxintation", "section_title": "Graphic Befrisxintation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2122-2743", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "snippets": [ "... e polygon of sine waves. Kirchhoff' s laws now assume, for alternating sine waves, the form : — a.) The resultant of all the E.M.Fs. in a closed circuit, as found by thq parallelogram of sine waves, is zero if the counter E.M.Fs. of resistance and of reactance are included. b.) The resultant of all the currents flowing towards a §17] GRAPHIC REPRESENTATION. 23 distributing point, as found by the parallelogram of sine waves, is zero. The energy equation expressed graphically is as follows : The power of ...", "... uct of the current ; /, into the projection of the E.M.F., Ey upon the current, or by the E.M.F., E, into the projection of the current, /, upon the E.M.F., or IE cos (/j^). 17. Suppose, as an instance, that over a line having the resistance, r, and the reactance, x = 2irNLy — where A^ = frequency and L = inductance, — a current of / amperes be sent into a non-inductive circuit at an E.M.F. of E ,Er E • ^^ J • \\ 1 Vi \\ E. \"e. — ~^^E. Fig. 12. volts. What will be the E.M.F. requir ...", "... presented by a vector, OE. To overcome the resistance, r, of the line, an E.M.F., /r, is required in phase with the current, repre- sented by OE^ in the diagram. The self-inductance of the line induces an E.M.F. which is proportional to the current / and reactance -r, and lags a quarter of a period, or 90°, behind the current. To overcome this counter E.M.F. /' 24 ALTERNATING-CURRENT PHENOMENA. [§18 of self-induction, an E.M.F. of the value Ix is required, in phase 90® ahead of the current, hence repre ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-04", "section_label": "Chapter 4: Graphic Representation", "section_title": "Graphic Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 1743-2321", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "snippets": [ "... Jie polygon of sine waves. Kirchhoff's laws now assume, for alternating sine waves, the form : — a.) The resultant of all the E.M.Fs. in a closed circuit, as found by the parallelogram of sine waves, is zero if the counter E.M.Fs. of resistance and of reactance are included. b.} The resultant of all the currents flowing towards a GRAPHIC REPRESENTATION. 23 distributing point, as found by the parallelogram of sine waves, is zero. The energy equation expressed graphically is as follows : The power of a ...", "... roduct of the current , /, into the projection of the E.M.F., E, upon the current, or by the E.M.F., E, into the projection of the current, /, upon the E.M.F., or by IE cos 17. Suppose, as an instance, that over a line having the resistance, r, and the reactance, x = ZirNL, — where N = frequency and L = inductance, — a current of / amperes be sent into a non-inductive circuit at an E.M.F. of E Fig. 12. volts. What will be the E.M.F. required at the generator end of the line ? In the polar diagram, Fig. 12, ...", "... presented by a vector, OE. To overcome the resistance, r, of the line, an E.M.F., Ir, is required in phase with the current, repre- sented by OEr in the diagram. The self-inductance of the line induces an E.M.F. which is proportional to the current / and reactance x, and lags a quarter of a period, or 90°, behind the current. To overcome this counter E.M.F. 24 ALTERNA TING-CURRENT PHENOMENA. of self-induction, an E.M.F. of the value Ix is required, in phase 90° ahead of the current, hence represented by vec ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "CHAPTER XIII. DISTRIBUTED CAPACITY, INDUCTANCE, RESISTANCE, AND LEAKAGE. 107. As far as capacity has been considered in the foregoing chapters, the assumption has been made that the condenser or other source of negative reactance is shunted across the circuit at a definite point. In many cases, how- ever, the capacity is distributed over the whole length of the conductor, so that the circuit can be considered as shunted by an infinite number of infinitely small condensers infi ni ...", "... crofarads, where K = dielectric constant of the surrounding medium = 1 in air ; / = length of conductor = 5 x 106 cm. ; d = distance of conductors from each other = 50 cm. ; 8 = diameter of conductor = 1 cm. Since C = .3 microfarads, the capacity reactance is x — 106 / 2 TT NC ohms, 160 ALTERNATING-CURRENT PHENOMENA. where N '= frequency; hence, at N = 60 cycles, x = 8,900 ohms ; and the charging current of the line, at E = 20,000 volts, becomes, ^ = E / x = 2.25 amperes. The resistance of 100 km of ...", "... In this case, the condenser current thus amounts to less than 2^ per cent., and hence can still be represented by the approximation of one condenser shunted across the line. If the length of transmission is 150 km., and the voltage, 30,000, capacity reactance at 60 cycles, x = 2,970 ohms ; charging current, i0 = 10.1 amperes ; line resistance, r = 66 ohms ; main current at 10 per cent loss, 7= 45.5 amperes. The condenser current is thus about 22 per cent of the main current, and the approximate calculatio ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-09", "section_label": "Theory Section 9: Vector Diagrams", "section_title": "Vector Diagrams", "kind": "theory-section", "sequence": 9, "number": 9, "location": "lines 2865-3233", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-09/", "snippets": [ "... l components of e.m.f. are power components, all vertical components are reac- tive components. With the e.m.f. as zero vector, all horizontal components of current are power components, all vertical components of current are reactive components. By measurement from the vector diagram numerical values can hardly ever be derived with sufficient accuracy, since the magnitudes of the different quantities used in the same diagram are usually by far too diffe ...", "... or shall be maintained constant at all loads, and the voltage regulation effected by producing lagging or leading currents with a synchronous motor in the receiving cir- cuit. The line has a resistance rx = 7.6 ohms and a reactance Xi = 4.35 ohms per wire, the generator is star connected, the resistance per circuit being r2 = 0.71, and the (synchronous) reactance is x2 = 25 ohms. ^ What must be the wattless or re- active component of the current, ...", "... onous motor in the receiving cir- cuit. The line has a resistance rx = 7.6 ohms and a reactance Xi = 4.35 ohms per wire, the generator is star connected, the resistance per circuit being r2 = 0.71, and the (synchronous) reactance is x2 = 25 ohms. ^ What must be the wattless or re- active component of the current, and therefore the total current and its phase relation at no load, one-quarter load, one-half load, three-quarters load, and full load, ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-13", "section_label": "Theory Section 13: Alternating-current Transformer", "section_title": "Alternating-current Transformer", "kind": "theory-section", "sequence": 13, "number": 13, "location": "lines 4465-5263", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-13/", "snippets": [ "... of one mag- netic circuit interlinked with two electric circuits, the primary circuit which receives energy, and the secondary circuit which delivers energy. Let TI = resistance, x\\ = 2TrfSz = self-inductive or leakage reactance of secondary circuit, r0 = resistance, XQ = 2irfSi = self -inductive or leakage reactance of primary circuit, where S2 and Si refer to that magnetic flux which is interlinked with the one but not with the other circui ...", "... receives energy, and the secondary circuit which delivers energy. Let TI = resistance, x\\ = 2TrfSz = self-inductive or leakage reactance of secondary circuit, r0 = resistance, XQ = 2irfSi = self -inductive or leakage reactance of primary circuit, where S2 and Si refer to that magnetic flux which is interlinked with the one but not with the other circuit. Let a ratio of — — • — - turns (ratio of transformation), primary An alternating e ...", "... NG terminal voltage, 01 1 = l\\ is the secondary current lagging by the angle EOI = 61. The e.m.f. consumed by the secondary resistance 7*1 is OE'i = E'i = Iiri in phase with /i. The e.m.f. consumed by the secondary reactance Xi is OE\"\\ = E'\\ = I&i, 90 degrees ahead of /i. Thus the e.m.f. con- sumed by the secondary impedance z\\ = Vn2 + Xi2 is the resultant of OE'i and OE\"i, or OE\"\\ = E\"\\ =JiZi. OE'\"\\ combined with the terminal voltage ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "section_label": "Chapter 14: Dielectric Losses", "section_title": "Dielectric Losses", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "CHAPTER XIV DIELECTRIC LOSSES Dielectric Hysteresis 116. Just as magnetic hysteresis and eddy currents give a power component in the inductive reactance, as \"effective resistance,\" so the energy losses in the dielectric lead to a power component in the condensive reactance, which may be repre- sented by an \"effective resistance of dielectric losses\" or an \"effective conductance of dielectric losses.\" In ...", "... HAPTER XIV DIELECTRIC LOSSES Dielectric Hysteresis 116. Just as magnetic hysteresis and eddy currents give a power component in the inductive reactance, as \"effective resistance,\" so the energy losses in the dielectric lead to a power component in the condensive reactance, which may be repre- sented by an \"effective resistance of dielectric losses\" or an \"effective conductance of dielectric losses.\" In the alternating magnetic field, power is consumed by mag- netic hysteresis. This is proportional to the frequency, and to ...", "... (1) 154 AL TERN A TING-C URREN T PHENOMENA Y = g -\\- jh = admittance, thus : Z =y = r — jx = impedance, where: 9 r = ^ = vector resistance (not ohmic resistance, but energy component of impedance, T see paragraph 89.) X = r = vector reactance, and (2) y = y/g^ + &^ = absolute admittance, (z = -y/r^ -\\- x^ = absohite impedance.) If then. El = potential drop across the first, E^ = potential drop across the second layer of dielectric, E = El -\\- Eo = voltage impressed upon the dielectric. ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-18", "section_label": "Chapter 18: Polyphase Induction Motors", "section_title": "Polyphase Induction Motors", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17717-20445", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-18/", "snippets": [ "... A if I' I = secondary current per circuit, Ii = -J- = secondary current per circuit reduced to primary system ; if r'l = secondary resistance per circuit, Vi = a-hr'i = secondary resistance per circuit reduced to pri- mary system; if x'l = secondary reactance per circuit, Xi = a^bx'i = secondary reactance per circuit reduced to pri- mary system; if z'l = secondary impedance per circuit, 2i = a^hz'i = secondary impedance per circuit reduced to pri- mary system; that is, the number of secondary circuits and ...", "... = -J- = secondary current per circuit reduced to primary system ; if r'l = secondary resistance per circuit, Vi = a-hr'i = secondary resistance per circuit reduced to pri- mary system; if x'l = secondary reactance per circuit, Xi = a^bx'i = secondary reactance per circuit reduced to pri- mary system; if z'l = secondary impedance per circuit, 2i = a^hz'i = secondary impedance per circuit reduced to pri- mary system; that is, the number of secondary circuits and of turns per sec- ondary circuit is assumed the ...", "... If (R = reluctance of magnetic circuit per pole, as discussed in Chapter XII, it is V2 Thus, from the hysteretic loss, and the reluctance, the con- stants, g and h and thus the admittance, Y, are derived. Let To = resistance per primary circuit; Xo = reactance per primary circuit; thus, Zo = To -}- jxo = impedance per primary circuit; ri = resistance per secondary circuit reduced to primary system; Xi = reactance per secondary circuit reduced to primary system, at full frequency/; 1 Complete discussion ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-26", "section_label": "Chapter 26: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 32540-33010", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-26/", "snippets": [ "... e in a circuit supplied by such a wave will be the combined effect of the different waves. Thus in a non-inductive circuit the current and the potential difference across the different parts of the circuit are of the same shape as the impressed e.m.f. If inductive reactance is inserted in series with a non-inductive circuit, the self-inductive reactance consumes more e.m.f. of the higher harmonics, since the reactance is proportional to the frequency, and thus the current and the e.m.f. in the non-inductive part of the circu ...", "... nt waves. Thus in a non-inductive circuit the current and the potential difference across the different parts of the circuit are of the same shape as the impressed e.m.f. If inductive reactance is inserted in series with a non-inductive circuit, the self-inductive reactance consumes more e.m.f. of the higher harmonics, since the reactance is proportional to the frequency, and thus the current and the e.m.f. in the non-inductive part of the circuit show the higher harmonics in a reduced amplitude. That is, self-inductive reac ...", "... fference across the different parts of the circuit are of the same shape as the impressed e.m.f. If inductive reactance is inserted in series with a non-inductive circuit, the self-inductive reactance consumes more e.m.f. of the higher harmonics, since the reactance is proportional to the frequency, and thus the current and the e.m.f. in the non-inductive part of the circuit show the higher harmonics in a reduced amplitude. That is, self-inductive react- ance in series with a non-inductive circuit reduces the higher ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "section_label": "Chapter 16: Induction Motor", "section_title": "Induction Motor", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "... mary system; if // = secondary current per circuit, fl= — = secondary current per circuit reduced to primary system ; if r^ = secondary resistance per circuit, rt = a2 r{ = secondary resistance per circuit reduced to primary system ; if x± = secondary reactance per circuit, xt = a2 x\\ = secondary reactance per circuit reduced to primary system ; if £/ = secondary impedance per circuit, z1 = azz\\ = secondary impedance per circuit reduced to primary system ; that is, the number of secondary circuits and of turn ...", "... cuit, fl= — = secondary current per circuit reduced to primary system ; if r^ = secondary resistance per circuit, rt = a2 r{ = secondary resistance per circuit reduced to primary system ; if x± = secondary reactance per circuit, xt = a2 x\\ = secondary reactance per circuit reduced to primary system ; if £/ = secondary impedance per circuit, z1 = azz\\ = secondary impedance per circuit reduced to primary system ; that is, the number of secondary circuits and of turns per secondary circuit is assumed the same as ...", "... ., it is A^^ft*. * Complete discussion hereof, see Chapter XXV. INDUCTION MOTOR. 241 Thus, from the hysteretic loss, and the reluctance, the constants, g and b, and thus the admittance, Fare derived. Let rQ = resistance per primary circuit ; XQ = reactance per primary circuit ; thus, •^o = ro — j XQ = impedance per primary circuit; rv = resistance per secondary circuit reduced to pri- mary system ; xv = reactance per secondary circuit reduced to primary system, at full frequency, .A7\"; hence, sx! = ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-19", "section_label": "Chapter 19: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 18053-19457", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "snippets": [ "... .M.Fs. are acting in circuit 322 ALTERNATING-CURRENT PHENOMENA. with the same current, it is convenient to use the current, /, as zero line OI of the polar diagram. Fig. 188. If I=i= current, and Z = impedance, r = effective resistance, x = effective reactance, and s = Vr2 -f x2 = absolute value of impedance, then the E.M.F. consumed by the resistance is E,, = ri, and in phase with the cur- rent, hence represented by vector OE,, ; and the E.M.F. consumed by the reactance is E2 = xi, and 90° ahead of the curren ...", "... r = effective resistance, x = effective reactance, and s = Vr2 -f x2 = absolute value of impedance, then the E.M.F. consumed by the resistance is E,, = ri, and in phase with the cur- rent, hence represented by vector OE,, ; and the E.M.F. consumed by the reactance is E2 = xi, and 90° ahead of the current, hence the E.M.F. consumed by the impedance is E = V(£,,)2 + (E2f, or = i Vr2 + x* = is, and ahead of the current by the angle 8, where tan 8 = x / r. We have now acting in circuit the E.M.Fs., E, Elf EQ; or El a ...", "... sight into the interdependence of the different quantities, for numerical calculation it is preferable to ex- press the diagrams analytically. For this purpose, Let z = Vr2 -j- x2 = impedance of the circuit of (equivalent) resistance r and (equivalent) reactance x = 2 TT NL, containing the impressed E.M.F. e0* and the counter E.M.F. et of the syn- chronous motor; that is, the E.M.F. induced in the motor arma- ture by its rotation through the (resultant) magnetic field. Let i = current in the circuit (effective v ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-30", "section_label": "Chapter 8: Low Frequency Surges In High Potential Systems", "section_title": "Low Frequency Surges In High Potential Systems", "kind": "chapter", "sequence": 30, "number": 8, "location": "lines 7826-9227", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "snippets": [ "... have c Z X (2) 65. These equations (1) and (2) can be essentially simplified by neglecting terms of secondary magnitude. xc is in high potential transmission lines or cables always very large compared with r and x. The full-load resistance and reactance voltage may vary from less than 5 per cent to about 20 per cent of the impressed e.m.f., the charging current of the line from 5 per cent to about 20 per cent of full-load current, at normal voltage and frequency. In this case, xc is from 25 to more tha ...", "... t which the oscillation begins, s c is the decrement of the oscillation. 66. The frequency of oscillation is where / is the impressed frequency. That is, the frequency of oscillation equals the impressed frequency times the square root of the ratio of condensive reactance and inductive reactance of the circuit, or is the impressed frequency divided by the square root of inductance voltage and capacity current, as fraction of impressed voltage and full-load current. Since the frequency of oscillation is that is, is in ...", "... begins, s c is the decrement of the oscillation. 66. The frequency of oscillation is where / is the impressed frequency. That is, the frequency of oscillation equals the impressed frequency times the square root of the ratio of condensive reactance and inductive reactance of the circuit, or is the impressed frequency divided by the square root of inductance voltage and capacity current, as fraction of impressed voltage and full-load current. Since the frequency of oscillation is that is, is independent of the frequen ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-01-recommendations", "section_label": "Report Section 2: Recommendations", "section_title": "Recommendations", "kind": "report-section", "sequence": 2, "number": 2, "location": "PDF pages 7-12, lines 145-720", "status": "pdf-text-extracted-candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "snippets": [ "... serious. I would recommend that 0.9 ohm, or at least 0.7 ohm feeder reactors (5.2% to 4% for a 300 ampere line) be installed, and the circuit breakers be set to cut off as quickly as possible, in case of a short circuit in the feeder. I believe such a feeder reactance would in no way adversely affect the operation of the substations, but it would limit the short circuit to about 100,000 KVA. If then the circuit breakers can be made to open this short in less than a second, the station voltage will be only a little affected ...", "... orter time limit, it also greatly reduces the duration of such short circuit and thereby correspondingly reduces the liability of dropping synchronous apparatus and spreading the trouble beyond the feeder directly involved. 4.) Install a power limiting busbar reactance between the two sec- tions of Fisk Street Station, so as to tie the three station sections : Fisk Street A, Quarry Street and Fisk B, together into a ring. This should increase the synchronizing power between these stations. It should also guard against the s ...", "... two parts out of synchron- ism with each other, in case that a short circuit at the busbars of an intermediary section (Quarry Street or Fisk Street B), drops the volt- age of this section to zero and thereby destroys its synchronizing power. The same size of reactance as now used, of about 1.75 ohms, would be recommended. [[END_PDF_PAGE:9]] [[PDF_PAGE:10]] 4 Report of Charles P. Steinmetz 5.) I should recommend strongly to endeavor to change the present connection between the Northwest Station and the rest of the system, ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-02", "section_label": "Lecture 2: General Distribution", "section_title": "General Distribution", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 566-982", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-02/", "snippets": [ "... of the conductor, hence decreases rapidly with increasing current: a conductor of one million circular mils is one-tenth the resistance of a conductor of 100,000 circular mils, and so can carry ten times the direct current with the same voltage drop. The reactance of a conductor, however, and so the voltage consumed by self-induction, de- creases only very little with the increasing size of a conductor, as seen from the table of resistances and reactances of conductors. A wire No. 000 B & S G is eight times the sec ...", "... ery little with the increasing size of a conductor, as seen from the table of resistances and reactances of conductors. A wire No. 000 B & S G is eight times the section of a wire No. 7, and therefore one-eighth (the resistance; but the wire No. 000 has a reactance of .109 ohms per 1000 feet, the wire No. 7 has a reactance of .133 oms, or only 1.22 times as large. Hence, while in the wire No. 7, the reactance, at 60 cycles, is only .266 times the resistance and therefore not of serious importance, in a wire No. 000 ...", "... from the table of resistances and reactances of conductors. A wire No. 000 B & S G is eight times the section of a wire No. 7, and therefore one-eighth (the resistance; but the wire No. 000 has a reactance of .109 ohms per 1000 feet, the wire No. 7 has a reactance of .133 oms, or only 1.22 times as large. Hence, while in the wire No. 7, the reactance, at 60 cycles, is only .266 times the resistance and therefore not of serious importance, in a wire No. 000 the reactance is 1.76 times the resistance, and the latter ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-38", "section_label": "Apparatus Section 17: Synchronous Machines: Short-circuit Currents of Alternators", "section_title": "Synchronous Machines: Short-circuit Currents of Alternators", "kind": "apparatus-section", "sequence": 38, "number": 17, "location": "lines 10190-10429", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-38/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-38/", "snippets": [ "... of the armature current, and the gen- SYNCHRONOUS MACHINES 161 erated e.m.f. thereby reduced from the nominal value EQ to the virtual value Ez; the latter is consumed by the armature self- inductive impedance z, or self-inductive reactance, which is practically the same in most cases. The armature self-inductance is instantaneous, since the magnetic field rises simultaneously with the armature current which produces it; armature reaction, however, requires an ap ...", "... would pass through zero. The momentary short-circuit current of an alternator thus represents one of the few cases in which armature self-induc- tance and armature reaction do not act in the same manner, and the synchronous reactance can be split into two components, thus, XQ = x -\\- x', where x = self-inductive reactance, which is due to a true self-inductance, and x' = effective reactance of armature reaction, which is not instantaneous. 32. In ma ...", "... represents one of the few cases in which armature self-induc- tance and armature reaction do not act in the same manner, and the synchronous reactance can be split into two components, thus, XQ = x -\\- x', where x = self-inductive reactance, which is due to a true self-inductance, and x' = effective reactance of armature reaction, which is not instantaneous. 32. In machines of high self-inductance and low armature re- action, as high frequency alternators, this ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-15", "section_label": "Chapter 15: Induction Motob", "section_title": "Induction Motob", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 14919-17024", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "snippets": [ "... if Ii = secondary current per circuit, /^ = _L a = secondary current per circuit reduced to primary system ; if r/ = secondary resistance per circuit, r, = a^ r^ = secondary resistance per circuit reduced to pri- mary system ; if Xx =- secondary reactance per circuit, Xi = a^ Xi^ = secondary reactance per circuit reduced to pri- mary system ; I 142] INDUCTION MOTOR. 209 if 0/ = secondary impedance per circuit, z^ = a^ z^ = secondary impedance per circuit reduced to pri- mary system ; that is, the ...", "... a = secondary current per circuit reduced to primary system ; if r/ = secondary resistance per circuit, r, = a^ r^ = secondary resistance per circuit reduced to pri- mary system ; if Xx =- secondary reactance per circuit, Xi = a^ Xi^ = secondary reactance per circuit reduced to pri- mary system ; I 142] INDUCTION MOTOR. 209 if 0/ = secondary impedance per circuit, z^ = a^ z^ = secondary impedance per circuit reduced to pri- mary system ; that is, the number of secondary circuits and of turns per se ...", "... e of magnetic circuit per pole, as dis- cussed in Chapter X., it is V2 nbe = (R<^. Thus, from the hysteretic loss, and the reluctance, the constants, g and b, and thus the admittance, K are derived. Let r = resistance per primary circuit ; z = reactance per primary circuit ; thus, Z '=^ r — y .r = impedance per primary circuit ; * Complete discussion hereof, see Chapter XXIII. § 143J INDUCTION MOTOR, 211 ri = resistance per secondary circuit reduced to primary sys- tem; Xi = reactance per secon ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-18", "section_label": "Chapter 16: Il", "section_title": "Il", "kind": "chapter", "sequence": 18, "number": 16, "location": "lines 19346-21338", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-18/", "snippets": [ "... everal E.M.Fs. are acting in circuit § 177] sy.\\ci//^ONOUs motor. 259 with the same current, it is convenient to use the current, /, as zero line 01 of the polar diagram. If I = i z= current, and Z = impedance, r = effective resistance, x = effective reactance, and s = Vr*-^ + ^2 __ absolute value of impedance, then the E.M.F. consumed by the resistance is i?i = r/, and in phase with the cur- rent, hence represented by vector 0E^\\ and the E.M.F. consumed by the reactance is E^ = xi^ and 90° ahead of the curren ...", "... r = effective resistance, x = effective reactance, and s = Vr*-^ + ^2 __ absolute value of impedance, then the E.M.F. consumed by the resistance is i?i = r/, and in phase with the cur- rent, hence represented by vector 0E^\\ and the E.M.F. consumed by the reactance is E^ = xi^ and 90° ahead of the current, hence the E.M.F. consumed by the impedance is E = \\/'{E^f + (E^f, or = /\" V/-^ -|- x^ = /-c, and ahead of the current by the angle 8, where tan 8 = x / r. We have now acting in circuit the E.M.Fs., E, E^, E^; or ...", "... nsight into the interdependence of the different quantities, for numerical calculation it is preferable to ex- press the diagrams analytically. For this purpose. Let z = V/^ + x^ = impedance of the circuit of (equivalent) resistance r and (equivalent) reactance x = 2irJVZ, containing the impressed E.M.F. e^* and the counter E.M.F. tTi of the syn- chronous motor; that is, the E.M F. induced in the motor arma- ture by its rotation through the (resultant) magnetic field. Let / = current in the circuit (effective v ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "... magnetic flux inside the conductor is , 27T . CR . TTiR* I From this we get, as the excess of counter E.M.F. at the axis of the conductor over that at the surface — &E = V27r^0> 10 ~8 = V27r7W10 -9, per unit length, and the reactivity, or specific reactance at the center of the conductor, becomes k = &E / i = V2 i^NR* 10 ~9. Let p = resistivity, or specific resistance, of the material of the conductor. We have then, k/p = V^TrW^lO-9/?; and p/ VFT7, the ratio of current densities at center and at peripher ...", "... alogously as in the chapter •on eddy currents, by the introduction of an energy com- FOUCAULT OR EDDY CURRENTS. 143 ponent, representing the loss of power, and a wattless component, representing the decrease of self-inductance. Let — x = 2 TT N L = reactance of main circuit ; that is, L = total number of interlinkages with the main conductor, of the lines of magnetic force produced by unit current in that conductor ; .#! = 2-jrNL1 = reactance of secondary circuit ; that is, Ll = total number of interlinkage ...", "... esenting the decrease of self-inductance. Let — x = 2 TT N L = reactance of main circuit ; that is, L = total number of interlinkages with the main conductor, of the lines of magnetic force produced by unit current in that conductor ; .#! = 2-jrNL1 = reactance of secondary circuit ; that is, Ll = total number of interlinkages with the secondary conductor, of the lines of magnetic force produced by unit current in that conductor ; xm = 2 TT N Lm = mutual inductance of circuits ; that is, Lm = total number of i ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... long distances, by overhead conductors or underground cables, or with very feeble currents at extremely high frequency, such as telephone currents, the consideration of the line resistance, which consumes e.m.fs. in phase with the current, and of the line reactance, which consumes e.m.fs. in quadrature with the current, is not sufficient for the explanation of the phenomena taking place in the line, but several other factors have to be taken into account. In long lines, especially at high potentials, the electrosta ...", "... nt approximately proportional and in phase with the e.m.f. of the line. This current represents consumption of power, and is therefore analogous to the e.m.f. consumed by resistance, while the condenser current and the e.m.f. of inductance are wattless or reactive. Furthermore, the alternating current passing over the line pro- duces in all neighboring conductors secondary currents, which react upon the primary current and thereby introduce e.m.fs. of mutual inductance into the primary circuit. Mutual induc- tanc ...", "... utual induc- tance is neither in phase nor in quadrature with the current, 282 TRANSIENT PHENOMENA and can therefore be resolved into a power component of mutual inductance in phase with the current, which acts as an increase of resistance, and into a reactive component in quadrature with the current, which decreases the self-inductance. This mutual inductance is not always negligible, as, for instance, its disturbing influence in telephone circuits shows. The alternating potential of the line induces, by ele ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-14", "section_label": "Lecture 14: Alternating Current Railway Motor", "section_title": "Alternating Current Railway Motor", "kind": "lecture", "sequence": 14, "number": 14, "location": "lines 8649-9342", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-14/", "snippets": [ "... ondary to the field coil of the motor as primary of a transformer ; and as primary and secondary ampere turns in a transformer are approximately equal, the current in -the armature turn during commutation is very large; if not limited by the resistance or reactance of the coil, it is as many times greater than the full load current, as the field coil has turns. This causes serious sparking, if not taken care of. One way of mitigating the effect of this short circuit cur- rent is to reduce it by interposing resista ...", "... e coil, it is as many times greater than the full load current, as the field coil has turns. This causes serious sparking, if not taken care of. One way of mitigating the effect of this short circuit cur- rent is to reduce it by interposing resistance or reactance ; that is by making the leads between the armature turns and the commutator bars of high resistance or high reactance. Obvi- ously this arrangement can merely somewhat reduce the spark- 1 88 GENERAL LECTURES ing by reducing the current in the short ci ...", "... ng, if not taken care of. One way of mitigating the effect of this short circuit cur- rent is to reduce it by interposing resistance or reactance ; that is by making the leads between the armature turns and the commutator bars of high resistance or high reactance. Obvi- ously this arrangement can merely somewhat reduce the spark- 1 88 GENERAL LECTURES ing by reducing the current in the short circuited coil, but can not eliminate it ; and it has the disadvantage, that in the moment of starting, if the motor doe ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-35", "section_label": "Chapter 35: Balanced Symmetrical Polyphase Systems", "section_title": "Balanced Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 35, "number": 35, "location": "lines 37453-37957", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-35/", "snippets": [ "... ms. The inductance of wire No. 0, with d = 0.325 in. diameter, and 6 ft. = 72 in. distance from the return conductor, is calculated from the formula of line inductance^ as, 2.3 mil-henrys per mile; hence, per circuit, L - 0.23 henry, and herefrom the reactance, X = 2TrfL = 88 ohms. The capacity of the transmission line may be calculated directly, or more conveniently it may be derived from the inductance. If C is the capacity of the circuit, of which the inductance is L, then is the fundamental frequency ...", "... of the m.m.f., and thus two-thirds of the exciting admittance, as equivalent single-phase circuit of a three-phase motor, which it would require, if as independent single-phase circuit it had to produce the entire m.m.f. 307. The same applies to the self-inductive reactance: as the self-inductive or leakage flux, which consumes the reactance voltage, is produced by the resultant of the currents of all three phases, and this resultant is 1.5 times the maximum of one phase, each phase produces only two-thirds, that is, the imp ...", "... ngle-phase circuit of a three-phase motor, which it would require, if as independent single-phase circuit it had to produce the entire m.m.f. 307. The same applies to the self-inductive reactance: as the self-inductive or leakage flux, which consumes the reactance voltage, is produced by the resultant of the currents of all three phases, and this resultant is 1.5 times the maximum of one phase, each phase produces only two-thirds, that is, the impedance current of each phase of the motor on three-phase voltage supp ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-01", "section_label": "Chapter 1: Speed Control Of Induction Motors", "section_title": "Speed Control Of Induction Motors", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1368-3542", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-01/", "snippets": [ "... e device leaves it unchanged. The foremost disadvantage of the use of the hysteresis device is the impairment of the power-factor, as seen in Fig. Z as p. The introduction of the effective resistance representing the hysteresis of necessity introduces a reactance, which is higher than the resistance, and thereby impairs the motor characteristics. Comparing Fig. 3 with Fig. 176, page 319 of \"Theoretical INDUCTION MOTOR Y6 = .oa-.9j: Z, -.05+155. e,-100 Z,-(.05+.ll») + .335 ja SPEED CONTROL BY MYSTEHESIS SPEE ...", "... - ance. With increasing motor speed and thus deereMlllg secondary frequency, the current penetrates deeper into the bar, until at full speed it passes practically uniformly throughout the entire bar, in a cireuit of low resistance— but somewhat increased reactance. The deep-bar construction, the eddy-current starting device and the double squirrel-cage construction thus are very similar in the motor-performance curves, and the double squirrel cage, which usually is the most economical arrangement, thus will be di ...", "... ductors in the motor armature. The only objection to the use of such pyro-electric resistances is the difficulty of producing stable pyro-electric conductors, and permiiiiriit terminal connections on such conductors. B. Condenser Speed Control 11. The reactance of a condenser is inverse proportional to the frequency, that of an inductance is directly proportional to the frequency. In the secondary of the induction motor, the Frequency varies from zero at synchronism, to full frequency at standstill. If, therefor ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-08", "section_label": "Lecture 8: Generation", "section_title": "Generation", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 3781-4217", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-08/", "snippets": [ "... hrough the field. This magnetism induces an e. m. f. in the armature, which opposes or assists the e. m. f . produced by the field magnetism, according to the phase of the armature current, and so lowers or raises the voltage. Self-induction, or \"armature reactance\" therefore is expressed in ohms. Armature reaction and self-induction therefore act in the same manner, lowering the voltage with lagging and raising the voltage with leading current. In calculating alternators, either the armature reaction and the sel ...", "... nsidered, which makes the calculation more complicated; or the armature reaction may be neglected and the self-induction made so much larger as to allow for the armature reaction. This self-induction is then no GENERAL LECTURES called the \"synchronous reactance\" and, combined with the armature resistance, the \"synchronous impedance\" of the ma- chine. Or the self-induction may be neglected and only the armature reaction considered, but which is increased to allow for the self-induction. The last way (armature r ...", "... nce\" of the ma- chine. Or the self-induction may be neglected and only the armature reaction considered, but which is increased to allow for the self-induction. The last way (armature reaction), is used in designing machines; the second way (synchronous reactance) in calcula- tions with machines and systems. In the momentary short circuit current of alternators, however, the armature reaction and the self-induction must be considered separately, since they act differently. In the moment of short circuiting an a ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-102", "section_label": "Apparatus Section 5: Alternating-current Transformer: Short-circuit Current", "section_title": "Alternating-current Transformer: Short-circuit Current", "kind": "apparatus-section", "sequence": 102, "number": 5, "location": "lines 18398-18460", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-102/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-102/", "snippets": [ "... with f = 0.02 + 0.02 j, hence f =0.028 0.01 + 0.04 j 0.04 0.01 + 0.08 j 0.08 the short-circuit current thus is 36, 25 and 12.5 times full-load current, respectively. As seen, with the exception of very low reactance transformers, it is essentially the reactance which determines the total im- pedance and thus the short-circuit current. 121. Primary current and secondary current in the trans- former, being opposite in phase, repel each othe ...", "... .028 0.01 + 0.04 j 0.04 0.01 + 0.08 j 0.08 the short-circuit current thus is 36, 25 and 12.5 times full-load current, respectively. As seen, with the exception of very low reactance transformers, it is essentially the reactance which determines the total im- pedance and thus the short-circuit current. 121. Primary current and secondary current in the trans- former, being opposite in phase, repel each other. This repul- sion is proportional to the ...", "... condary current are (ap- 19 294 ELEMENTS OF ELECTRICAL ENGINEERING proximately) proportional to each other, the repulsion is pro- portional to the square of the current. The repulsion is small at full load, but in low-reactance transformers, with 'short-circuit currents from forty to fifty times full-load current, the mechanical forces have increased 1600 to 2500 fold, and then, with large power transformers, reach formidable values, amounting to many ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-36", "section_label": "Apparatus Section 15: Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "section_title": "Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "kind": "apparatus-section", "sequence": 36, "number": 15, "location": "lines 9918-10123", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-36/", "snippets": [ "... OE\\ and OE2 of the machines, if these latter two e.m.fs. are equal to each other. The cross current between the machines lags behind the e.m.f. producing it, OE* ', by the angle co, where tan w = — , and XQ = 7*0 reactance, r0 = effective resistance of alternator armature. The energy component of this cross current, or component in phase with OEfj is thus in quadrature with the machine voltages OEi and OE2, that is, transfers no power betwee ...", "... in phase with OEfj is thus in quadrature with the machine voltages OEi and OE2, that is, transfers no power between them. The power transfer or equalization of load between the two machines takes place by the wattless or reactive component of cross current, E' 158 ELEMENTS OF ELECTRICAL ENGINEERING that is, the component which is in quadrature with OE', and thus in phase with one and in opposition with the other of the machine e.m.fs. OEi ...", "... 8 ELEMENTS OF ELECTRICAL ENGINEERING that is, the component which is in quadrature with OE', and thus in phase with one and in opposition with the other of the machine e.m.fs. OEi and OE^. 29. Hence, machines without reactance would have no syn- chronizing power, or could not be operated in parallel. The theoretical maximum synchronizing power exists if the reactance equals the resistance: XQ = r0. This condition, however, cannot be realized, and ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-85", "section_label": "Apparatus Section 6: Synchronous Converters: Reactive Currents and Compounding", "section_title": "Synchronous Converters: Reactive Currents and Compounding", "kind": "apparatus-section", "sequence": 85, "number": 6, "location": "lines 15476-15585", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-85/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-85/", "snippets": [ "VI. Reactive Currents and Compounding 96. Since the polarization due to the power component of the alternating current as synchronous motor is in quadrature ahead of the field magnetization, the polarization or magnetizing effect of the ...", "... e action, however, is different; and the compounding takes place not in the machine as with a direct-current generator, but in the alternating lines leading to the machine, in which self-inductance becomes essential. As the reactance of the transmission line is rarely sufficient to give phase control over a wide range without excessive reac- tive currents, it is customary, especially at 25 cycles, to insert reactive coils into the leads between the conv ...", "... -inductance becomes essential. As the reactance of the transmission line is rarely sufficient to give phase control over a wide range without excessive reac- tive currents, it is customary, especially at 25 cycles, to insert reactive coils into the leads between the converter and its step- down transformers, in those cases in which automatic phase control by converter series fields is desired, as in power trans- mission for suburban and interurban railwa ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-13", "section_label": "Chapter 13: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 13484-14333", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-13/", "snippets": [ "... ux inside the conductor is Jo 10 Jo 10 10 From this we get, as the excess of counter e.mi. at the axis of the conductor over that at the surface, AE = \\/2 7r/$ 10^8 ^ -v/2x// 10~9, per unit length, = V2 Try? 7^2 10-9; and the reactivity, or specific reactance at the center of the con- A J^ ductor, becomes k = —r- = \\/2 w^fR^ 10~^. Let p = resistivity, or specific resistance, of the material of the conductor. We have then, ^ _ V2ir^fRnO-\\ P P and P the ratio of current densities at center and at per ...", "... ect on the primary circuit be con- sidered analogously as in the chapter on eddy currents by the introduction of a power component, representing the loss of power, and a wattless component, representing the decrease of self-induction. Let X = 2 7r/L = reactance of main circuit; that is, L = total num- ber of interlinkages with the main conductor, of the lines of magnetic force produced by unit current in that conductor; Xi — 2 tt/Li = reactance of secondary circuit; that is, Li = total number of interlinkages w ...", "... , representing the decrease of self-induction. Let X = 2 7r/L = reactance of main circuit; that is, L = total num- ber of interlinkages with the main conductor, of the lines of magnetic force produced by unit current in that conductor; Xi — 2 tt/Li = reactance of secondary circuit; that is, Li = total number of interlinkages with the secondary conductor, of the lines of magnetic force produced by unit current in that con- ductor; Xm = 2x/Li = mutual inductive reactance of the circuits; that is, L„i = total nu ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 3230-3545", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-06/", "snippets": [ "... ., E^, passes through a circuit, the counter E.M.F. of resistance, r, is E^ = /r, in opposition to /^ or E^^ 135] TOPOGRAPHIC METHOD. 47 and hence represented in the diagram by point £\",, and its combination with E^ by E(. The counter E,M.F. of reactance, x, is E^ = Ix, 90' behind the current /j, or E.M.F., E^, and therefore represented by point E^, and giving, by its combination with E^, the terminal potential of the generator E^, which, as seen, is less than the E.M.F., £■,. If all the three branches ...", "... . 30, by the points E-^, E^, E^, equidistant from each other, and equidistant from the zero point, O), the counter E.M.Fs. of resistance, fr, are repre- sented by the distances EE', as EyE.^, etc., in phase with the currents, /; and the counter E.M.Fs. of reactance, /^, are represented by the distance, E'E\" in quadrature with the current, thereby giving, at the generator E.M.Fs., the points £\",\", Ej\", E^. Thus, the triangle of generator E.M.Fs. E^'E^E^, pro- •duces, with equal load on the three branches and non- ...", "... with E^E^ the angle «> — 20° ; that is, the current in E^ is 01^, and the current in E^ is Ot^ , the return current of 01^, Hence the potential at the first terminal is E^, as de- rived by combining with E{ the resistance E.M.F., E{E^^ in phase, and the reactance, E.M.F., E^E^, in quadrature, with the current; and in the same way, the E.M.F. at the 536] TOPOGRAPHIC METHOD. 49 second terminal is E^^ derived by the combination of E^ with E^E^ in phase, and E^E^ in quadrature, with the current. Hence the three ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "section_title": "Dibtbisnted Capacity, Inductance, Besistance, And", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "CHAPTER XII. DIBTBISnTED CAPACITY, INDUCTANCE, BESISTANCE, AND liEAKAGE. 102. As far as capacity has been considered in the foregoing chapters, the assumption has been made that the condenser or other source of negative reactance is shunted across the circuit at a definite point. In many cases, how- ever, the capacity is distributed over the whole length of the conductor, so that the circuit can be considered as shunted by an infinite number of infinitely small condensers infi. n ...", "... nat -^ where K = dielectric constant of the surrounding medium = 1 in air ;. / = length of conductor = 5 X 10* cm. ; d = distance of conductors from each other = 50 cm. ; 8 = diameter of conductor = 1 cm. Since C = .3 microfarads, the capacity reactance is 10« . 152 AL TERN A TING-CURRENT PHENOMENA, [$ 104 where N = frequency ; hence, at iV = 60 cycles, X = 8,900 ohms ; and the charging current of the line, at -£* = 20,000 volts, becomes, ^ to = — = 2.25 amperes. X The resistance of 100 km ...", "... his case, the condenser current thus amounts to less than 2\\ per cent., and hence can still be represented by the approximation of one condenser shunted across the line. If, however, the length of transmission is 150 km and the voltage 30,000, capacity reactance at 60 cycles, x = 2,970 ohms ; charging current, /'o = 10.1 amperes ; line resistance, r = (S^ ohms ; main current at 10 per cent loss, / = 45.5 amperes. The condenser current is thus about 22 per cent, of the main current. At 300 km length of tran ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-19", "section_label": "Chapter 19: Commutatob Motobs", "section_title": "Commutatob Motobs", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 21339-22387", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "snippets": [ "... g out of this position, is replaced by other secondary circuits entering this position of 45° displacement. For simplicity, in the following all the secondary quan- 296 AL TERN A TJNG-CURRENT PHENOMENA. [ § 196 titles, as E.M.F., current, resistance, reactance, etc., are assumed as reduced to the primary circuit by the ratio of turns, in the same way as done in the chapter on Induction Motors. 196. Let ^ = maximum magnetic flux per field pdle ; e = effective E.M.F. induced thereby in the field turns; thus ...", "... = /\" > 302 AL TEKA'A TING-CURRENT PHENOMENA, [§199 Armature magnetism : vi = -^ . Substituting these values, J' j^, ^ 2 irptl^NI , P ' E{ = * ; Thus the impressed E.M.F., ^^\"i^L^ + . + ..y+4^A'«(/^+'^;j; or, smce ^ = 2 w N^-^ = reactance of field ; //,^ OTi = 2 fl- A'' — ^ = reactance of armature ; and ^» - v/(i^?2' a \\Til P\"' ,'1^^'' =v/(^^+'-+^'Y+(-^+-') a ^« =v/(r^ f ^+'- +'■■)\"+ (^•+^-^- 1*200] COMMUTATOR MOTORS, 303 200. The power output at armature sha ...", "... [§199 Armature magnetism : vi = -^ . Substituting these values, J' j^, ^ 2 irptl^NI , P ' E{ = * ; Thus the impressed E.M.F., ^^\"i^L^ + . + ..y+4^A'«(/^+'^;j; or, smce ^ = 2 w N^-^ = reactance of field ; //,^ OTi = 2 fl- A'' — ^ = reactance of armature ; and ^» - v/(i^?2' a \\Til P\"' ,'1^^'' =v/(^^+'-+^'Y+(-^+-') a ^« =v/(r^ f ^+'- +'■■)\"+ (^•+^-^- 1*200] COMMUTATOR MOTORS, 303 200. The power output at armature shaft is, P^ EI ( ( - ^ ^ •'^ + '- + '■lY + (•* ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-20", "section_label": "Chapter 20: Commutator Motors", "section_title": "Commutator Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 19458-20501", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "snippets": [ "... ly the same, when moving out of this position, is replaced by other secondary circuits entering this position of 45° displacement. For simplicity, in the following all the secondary quan- COMMUTATOR MOTORS. 359 titles, as E.M.F., current, resistance, reactance, etc., are assumed as reduced to the primary circuit by the ratio of turns, in the same way as done in the chapter on Induction Motors. 217. Let $ = maximum magnetic flux per field pole ; e = effective E.M.F. induced thereby in the field turns ; thus ...", "... , produced by the armature reaction. COMMUTATOR MOTORS. 365 Armature magnetism : Wj/108 1 = \"V\"; Substituting these values, (R ptfNI E' = (R E1 = ^^niNI . Er = (r + rj) / Thus the impressed E.M.F., or, since i,2 x = 2 TT N^- = reactance of field ; (R 2-n-jV— = reactance of armature fti and / « • «, 366 AL TERNA TING-CURRENT PHENOMENA. 221. The power output at armature shaft is, J>= El \\ (R (R fi- *Ef 7T « 7V^ /2 n± N± x _j_ r _^_ The displacement of phase be ...", "... COMMUTATOR MOTORS. 365 Armature magnetism : Wj/108 1 = \"V\"; Substituting these values, (R ptfNI E' = (R E1 = ^^niNI . Er = (r + rj) / Thus the impressed E.M.F., or, since i,2 x = 2 TT N^- = reactance of field ; (R 2-n-jV— = reactance of armature fti and / « • «, 366 AL TERNA TING-CURRENT PHENOMENA. 221. The power output at armature shaft is, J>= El \\ (R (R fi- *Ef 7T « 7V^ /2 n± N± x _j_ r _^_ The displacement of phase between current and E.M.F. tan CD = ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-48", "section_label": "Chapter 8: Velocity Of Propagation Of Electric Field", "section_title": "Velocity Of Propagation Of Electric Field", "kind": "chapter", "sequence": 48, "number": 8, "location": "lines 26095-27002", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "snippets": [ "... 0, (14) the e.m.f. consumed by the magnetic field beyond distance I, or e.m.f. of inductance, contains a component in phase with the current, or power component, e, == 4 TT///O col al cos 0, (15) and a component in quadrature with the current, or reactive com- ponent, e2 = — 4 nfll0 sil a/ sin 0, (16) which latter leads the current by a quarter period. The reactive component e2 is a true self-induction, that is, rep- resents a surging of energy between the conductor and its electric field, but no ...", "... n phase with the current, or power component, e, == 4 TT///O col al cos 0, (15) and a component in quadrature with the current, or reactive com- ponent, e2 = — 4 nfll0 sil a/ sin 0, (16) which latter leads the current by a quarter period. The reactive component e2 is a true self-induction, that is, rep- resents a surging of energy between the conductor and its electric field, but no power consumption. The effective component elt however, represents a power consumption p = eti = 4 nfPl0 col al cos2# ...", "... (17) by the magnetic field of the conductor, due to its finite velocity; that is, it represents the power radiated into space by the conductor. The energy component et gives rise to an effective resistance, r = % = 4 ;r/70 col al, (18) ^ and the reactive component gives rise to a reactance, 4K/4 sil al, (19) 394 TRANSIENT PHENOMENA When considering the finite velocity of propagation of the electric field, self-inductance thus is not wattless, but contains an energy component, and so can be represente ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... nt to operating mechanism 131 machine 230 as rectifier 221 current control 220 properties 249 rectification 249 rectifiers 222 resistivities 9 starting 249 Arcing ground on lines and cables, as periodic transient phenomenon . . 23 Armature reactance, reaction and short-circuit current of alternator 199 Attenuation of alternating magnetic flux in iron 361 constants 434 of traveling wave, and loading 462 Booster, response to change of load 158 Brush arc machine 221, 230, 242, 248 Building up of ...", "... rent of condenser discharge 70 voltage and power of oscillating-current generator. . . 81 layer of alternating-current conductor 377 penetration of alternating current in conductor 376, 378 power of complex circuit 514 of cpndenser oscillation '70 reactance of armature reaction 200 561 INDEX PAGE Effective resistance of alternating-current distribution in conductor, 370, 376 voltage of condenser oscillation 70 Efficiency of condenser oscillation 72 Electric circuit, general equations 428 field, ve ...", "... eld, excitation 27 Multigap lightning arrester '. 348 Mutual impedance and velocity of propagation 399 inductance, equations 143 and velocity of propagation 397 inductive circuit with capacity 161 without capacity 144 of solid magnet poles 155 reactance : 143 Nominal generated e.m.f. and short-circuit current 200 Noninductive condenser circuit 54 shunt to inductive circuit 129 Nonoscillatory, see Gradual or Logarithmic. Open-circuit rectification 230 Opening of cable or transmission line under lo ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3721-4369", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-06/", "snippets": [ "... a circuit of distributed capacity, inductance, and resistance), Zq is high and 2/0 low. That is, a high transient voltage can produce only moderate transient currents, but even a small transient cur- rent produces high voltages. Thus reactances, and other reactive apparatus, as transformers, stop the passage of large oscillating currents, but do so by the production of high oscillating voltages. Inversely, if L is low and C high, as in an underground cable, Zq is low but yo high, and even moderate oscillating volt ...", "... a transformer, gives only very low DOUBLE-ENERGY TRANSIENTS. 63 oscillating voltages, that is, acts as a short circuit for the trans- former oscillation, and therefore protects the latter. Inversely, if the large oscillating current of a cable enters a reactive device, as a current transformer, it produces enormous voltages therein. Thus, cable oscillations are more liable to be destructive to the reactive apparatus, transformers, etc., connected with the cable, than to the cable itself. A transmission line is ...", "... llation, and therefore protects the latter. Inversely, if the large oscillating current of a cable enters a reactive device, as a current transformer, it produces enormous voltages therein. Thus, cable oscillations are more liable to be destructive to the reactive apparatus, transformers, etc., connected with the cable, than to the cable itself. A transmission line is intermediate in the values of Zq and t/o between the cable and the reactive apparatus, thus acting like a reactive apparatus to the former, like a c ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "... , but there is a surge of power, of double frequency. That is, power flows first one way, during one-quarter cycle, and then in the opposite direction, during the next quarter- cycle, etc. Such a transient wave thus is analogous to the permanent wave of reactive power. As in a stationary wave, current and voltage are in quadrature with each other, the question then arises, whether, and what 88 TRAVELING WAVES. 89 physical meaning a wave has, in which current and voltage are in phase with each other: ...", "... power transfer between the sections of the circuit.* A traveling wave, equation (4), would correspond to the case of effective power in a permanent alternating-current circuit, while the stationary wave of the uniform circuit corresponds to the case of reactive power. Since one of the most important applications of the traveling wave is the investigation of the compound circuit, it is desirable * In oscillogram Fig. 41, the current wave is shown reversed with regard to the voltage wave for greater clearness. ...", "... f the time angle 0, to the standard form given in \"Transient Phenomena,\" Section III. 36. Obviously, traveling waves and standing waves may occur simultaneously in the same circuit, and usually do so, just as in alternating-current circuits effective and reactive waves occur simultaneously. In an alternating-current circuit, that is, in permanent condition, the wave of effective power (current in phase with the voltage) and the wave of reactive power (current in quadrature with the voltage) are combined into a sin ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3287-3955", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "snippets": [ "... a circuit of distributed capacity, inductance, and resistance), z0 is high and T/O low. That is, a high transient voltage can produce only moderate transient currents, but even a small transient cur- rent produces high voltages. Thus reactances, and other reactive apparatus, as transformers, stop the passage of large oscillating currents, but do so by the production of high oscillating voltages. Inversely, if L is low and C high, as in an underground cable, ZQ is low but 2/0 high, and even moderate oscillating vol ...", "... a transformer, gives only very low DOUBLE-ENERGY TRANSIENTS. 63 oscillating voltages, that is, acts as a short circuit for the trans- former oscillation, and therefore protects the latter. Inversely, if the large oscillating current of a cable enters a reactive device, as a current transformer, it produces enormous voltages therein. Thus, cable oscillations are more liable to be destructive to the reactive apparatus, transformers, etc., connected with the cable, than to the cable itself. A transmission line is ...", "... llation, and therefore protects the latter. Inversely, if the large oscillating current of a cable enters a reactive device, as a current transformer, it produces enormous voltages therein. Thus, cable oscillations are more liable to be destructive to the reactive apparatus, transformers, etc., connected with the cable, than to the cable itself. A transmission line is intermediate in the values of z0 and yQ between the cable and the reactive apparatus, thus acting like a reactive apparatus to the former, like a ca ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 4745-5520", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "snippets": [ "... , but there is a surge of power, of double frequency. That is, power flows first one way, during one-quarter cycle, and then in the opposite direction, during the next quarter- cycle, etc. Such a transient wave thus is analogous to the permanent wave of reactive power. As in a stationary wave, current and voltage are in quadrature with each other, the question then arises, whether, and what TRAVELING WAVES. 89 physical meaning a wave has, in which current and voltage are in phase with each other: i = l ...", "... power transfer between the sections of the circuit.* A traveling wave, equation (4), would correspond to the case of effective power in a permanent alternating-current circuit, while the stationary wave of the uniform circuit corresponds to the case of reactive power. Since one of*the most important applications of the traveling wave is the investigation of the compound circuit, it is desirable * In oscillogram Fig. 41, the current wave is shown reversed with regard to the voltage wave for greater clearness. ...", "... the time angle , to the standard form given in \"Transient Phenomena,\" Section III. 36. Obviously, traveling waves and standing waves may occur simultaneously in the same circuit, and usually do so, just as in alternating-current circuits effective and reactive waves occur simultaneously. In an alternating-current circuit, that is, in permanent condition, the wave of effective power (current in phase with the voltage) and 'the wave of reactive power (current in quadrature with the voltage) are combined into a si ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-111", "section_label": "Apparatus Section 5: Induction Machines: Induction Booster", "section_title": "Induction Machines: Induction Booster", "kind": "apparatus-section", "sequence": 111, "number": 5, "location": "lines 21589-21646", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-111/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-111/", "snippets": [ "... nd definite slip s, either positive or negative, the induction machine acts like a constant impedance. 350 ELEMENTS OF ELECTRICAL ENGINEERING The apparent impedance and its components, the apparent resistance and apparent reactance represented by the induction machine, vary with the slip. At synchronism apparent impe- dance, resistance, and reactance are a maximum. They decrease with increasing positive slip. With increasing negative slip the apparent imp ...", "... OF ELECTRICAL ENGINEERING The apparent impedance and its components, the apparent resistance and apparent reactance represented by the induction machine, vary with the slip. At synchronism apparent impe- dance, resistance, and reactance are a maximum. They decrease with increasing positive slip. With increasing negative slip the apparent impedance and reactance decrease also, the apparent FIG. 191. — Effective impedance of three-phase induction machine. resis ...", "... by the induction machine, vary with the slip. At synchronism apparent impe- dance, resistance, and reactance are a maximum. They decrease with increasing positive slip. With increasing negative slip the apparent impedance and reactance decrease also, the apparent FIG. 191. — Effective impedance of three-phase induction machine. resistance decreases to zero and then increases again in negative direction as shown in Fig. 191, which gives the apparent impe- ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-20", "section_label": "Chapter 20: Single-Phase Induction Motors", "section_title": "Single-Phase Induction Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 21538-22301", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-20/", "snippets": [ "... ed, as by transformation. The impedances of these circuits are made different from each other as much as possible to produce a phase displacement between them. This can be done either by inserting external impedances in the circuits, as a condenser and a reactive coil, or by making the internal impedances of the motor circuits different, as by making one coil of high and the other of low resistance. 2. Inductive Devices. The different primary circuits of the motor are inductively related to each other in such a w ...", "... ature ' with the main e.m.f. and impressed upon the motor, either directly or after com- bination with the single-phase main e.m.f. Such wattless quadrature e.m.f. can be produced by the common connection of two impedances of different power-factor, as an inductive reactance and a resistance, or an inductive and a condensive reactance connected in series across the mains. The investigation of these starting-devices offers a very instructive application of the symbolic method of investiga- tion of alternating-current phenomen ...", "... ither directly or after com- bination with the single-phase main e.m.f. Such wattless quadrature e.m.f. can be produced by the common connection of two impedances of different power-factor, as an inductive reactance and a resistance, or an inductive and a condensive reactance connected in series across the mains. The investigation of these starting-devices offers a very instructive application of the symbolic method of investiga- tion of alternating-current phenomena, and a study thereof is thus recommended to the reader.^ ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... ide the conductor is Jo 10 Jo 10 10 From this we get, as the excess of counter E.M.F. at the axis of the conductor over that at the surface — A^== V2irA^*10-»= V2 TT A^/ 10 -•, per unit length, = V2ir^A^/(R«10-»; and the reactivity, or specific reactance at the center of the conductor, becomes ■ Let p = resistivity, or specific resistance, of the material of the conductor. We have then, b V2,r2iV/'nO-» ^■-^ \"~\" I, . • A P P ' and ^ Vk^ + p'' the percentage decrease of current density at ce ...", "... sly as in the chapter on eddy currents, by the introduction of an energy com- ■$971 FOUCAULT OR EDDY CURRENTS. 143 ponent, representing the loss of power, and a wattless •component, representing the decrease of self-inductance. Let — jr = 2 IT NL = reactance of main circuit ; that is, L = total number of interlinkages with the main conductor, of the lines of magnetic force produced by unit current in that conductor ; x^ = 2tc N L^ = reactance of secondary circuit ; that is, Z^ = total number of interlinkage ...", "... esenting the decrease of self-inductance. Let — jr = 2 IT NL = reactance of main circuit ; that is, L = total number of interlinkages with the main conductor, of the lines of magnetic force produced by unit current in that conductor ; x^ = 2tc N L^ = reactance of secondary circuit ; that is, Z^ = total number of interlinkages with the secondary conductor, of the lines of magnetic force produced by unit current in that conductor ; ;r„ = 2 IT N L^ = mutual inductance of circuits ; that is, L^ = total number of ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-110", "section_label": "Apparatus Section 4: Induction Machines: Induction Generator", "section_title": "Induction Machines: Induction Generator", "kind": "apparatus-section", "sequence": 110, "number": 4, "location": "lines 21158-21588", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-110/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-110/", "snippets": [ "... es with the load. In the calculation of these induction generator curves for con- INDUCTION MACHINES 343 slant speed the change of frequency with the load has obviously to be considered, that is, in the equations the reactance x0 has to be replaced by the reactance XQ (1 — s), otherwise the equa- tions remain the same. FIG. 187. — Induction generator load curves. 3. POWER-FACTOR OF INDUCTION GENERATOR 155. The induction generator differs 'esse ...", "... these induction generator curves for con- INDUCTION MACHINES 343 slant speed the change of frequency with the load has obviously to be considered, that is, in the equations the reactance x0 has to be replaced by the reactance XQ (1 — s), otherwise the equa- tions remain the same. FIG. 187. — Induction generator load curves. 3. POWER-FACTOR OF INDUCTION GENERATOR 155. The induction generator differs 'essentially from a syn- chronous alternator (t ...", "... ent and voltage in the external circuit must be such as required by the induction generator at that particular load. Induction generators can operate only on circuits with lead- ing current or circuits of negative effective reactance. 344 ELEMENTS OF ELECTRICAL ENGINEERING In Fig. 188 are given for the constant-speed induction gen- erator in Fig. 230 as function of the impedance of the external circuit z = -?• as abscissas (where eQ = terminal ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-23", "section_label": "Apparatus Section 2: Synchronous Machines: Electromotive Forces", "section_title": "Synchronous Machines: Electromotive Forces", "kind": "apparatus-section", "sequence": 23, "number": 2, "location": "lines 8658-8740", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-23/", "snippets": [ "... inductance, have no real and independent existence, but are merely fictitious components of the real or resultant generated e.m.f. EI. The virtual generated e.m.f. is Ei = Et + jlx, where x is the self -inductive armature reactance, and the e.m.f consumed by self-inductance Ix is to be combined with the real generated e.m.f. EI in the proper phase relation. 7. The nominal generated e.m.f. EQ is the e.m.f. which would be generated by the field exci ...", "... fictitious quantity, which, however, is very useful for the investigation of alternators by allowing the combination of armature reaction and self-inductance into a single effect by a (fictitious) self-inductance or synchronous reactance XQ. The nominal generated e.m.f. would be the terminal voltage with open circuit and load excitation if the saturation curve were a straight line. The synchronous reactance XQ is thus a quantity combining armature reaction ...", "... ct by a (fictitious) self-inductance or synchronous reactance XQ. The nominal generated e.m.f. would be the terminal voltage with open circuit and load excitation if the saturation curve were a straight line. The synchronous reactance XQ is thus a quantity combining armature reaction and self-inductance of the alternator. It is the only quantity which can easily be determined by experiment by running the alternator on short circuit with excited field. If ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-37", "section_label": "Apparatus Section 16: Synchronous Machines: Higher Frequency Cross Currents Between Synchronous Machines", "section_title": "Synchronous Machines: Higher Frequency Cross Currents Between Synchronous Machines", "kind": "apparatus-section", "sequence": 37, "number": 16, "location": "lines 10124-10189", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-37/", "snippets": [ "... e system to which they are connected. The intensity of these cross currents is the difference of the corresponding harmonics of the machines divided by the impe- dance between the machines. This impedance includes the self- inductive reactance of the machine armatures. The reactance obviously is that at the frequency of the harmonic, that is, if x = reactance at fundamental frequency, it is nx for the nth harmonic. In most cases these cross currents are very ...", "... ity of these cross currents is the difference of the corresponding harmonics of the machines divided by the impe- dance between the machines. This impedance includes the self- inductive reactance of the machine armatures. The reactance obviously is that at the frequency of the harmonic, that is, if x = reactance at fundamental frequency, it is nx for the nth harmonic. In most cases these cross currents are very small and negli- gible. With machines of ...", "... the machines divided by the impe- dance between the machines. This impedance includes the self- inductive reactance of the machine armatures. The reactance obviously is that at the frequency of the harmonic, that is, if x = reactance at fundamental frequency, it is nx for the nth harmonic. In most cases these cross currents are very small and negli- gible. With machines of distributed armature winding, the in- tensity of the harmonic is low, that is, ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-02", "section_label": "Chapter 2: Electric Conduction. Gas And Vapor", "section_title": "Electric Conduction. Gas And Vapor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3895-5444", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-02/", "snippets": [ "... nescence accompanies the con- duction, that is, conversion of electric energy into light. Thus, gas and vapor conductors are unstable on constant- potential supply, but stable on constant current. On constant potential they require a series resistance or reactance, to produce stability. Such conduction may be divided into three distinct types: spark conduction, arc conduction, and true electronic conduction. In spark conduction, the gas or vapor which fills the space be- tween the electrodes is the conductor. Th ...", "... t — spark con- duction is produced at atmospheric pressure by capacity in series to the gaseous conductor, on an alternating-voltage supply, as corona, and as Geissler tube conduction at a partial vacuum, by an alternating-supply voltage with considerable reactance or resistance in series, or from a direct-current source of very high voltage and very Umited current, as an electrostatic machine. In the Geissler tube or vacuum tube, on alternating-voltage supply, the effective voltage consumed by the tube, at constan ...", "... temperature and constant gas pressure, is approximately con- stant and independent of the effective current, that is, the volt- ampere characteristic a straight horizontal line. The Geissler tube thus requires constant current or a steadying resistance or reactance for its operation. The voltage consumed by the Geiss- ler tube consists of a potential drop at the terminals, the \"termi- nal drop, \" and a voltage consumed in the luminous stream, the *' stream voltage.'* Both greatly depend on the gas pressure, and vary ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-26", "section_label": "Chapter 4: Inductance And Resistance In Alternating Current Circuits", "section_title": "Inductance And Resistance In Alternating Current Circuits", "kind": "chapter", "sequence": 26, "number": 4, "location": "lines 3515-4071", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-26/", "snippets": [ "CHAPTER IV. INDUCTANCE AND RESISTANCE IN ALTERNATING- CURRENT CIRCUITS. • 26. In alternating-current circuits, the inductance L, or, as it is usually employed, the reactance x = 2 nfL, where / = fre- quency, enters the expression of the transient as well as the permanent term. At the moment 0 = 0, let the e.m.f. e = E cos (0 — 00) be impressed upon a circuit of resistance r and inductance L, thus inductive reactance x = 2 x ...", "... lly employed, the reactance x = 2 nfL, where / = fre- quency, enters the expression of the transient as well as the permanent term. At the moment 0 = 0, let the e.m.f. e = E cos (0 — 00) be impressed upon a circuit of resistance r and inductance L, thus inductive reactance x = 2 xfL; let the time 6 = 2 xft be counted from the moment of closing the circuit, and 00 be the phase of the impressed e.m.f. at this moment. In this case the e.m.f. consumed by the resistance = ir, where i = instantaneous value of current. The e.m. ...", "... ^)-cos (00 + 0,)- e* . (10) 27. The equation of current (9) contains a permanent term E — cos (0 — 00 — dj, which usually is the only term considered, E -~e and a transient term — e x cos (00 + 0t). z The greater the resistance r and smaller the reactance x, the more rapidly the term :- e ;c cos (00 -f 0t) disappears. This transient term is a maximum if the circuit is closed at the moment 00 = — 6V that is, at the moment when the E permanent value of current, — cos (0 — 00 — 0t), should be a maximum ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-27", "section_label": "Chapter 5: Resistance, Inductance, And Capacity In Series Condenser Charge And Discharge", "section_title": "Resistance, Inductance, And Capacity In Series Condenser Charge And Discharge", "kind": "chapter", "sequence": 27, "number": 5, "location": "lines 4072-5311", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "snippets": [ "... (48) (50) 42. If the resistance r can be neglected, that is, if r2 is small compared with — , the following equations are approximately exact: and r _ __ _ _ J ' 2 n VW (54) (55) 64 TRANSIENT PHENOMENA Introducing now x = 2 TT/L = inductive reactance and x' = ^- = capacity reactance, and substituting (55), we 2 TT/ C have and 0 hence, xf = x, that is, the frequency of oscillation of a circuit containing inductance and capacity, but negligible resistance, is that frequency / which makes t ...", "... be neglected, that is, if r2 is small compared with — , the following equations are approximately exact: and r _ __ _ _ J ' 2 n VW (54) (55) 64 TRANSIENT PHENOMENA Introducing now x = 2 TT/L = inductive reactance and x' = ^- = capacity reactance, and substituting (55), we 2 TT/ C have and 0 hence, xf = x, that is, the frequency of oscillation of a circuit containing inductance and capacity, but negligible resistance, is that frequency / which makes the condensive reactance xf = — — — ...", "... d x' = ^- = capacity reactance, and substituting (55), we 2 TT/ C have and 0 hence, xf = x, that is, the frequency of oscillation of a circuit containing inductance and capacity, but negligible resistance, is that frequency / which makes the condensive reactance xf = — — — 2 7T/C equal the inductive reactance x = 2 nfL : (56) Then (54), q = 2x, (57) and the general equations (52) and (53) are i = s 2ar ] i0cos^ + - - sin/9 [ ; (58) 4 ic -e0) cos 0 + r g~c*~2a\"Bin 0 1 • (59) ^ x x- (56) and ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-33", "section_label": "Chapter 40: General System Of Circuits", "section_title": "General System Of Circuits", "kind": "chapter", "sequence": 33, "number": 40, "location": "lines 12217-12884", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-33/", "snippets": [ "... t the transient term. 96. As an example of the application of this method may be considered the following case, sketched diagrammatically in Fig. 42: An alternator of e.m.f. E cos (6 - 00) feeds over resistance rl the primary of a transformer of mutual reactance xm. The secondary of this transformer feeds over resistances r2 and rs the primary of a second transformer of mutual reactance xmo, and the secondary of this second transformer is closed by resist- ance r4. Across the circuit between the two transformers ...", "... ammatically in Fig. 42: An alternator of e.m.f. E cos (6 - 00) feeds over resistance rl the primary of a transformer of mutual reactance xm. The secondary of this transformer feeds over resistances r2 and rs the primary of a second transformer of mutual reactance xmo, and the secondary of this second transformer is closed by resist- ance r4. Across the circuit between the two transformers and the two resistances r2 and r3, is connected a continuous-current 172 TRANSIENT PHENOMENA e.m.f., e0, as a battery, ...", "... ondary of this second transformer is closed by resist- ance r4. Across the circuit between the two transformers and the two resistances r2 and r3, is connected a continuous-current 172 TRANSIENT PHENOMENA e.m.f., e0, as a battery, in series with an inductive reactance x. The transformers obviously must be such as not to be saturated magnetically by the component of continuous current which traverses them, must for instance be open core transformers. Fig. 42. Alternating-current circuit containing mutual and self-indu ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-43", "section_label": "Chapter 3: The Natural Period Of The Transmission Line", "section_title": "The Natural Period Of The Transmission Line", "kind": "chapter", "sequence": 43, "number": 3, "location": "lines 21721-23178", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "snippets": [ "... a transmission line, a sufficiently close approximation is 320 NATURAL PERIOD OF TRANSMISSION LINE 321 obtained by neglecting the resistance of the line, which, at the relatively high frequency of oscillating discharges, is small com- pared with the reactance. This assumption means that the dying out of the discharge current through the influence of the resistance of the circuit is neglected, and the current assumed as an alternating current of approximately the same frequency and the same intensity as the ini ...", "... sity as the initial waves of the oscillating discharge current. By this means the problem is essentially simplified. 28. Let 10 = total length of a transmission line; I = the dis- tance from the beginning of the line; r = resistance per unit length; x = reactance per unit length = 2 nfL, where L = inductance per unit length; g = conductance from line to return (leakage and discharge into the air) per unit length; b = capacity susceptance per unit length = 2 nfC, where C = capacity per unit length. Neglecting the ...", "... it has no end but is closed upon itself. (4) The current is in quadrature with the voltage. This case does not represent a free oscillation, since the frequency depends also on the connected circuit, but rather represents a line supply- ing a wattless or reactive load. In free oscillation the circuit thus must be either open or grounded at its ends or closed upon itself. (1) Circuit open at one end, grounded at other end. 29. Assuming the circuit grounded at I = 0, open at / = Z0, we have for I = 0, # = #o = ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-47", "section_label": "Chapter 7: Distribution Of Alternating-Current Density In Conductor", "section_title": "Distribution Of Alternating-Current Density In Conductor", "kind": "chapter", "sequence": 47, "number": 7, "location": "lines 24981-26094", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "snippets": [ "... it length in the conductor after subtracting the e.m.f. consumed by the self- inductance of the external magnetic field of the conductor; thus, if El = the total supply voltage per unit length of conductor 372 TRANSIENT PHENOMENA and E2 = the external reactance voltage, or voltage consumed by the magnetic field outside of the conductor, between the con- ductors, we have Let 7=^4- ji2 = current density in conductor element dl, & = ^ + y&2 = magnetic density in conductor element dl, E = e.m.f. consumed in the ...", "... onductors gives for ml and m2 the values 63. As the result of the unequal current distribution in the conductor, the effective resistance is increased from the ohmic resistance R to the value R = R0mv R = cl0R0, and in addition thereto an effective reactance X = RQm2, or X = d0R0, is produced in the conductor. In the extreme case, where the current does not penetrate much below the surface of the conductor, the effective resistance and the effective reactance of the conductor are equal and are wher ...", "... R0, and in addition thereto an effective reactance X = RQm2, or X = d0R0, is produced in the conductor. In the extreme case, where the current does not penetrate much below the surface of the conductor, the effective resistance and the effective reactance of the conductor are equal and are where Rn is the ohmic resistance of the conductor. DISTRIBUTION OF ALTERNATING CURRENT 377 It follows herefrom that only -r of the conductor section is clQ effective; that is, the depth of the effective layer is ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 6125-6803", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-09/", "snippets": [ "... the greater is the difference between the currents and voltages of the two sections; that is, the more of current and voltage are reflected, the less transmitted, and if the change of constants is very great, as when entering from a trans- mission line a reactance of very low capacity, almost all the current is reflected, and very little passes into and through the reactance, but a high voltage is produced in the reactance.", "... t and voltage are reflected, the less transmitted, and if the change of constants is very great, as when entering from a trans- mission line a reactance of very low capacity, almost all the current is reflected, and very little passes into and through the reactance, but a high voltage is produced in the reactance.", "... , and if the change of constants is very great, as when entering from a trans- mission line a reactance of very low capacity, almost all the current is reflected, and very little passes into and through the reactance, but a high voltage is produced in the reactance." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 5521-6088", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "snippets": [ "... the greater is the difference between the currents and voltages of the two sections; that is, the more of current and voltage are reflected, the less transmitted, and if the change of constants is very great, as when entering from a trans- mission line a reactance of very low capacity, almost all the current is reflected, and very little passes into and through the reactance, but a high voltage is produced in the reactance. v/", "... t and voltage are reflected, the less transmitted, and if the change of constants is very great, as when entering from a trans- mission line a reactance of very low capacity, almost all the current is reflected, and very little passes into and through the reactance, but a high voltage is produced in the reactance. v/", "... , and if the change of constants is very great, as when entering from a trans- mission line a reactance of very low capacity, almost all the current is reflected, and very little passes into and through the reactance, but a high voltage is produced in the reactance. v/" ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "... k to the Geissler tube glow. In this experi- ment, a small condenser, a Leyden jar, is shunted across the high- potential terminals of the transformer, to guard against the disruptive conduction changing to continuous conduction, that is, to an arc, and a reactance inserted into the low-tension pri- mary of the step-up transformer, to limit the discharge current, as shown diagrammatically in Fig. 31. If the Geissler tube has a considerable diameter, 3 to 5 cm., the Geissler discharge with alternating current is str ...", "... LUMINESCENCE. 107 gas which fills the space between the terminals is mercury vapor. 1 now connect, as shown diagrammatically in Fig. 34, terminals 2 and 3 to the high potential coil of a step-up transformer — the low potential circuit contains a reactance to limit the current - and you see the striated Geissler discharge through mercury FIG. 33. vapor appear between terminals 2 and 3, giving the green light> of the mercury spectrum. The terminals are quiet, as they do not participate in the conduction. ...", "... age as a direct-current arc. Even materials like titanium carbide, in which the starting voltage is not much above the running voltage, maintain a steady alter- nating arc, as in starting, the voltage consumed during running in the steadying resistance or reactance is available. Alternating arcs thus can be maintained at moderate volt- ages only by a few materials of extremely high boiling points, as carbon and carbides, but by far the largest number of materials cannot be used as terminals of an alternating-curren ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-105", "section_label": "Apparatus Section 8: Alternating-current Transformer: Autotransformer", "section_title": "Alternating-current Transformer: Autotransformer", "kind": "apparatus-section", "sequence": 105, "number": 8, "location": "lines 18666-18812", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-105/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-105/", "snippets": [ "... transformer of (ei — e^) X i\\ primary, and ez X (i* — ii) secondary circuit. The regulation of an autotransformer is better, and the effi- ciency higher, than that of the same structure as transformer, and the per cent, reactance lower, that is the short-circuit current higher in the autotransformer than in the same structure as transformer. Very often it is difficult to build autotransformers with sufficiently high internal reactance, to make them sa ...", "... nd the per cent, reactance lower, that is the short-circuit current higher in the autotransformer than in the same structure as transformer. Very often it is difficult to build autotransformers with sufficiently high internal reactance, to make them safe under momentary short circuit as autotransformers, while they may be . perfectly safe as transformers, where the reactance is higher. This is a serious objection to the use of autotransformers in high-powe ...", "... Very often it is difficult to build autotransformers with sufficiently high internal reactance, to make them safe under momentary short circuit as autotransformers, while they may be . perfectly safe as transformers, where the reactance is higher. This is a serious objection to the use of autotransformers in high-power systems." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-108", "section_label": "Apparatus Section 2: Induction Machines: Polyphase Induction Motor", "section_title": "Induction Machines: Polyphase Induction Motor", "kind": "apparatus-section", "sequence": 108, "number": 2, "location": "lines 19166-20427", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-108/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-108/", "snippets": [ "... l standstill of the motor. We then have 1 — s = speed of the motor secondary as fraction of syn- chronous speed, sf = frequency of the secondary currents, where / = frequency impressed upon the primary; 1 The self -inductive reactance refers to that flux which surrounds one of the electric circuits only, without being interlinked with the other circuits. 312 ELEMENTS OF ELECTRICAL ENGINEERING hence, . se = e.m.f. generated in the secondary. The a ...", "... = 5 ohms additional resistance. The best values of torque efficiency are found beyond the maximum torque point. The same Fig. 180 also shows the torque with resistance in- serted into the primary circuit. The insertion of reactance, either in the primary or in the secondary, is just as unsatisfactory as the insertion of resistance in the primary circuit. 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 FIG. 180. — Inductio ...", "... ction motor starting torque with resistance secondary. in the Capacity inserted in the secondary very greatly increases the torque within the narrow range of capacity corresponding to resonance with the internal reactance of the motor, and the torque which can be produced in this way is far in excess of the maximum torque of the motor when running or when starting with resistance in the secondary. 326 ELEMENTS OF ELECTRICAL ENGINEERI ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-15", "section_label": "Theory Section 15: Load Characteristic of Transmission Line", "section_title": "Load Characteristic of Transmission Line", "kind": "theory-section", "sequence": 15, "number": 15, "location": "lines 5832-6221", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-15/", "snippets": [ "... ristic of a transmission line is the curve of volts and watts at the receiving end of the line as function of the amperes, and at constant e.m.f . impressed upon the generator end of the line. Let r = resistance, x = reactance of the line. Its impedance z = -y/r2 + x2 can be denoted symbolically by Z = r + jx. Let EQ = e.m.f. impressed upon the line. Choosing the e.m.f. at the end of the line as horizontal com- ponent in the vector diag ...", "... jx, (10) or, zo = V(r + z)2 + z2. (11) Thus the current is *o V(r + z)2 + x2 and the power transmitted is Eo2z (r that is, the maximum power which can be transmitted over a line of resistance r and reactance x is the square of the impressed e.m.f. divided by twice the sum of resistance and impedance of the line. At x = 0, this gives the common formula, Inductive Load 72. With an inductive receiving circuit of lag angle ...", "... a transmission line of impedance Z = r + jx = 20 + 50 j. How do the voltage \\ \\ \\ V son mo VOLTS 11000 9000 7000 4000 20 40 60 80 100 120 140 160 .180 200 220 FIG. 39. — Non-reactive load characteristic^ of a transmission line. Con- stant impressed e.m.f. and the output in the receiving circuit vary with the current with non-inductive load? Let e = voltage at the receiving end of the line, i = cur ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-25", "section_label": "Apparatus Section 4: Synchronous Machines: Self-inductance", "section_title": "Synchronous Machines: Self-inductance", "kind": "apparatus-section", "sequence": 25, "number": 4, "location": "lines 8907-9034", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-25/", "snippets": [ "... npon the e.m.f. of an alternating-current generator. Let E — terminal voltage per machine circuit, 7 = current per machine circuit, and 0 = lag of the current behind the terminal voltage. Let r = resistance, x = reactance of the alternator armature. FIG. 51. — Diagram showing combined effect of armature reaction and arma- ture self-inductance. Then, in the vector diagram, Fig. 51, OE = E, the terminal voltage, assumed as zero vector. 01 = ...", "... r diagram, Fig. 51, OE = E, the terminal voltage, assumed as zero vector. 01 = I, the current, lagging by the angle EOI = 0. _The e.m.f. consumed by resistance is OE \\ = Ir in phase with 01. The e-m-i^ consumed by reactance is OEfz — Ix, 90 degrees ahead of 01. The real generated e.m.f. is found by combining OE and OE\\ to SYNCHRONOUS MACHINES 135 The virtual generated e.m.f. is OEi and OE'Z combined to = E2. The m.m.f. required ...", "... S MACHINES 135 The virtual generated e.m.f. is OEi and OE'Z combined to = E2. The m.m.f. required to produce -this e.m.f. Ez is OF = F, Fa I E, FIG. 52. — Diagram of generator e.m.fs. and m.m.fs. for non-reactive load. 90 deg. ahead of OE2. It is the resultant of the armature m.m.f. or armature reaction and of the impressed m.m.f. or field excita- tion. The armature m.m.f. is in phase with the cur- rent 7, and is nl in a s ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-28", "section_label": "Apparatus Section 7: Synchronous Machines: Synchronous Motor", "section_title": "Synchronous Machines: Synchronous Motor", "kind": "apparatus-section", "sequence": 28, "number": 7, "location": "lines 9292-9398", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-28/", "snippets": [ "... al voltage depends upon the field excitation and the load. Thus, if E = terminal voltage or impressed e.m.f., I = current, 6 = lag of current behind impressed e.m.f. in a synchronous motor of resistance r and synchronous reactance XQ, the polar diagram is as follows, Fig. 62. OE = E is the terminal voltage assumed as zero vector. The current 01 = I lags by the angle EOI = 6. The e.m.f. consumed by resistance isj9#'i = Ir. The e.m.f. consumed ...", "... diagram is as follows, Fig. 62. OE = E is the terminal voltage assumed as zero vector. The current 01 = I lags by the angle EOI = 6. The e.m.f. consumed by resistance isj9#'i = Ir. The e.m.f. consumed by synchronous reactance, OE'o = IxQ. Thus, com- 142 ELEMENTS OF ELECTRICAL ENGINEERING bining OE'i and OE'o gives OE', the e.m.f. consumed by the synchronous impedance. The e.m.f. consumed by the synchro- nous impedance OE' and the e.m.f. co ...", "... current and wattless components in quadrature with the current i, we have: the terminal voltage, E = E cos 6 + jE sin 6 = Ep + jEq; the e.m.f. consumed by resistance, E/i = ir, and the e.m.f. consumed by synchronous reactance, E'Q = + jix0. Thus the e.m.f. consumed by the nominal counter-generated e.m.f. is Eo = E - E'i - E'Q = (E cos 0 - ir) + j (E sin 6 - ixQ) = (Ep - ir) + j(Eq - ixQ); SYNCHRONOUS MACHINES 143 or, in absolute ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-22", "section_label": "Chapter 20: Ri", "section_title": "Ri", "kind": "chapter", "sequence": 22, "number": 20, "location": "lines 24560-25119", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "snippets": [ "... potential difference across the different parts of the circuit are of the same shape as the impressed E.M.F\". If self- induction is inserted in series to a non-inductive circuit, the self-induction consumes more E.M.F. of the higher harmon- ics, since the reactance is proportional to the frequency, and thus the current and the E.M.F. in the non-inductive part of the circuit shows the higher harmonics in a reduced amplitude. That is, self-induction in series to a non-induc- tive circuit reduces the higher harmonics o ...", "... er shunted across the middle of the line. The E.M.F. at the generator terminals E is assumed as main- tained constant. The E.M.F. consumed by the resistance of the circuit from generator terminals to condenser is Ir = .06 £, or, r = .06 — . / The reactance E.M.F. between generator terminals and condenser is, for the fundamental frequency, /X = .15 £y or, X = .lo -— , thus the reactance corresponding to the frequency (2^ — 1) A^of the higher harmonic is : .r (2>t- 1) = .15(2^- 1) ^. The capacity curr ...", "... med by the resistance of the circuit from generator terminals to condenser is Ir = .06 £, or, r = .06 — . / The reactance E.M.F. between generator terminals and condenser is, for the fundamental frequency, /X = .15 £y or, X = .lo -— , thus the reactance corresponding to the frequency (2^ — 1) A^of the higher harmonic is : .r (2>t- 1) = .15(2^- 1) ^. The capacity current at fundamental frequency is : i = .21, hence, at the frequency: (2^ — 1) A'': i=.2{2k-l)e'L, E if: e' = E.M.F. of the (2 ^ ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-23", "section_label": "Chapter 23: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 21983-22448", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "snippets": [ "... potential difference across the different parts of the circuit are of the same shape as the impressed E.M.F. If self- induction is inserted in series to a non-inductive circuit, the self-induction consumes more E.M.F. of the higher harmon- ics, since the reactance is proportional to the frequency, and thus the current and the E.M.F. in the non-inductive part of the circuit shows the higher harmonics in a reduced amplitude. That is, self-induction in series to a non-induc- tive circuit reduces the higher harmonics o ...", "... denser shunted across the middle of the line. The E.M.F. at the generator terminals E is assumed as main- tained constant. The E.M.F. consumed by the resistance of the circuit from generator terminals to condenser is Ir = .06 £, or, r = .06 -| . The reactance E.M.F. between generator terminals and condenser is, for the fundamental frequency, Ix = .15 £, -IK E or, x = .15 — , thus the reactance corresponding to the frequency (2/£ — 1) N of the higher harmonic is : x(2k- 1) =.15(2£- 1) — . The capacity ...", "... by the resistance of the circuit from generator terminals to condenser is Ir = .06 £, or, r = .06 -| . The reactance E.M.F. between generator terminals and condenser is, for the fundamental frequency, Ix = .15 £, -IK E or, x = .15 — , thus the reactance corresponding to the frequency (2/£ — 1) N of the higher harmonic is : x(2k- 1) =.15(2£- 1) — . The capacity current at fundamental frequency is : hence, at the frequency : (2 k — 1) N: / = .2(2£-l)/Z, if: e' = E.M.F. of the (2 k — l)th harmonic a ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-05", "section_label": "Chapter 6: Induction-Motor Regulation And Stability", "section_title": "Induction-Motor Regulation And Stability", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 10583-12397", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-05/", "snippets": [ "... nduc- 123 124 ELECTRICAL APPARATUS tive impedance, Z, = 0.1 + 0.3 j; supply voltage, e0 = 110 volts, and rated output, 5000 waits per phase. Assuming this motor to be operated: 1. By transformers of about 2 per cent, resistance and 4 per cent, reactance voltage, that is, transformers of good regulation, with constant voltage at the transformer terminals. 2. By transformers of ahout 2 per cent, resistance and 15 per cent, reactance voltage, that is, very poorly regulating trans- formers, at constant supp ...", "... ted: 1. By transformers of about 2 per cent, resistance and 4 per cent, reactance voltage, that is, transformers of good regulation, with constant voltage at the transformer terminals. 2. By transformers of ahout 2 per cent, resistance and 15 per cent, reactance voltage, that is, very poorly regulating trans- formers, at constant supply voltage at the transformer primaries. 3. With constant voltage at the generator terminals, and about 8 per cent, resistance, 40 per cent, reactance voltage in line and transforme ...", "... t, resistance and 15 per cent, reactance voltage, that is, very poorly regulating trans- formers, at constant supply voltage at the transformer primaries. 3. With constant voltage at the generator terminals, and about 8 per cent, resistance, 40 per cent, reactance voltage in line and transformers between generator and motor. This gives, in complex quantities, the impedance between the motor terminals and the constant voltage supply: 1. Z - 0.04 + 0.08 j, 2. Z = 0.04 + 0.3 j\", 3. Z = 0.16 + 0.8,/. It is assu ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-44", "section_label": "Chapter 4: Distributed Capacity Of High-Potential Transformers", "section_title": "Distributed Capacity Of High-Potential Transformers", "kind": "chapter", "sequence": 44, "number": 4, "location": "lines 23179-23585", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "snippets": [ "... er of turns, a great length of conductor, and therefore its electrostatic capacity is appreciable, and such a coil thus represents a circuit of distributed resistance, inductance, and capacity somewhat similar to a transmission line. The same applies to reactive coils, etc., wound for very high voltages, and even in smaller reactive coils at very high frequency. This capacity effect is more marked in smaller transformers, where the size of the iron core and therewith the voltage per turn is less, and therefore t ...", "... c capacity is appreciable, and such a coil thus represents a circuit of distributed resistance, inductance, and capacity somewhat similar to a transmission line. The same applies to reactive coils, etc., wound for very high voltages, and even in smaller reactive coils at very high frequency. This capacity effect is more marked in smaller transformers, where the size of the iron core and therewith the voltage per turn is less, and therefore the number of turns greater than in very large transformers, and at the s ...", "... erefore the number of turns greater than in very large transformers, and at the same time the exciting cur- rent and the full-load current are less; that is, the charging current of the conductor more comparable with the load current of the transformer or reactive coil. However, even in large transformers and at moderately high voltages, capacity effects occur in transformers, if the frequency is sufficiently high, as is the case with the currents produced in overhead lines by lightning discharges, or by arcing gr ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-50", "section_label": "Chapter 1: General Equations", "section_title": "General Equations", "kind": "chapter", "sequence": 50, "number": 1, "location": "lines 27761-28694", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "snippets": [ "... inductance, representing the energy storage i2L depending upon the current, - — , as electromagnetic component & of the electric field; or the voltage generated due to the change of the current, L — , that is, with an alternating current, the at reactive voltage consumed in the circuit - jxi, where x = 2 nfL and / = frequency. g = effective (shunted) conductance, representing the power or rate of energy consumption depending upon the voltage, e*g; or the power component of the current consumed in the cir ...", "... ive capacity, representing the energy storage e*C depending upon the voltage, — , as electrostatic component of the electric field; or the current consumed by a change of the de voltage, C — , that is, with an alternating voltage, the (leading) dt reactive current consumed in the circuit - jbe, where 6 = 2 and / = frequency. 417 418 TRANSIENT PHENOMENA In the investigation of electric circuits, these four constants, r, L, g, C, usually are assumed as located separately from each other, or localized. A ...", "... where another circuit joins the circuit in question, the integration con- stants in the equations also change correspondingly. Special cases of these general equations then are all the phe- nomena of direct currents, alternating currents, discharges of reactive coils, high-frequency oscillations, etc., and the difference between these different circuits is due merely to different values of the integration constants. 2. In a circuit or a section of a circuit containing distributed resistance, inductance, conduct ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-02", "section_label": "Chapter 2: Potential Series And Exponential Function", "section_title": "Potential Series And Exponential Function", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3492-6063", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-02/", "snippets": [ "... ion. Very convenient for development into an infinite series of powers or roots, is the binomial theorem, (14) X * n(n-l) _ n(n-l)(n-2) ^ If II 4 where |w«-lX2x3X. . .Xm. Thus, for instance, in an alternating-current circuit of resistance r, reactance x, and supply voltage e, the curi-ent is. ^■v^T7^ \"^) 60 ENGINEERING MATHEMATICS. If this circuit is practically non-inductive, as an incandescent lighting circuit; that is, if x is small compared with r, (15) can be written in the form, ._ e e ...", "... with r, (15) can be written in the form, ._ e e h©T', . . . ae, and the square root can be developed by the binomial (14), thus, u= yyj ; n= --, and gives h(r)T*=-i(7)\"-s(r)'-f.(\")'-- <■:) In this series (17), if x = 0.1r or less; that is, the reactance is not more than 10 per cent of the resistance, the third term, Q ( - ) , is less than 0.01 per cent; hence, negligible, and the series is approximated with sufficient exactness by the fii-st two terms, and equation (16) of the current then gives -t ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-21", "section_label": "Apparatus Introduction 21: Introduction", "section_title": "Introduction", "kind": "apparatus-introduction", "sequence": 21, "number": null, "location": "lines 8292-8517", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-21/", "snippets": [ "... the mutual in- ductance between primary and secondary circuit, either elec- trically or magnetically. The stationary induction apparatus with one electric circuit are used for producing wattless lagging currents, as reactors, reactive or choke coils. (6) Condensers and polarization cells produce wattless leading currents, the latter, however, usually at a low efficiency, while the efficiency of the condenser is extremely high, frequently above 99 per ce ...", "... t, and a discussion of the numerous less common types of apparatus, which could not be included in the following, is given in \"Theory and Calculation of Electrical Apparatus.\" Some important features, as the nature of the reactance of apparatus, mechanical magnetic forces, wave shape distortions caused by some features of design, in apparatus, etc., are dis- cussed in \"Theory and Calculation of Electric Circuits.\" A. SYNCHRONOUS MACHINES" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-29", "section_label": "Apparatus Section 8: Synchronous Machines: Characteristic Curves of Synchronous Motor", "section_title": "Synchronous Machines: Characteristic Curves of Synchronous Motor", "kind": "apparatus-section", "sequence": 29, "number": 8, "location": "lines 9399-9553", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-29/", "snippets": [ "... four-phase characteristics a certain field excitation gives 146 ELEMENTS OF ELECTRICAL ENGINEERING minimum current, a lesser excitation gives lagging current, a greater excitation leading current. The higher the synchronous reactance XQ, and thus the armature reaction of the synchronous motor, the flatter are the phase characteristics; that is, the less sensitive is the synchronous motor for a change of field excitation or of impressed e.m.f. Thus a r ...", "... ttless currents, that is, synchronous motors or generators running light, with over-excited or under-excited field, are called synchronous condensers. They are used as exciters for induc- tion generators, as compensators for the reactive lagging currents SYNCHRONOUS MACHINES 147 of induction motors, for voltage control of transmission lines, etc. Sometimes they are called \"rotary condensers\" or \"dynamic condensers\" when used only for producing lead- ing cu ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-83", "section_label": "Apparatus Section 4: Synchronous Converters: Armature Current and Heating", "section_title": "Synchronous Converters: Armature Current and Heating", "kind": "apparatus-section", "sequence": 83, "number": 4, "location": "lines 13889-15160", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-83/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-83/", "snippets": [ "... he effective value of the alternating power current in the armature winding, or ring current, corresponding thereto, is n sn - n Let pi' = total power current, 'allowing for the losses of power in the converter; qlf = reactive current in the converter, assumed as positive when lagging, as negative when leading, and si' = total current, where s = Vp2 + tf2 is the ratio of total current to the load current, that is, power current corresponding ...", "... 1. 65 3.17 oo -phase: -v — 'v ' — r Jm jm ~ •*• = 0 20 0.22 0 32 0.49 0. 82 1. 45 2.82 92. The values are shown graphically in Figs. 137 and 138, SYNCHRONOUS CONVERTERS 243 reactive current , . with tan 6 = - TT~ as abscissas, and 7 as ordinates energy current in Fig. 137, T as ordinates in Fig. 138. As seen, with increasing phase displacement, irrespectively whether lag or lead, the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-90", "section_label": "Apparatus Section 12: Synchronous Converters: Conclusion", "section_title": "Synchronous Converters: Conclusion", "kind": "apparatus-section", "sequence": 90, "number": 12, "location": "lines 15983-16064", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-90/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-90/", "snippets": [ "... much larger than standard converters, but are smaller than motor generator sets, as half the power is converted in either machine. One advantage of this type of machine for phase control is that it requires no additional reactive coils, as the induction machine affords sufficient reactance. The use of the converter to change from alternating to alter- nating of a different phase, as, for instance, when using a quarter- phase converter to receive pow ...", "... motor generator sets, as half the power is converted in either machine. One advantage of this type of machine for phase control is that it requires no additional reactive coils, as the induction machine affords sufficient reactance. The use of the converter to change from alternating to alter- nating of a different phase, as, for instance, when using a quarter- phase converter to receive power by one pair of its collector rings from a single-phase ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-95", "section_label": "Apparatus Section 1: Alternating-current Transformer: General", "section_title": "Alternating-current Transformer: General", "kind": "apparatus-section", "sequence": 95, "number": 1, "location": "lines 16804-16911", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-95/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-95/", "snippets": [ "... n2 This ratio is called the ratio of transformation. The ratio of transformation of a transformer is the ratio of turns of primary and secondary windings. In addition to the induced e.m.fs. e'i and e\\, resistance r and reactance x consume voltage in primary and secondary wind- ings. The voltage consumed by the resistance represents waste of power; the voltage consumed by reactance is wattless, but causes lag of current, that is, lowers the power fa ...", "... gs. In addition to the induced e.m.fs. e'i and e\\, resistance r and reactance x consume voltage in primary and secondary wind- ings. The voltage consumed by the resistance represents waste of power; the voltage consumed by reactance is wattless, but causes lag of current, that is, lowers the power factor; while the in- duced voltages give the power transfer from primary to sec- ondary. Efficiency therefore requires to make the former vol- tages as small ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-03", "section_label": "Chapter 3: Law Of Electromagnetic Induction", "section_title": "Law Of Electromagnetic Induction", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 2012-2148", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-03/", "snippets": [ "... mperes maximum, is therefore n$ = LIV2 108; 18 ALTERNATING-CURRENT PHENOMENA and consequently the effective e.m.f. of self-induction is E = V2 7rn$/10-8 = 2 wfLI volts. The product, x = 2 7r/L, is of the dimension of resistance, and is called the inductive reactance of the circuit; and the e.m.f. of self-induction of the circuit, or the reactance voltage, is E = Ix, and lags 90° behind the current, since the current is in phase with the magnetic flux produced by the current, and the e.m.f. lags 90° behind the magn ...", "... quently the effective e.m.f. of self-induction is E = V2 7rn$/10-8 = 2 wfLI volts. The product, x = 2 7r/L, is of the dimension of resistance, and is called the inductive reactance of the circuit; and the e.m.f. of self-induction of the circuit, or the reactance voltage, is E = Ix, and lags 90° behind the current, since the current is in phase with the magnetic flux produced by the current, and the e.m.f. lags 90° behind the magnetic flux. The e.m.f. lags 90° behind the magnetic flux, as it is proportional to ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 3267-3618", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-06/", "snippets": [ "... of impedance, Zi = ri -{- jxi, from a generator of internal impedance, Zo = ro + jxo. In phase OEi the voltage consumed by resistance ri is repre- sented by the distance, EiEi^ = Iri, in phase, that is, parallel with current OIi. The voltage consumed by reactance Xi is represented by Ei^Ei^^ = Ixi, 90° ahead of current OTu The same applies to the other two phases, and it thus follows that to produce the voltage triangle, E1E2E3, at the terminals of the consumer's circuit, the voltage triangle, Ei^^Ez^^Ea^^, is req ...", "... phase angle, 6. Considering again as in §3 the transmission line, element by element, we have in every element a voltage, EiEi^, consumed by the resistance in phase with the current. Oh, and proportional thereto, and a voltage, Ei^, iJi\", consumed by the reactance of the Hne element, 90° ahead of the current, Oh, and proportional thereto. In the same Hne element we have a current, hh^, in phase with the voltage, OEi, and proportional thereto, representing 44 ALTERNATING-CURRENT PHENOMENA the loss of curre ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-07", "section_label": "Chapter 7: Polar Coordinates And Polar Diagrams", "section_title": "Polar Coordinates And Polar Diagrams", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 3619-4087", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-07/", "snippets": [ "... INATES AND POLAR DIAGRAMS 49 Kirchhoff's laws now assume, for alternating sine waves, the form : (o) The resultant of all the e.m.fs. in a closed circuit, as found by the parallelogram of sine waves, is zero if the counter e.m.fs. of resistance and of reactance are included. (6) The resultant of all the currents toward a distributing point, as found by the parallelo- gram of sine waves, is zero. The power equation expressed graphically is as follows: The power of an alternating- current circuit is represe ...", "... sformed into it by reversing right and left, or top and bottom. So the crank diagram, Fig. 47, is the image of the polar diagram, Fig. 46. In symbolic representation, based upon the crank diagram, the impedance was denoted by Z = r -\\- jx, where x == inductive reactance. In the polar diagram, the impedance thus is denoted by: Z = r — jx since the latter is the mirror image of the crank diagram, that is, differs from it symbolically by the interchange of + j and — j. A treatise written in the symbolic repre- sentation ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-03", "section_label": "Chapter 3: Iiaw Of Eucctbo-Maonimc Induction", "section_title": "Iiaw Of Eucctbo-Maonimc Induction", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 1973-2121", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-03/", "snippets": [ "... flux, *, produced by a current of / amperes effective, or/V2 amperes maximum, is therefore — and consequently the effective E.M.F. of self-inductance is: = 2 IT NLI volts. The product, jr = 2 irNLy is of the dimension of resistance, and is called the reactance of the circuit ; and the E.M.F. of self-inductance of the circuit, or the reactance voltage, is E = Ix, and lags 90** behind the current, since the current is in phase with the magnetic flux produced by the current, and the E.M.F. lags 90° behind the m ...", "... erefore — and consequently the effective E.M.F. of self-inductance is: = 2 IT NLI volts. The product, jr = 2 irNLy is of the dimension of resistance, and is called the reactance of the circuit ; and the E.M.F. of self-inductance of the circuit, or the reactance voltage, is E = Ix, and lags 90** behind the current, since the current is in phase with the magnetic flux produced by the current, and the E.M.F. lags 90° behind the magnetic flux. The E.M.F. lags 90° behind the magnetic flux, as it is propor- tional ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-03", "section_label": "Chapter 3: Law Of Electro-Magnetic Induction", "section_title": "Law Of Electro-Magnetic Induction", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 1606-1742", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-03/", "snippets": [ "... rrent of / amperes effective, or / V2 amperes maximum, is therefore — n® =Z/V2 108; and consequently the effective E.M.F. of self-inductance is: E = V2 =' 2 TT NLI volts. The product, x = 2 vNL, is of the dimension of resistance, and is called the reactance of the circuit ; and the E.M.F. of self-inductance of the circuit, or the reactance voltage, is E = Ix, and lags 90° behind the current, since the current is in phase with the magnetic flux produced by the current, and the E.M.F. lags 90° behind the ma ...", "... ; and consequently the effective E.M.F. of self-inductance is: E = V2 =' 2 TT NLI volts. The product, x = 2 vNL, is of the dimension of resistance, and is called the reactance of the circuit ; and the E.M.F. of self-inductance of the circuit, or the reactance voltage, is E = Ix, and lags 90° behind the current, since the current is in phase with the magnetic flux produced by the current, and the E.M.F. lags 90° behind the magnetic flux. The E.M.F. lags 90° behind the magnetic flux, as it is propor- tional ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-12", "section_label": "Chapter 14: Phase Conversion And Single-Phase Generation", "section_title": "Phase Conversion And Single-Phase Generation", "kind": "chapter", "sequence": 12, "number": 14, "location": "lines 17125-18412", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-12/", "snippets": [ "... ocyclic generators built. These were .^iriulr-pluisi' alternating-eurrenl generators, having a small quadrature phase of high inductance, which combined with the main phase gives three-phase or quarter- phase voltages. The auxiliary phase was of such high reactance as to limit the quadra- < i < ti ■ poWCI and thus make the flow of energy essentially single- phase, that is, monocyclic. The purpose hereof was to permit the use of a small quadrature coil on the generator, and thereby to preserve the whole generator cap ...", "... gives the currents: eY0 (Yx - Yt) /o = -— z^rl Fi + F2 + 2 Fo f = ? (Z?7a_+ y*y* + 2YjY2) /l = /* = Y1 + Yi + 2Yo eYx (y, + r0) yi +\"y2 + 2 yV ey, (y! + y0) (8) y1 + y2 + 2 y0 129. For a combination of equal resistance and reactance : RESISTANCE-INDUCTANCE MONOCYCLIC SQUARE r- « -7.07 OHMS 0 - 100 VOLTS E 1, that is, when passing from ci a section of low inductance and high capacity into a section of high inductance and low capacity, as from a transmission line into a transformer or a reactive coil, the voltage of the wave is s* increased; if — < 1, that is, when passing from a section of high ci inductance and low capacity into a section of low inductance and high capacity, as from a transformer to a transmission line, the voltage of the ..." ] } ] }, { "id": "synchronism", "label": "Synchronism", "aliases": [ "Synchronism", "synchronising", "synchronism", "synchronizing", "synchronous" ], "total_occurrences": 2261, "matching_section_count": 163, "matching_source_count": 12, "source_totals": [ { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 732, "section_count": 21 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 408, "section_count": 55 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 300, "section_count": 21 }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 245, "section_count": 4 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 233, "section_count": 17 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 135, "section_count": 15 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 96, "section_count": 6 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 54, "section_count": 9 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 21, "section_count": 6 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 16, "section_count": 3 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 12, "section_count": 2 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 9, "section_count": 4 } ], "section_hits": [ { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 156, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "CHAPTER IV INDUCTION MOTOR WITH SECONDARY EXCITATION 38. While in the typical synchronous machine and eommu- tating machine the magnetic field is excited by a direct current, characteristic of the induction machine is, that the magnetic field is excited by an alternating current derived from the alter- nating supply voltage, just as in the alt ...", "... -.SJ Z,-.l+.3j -'I-. 1 — i- m v. / :> -350 J- > PS j / 1 i 1 1 i 1 I 0 1 0 1 0 1 Fio. 20. — Low-epecd induction motor, load c : the Elements of Electrical Engineering,\" 4th edition, difference. 39. In the synchronous machine usually the stator, in com- mutating machines the rotor is the armature, that is, the element to -which electrical power is supplied, and in which electrical power is converted into the mechanical power output of the motor. The rotor of the typica ...", "... achine usually the stator, in com- mutating machines the rotor is the armature, that is, the element to -which electrical power is supplied, and in which electrical power is converted into the mechanical power output of the motor. The rotor of the typical synchronous machine, and the stator of the com mutating machine are the held, that is, in them no electric power is consumed by conversion into mechanical work, but their purpose is to produce the magnetic field flux, through which the armature rotates. In the indu ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-appendix-01-synchronous-operation", "section_label": "Mathematical Appendix 5: Appendix: Synchronous Operation", "section_title": "Appendix: Synchronous Operation", "kind": "mathematical-appendix", "sequence": 5, "number": 5, "location": "PDF pages 27-68, lines 2165-5013", "status": "pdf-text-extracted-candidate", "occurrence_count": 127, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "snippets": [ "Appendix [[END_PDF_PAGE:27]] [[PDF_PAGE:28]] 22 Report of Charles P. Steinmetz APPENDIX Synchronous Operation A Consider the case of two alternators or groups of alternators such as station sections, which are running in synchronism with each other, that is, have the same frequency f, but are connected together while out of phase with each other by angle 2w ...", "Appendix [[END_PDF_PAGE:27]] [[PDF_PAGE:28]] 22 Report of Charles P. Steinmetz APPENDIX Synchronous Operation A Consider the case of two alternators or groups of alternators such as station sections, which are running in synchronism with each other, that is, have the same frequency f, but are connected together while out of phase with each other by angle 2w. That is, the one alternator has the voltage phase ( to), the other the voltage phase (0+w). We may assume the alternators as of ...", "... e connected together while out of phase with each other by angle 2w. That is, the one alternator has the voltage phase ( to), the other the voltage phase (0+w). We may assume the alternators as of equal voltage, since a voltage difference superposes on the synchronizing energy current due to the phase difference, a reactive magnetizing current due to the voltage difference without materially changing the energy relations. The EMFs of the two alternators then may be represented by: ei = E cos (0 co) 1 e2 = Ecos (0+co) / (1) a ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-11", "section_label": "Chapter 12: Frequency Converter Or General Alternating Current Transformer", "section_title": "Frequency Converter Or General Alternating Current Transformer", "kind": "chapter", "sequence": 11, "number": 12, "location": "lines 14897-17124", "status": "candidate", "occurrence_count": 101, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-11/", "snippets": [ "... primary n r thus, if: / = primary frequency, or frequency of impressed e.m.f., sf = secondary frequency; and the e.m.f. generated per secondary turn by the mutual flux has to the e.m.f. generated per primary turn the ratio, «, s = 0 represents synchronous motion of the secondary; s < 0 represents motion above synchronism — driven by external mechanical power, as will be seen; 8 = 1 represents standstill; s > 1 represents backward motion of the secondary, that is, motion against the mechanical force act ...", "... impressed e.m.f., sf = secondary frequency; and the e.m.f. generated per secondary turn by the mutual flux has to the e.m.f. generated per primary turn the ratio, «, s = 0 represents synchronous motion of the secondary; s < 0 represents motion above synchronism — driven by external mechanical power, as will be seen; 8 = 1 represents standstill; s > 1 represents backward motion of the secondary, that is, motion against the mechanical force acting between primary and secondary (thus representing driving by exte ...", "... r) + js (X! + x) 1 This applies to the case where the secondary contains inductive react- ance only; or, rather, that kind of reactance which is proportional to the frequency. In a condenser the reactance is inversely proportional to the frequency, in a synchronous motor under circumstances independent of the frequency. Thus, in general, we have to set, x = x' -f x\" + s'\", where x' is that part of the reactance which is proportional to the frequency, x\" that part of the reactance independent of the frequency, and x'\" ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-24", "section_label": "Chapter 24: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 25682-29374", "status": "candidate", "occurrence_count": 95, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-24/", "snippets": [ "CHAPTER XXIV SYNCHRONOUS MOTOR 212. In the chapter on synchronizing alternators we have seen that when an alternator running in synchronism is connected with a system of given voltage, the work done by the alternator can be either positive or negative. In the latter case the alt ...", "CHAPTER XXIV SYNCHRONOUS MOTOR 212. In the chapter on synchronizing alternators we have seen that when an alternator running in synchronism is connected with a system of given voltage, the work done by the alternator can be either positive or negative. In the latter case the alternator consumes electrical, and consequentl ...", "CHAPTER XXIV SYNCHRONOUS MOTOR 212. In the chapter on synchronizing alternators we have seen that when an alternator running in synchronism is connected with a system of given voltage, the work done by the alternator can be either positive or negative. In the latter case the alternator consumes electrical, and consequently produces mechanical, power; that is, runs as a synchronous motor, so t ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "section_label": "Chapter 16: Induction Motor", "section_title": "Induction Motor", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 94, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "... e frequency as the E.M.Fs. impressed upon the primary, but of a frequency which is the difference between the impressed frequency 238 ALTERNATING-CURRENT PHENOMENA. and the frequency of rotation, or equal to the \"slip,\" that is, the difference between synchronism and speed (in cycles). Hence, if N = frequency of main or primary E.M.F., and s = percentage slip ; sJV = frequency of armature or secondary E.M.F., and (1 — s) N= frequency of rotation of armature. In its reaction upon the primary circuit, however ...", "... the motor,\" or \" Counter E.M.F.\" Since the secondary frequency is s N, the secondary in- duced E.M.F. (reduced to primary system) is El = — se. Let I0 = exciting current, or current passing through the motor, per primary circuit, when doing no work (at synchronism), and K= g -j- j 'b = orimary admittance per circuit = — . We thus have, ge = magnetic energy current, ge* = loss of power oy hysteresis (and eddy currents) per primary coil. Hence = total loss of energy by hysteresis and eddys, as calculated ...", "... motor passes the maximum torque point st, it \" falls out of step,\" and comes to a standstill. Inversely, the torque of the motor, when starting from rest, will increase with increasing speed, until the maximum torque point is reached. From there towards synchronism the torque decreases again. In consequence hereof, the part of the torque-speed curve below the maximum torque point is in general un- stable, and can be observed only by loading the motor with an apparatus, whose countertorque increases with the speed ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-03-record", "section_label": "Report Record 4: Record of Four Troubles", "section_title": "Record of Four Troubles", "kind": "report-record", "sequence": 4, "number": 4, "location": "PDF pages 16-27, lines 1139-2164", "status": "pdf-text-extracted-candidate", "occurrence_count": 69, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-03-record/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-03-record/", "snippets": [ "... are no power limiting reactors between Fisk B and North- west Station, and the six tie cables between these stations are of very low resistance, the Northwest Station was just as seriously affected as Fisk B, and indeed acted like a part of Fisk B. b) All the synchronous machines on Fisk Street B, and on North- west Station dropped out, and many synchronous machines on Fisk A and Quarry Street: 44 synchronous machines on Fisk B and 18 on Northwest are recorded as shut down. Of 26 machines on Fisk A, 12 dropped out and 14 stay ...", "... ables between these stations are of very low resistance, the Northwest Station was just as seriously affected as Fisk B, and indeed acted like a part of Fisk B. b) All the synchronous machines on Fisk Street B, and on North- west Station dropped out, and many synchronous machines on Fisk A and Quarry Street: 44 synchronous machines on Fisk B and 18 on Northwest are recorded as shut down. Of 26 machines on Fisk A, 12 dropped out and 14 stayed in; of 8 machines on Quarry Street, 4 dropped out and 4 stayed in. [[END_PDF_PAGE:16] ...", "... ce, the Northwest Station was just as seriously affected as Fisk B, and indeed acted like a part of Fisk B. b) All the synchronous machines on Fisk Street B, and on North- west Station dropped out, and many synchronous machines on Fisk A and Quarry Street: 44 synchronous machines on Fisk B and 18 on Northwest are recorded as shut down. Of 26 machines on Fisk A, 12 dropped out and 14 stayed in; of 8 machines on Quarry Street, 4 dropped out and 4 stayed in. [[END_PDF_PAGE:16]] [[PDF_PAGE:17]] Report of Charles P. Steinmetz 11 ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-18", "section_label": "Chapter 20: Single-Phase Commutator Motors", "section_title": "Single-Phase Commutator Motors", "kind": "chapter", "sequence": 18, "number": 20, "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 68, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "... for single-phase railroading, and as con- stant-speed motors or adjustable-speed motors, where efficient acceleration under heavy torque is necessary. As generators, they would be of advantage for the generation of very low fre- quency, since in this case synchronous machines are uneconom- ical, due to their very low speed, resultant from the low frequency. The direction of rotation of a direct-current motor, whether shunt or series motor, remains the same at a reversal of the im- pressed e.m.f., as in this case the ...", "... es is generally the highest frequency considered for large commutating motors. High ni and low n0 means high armature reaction and low field excitation, that is, just the opposite conditions from that required for good commutator-motor design. Assuming synchronism, /o = /, as average motor speed — 750 revolutions with a four-pole 25-cyclc motor — an armature reac- 334 ELECTRICAL APPARATUS tion, n,, equal to the field excitation, n0, would then give tan 6 = 1, 9 = 45°, or 70.7 per cent, power-factor; that is, ...", "... 0.10 to 0.15 in. as the smallest safe value in railway work, b can not well be made larger than about 4. Assuming, then, 6 = 4, gives q = 2, that is, twice as many armature turns as field turns; rti = 2 n0. The angle of lag in this case is, by (12), at synchronism:/© = /, tan 0O = 1, giving a power-factor of 70.7 per cent. It follows herefrom that it is not possible, with a mechanically 336 ELECTRICAL APPARATUS safe construction, at 25 cycles to get a good power-factor moderate speed, from a straight series ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-110", "section_label": "Apparatus Section 4: Induction Machines: Induction Generator", "section_title": "Induction Machines: Induction Generator", "kind": "apparatus-section", "sequence": 110, "number": 4, "location": "lines 21158-21588", "status": "candidate", "occurrence_count": 53, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-110/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-110/", "snippets": [ "IV. Induction Generator 1. INTRODUCTION 163. In the range of slip from s = 0 to s = 1, that is, from synchronism to standstill, torque, power output, and power input of the induction machine are positive, and the machine thus acts as a motor, as discussed before. Substituting, however, in the equations in paragraph 1 for s values > ...", "... M CONSTANT FREQUENCY CONSTANT TERMINAL VOLTAGE OF 110 Z0- Y - 0.01 - 0.4 05 060 160 140 100. FIG. 186. — Induction machine speed curves. Substituting for s negative values, corresponding to a speed above synchronism, torque and power output and power input 342 ELEMENTS OF ELECTRICAL ENGINEERING become negative, and a load curve can be plotted for the induc- tion generator which is very similar, but the negative counter- part of th ...", "... e curve, for s < 0, is of the same char- acter as the motor part, s > 0, but the maximum torque and maximum output of the machine as generator are greater than as motor. Thus an induction motor when speeded up above synchronism acts as a powerful brake by returning energy into the lines, and the maximum braking effort and also the maximum electric power returned by the machine will be greater than the maxi- mum motor torque or output. 2. CONSTA ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-21", "section_label": "Chapter 23: Review", "section_title": "Review", "kind": "chapter", "sequence": 21, "number": 23, "location": "lines 32138-32819", "status": "candidate", "occurrence_count": 52, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-21/", "snippets": [ "... . Comprises an inductor disk of very many teeth, revolving at very high speed between two radial armatures. Used for producing very high frequencies, from 20,000 to 200,000 cycles per second. Amortisseur. — Squirrel-cage winding in the pole faces of the synchronous machine, proposed by Leblanc to oppose the hunt- ing tendency, and extensively used. Amplifier. — 161. An apparatus to intensify telephone and radio telephone currents. High-frequency inductor alternator excited by the telephone current, usually by armat ...", "... returned to direct current, the development of the mercury-arc rectifier superseded the arc machine. Asynchronous Motor. — Name used for all those types of alternating-current (single-phase or polyphase) motors or motor couples, which approach a definite synchronous speed at no-load, and slip below this speed with increasing load. 459 400 ELECTRICAL APPARATUS Brush Arc Machine. — (Sec1 \"Are Machines.'1} Compound Alternator. — 138. Alternator with rectifying com- mutator, connected in Beriea to the armature, ...", "... otor railroading, it has the advantage of greater simplicity. The internally concatenated motor {Hunt mtttt>r), 36. I' H more efficient than the concatenated couple or the multispeed motor, but limited in design to certain speeds and speed ratios. 2. A Synchronous Machine. — The couple then is synchronous. Hereto belong: The synchronous frequency converter, XII, 103. It has a defi- nite frequency ratio, while that of the induction frequi REVIEW 461 verter slightly changes with the load, by the slip of the indu ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-19", "section_label": "Chapter 19: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 18053-19457", "status": "candidate", "occurrence_count": 45, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "snippets": [ "CHAPTER XIX. SYNCHRONOUS MOTOR. 198. In the chapter on synchronizing alternators we have seen that when an alternator running in synchronism is connected with a system of given E.M.F., the work done by the alternator can be either positive or negative. In the latter case the al ...", "CHAPTER XIX. SYNCHRONOUS MOTOR. 198. In the chapter on synchronizing alternators we have seen that when an alternator running in synchronism is connected with a system of given E.M.F., the work done by the alternator can be either positive or negative. In the latter case the alternator consumes electrical, and consequentl ...", "CHAPTER XIX. SYNCHRONOUS MOTOR. 198. In the chapter on synchronizing alternators we have seen that when an alternator running in synchronism is connected with a system of given E.M.F., the work done by the alternator can be either positive or negative. In the latter case the alternator consumes electrical, and consequently produces mechanical, power ; that is, runs as a synchronous motor, so ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-11", "section_label": "Chapter 11: Instability Of Circuits: Induction And Syn Chronous Motors", "section_title": "Instability Of Circuits: Induction And Syn Chronous Motors", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 21382-22633", "status": "candidate", "occurrence_count": 42, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-11/", "snippets": [ "... zed by the central stations since the early days, and good partial load efficiencies and power-factors secured. 104. The induction motor speed-torque curve thus has on a constant-torque load a stable branch, from the maximum torque point, c. Fig. 102, to synchronism; and an unstable branch, from standstill to the maximum torque point. However, it would be incorrect to ascribe the stability or in- stability to the induction motor-speed curve; but it is the char- acter of the load, the requirement of constant torque, ...", "... \\ , V'<^< ^ ^-.ll ,. , . . . , dS - dS\" Thus, with this character of load, a torque required propor- tional to the speed, and the motor-torque curve, 2>, no instability exists, but conditions are stable from standstill to synchronism, just as in Fig. 101. That is, with increasing load, the speed de- creases and increases again with decreasing load. If, however, the motor curve is as shown by Do in Fig. 103, that is, low starting torque and a maximum torque point close to synchronism ...", "... synchronism, just as in Fig. 101. That is, with increasing load, the speed de- creases and increases again with decreasing load. If, however, the motor curve is as shown by Do in Fig. 103, that is, low starting torque and a maximum torque point close to synchronism, as corresponds to an induction motor with low resistance secondary, then for a certain range of load, between INSTABILITY OF CIRCUITS 207 D' and D'o, the load-torque line, D'2, intersects the motor curve, Do, in three points 62, ^2, /12. At 62, S = ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-18", "section_label": "Chapter 16: Il", "section_title": "Il", "kind": "chapter", "sequence": 18, "number": 16, "location": "lines 19346-21338", "status": "candidate", "occurrence_count": 39, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-18/", "snippets": [ "CHAPTER XVIil. SYNCHRONOUS MOTOR. 177. In the chapter on synchronizing alternators we have seen that when an alternator running in synchronism is connected with a system of given E.M.F., the work done by the alternator can be either positive or negative. In the latter case the al ...", "CHAPTER XVIil. SYNCHRONOUS MOTOR. 177. In the chapter on synchronizing alternators we have seen that when an alternator running in synchronism is connected with a system of given E.M.F., the work done by the alternator can be either positive or negative. In the latter case the alternator consumes electrical, and consequentl ...", "CHAPTER XVIil. SYNCHRONOUS MOTOR. 177. In the chapter on synchronizing alternators we have seen that when an alternator running in synchronism is connected with a system of given E.M.F., the work done by the alternator can be either positive or negative. In the latter case the alternator consumes electrical, and consequently produces mechanical, power ; that is, runs as a synchronous motor, so ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-02", "section_label": "Chapter 2: Multiple Squirrel-Cage Induction Motor", "section_title": "Multiple Squirrel-Cage Induction Motor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3543-5554", "status": "candidate", "occurrence_count": 39, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-02/", "snippets": [ "... g is high, and the high-resistance squirrel cage thus carries con- siderable current, gives good torque and torque efficiency, while the low-resistance squirrel cage is ineffective, due to its high reactance at the high armature frequency. At speeds near synchronism, the secondary frequency, being that of slip, is low, and the secondary induced voltage correspondingly low. The high-resistance squirrel cage thus carries little current and gives little torque. In the low-resistance squirrel cage, due to its low reactan ...", "... ue. Such double squirrel -cage induc- tion motor thus gives a torque curve, which to some extent is a superposition of the torque curve of the high-resistance and that of the low-resistance squirrel cage, has two maxima, one at low speed, Mid another near synchronism, therefore gives a fairly good torque and torque efficiency over the entire speed range from standstill to full speed, that is, combines the good features of both types. Where a very high starting torque requires locating the first torque maximum near sta ...", "... om standstill to full speed, that is, combines the good features of both types. Where a very high starting torque requires locating the first torque maximum near standstill, and large size and high efficiency brings the second torque maximum very close to synchronism, the drop of torque between the two maxima may be considerable. This is still more the ease, when the motor is required to reverse at full speed and full power, that is, a very- high torque is required at full speed backward, or at or near slip s — 2. In ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-17", "section_label": "Chapter 19: Alternating- Current Motors In General", "section_title": "Alternating- Current Motors In General", "kind": "chapter", "sequence": 17, "number": 19, "location": "lines 21713-23905", "status": "candidate", "occurrence_count": 37, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-17/", "snippets": [ "... s of stator and rotor. In the latter a cycle of rotation exists, and therefrom the tendency of the motor results to lock at a speed giving a definite ratio between the frequency of rotation and the frequency of impressed e.m.f. Such motors, therefore, are synchronous motors. The main types of synchronous motors are as follows: 1. One member supplied with alternating and the other with direct current — polyphase or single-phase synchronous motors, 2. One member excited by alternating current, the other taining a si ...", "... ycle of rotation exists, and therefrom the tendency of the motor results to lock at a speed giving a definite ratio between the frequency of rotation and the frequency of impressed e.m.f. Such motors, therefore, are synchronous motors. The main types of synchronous motors are as follows: 1. One member supplied with alternating and the other with direct current — polyphase or single-phase synchronous motors, 2. One member excited by alternating current, the other taining a single circuit closed upon itself — synchr ...", "... of rotation and the frequency of impressed e.m.f. Such motors, therefore, are synchronous motors. The main types of synchronous motors are as follows: 1. One member supplied with alternating and the other with direct current — polyphase or single-phase synchronous motors, 2. One member excited by alternating current, the other taining a single circuit closed upon itself — synchronous induction motors. 3. One member excited by alternating current, the other of different magnetic reluctance iii different direction ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-13", "section_label": "Chapter 15: Synchronous Rectifier", "section_title": "Synchronous Rectifier", "kind": "chapter", "sequence": 13, "number": 15, "location": "lines 18413-19373", "status": "candidate", "occurrence_count": 36, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-13/", "snippets": [ "CHAPTER XV SYNCHRONOUS RECTIFIER Self-compounding Alternators— Self-starting Synchro- nous Motors — Arc Rectifier — Brush and Thomson Houston Arc Machine — Leblanc Panchahuteur — Permutator — Synchronous Converter 138. Rectifiers ffir converting alternating into direct curr ...", "CHAPTER XV SYNCHRONOUS RECTIFIER Self-compounding Alternators— Self-starting Synchro- nous Motors — Arc Rectifier — Brush and Thomson Houston Arc Machine — Leblanc Panchahuteur — Permutator — Synchronous Converter 138. Rectifiers ffir converting alternating into direct current have been designed and built since many years. As mechanical rectifiers, mainly single-phase, they have found a limited use for small powers since a long time, and during the last ...", "... d during the last years arc rectifiers have found extended use for small and moderate powers, for storage-battery charging and for series arc lighting by constant direct current. For large powers, however, the rectifier does not appear applicable, but the synchronous converter takes its place. The two most important types of direct-current arc-light ma- chines, however, have in reality been mechanical rectifiers, and for compounding alternators, and for starting synchronous motors, rectifying commutators have been use ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-02-discussion-of-recommendations", "section_label": "Report Section 3: Discussion of Recommendations", "section_title": "Discussion of Recommendations", "kind": "report-section", "sequence": 3, "number": 3, "location": "PDF pages 12-16, lines 721-1138", "status": "pdf-text-extracted-candidate", "occurrence_count": 34, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-02-discussion-of-recommendations/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-02-discussion-of-recommendations/", "snippets": [ "... e, but in a large part of the system (Fisk Street B and Northwest) the voltage remained practically zero for about a quarter of an hour after the trouble had been cleared. It appears, as the result of the momentary short circuit the stations had broken out of synchronism with each other and were not able to pull back into synchronism, but kept drifting past each other indefinitely, short circuiting each other and thus keeping the voltage down to practically zero. In these very large power systems, it is essential for the safe ...", "... t) the voltage remained practically zero for about a quarter of an hour after the trouble had been cleared. It appears, as the result of the momentary short circuit the stations had broken out of synchronism with each other and were not able to pull back into synchronism, but kept drifting past each other indefinitely, short circuiting each other and thus keeping the voltage down to practically zero. In these very large power systems, it is essential for the safety of operation to limit the possible local concentration of pow ...", "... eir purposes, these reactors must be fairly large, and the value of 1.75 ohms used in the power limiting busbar reactors of the Commonwealth Edison Company of Chicago, is by no means too high. Necessarily, however, these power limiting reactors also limit the synchronizing power be- tween the station sections. Thus if in a station section as Fisk Street A, which is connected by one power limiting reactor to the rest of the system, full load of 60,000 KW is suddenly thrown off as by a short circuit at the busbars dropping out th ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-13", "section_label": "Chapter 13: Reactance Of Synchronous Machines", "section_title": "Reactance Of Synchronous Machines", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 23466-24022", "status": "candidate", "occurrence_count": 32, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-13/", "snippets": [ "CHAPTER XIII REACTANCE OF SYNCHRONOUS MACHINES 119. The synchronous machine — ^alternating-current generator, synchronous motor or synchronous condenser — consists of an armature containing one or more electric circuits traversed by alternating currents and synchronously revolving relative ...", "CHAPTER XIII REACTANCE OF SYNCHRONOUS MACHINES 119. The synchronous machine — ^alternating-current generator, synchronous motor or synchronous condenser — consists of an armature containing one or more electric circuits traversed by alternating currents and synchronously revolving relative to a unidirectional magnetic fie ...", "CHAPTER XIII REACTANCE OF SYNCHRONOUS MACHINES 119. The synchronous machine — ^alternating-current generator, synchronous motor or synchronous condenser — consists of an armature containing one or more electric circuits traversed by alternating currents and synchronously revolving relative to a unidirectional magnetic field, excited by direct current. The armature circuit, l ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-16", "section_label": "Chapter 18: Surging Of Synchronous Motors", "section_title": "Surging Of Synchronous Motors", "kind": "chapter", "sequence": 16, "number": 18, "location": "lines 20975-21712", "status": "candidate", "occurrence_count": 31, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-16/", "snippets": [ "CHAPTER XVIII SURGING OF SYNCHRONOUS MOTORS 166. In the theory of the synchronous motor the assumption is made that the mechanical output of the motor equals the power developed by it. This is the case only if the motor runs at constant speed. If, however, it accelerates, the power input is ...", "CHAPTER XVIII SURGING OF SYNCHRONOUS MOTORS 166. In the theory of the synchronous motor the assumption is made that the mechanical output of the motor equals the power developed by it. This is the case only if the motor runs at constant speed. If, however, it accelerates, the power input is greater; if it decelerates, less than the pow ...", "... ed. If, however, it accelerates, the power input is greater; if it decelerates, less than the power output, by the power stored in and returned by the momentum. Obviously, the motor can neither constantly accelerate nor decelerate, without breaking out of synchronism. If, for instance, at a certain moment the power prod wed by the motor exceeds the mechanical load (as in the moment of throwing off a part of the load), the excess power is consumed by the momentum as acceleration, causing an increase of speed. The res ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-18", "section_label": "Chapter 18: Polyphase Induction Motors", "section_title": "Polyphase Induction Motors", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17717-20445", "status": "candidate", "occurrence_count": 29, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-18/", "snippets": [ "... the motor armature are not of the same frequency as the e.m.fs. impressed upon the primary, but of a frequency which is the difference between the impressed frequency and the frequency of rotation, or equal to the \"slip,\" that is, the difference between synchronism and speed (in cycles). 208 POLYPHASE INDUCTION MOTORS 209 Hence, if / = frequency of main or primary e.m.f., 5 = slip as fraction of synchronous speed, sf = frequency of armature or secondary e.m.f., and (1 — s) / = frequency of rotation of armat ...", "... essed frequency and the frequency of rotation, or equal to the \"slip,\" that is, the difference between synchronism and speed (in cycles). 208 POLYPHASE INDUCTION MOTORS 209 Hence, if / = frequency of main or primary e.m.f., 5 = slip as fraction of synchronous speed, sf = frequency of armature or secondary e.m.f., and (1 — s) / = frequency of rotation of armature. In its reaction upon the primary circuit, however, the arma- ture current is of the same frequency as the primary current, since it is carried aro ...", "... r e.m.f.\" Since the secondary frequency is sf, the secondary induced e.m.f. (reduced to primary system) is Ei = — se. POLYPHASE INDUCTION MOTORS 211 Let 7o = exciting current, or current through the motor, per primary circuit, when doing no work (at synchronism), and F = g — j6 = primary exciting admittance per circuit = — • We thus have, ge = magnetic power current, ge~ = loss of power by hysteresis (and eddy currents) per primary coil. Hence Poge^ = total loss of power by hysteresis and eddies, as calcul ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-14", "section_label": "Chapter 16: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 14, "number": 16, "location": "lines 19374-20293", "status": "candidate", "occurrence_count": 29, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-14/", "snippets": [ "CHAPTER XVI REACTION MACHINES 147. In the usual treatment of synchronous machines and induction machines, the assumption is made that the reactance, x, of the machine is a constant. While this is more or less approximately the case in many alternators, in others, especially in machines of large armature reaction, the reactance ...", "... the different positions of the armature coils in the magnetic circuit. This variation of the reactance causes phenomena which do not find their explanation by the theoretical calculations made under the assumption of constant reactance. It is known that synchronous motors or converters of large and variable reactance keep in synchronism, and are able to do a considerable amount of work, and even carry under circum- stances full load, if the field-exciting circuit is broken, and thereby the counter e.m.f., E,, reduce ...", "... is variation of the reactance causes phenomena which do not find their explanation by the theoretical calculations made under the assumption of constant reactance. It is known that synchronous motors or converters of large and variable reactance keep in synchronism, and are able to do a considerable amount of work, and even carry under circum- stances full load, if the field-exciting circuit is broken, and thereby the counter e.m.f., E,, reduced to zero, and sometimes even if the field circuit is reversed and the co ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-22", "section_label": "Chapter 22: Armature Reactions Of Alternators", "section_title": "Armature Reactions Of Alternators", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 23971-25134", "status": "candidate", "occurrence_count": 28, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-22/", "snippets": [ "... ction, that is, instead of the counter m.m.f. of the armature reaction, the e.m.f. considered, which would be generated by the magnetic flux, which the arma- ture reaction would produce. That is, both effects are com- bined in an effective reactance, the \"synchronous reactance.\" While armature reaction and self-inductance are similar in ARMATURE REACTIONS OF ALTERNATORS 273 effect, in some cases they differ in their action; the e.m.f. of self-inductance is instantaneous, that is, appears and disappears with the c ...", "... m.f.; therefore, (9ni = magnetic flux produced thereby, and, a(9n.i = e.m.f. generated in the armature bj'^ the magnetic flux of armature reaction, hence, a(Pn = Xi = effective reactance, representing the armature reaction, and Xo = a(Pn + x (16) = synchronous reactance, that is, the effective reactance representing the combined effect of armature self-induction and armature reaction. Substituting (15) and (16) in (14) gives, £' = (eo — a:o^2 — rii) — jix^ii — rio) (17) It follows herefrom: In an altern ...", "... rmature turns, effective, /\"o = field excitation, in ampere-turns, a = 2TfnlO-\\ (7) (P = magnetic permeance of the field structure at a magnetic flux in the field-poles corresponding to the virtual generated e.m.f., E2. The introduction of the term \"synchronous reactance,\" Xo, and \"nominal generated e.m.f.,\" eo, is hereby justified, when dealing with the permanent condition of the electric circuit. The case of the transient phenomena of momentary short- circuit currents, etc., is discussed in a chapter on \"Trans ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-05", "section_label": "Chapter 6: Induction-Motor Regulation And Stability", "section_title": "Induction-Motor Regulation And Stability", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 10583-12397", "status": "candidate", "occurrence_count": 27, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-05/", "snippets": [ "... , with a secondary resistance giving maximum torque in starting, at constant tcr- INDUCTION -MOTOR REGULATION 129 rainal voltage, with high impedance in the supply, the starting torque drops so much that the maximum torque is shifted to about half synchronism. In induction motors, especially at overloads ami in starting, it therefore is important to have as low impedance as pos- sible between the point of constant voltage and the motor terminals. _>j^_ \\^&% °yo^?I L-.K! g I p Friction of Synchr ...", "... e shown, in Fig. 50, the values of current and of torque for maximum and minimum frequency, and for the average frequency, for p = 0.025, that is, 2.5 per cent, pulsa- tion of frequency from the average. As seen, the pulsation of current is moderate until synchronism is approached, but be- 132 ELECTRICAL APPARATUS comes very large near synchronism, and from slip, s = 0.025, op to synchronism the average current remains practically con- stant, thus at synchronism is very much higher than the current at constant ...", "... , and for the average frequency, for p = 0.025, that is, 2.5 per cent, pulsa- tion of frequency from the average. As seen, the pulsation of current is moderate until synchronism is approached, but be- 132 ELECTRICAL APPARATUS comes very large near synchronism, and from slip, s = 0.025, op to synchronism the average current remains practically con- stant, thus at synchronism is very much higher than the current at constant Frequency. The average torque also drops some- what below the torque corresponding to con ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-06", "section_label": "Chapter 7: Higher Harmonics In Induction Motors", "section_title": "Higher Harmonics In Induction Motors", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 12398-13955", "status": "candidate", "occurrence_count": 27, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-06/", "snippets": [ "... n motor, and due to the fundamental voltage wave: ei cos 0 ] Iju *\\ (3) d cos \\ ~ 2) is shown as T\\ in Fig. 55, of the usual shape, increasing from standstill, with increasing speed, upj to a maximum torque, and then decreasing again to zero at synchronism. The third harmonics of the voltage waves are : e3cos(3 0 — a3), j e3cos(3 0- «» + 5)-| (4) As seen, these also constitute a quarter-phase system of voltage, but the second wave, which is lagging in the funda- mental, is 90° leading in the third harm ...", "... ging in the funda- mental, is 90° leading in the third harmonic, or in other words, the third harmonic gives a backward rotation of the poles with triple frequency. It thus produces a torque in opposite direc- tion to the. fundamental, and would reach its synchronism, that is, zero torque, at one-third of synchronism in negative direction, or at the speed 1, backward driving. Pi becomes negative, repre- senting consumption of power, while ...", "... values, and the load curves for the machine shown as motor in Fig. 122, are shown in Fig. 125 for negative slip Si as induction generator. Again, a maximum torque point and a maximum output point are found, and the torque and power increase from zero at synchronism up to a maximum point, and then decrease again, while the current constantly increases. 174. The induction generator differs essentially from the ordinary synchronous alternator in so far as the induction generator has a definite power-factor, while the ...", "... t and a maximum output point are found, and the torque and power increase from zero at synchronism up to a maximum point, and then decrease again, while the current constantly increases. 174. The induction generator differs essentially from the ordinary synchronous alternator in so far as the induction generator has a definite power-factor, while the synchronous alternator has not. That is, in the synchronous alternator the phase relation between current and terminal voltage entirely depends upon the condition of th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-23", "section_label": "Chapter 23: Synchronizing Alternators", "section_title": "Synchronizing Alternators", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 25135-25681", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-23/", "snippets": [ "CHAPTER XXIII SYNCHRONIZING ALTERNATORS 203. All alternators, when brought to synchronism with each other, operate in parallel more or less satisfactorily. This is due to the reversibility of the alternating-current machine; that is, its ability to operate as synchronous motor. In ...", "CHAPTER XXIII SYNCHRONIZING ALTERNATORS 203. All alternators, when brought to synchronism with each other, operate in parallel more or less satisfactorily. This is due to the reversibility of the alternating-current machine; that is, its ability to operate as synchronous motor. In consequence thereof, if the driving power of one of several par ...", "... R XXIII SYNCHRONIZING ALTERNATORS 203. All alternators, when brought to synchronism with each other, operate in parallel more or less satisfactorily. This is due to the reversibility of the alternating-current machine; that is, its ability to operate as synchronous motor. In consequence thereof, if the driving power of one of several parallel-operating generators is withdrawn, this generator will keep revolving in synchronism as a synchronous motor; and the power with which it tends to' remain in synchronism is the ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-22", "section_label": "Chapter 24: Conclusion", "section_title": "Conclusion", "kind": "chapter", "sequence": 22, "number": 24, "location": "lines 32820-33531", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-22/", "snippets": [ "... ole (\"interpole\") in direct-current machines has been known since very many years, has been discussed and recommended, but used very little, in short was of practically no industrial importance, while now practically all larger direct-current machines and synchronous converters use commutating poles. For many years, with tin- types of direct-current machines in use, the advantage of tin commutating pole did not appear sufficient to compensate to* the disadvantage of the complication and resuliunt increase o4 size and ...", "... today. However, we are only in the beginning of the water- power development, and thus far have considered only the largest and most concentrated powers, and for these, as best adapted, has been developed a certain type of generating station, compris- ing synchronous generators, with direct-current exciting circuits, switches, circuit-breakers, transformers and protective devices, etc., and requiring continuous attendance of expert operating engineers. This type of generating station is feasible only with large water ...", "... velopment of an entirely different type of generating station: induction generators driven by small and cheap waterwheels, at low voltage, and permanently connected through step-up transformers to a collecting line, which is con- trolled from some central synchronous station. A cheap hy- draulic development, no regulation of waterwheel speed or gen- erator voltage, no attendance in the station beyond an occasional inspection, in short an automatically operating induction gen- erator station controlled from the central ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-11", "section_label": "Chapter 11: Phase Control", "section_title": "Phase Control", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 9767-10717", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-11/", "snippets": [ "... circuit supplied over an induc- tive line, by varying the phase relation of the current in the circuit, has been called \"phase control,\" and is used to a great extent, especially in the transmission of three-phase power for conversion to direct current by synchronous converters for 7 97 98 ALTERNATING-CURRENT PHENOMENA railroading, and in the voltage control at the receiving end of very long high voltage transmission lines. It requires a receiving circuit in which, independent of the load, a lagging or leading c ...", "... ading, and in the voltage control at the receiving end of very long high voltage transmission lines. It requires a receiving circuit in which, independent of the load, a lagging or leading component of current can be produced at will. Such is the case in synchronous motors or converters: in a synchronous motor a lagging current can be produced by decreasing, a leading current by increasing, the field excitation. 81. If in a direct-current motor, at constant impressed voltage, the field excitation and therefore the f ...", "... receiving end of very long high voltage transmission lines. It requires a receiving circuit in which, independent of the load, a lagging or leading component of current can be produced at will. Such is the case in synchronous motors or converters: in a synchronous motor a lagging current can be produced by decreasing, a leading current by increasing, the field excitation. 81. If in a direct-current motor, at constant impressed voltage, the field excitation and therefore the field magnetism is decreased, the motor ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-07", "section_label": "Chapter 8: Synchronizing Induction Motors", "section_title": "Synchronizing Induction Motors", "kind": "chapter", "sequence": 7, "number": 8, "location": "lines 13956-14465", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-07/", "snippets": [ "CHAPTER VIII SYNCHRONIZING INDUCTION MOTORS 94. Occasionally two or more induction motors are operated in parallel on the same load, as for instance in three-phase rail- roading, or when securing several speeds by concatenation. In this case the secondaries of the induction motors ...", "... veral speeds by concatenation. In this case the secondaries of the induction motors may be connected in multiple and a single rheostat used for starting . and speed control. Thus, when using two motors in concatena- tion for speeds from standstill to half synchronism, from half synchronism to full speed, the motors may also be operated on a single rheostat by connecting their secondaries in parallel. As in parallel connection the frequency of the secondaries must be the same, and the secondary frequency equals the sli ...", "... ation. In this case the secondaries of the induction motors may be connected in multiple and a single rheostat used for starting . and speed control. Thus, when using two motors in concatena- tion for speeds from standstill to half synchronism, from half synchronism to full speed, the motors may also be operated on a single rheostat by connecting their secondaries in parallel. As in parallel connection the frequency of the secondaries must be the same, and the secondary frequency equals the slip, it follows that the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-17", "section_label": "Chapter 17: Synchbonizino Aiitebkatobs", "section_title": "Synchbonizino Aiitebkatobs", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 18829-19345", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-17/", "snippets": [ "CHAPTER XVII. SYNCHBONIZINO AIiTEBKATOBS. 168. All alternators, when brought to synchronism with each other, will operate in parallel more or less satisfactorily. This is due to the reversibility of the alternating-current machine ; that is, its ability to operate as synchronous motor. In consequence thereof, if the driving power of one of sev- ...", "... SYNCHBONIZINO AIiTEBKATOBS. 168. All alternators, when brought to synchronism with each other, will operate in parallel more or less satisfactorily. This is due to the reversibility of the alternating-current machine ; that is, its ability to operate as synchronous motor. In consequence thereof, if the driving power of one of sev- eral parallel-operating generators is withdrawn, this gene- rator will keep revolving in synchronism as a synchronous motor ; and the power with which it tends to remain in synchronism is ...", "... e reversibility of the alternating-current machine ; that is, its ability to operate as synchronous motor. In consequence thereof, if the driving power of one of sev- eral parallel-operating generators is withdrawn, this gene- rator will keep revolving in synchronism as a synchronous motor ; and the power with which it tends to remain in synchronism is the maximum power which it can furnish as synchronous motor under the conditions of running. 169. The principal and foremost condition of parallel operation of altern ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-08", "section_label": "Chapter 9: Synchronous Induction Motor", "section_title": "Synchronous Induction Motor", "kind": "chapter", "sequence": 8, "number": 9, "location": "lines 14466-14550", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-08/", "snippets": [ "CHAPTER IX SYNCHRONOUS INDUCTION MOTOR 97. The typical induction motor consists of one or a number df primary circuits acting upon an armature movable thereto, which contains a number of closed secondary circuits, displaced from each other in space so as to offer a resultant c ...", "... d as a transformer, having to each primary circuit a corresponding secondary cir- cuit— a secondary coil, moving out of the field of the primary coil,* being replaced by another secondary coil moving into the field. In such a motor the torque is zero a) synchronism, positive below, and negative above, synchronism. If, however, the movable armature contains one closed cir- cuit only, it offers a closed secondary circuit only in the direc- tion of the axis of the armature coil, but no secondary circuit at right angl ...", "... t a corresponding secondary cir- cuit— a secondary coil, moving out of the field of the primary coil,* being replaced by another secondary coil moving into the field. In such a motor the torque is zero a) synchronism, positive below, and negative above, synchronism. If, however, the movable armature contains one closed cir- cuit only, it offers a closed secondary circuit only in the direc- tion of the axis of the armature coil, but no secondary circuit at right angles therewith. That is, with the rotation of the ar ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-109", "section_label": "Apparatus Section 3: Induction Machines: Single -phase Induction Motor", "section_title": "Induction Machines: Single -phase Induction Motor", "kind": "apparatus-section", "sequence": 109, "number": 3, "location": "lines 20428-21157", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-109/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-109/", "snippets": [ "... A number of secondary circuits displaced in position must be used so as to offer to the primary circuit a short-circuited sec- ondary in any position of the armature. If only one secondary coil is used, the motor is a synchronous induction motor and belongs to the class of reaction machines. A single-phase induction motor will not start from rest, but when started in either direction will accelerate with increasing torque and approach synchronism. W ...", "... a synchronous induction motor and belongs to the class of reaction machines. A single-phase induction motor will not start from rest, but when started in either direction will accelerate with increasing torque and approach synchronism. When running at or very near synchronism, the magnetic field of the single-phase induction motor is practically identical with that of a polyphase motor, that is, can be represented by the theory of the rotating field. T ...", "... to the class of reaction machines. A single-phase induction motor will not start from rest, but when started in either direction will accelerate with increasing torque and approach synchronism. When running at or very near synchronism, the magnetic field of the single-phase induction motor is practically identical with that of a polyphase motor, that is, can be represented by the theory of the rotating field. Thus, in a turn wound under angle r to the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-21", "section_label": "Apparatus Introduction 21: Introduction", "section_title": "Introduction", "kind": "apparatus-introduction", "sequence": 21, "number": null, "location": "lines 8292-8517", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-21/", "snippets": [ "... tric generator can be used as motor, and conversely, and frequently one and the same machine is used for either purpose. Where a difference is made in the construction, it is either only quantitative, as, for instance, in synchronous motors a higher armature reaction is often used than in synchro- nous generators, or it is in minor features, as direct-current motors usually have only one field winding, either shunt or series, while in generators frequent ...", "... nt motors usually have only one field winding, either shunt or series, while in generators frequently a compound field is employed. Further- more, apparatus have been introduced which are neither motors nor generators, as the synchronous machine producing wattless lag- ging or leading current, etc., and the different types of converters. The subdivision into direct-current and alternating-current apparatus is unsatisfactory, since it includes in the same class ...", "... and between electric and mechanical power. 1st. Commutating machines, consisting of a magnetic field and a closed-coil armature, connected with a multi-segmental commutator. 121 122 ELEMENTS OF ELECTRICAL ENGINEERING 2d. Synchronous machines, consisting of a undirectional mag- netic field and an armature revolving relatively to the mag- netic field at a velocity synchronous with the frequency of the alternating-current circuit connected thereto. . 3d. Rect ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-29", "section_label": "Apparatus Section 8: Synchronous Machines: Characteristic Curves of Synchronous Motor", "section_title": "Synchronous Machines: Characteristic Curves of Synchronous Motor", "kind": "apparatus-section", "sequence": 29, "number": 8, "location": "lines 9399-9553", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-29/", "snippets": [ "VIII. Characteristic Curves of Synchronous Motor 17. In Fig. 66 are shown, at constant impressed e.m.f. E, the nominal counter-generated e.m.f. EQ and thus the field excitation FQ required, 1. At no phase displacement, 6 = 0, or for the condition of minimum inp ...", "... g. 67 are shown, with the power output PI = i (Ep — ir) — (iron loss and friction) as abscissas, and the same constants 1= E = =0.1, 000 XQ= 1100 20 40 60 80 100 120 140 160 180 200 FIG. 66. — Synchronous motor compounding curves. r = 0.1, XQ = 5, E = 1000, and constant field excitation F0' that is, constant nominal counter-generated e.m.f. EQ = 1109 (corresponding to p = 1, # = 0 at 7 = 100), the values of current I ...", "... e.m.f. EQ = 1109 (corresponding to p = 1, # = 0 at 7 = 100), the values of current I and power-factor p. As iron loss is assumed 3000 watts, as friction 2000 watts. Such curves are called load characteristics of the synchronous motor. 18. In Fig. 68 are shown, with constant power output = PO, SYNCHRONOUS MACHINES 145 i (Ep — ir), and the same constants, r = 0.1, XQ = 5, E = 1000, and with the nominal counter-generated voltage E0, that ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-81", "section_label": "Apparatus Section 1: Synchronous Converters: General", "section_title": "Synchronous Converters: General", "kind": "apparatus-section", "sequence": 81, "number": 1, "location": "lines 13189-13795", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-81/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-81/", "snippets": [ "... system. Thus, where power is derived from an alternating system, transforming devices are required to convert from alternating to direct current. This can be done either by a direct-current generator driven by an alternating synchronous or induction motor, or by a single machine consuming alternating and pro- ducing direct current in one and the same armature. Such a machine is called a converter, and combines, to a certain extent, the features of a dire ...", "... achine consuming alternating and pro- ducing direct current in one and the same armature. Such a machine is called a converter, and combines, to a certain extent, the features of a direct-current generator and an alternating synchronous motor, differing, however, from either in other features. Since in the converter the alternating and the direct current are in the same armature conductors, their e.m.fs. stand in a definite relation to each other, which i ...", "... s are necessary to generate the required alternating voltage. Comparing thus the converter with the combination of syn- chronous or induction motor and direct-current generator, the converter requires step-down transformers; the synchronous motor, if the alternating line voltage is considerably above 10,000 volts, generally requires step-down transformers also; with voltages of 1000 to 10,000 volts, however, , usually the synchronous motor and frequently the induc ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-14", "section_label": "Lecture 14: Alternating Current Railway Motor", "section_title": "Alternating Current Railway Motor", "kind": "lecture", "sequence": 14, "number": 14, "location": "lines 8649-9342", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-14/", "snippets": [ "... and frequency times main field must equal speed times commutating field. That is : N F = No Fo or in other words, the commutating field must be : or equal to the main field times the ratio of frequency to speed, and in quadrature therewith. Hence, at synchronism: N© = N, the commutating field must be equal to the main field; at half synchronism: No = 2 N, it must be twice ; at double synchronism : No = 2 N, it must be one-half the main field. The problem of controlling the commutation of the alter- nating curr ...", "... N F = No Fo or in other words, the commutating field must be : or equal to the main field times the ratio of frequency to speed, and in quadrature therewith. Hence, at synchronism: N© = N, the commutating field must be equal to the main field; at half synchronism: No = 2 N, it must be twice ; at double synchronism : No = 2 N, it must be one-half the main field. The problem of controlling the commutation of the alter- nating current motor therefore requires the production of a commutating field of proper strengt ...", "... must be : or equal to the main field times the ratio of frequency to speed, and in quadrature therewith. Hence, at synchronism: N© = N, the commutating field must be equal to the main field; at half synchronism: No = 2 N, it must be twice ; at double synchronism : No = 2 N, it must be one-half the main field. The problem of controlling the commutation of the alter- nating current motor therefore requires the production of a commutating field of proper strength, in quadrature phase with the main field of the mot ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-28", "section_label": "Apparatus Section 7: Synchronous Machines: Synchronous Motor", "section_title": "Synchronous Machines: Synchronous Motor", "kind": "apparatus-section", "sequence": 28, "number": 7, "location": "lines 9292-9398", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-28/", "snippets": [ "VII. Synchronous Motor 16. As seen in the preceding, in an alternating-current gen- erator the field excitation required for a given terminal voltage and current depends upon the phase relation of the external circuit or the load. Inversely ...", "... 16. As seen in the preceding, in an alternating-current gen- erator the field excitation required for a given terminal voltage and current depends upon the phase relation of the external circuit or the load. Inversely, in a synchronous motor the phase relation of the current into the armature at a given ter- minal voltage depends upon the field excitation and the load. Thus, if E = terminal voltage or impressed e.m.f., I = current, 6 = lag of current ...", "... he current into the armature at a given ter- minal voltage depends upon the field excitation and the load. Thus, if E = terminal voltage or impressed e.m.f., I = current, 6 = lag of current behind impressed e.m.f. in a synchronous motor of resistance r and synchronous reactance XQ, the polar diagram is as follows, Fig. 62. OE = E is the terminal voltage assumed as zero vector. The current 01 = I lags by the angle EOI = 6. The e.m.f. consumed ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-27", "section_label": "Chapter 27: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 33011-34776", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-27/", "snippets": [ "... s before discussed, that is, a sine wave of equal effective intensity and equal power, while sufficiently accurate in many cases, completely fails in other cases, especially in circuits con- taining capacity, or in circuits containing periodically (and in synchronism with the wave) varying resistance or reactance (as alternating arcs, reaction machines, synchronous induction motors, oversaturated magnetic circuits, etc.). Since, however, the individual harmonics of the general alter- nating wave are independent of ea ...", "... ently accurate in many cases, completely fails in other cases, especially in circuits con- taining capacity, or in circuits containing periodically (and in synchronism with the wave) varying resistance or reactance (as alternating arcs, reaction machines, synchronous induction motors, oversaturated magnetic circuits, etc.). Since, however, the individual harmonics of the general alter- nating wave are independent of each other, that is, all products of different harmonics vanish, each term can be represented by a co ...", "... -{- xo -\\- Xc) is the impedance of the fundamental harmonic, where Xm is that part of the reactance which is proportional to the frequency (inductance, etc.), ^ Xo is that part of the reactance which is independent of the frequency (mutual inductance, synchronous motion, etc.). Xc is that part of the reactance which is inversely propor- tional to the frequency (capacity, etc.). The impedance for the nth harmonic is + jn (nxr^ + a^o + -^ ) This term can be considered as the general symbolic expression of th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "... before discussed, that is a sine wave of equal effective intensity and equal power, while sufficiently accu- rate in many cases, completely fails in other cases, espe- cially in circuits containing capacity, or in circuits containing periodically (and in synchronism with the wave) varying resistance or reactance (as alternating arcs, reaction ma- chines, synchronous induction motors, oversaturated mag- netic circuits, etc.). Since, however, the individual harmonics of the general alternating wave are independent of ...", "... accu- rate in many cases, completely fails in other cases, espe- cially in circuits containing capacity, or in circuits containing periodically (and in synchronism with the wave) varying resistance or reactance (as alternating arcs, reaction ma- chines, synchronous induction motors, oversaturated mag- netic circuits, etc.). Since, however, the individual harmonics of the general alternating wave are independent of each other, that is, all products of different harmonics vanish, each term can be represented by a co ...", "... ent by, if, is the impedance of the fundamental harmonic, where xm is that part of the reactance which is proportional to the frequency (inductance, etc.). x0 is that part of the reactance which is independent of the frequency (mutual induction, synchronous motion, etc.). xc is that part of the reactance which is inversely pro- portional to the frequency (capacity, etc.). The impedance for the nth harmonic is, r —Jnn xm This term can be considered as the general symbolic expression of the impedance o ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-12", "section_label": "Chapter 14: Phase Conversion And Single-Phase Generation", "section_title": "Phase Conversion And Single-Phase Generation", "kind": "chapter", "sequence": 12, "number": 14, "location": "lines 17125-18412", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-12/", "snippets": [ "... has become of considerable importance in the last years, for the purpose of taking targe single-phase loads, for electric railway, furnace work, etc., from a three-phase supply system as a central station or transmission line. For this pur- pose, usually synchronous phase converters with synchronous phase balancers are used. As illustration may thus be considered in the following the monocyclic device, the induction phase converter, and the synchronous phase converter and balancer. Monocyclic Devices 127. The na ...", "... ance in the last years, for the purpose of taking targe single-phase loads, for electric railway, furnace work, etc., from a three-phase supply system as a central station or transmission line. For this pur- pose, usually synchronous phase converters with synchronous phase balancers are used. As illustration may thus be considered in the following the monocyclic device, the induction phase converter, and the synchronous phase converter and balancer. Monocyclic Devices 127. The name \"monocyclic\" is applied to a po ...", "... ntral station or transmission line. For this pur- pose, usually synchronous phase converters with synchronous phase balancers are used. As illustration may thus be considered in the following the monocyclic device, the induction phase converter, and the synchronous phase converter and balancer. Monocyclic Devices 127. The name \"monocyclic\" is applied to a polyphase sys- tem of voltages (whether symmetrical or unsymmetrical), in which the flow of energy is essentially single- phase. For instance, if, as shown dia ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-01-recommendations", "section_label": "Report Section 2: Recommendations", "section_title": "Recommendations", "kind": "report-section", "sequence": 2, "number": 2, "location": "PDF pages 7-12, lines 145-720", "status": "pdf-text-extracted-candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "snippets": [ "... wer limiting reactors are used in the feeders, and as the result, any short circuit in a feeder cable, near the generating station, is practically a short circuit on the busbars, that is, pulls the voltage of the station section down to nothing, drops out the synchronous apparatus and thus gives serious and wide- [[END_PDF_PAGE:8]] [[PDF_PAGE:9]] Report of Charles P. Steinmetz spread trouble. Such short circuits in the feeder cable near the gen- erating stations, however, may be expected to be more frequent than short circui ...", "... de to open this short in less than a second, the station voltage will be only a little affected during the short, due to the great sluggishness of the turbo-alternator fields, and immediately come back to practically normal, so that it may be expected that no synchronous apparatus will be dropped out, that is, the trouble limited to the short circuited feeder cable and its substations. If, however, the short circuit holds on for several seconds, an appreciable voltage drop must be expected in the generating stations, and at l ...", "... e dropped out, that is, the trouble limited to the short circuited feeder cable and its substations. If, however, the short circuit holds on for several seconds, an appreciable voltage drop must be expected in the generating stations, and at least some of the synchronous apparatus supplied from this generating station would be dropped out. The advantage of feeder reactors thus not merely consists in limiting the short circuit current and thereby the voltage drop and in general the shock on the system, but, by permitting to se ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-09", "section_label": "Lecture 9: Hunting Of Synchronous Machines", "section_title": "Hunting Of Synchronous Machines", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 4218-4594", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-09/", "snippets": [ "NINTH LECTURE HUNTING OF SYNCHRONOUS MACHINES C\"^ROSS currents can flow between alternators due to dif- ferences in voltage, that is, differences in excitation; ■—^ and due to differences in phase, that is, differences in position of their rotors. Cross currents due to differences in exc ...", "... field, ithat is, they increase the magnetic density at the one and decrease it at the other pole corner. If two machines are thrown together out of phase, or brought out of the phase by some cause (as the beat of an en- gine, or the change of load of a synchronous motor) then the two machines pull each other in phase again, oscillate a few times against each other, which oscillation gradually decreases and dies out, and the machines run steadily. If the oscillations do not decrease, but continue, the machines are ...", "... itation. 2nd. If the speed of the engine varies during the rota- tion, rising and falling with the steam impulses, then the alternator speed and the frequency also pulsate with a speed equal to, or a multiple of the engine speed. If now two HUNTING OF SYNCHRONOUS MACHINES 117 such alternators happen to be thrown together so that the moment of maximum frequency of one coincides with the moment of minimum frequency of the other, the two machines cannot run in perfect phase with each other, but pulsate, alter- nati ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-113", "section_label": "Apparatus Section 7: Induction Machines: Frequency Converter or General Alternating-current Transformer", "section_title": "Induction Machines: Frequency Converter or General Alternating-current Transformer", "kind": "apparatus-section", "sequence": 113, "number": 7, "location": "lines 21813-21922", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-113/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-113/", "snippets": [ "VH. Frequency Converter or General Alternating-current Transformer 159. The e.m.fs. generated in the secondary of the induction machine are of the frequency of slip, that is, synchronism minus speed, thus of lower frequency than the impressed e.m.f. in the range from standstill to double synchronism; of higher frequency outside of this range. ' Thus, by opening the secondary circuits of the induction machin ...", "... 159. The e.m.fs. generated in the secondary of the induction machine are of the frequency of slip, that is, synchronism minus speed, thus of lower frequency than the impressed e.m.f. in the range from standstill to double synchronism; of higher frequency outside of this range. ' Thus, by opening the secondary circuits of the induction machine and connecting them to an external or consumer's cir- cuit, the induction machine can be used to transform from ...", "... rnal or consumer's cir- cuit, the induction machine can be used to transform from one frequency to another, as frequency converter. It lowers the frequency with the secondary running at a speed between standstill and double synchronism, and raises the fre- quency with the secondary either driven backward or above double synchronism. Obviously, the frequency converter can at the same time change the e.m.f. by using a suitable number of primary and secondar ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-33", "section_label": "Apparatus Section 12: Synchronous Machines: Starting of Synchronous Motors", "section_title": "Synchronous Machines: Starting of Synchronous Motors", "kind": "apparatus-section", "sequence": 33, "number": 12, "location": "lines 9749-9820", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-33/", "snippets": [ "XII. Starting of Synchronous Motors 24. In starting, an essential difference exists between the single- phase and the polyphase synchronous motor, in so far as the for- mer is not self-starting but has to be brought to complete syn- chronism, or in s ...", "XII. Starting of Synchronous Motors 24. In starting, an essential difference exists between the single- phase and the polyphase synchronous motor, in so far as the for- mer is not self-starting but has to be brought to complete syn- chronism, or in step with the generator, by external means before it can develop torque, while the polyphase synchronous motor s ...", "... olyphase synchronous motor, in so far as the for- mer is not self-starting but has to be brought to complete syn- chronism, or in step with the generator, by external means before it can develop torque, while the polyphase synchronous motor starts from rest and runs up to synchronism with more or less torque. In starting, the field excitation of the polyphase synchronous motor should be zero or very low. The starting torque is due to the magnetic at ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... ne waves, 31 Compensation for lagging currents by condensance, 72 Condensance in symbolic expression, 36 Condenser as reactance and suscep- tance, 96 with distorted wave, 384 motor on distorted wave, 392 motor, single-phase induction, 249, 257 synchronous, 339 Conductance of circuit with induc- tive line, 84 direct current, 55 due to eddy currents, 137 effective, 111 due to hysteresis, 126 parallel and series connection, 54 Conductivity, dielectric, 153 of dielectric circuit, 160 Constant current f ...", "... ith induc- tive line, 84 direct current, 55 due to eddy currents, 137 effective, 111 due to hysteresis, 126 parallel and series connection, 54 Conductivity, dielectric, 153 of dielectric circuit, 160 Constant current from constant po- tential, 76 synchronous motor, 337 potential constant current trans- formation, 76 Consumed voltage, by resistance, re- actance, impedance, 23 Control of voltage by shunted sus- ceptance, 89 Corona, 112, 161 of line, 174 Counter e.m.f. of impedance, react- a,nce, resista ...", "... current trans- formation, 76 Consumed voltage, by resistance, re- actance, impedance, 23 Control of voltage by shunted sus- ceptance, 89 Corona, 112, 161 of line, 174 Counter e.m.f. of impedance, react- a,nce, resistance, self-induc- tion, 23 of synchronous motor, 24, 315 Crank diagram, 19 and polar diagram, comparison, 51 Critical voltage of corona, 166 Cross currents in alternators, 293 Cross flux, magnetic of transformer, 187 Cycle, magnetic or hysteresis, 114 475 476 tstntK Delta connec ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-17", "section_label": "Chapter 17: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16362-17596", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "snippets": [ "... in general, symmetrical. An exception from this statement may take place only in those types of alternators where the magnetic reluctance of the armature is different in different directions ; thereby, 298 AL TERNA TING-CURRENT PHENOMENA. during the synchronous rotation of the armature, a pulsa- tion of the magnetic flux passing through it is produced. This pulsation of the magnetic flux induces E.M.F. in the field spools, and thereby makes the field current pulsating also. Thus, we havet in this case, even on o ...", "... ture reaction of the alternator strengthens the field, and thereby, at con- stant-field excitation, increases the voltage ; with lagging current it weakens the field, and thereby decreases the vol- tage in a generator. Obviously, the opposite holds for a synchronous motor, in which the armature current flows in the opposite direction ; and thus a lagging current tends to magnetize, a leading current to demagnetize, the field. 183. The E.M.F. induced in the armature by the re- sultant magnetic flux, produced by the r ...", "... ure reaction. For this reason both actions can be combined in one, and represented by what is called the syn- cJironous reactance of the alternator. In the following, we shall represent the total reaction of the armature of the alternator by the one term, synchronous reactance. While this is not exact, as stated above, since the reactance should be resolved into the magnetic reaction due to the magnet- izing action of the armature current, and the electric reac- tion due to the self-induction of the armature current, ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-01", "section_label": "Chapter 1: Speed Control Of Induction Motors", "section_title": "Speed Control Of Induction Motors", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1368-3542", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-01/", "snippets": [ "... ation; and to produce an approximately constant speed for a wide range of load, for constant-speed operation. In its characteristics, the induction motor is a shunt motor, that is, it runs at approximately constant speed for all loads, and this speed is synchronism at no-load. At speeds below full speed, and at standstill, the torque of the motor is low and the current high, that is, the starting-torque efficiency and especially the apparent starting-torque efficiency are low. Where starting with considerable load, ...", "... sistance as curve A ; r\\ = 0.1, at light- load, where iL is small and the external part of the resistance cold. But with increasing load the resistance, r'i, increases, and the motor gives the curve shown as C in Fig. 1. As seen, curve C is the same near synchronism as A, but in starting gives twice as much torque as A, due to the increased resistance, C and .-1 thus are directly comparable: both have the same constants mid same speed regulation and other performance, at speed, but C gives much higher torque at sta ...", "... us will be discussed more fully in Chapter II. II. CONSTANT -SPEED OPERATION 8. The standard induction motor is essentially a constant-speed motor, that is, its speed is practically constant for all loads, decreasing slightly with increasing load, from synchronism at no-load. It thus has the same speed characteristics as the direct- current shunt motor, and in principle is a shunt motor. In the direct-current shunt motor, the speed may be changed by: resistance in the armature, resistance in the field, change of ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-26", "section_label": "Apparatus Section 5: Synchronous Machines: Synchronous Reactance", "section_title": "Synchronous Machines: Synchronous Reactance", "kind": "apparatus-section", "sequence": 26, "number": 5, "location": "lines 9035-9169", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-26/", "snippets": [ "V. Synchronous Reactance 14. In general, both effects, armature self-inductance and armature reaction, can be combined by the term \" synchronous reactance.\" FIG. 55. — Diagram showing effect of synchronous reactance. FIG. 56. — Diagram o ...", "V. Synchronous Reactance 14. In general, both effects, armature self-inductance and armature reaction, can be combined by the term \" synchronous reactance.\" FIG. 55. — Diagram showing effect of synchronous reactance. FIG. 56. — Diagram of generator e.m.f s. showing affect of synchronous reactance with non-reactive load. In a polyphase machine, the synchronous react ...", "V. Synchronous Reactance 14. In general, both effects, armature self-inductance and armature reaction, can be combined by the term \" synchronous reactance.\" FIG. 55. — Diagram showing effect of synchronous reactance. FIG. 56. — Diagram of generator e.m.f s. showing affect of synchronous reactance with non-reactive load. In a polyphase machine, the synchronous reactance is different, and lower, with one phase only loaded, as ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-86", "section_label": "Apparatus Section 7: Synchronous Converters: Variable Ratio Converters (\"split Pole\" Converters)", "section_title": "Synchronous Converters: Variable Ratio Converters (\"split Pole\" Converters)", "kind": "apparatus-section", "sequence": 86, "number": 7, "location": "lines 15586-15734", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-86/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-86/", "snippets": [ "... onverters (\"Split Pole\" Converters) 98. With a sine wave of alternating voltage, and the com- mutator brushes set at the magnetic neutral, that is, at right angles to the resultant magnetic flux, the direct voltage of a SYNCHRONOUS CONVERTERS 253 converter is constant at constant impressed alternating voltage. It equals the maximum value of the alternating voltage between two diametrically opposite points of the commutator, or \"dia- metrical voltage, ...", "... ary. Vm. Starting 99. The polyphase converter is self-starting from rest; that is, when connected across the polyphase circuit it starts, acceler- 254 ELEMENTS OF ELECTRICAL ENGINEERING ates, and runs up to complete synchronism. The e.m.f. between the commutator brushes is alternating in starting, with the fre- quency of slip below synchronism. Thus a direct-current volt- meter or incandescent lamps connected across the commutator brushes indicate by ...", "... phase circuit it starts, acceler- 254 ELEMENTS OF ELECTRICAL ENGINEERING ates, and runs up to complete synchronism. The e.m.f. between the commutator brushes is alternating in starting, with the fre- quency of slip below synchronism. Thus a direct-current volt- meter or incandescent lamps connected across the commutator brushes indicate by their beats the approach of the converter to synchronism. When starting, the field circuit of the converter has to b ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-16", "section_label": "Chapter 16: Aiitebnatingh-Current Osnebator", "section_title": "Aiitebnatingh-Current Osnebator", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 17025-18828", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "snippets": [ "... al, symmetrical. An exception from this statement may take place only in those types of alternators where the magnetic reluctance of the armature is different in different directions ; thereby, 1 160] AL TERN A TING-CURRENT GENERA TOR. 235 during the synchronous rotation of the armature, a pulsa- tion of the magnetic flux passing through it is produced. This pulsation of the magnetic flux induces E.M.F. in the field spools, and thereby makes the field current pulsating also. Thus, we have, in this case, even on o ...", "... ure reaction of the alternator strengthens the field, and thereby, at con- stant-field excitation, increases the voltage ; with lagging current it weakens the fi,eld, and thereby decreases the vol- tage in a generator. Obviously, the opposite holds for a synchronous motor, in which the direction of rotation is opposite ; and thus a lagging current tends to magnetize, a leading current to demagnetize, the field. 161. The E.M.F. induced in the armature by the re- sultant magnetic flux, produced by the resultant M.M.F. ...", "... ce increases the ter- minal voltage with a leading, and decreases it with a lagging current, or, in other words, acts in the same manner as the armature reaction. For this reason both actions can be combined in one, and represented by what is called the synchronous reactance of the alternator. In the following, we shall represent the total reaction of the armature of the alternator by the one term, synchronous reactance. While this is not exact, as stated above, since the reactance should be resolved into the magn ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... stic, 192 as unstable conductor, 167 Arcing ground on transmission lines, . 199 Area of BH relation, 53 Armature flux of alternator, 233 reactance flux of alternator, 232 reaction of alternator, 236 Attenuation constant, leaky con- ductor, 334 of synchronous machine oscil- lation, 213 B Balance of quarterphase system on singlephase load, 322 of singlephase load, 319 of threephase system on single- phase load, 325 of unbalanced power of system, 319 Bends in magnetic reluctivity curve, 49 Bismuth, ...", "... 2 Corona cbnduction, 29, 42 Creepage, magnetic, 57 Critical points of reluctivity curve, 46 Cumulative oscillation, cause, 166 produced by arc, 188 in transformer, 199 surge, 166 Current wave distorted by mag- netism, 126 D Damping power in synchronous^ motor oscillation, 210 winding in synchronous mi chines, 211 Danger of higher harmonics, 121 Decrement of oscillating wave, 34J Demagnetization by alternating ci^ :y, rent, 54 temperature, 78 Diffusion current of polarization, S Direct current prod ...", "... 57 Critical points of reluctivity curve, 46 Cumulative oscillation, cause, 166 produced by arc, 188 in transformer, 199 surge, 166 Current wave distorted by mag- netism, 126 D Damping power in synchronous^ motor oscillation, 210 winding in synchronous mi chines, 211 Danger of higher harmonics, 121 Decrement of oscillating wave, 34J Demagnetization by alternating ci^ :y, rent, 54 temperature, 78 Diffusion current of polarization, S Direct current producing even har- monics, 159 Discharges, oscilla ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-36", "section_label": "Apparatus Section 15: Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "section_title": "Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "kind": "apparatus-section", "sequence": 36, "number": 15, "location": "lines 9918-10123", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-36/", "snippets": [ "... aid to be synchronized. The parallel operation of the alternators is satisfactory in this case provided that the pulsations of engine speeds are of the same size and duration; but apparatus requiring constant fre- quency, as synchronous motors and rotary converters, when operated from such a system, will give a reduced maximum out- put, due to periodic cross currents between the generators of fluctuating frequency and the synchronous motors of constant frequ ...", "... constant fre- quency, as synchronous motors and rotary converters, when operated from such a system, will give a reduced maximum out- put, due to periodic cross currents between the generators of fluctuating frequency and the synchronous motors of constant frequency, and in an extreme case the voltage of the whole sys- tem will be caused to fluctuate periodically. Even with small fluctuations of engine speed the unsteadiness of current due to this source i ...", "... ant frequency, and in an extreme case the voltage of the whole sys- tem will be caused to fluctuate periodically. Even with small fluctuations of engine speed the unsteadiness of current due to this source is noticeable in synchronous motors and synchronous converters. If the alternators happen to be synchronized in such a position that the moment of maximum speed of the one coincides with the moment of minimum speed of the other, alternately the one ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-20", "section_label": "Chapter 20: Beactiox Machines", "section_title": "Beactiox Machines", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 22388-23273", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "snippets": [ "... he different positions of the armature coils in the magnetic circuit. This variation of the reactance causes phenomena which do not find their explanation by the theoretical cal- culations made under the assumption of constant reactance. It is known that synchronous motors of large and variable reactance keep in synchronism, and are able to do a considerable amount of work, and even carry under circumstances full load, if the field-exciting circuit is broken, and thereby the counter E.M.F. E^ reduced to zero, and so ...", "... circuit. This variation of the reactance causes phenomena which do not find their explanation by the theoretical cal- culations made under the assumption of constant reactance. It is known that synchronous motors of large and variable reactance keep in synchronism, and are able to do a considerable amount of work, and even carry under circumstances full load, if the field-exciting circuit is broken, and thereby the counter E.M.F. E^ reduced to zero, and sometimes even if the field circuit is reversed and the count ...", "... broken, or even reversed to a small negative value, in which latter case the current flows against the E.M.F. E^ of the generator. Furthermore, a shuttle armature without any winding will in an alternating magnetic field revolve when once brought up to synchronism, and do considerable work as a motor. These phenomena are not due to remanant magnetism nor to the magnetizing effect of Foucault currents, because 206, 206] REACTION MACHINES, 809 they exist also in machines with laminated fields, and exist if the ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2485-3386", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-04/", "snippets": [ "... reactance), etc., of the apparatus, resulting from the air gap in the magnetic circuit. 19. As instance of the use of the single-energy transient in engineering calculations may be considered the investigation of the momentary short-circuit phenomena of synchronous alter- nators. In alternators, especially high-speed high-power ma- chines as turboalternators, the momentary short-circuit current may be many times greater than the final or permanent short- circuit current, and this excess current usually decreases fai ...", "... armature self-induction. Under permanent condi- tion, both usually act in the same way, reducing the voltage at noninductive and still much more at inductive load, and increasing it at antiinductive load; and both are usually combined in one quantity, the synchronous reactance Xq. In the transients result- ing from circuit changes, as short circuits, the self-inductive armature reactance and the magnetic armature reaction act very differently:* the former is instantaneous in its effect, while the latter requires time. ...", "... re magnetic flux and the current which produces it must be simultaneous (the former being an integral part of the phenomenon of current flow, as seen in Lecture II), it thus follows that the armature reactance appears together * So also in their effect on synchronous operation, in hunting, etc. 38 ELECTRIC DISCHARGES, WAVES AND IMPULSES. with the armature current, that is, is instantaneous. The arma- ture reaction, however, is the m.m.f. of the armature current in its reaction on the m.m.f. of the field-exciting cu ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2162-2971", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "snippets": [ "... ng the transi- tion period can reach, is limited to less than double the final value, as is obvious from the construction of the 'field, Fig. 19. It is evident herefrom, however, that in apparatus containing rotating fields, as induction motors, polyphase synchronous machines, etc., the resultant field may under transient conditions reach nearly double value, and if then it reaches far above magnetic saturation, excessive momentary currents may appear, similar as in starting transformers of high magnetic density. In p ...", "... reactance), etc., of the apparatus, resulting from the air gap in the magnetic circuit. 19. As instance of the use of the single-energy transient in engineering calculations may be considered the investigation of the momentary short-circuit phenomena of synchronous alter- nators. In alternators, especially high-speed high-power mar chines as turboalternators, the momentary short-circuit current may be many times greater than the final or permanent short- circuit current, and this excess current usually decreases ver ...", "... rmature self-induction. Under permanent condi- tion, both usually act\" in the same way, reducing the voltage at noninductive and still much more at inductive load, and increasing it at antiinductive load; and both are usually combined in one quantity, the synchronous reactance XQ. In the transients result- ing from circuit changes, as short circuits, the self-inductive armature reactance and the magnetic armature reaction act very differently:* the former is instantaneous in its effect, while the latter requires time. ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-30", "section_label": "Apparatus Section 9: Synchronous Machines: Magnetic Characteristic or Saturation Curve", "section_title": "Synchronous Machines: Magnetic Characteristic or Saturation Curve", "kind": "apparatus-section", "sequence": 30, "number": 9, "location": "lines 9554-9650", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-30/", "snippets": [ "IX. Magnetic Characteristic or Saturation Curve 20. The dependence of the generated e.m.f., or terminal voltage at open circuit, upon the field excitation is called the magnetic characteristic, or saturation curve, of the synchronous 1000 2000 3000 4000 5000 FIG. 69. — Synchronous generator magnetic 7000 characteristics. machine. It has the same general shape as the curve of mag- netic flux density, consisting of a straight part below ...", "... endence of the generated e.m.f., or terminal voltage at open circuit, upon the field excitation is called the magnetic characteristic, or saturation curve, of the synchronous 1000 2000 3000 4000 5000 FIG. 69. — Synchronous generator magnetic 7000 characteristics. machine. It has the same general shape as the curve of mag- netic flux density, consisting of a straight part below saturation, a bend or knee, and a saturated part beyond the k ...", "... r knee, and a saturated part beyond the knee. Gener- ally the change from the unsaturated to the over-saturated por- tion of the curve is more gradual; thus the knee is less pronounced in the magnetic characteristic of the synchronous machines, since the different parts of the magnetic circuit approach saturation successively. The dependence of the terminal voltage upon the field excita- tion, at constant full-load current through the amature into a 148 ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-83", "section_label": "Apparatus Section 4: Synchronous Converters: Armature Current and Heating", "section_title": "Synchronous Converters: Armature Current and Heating", "kind": "apparatus-section", "sequence": 83, "number": 4, "location": "lines 13889-15160", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-83/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-83/", "snippets": [ "IV. Armature Current and Heating 88. The current in the armature conductors of a converter is the difference between the alternating-current input and the direct-current output. SYNCHRONOUS CONVERTERS 233 In Fig. 127, ai, a2 are two adjacent leads connected with the collector rings DI, D2 in an n-phase converter. The alternating e.m.f. between a\\ and a2, and thus the power component of the alternating cu ...", "... t wave, and consequently in this coil the power component of the alternating current and the rectan- gular direct current are in phase with each other, but opposite, as FIG. 127. — Diagram for study of armature heating in synchronous converters. FIG. 128. — Direct current and alternating current in armature coil d, Fig. 127. FIG. 129. — Resultant current in coil d, Fig. 127. shown in Fig. 128 as 7i and /, and the actual current is their difference ...", "... and a\\ or a* Fig. 127. FIG. 131. — Resultant of currents given in Fig. 130. FIG. 132. — Alternating current and direct current in coil between d and or a2, Fig. 127. FIG. 133. — Resultant of currents shown in 132. SYNCHRONOUS CONVERTERS 235 ture coils are successively displaced in phase from each other; and since the alternating current is the same in the whole section ai a2, and in phase with the rectangular current in the coil d, it become ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-21", "section_label": "Chapter 21: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 22302-23970", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-21/", "snippets": [ "... o distinctly different m.m.fs. are acting upon the alternator armature — the m.m.f. of the field due to the field-exciting spools, and the m.m.f. of the armature current. The former is constant, or approximately so, while the latter is alternating, and in synchronous motion relatively to the former; hence fixed in space relative to the field m.m.f., or uni- FiG. 129. directional; but pulsating in a single-phase alternator. In the polyphase alternator, when evenly loaded or balanced, the result- ant m.m.f. of the a ...", "... ion of the alternator strengthens the field, and thereby, at constant field excitation, increases the voltage; with lagging current it weakens Fig. 131. the field, and thereby decreases the voltage in a generator. Ob- viously, the opposite holds for a synchronous motor, in which the armature current is in the opposite direction; and thus a lagging current tends to magnetize, a leading current to demagnetize, the field. 186. The e.m.f. generated in the armature by the resultant magnetic flux, produced by the resu ...", "... ance increases the terminal voltage with a leading, and decreases it with a lagging current, or, in other words, acts in the same manner as the armature reaction. For this reason both actions can be combined in one, and repre- sented by what is called the synchronous reactance of the alter- nator. In the following, we shall represent the total reaction of the armature of the alternator by the one term, synchronous reactance. While this is not exact, as stated above, since the reactance should be resolved into the magn ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-21", "section_label": "Chapter 21: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 20502-21189", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-21/", "snippets": [ "... he different positions of the armature coils in the magnetic circuit. This variation of the reactance causes phenomena which do not find their explanation by the theoretical cal- culations made under the assumption of constant reactance. It is known that synchronous motors of large and variable reactance keep in synchronism, and are able to do a considerable amount of work, and even carry under circumstances full load, if the field-exciting circuit is broken, and thereby the counter E.M.F. E± reduced to zero, and so ...", "... circuit. This variation of the reactance causes phenomena which do not find their explanation by the theoretical cal- culations made under the assumption of constant reactance. It is known that synchronous motors of large and variable reactance keep in synchronism, and are able to do a considerable amount of work, and even carry under circumstances full load, if the field-exciting circuit is broken, and thereby the counter E.M.F. E± reduced to zero, and sometimes even if the field circuit is reversed and the count ...", "... broken, or even reversed to a small negative value, in which latter case the current flows against the E.M.F. EQ of the generator. Furthermore, a shuttle armature without any winding will in an alternating magnetic field revolve when once brought up to synchronism, and do considerable work as a motor. These phenomena are not due to remanent magnetism nor to the magnetizing effect of Foucault currents, because 372 AL TERNA TING-CURRENT PHENOMENA. they exist also in machines with laminated fields, and exist if ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-09", "section_label": "Chapter 10: Hysteresis Motor", "section_title": "Hysteresis Motor", "kind": "chapter", "sequence": 9, "number": 10, "location": "lines 14551-14761", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-09/", "snippets": [ "... ant. The apparent or volt-ampere input of the motor is: P ■ wiS*. Thus the apparent torque efficiency: Q = volt-ampere input, HYSTERESIS MOTOR 169 and the power of the motor is: P = (1 - s) D = (1 - s) m$$ sin a, where s = slip as fraction of synchronism. The apparent efficiency is: p n = (1 — *) sin a. Since in a magnetic circuit containing an air gap the angle, a, is small, a few degrees only, it follows that the apparent efficiency of the hysteresis motor is low, the motor consequently unsuitabl ...", "... motor the rotary iron structure has imi uniform reluctance in all directions — but is, for instance, bar- shaped or shuttle-shaped — on the hysteresis-motor effect is superimposed the effect of varying magnetic reluctance which tends to bring the motor to synchronism, and maintain it therein, as shall be more fully investigated under \"Reaction Machine\" in Chapter XVI. 100. In the hysteresis motor, consisting of an iron disk of uniform magnetic reluctance, which revolves in a uniformly rotating magnetic field, below ...", "... , and maintain it therein, as shall be more fully investigated under \"Reaction Machine\" in Chapter XVI. 100. In the hysteresis motor, consisting of an iron disk of uniform magnetic reluctance, which revolves in a uniformly rotating magnetic field, below synchronism, the magnetic mix rotates in the armature with the frequency of slip, and the resultant line of magnetic induction in the disk thus lags, in space, behind the synchronously rotating line of resultant m.m.f HYSTERESIS MOTOR 171 of the exciting coils, b ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-20", "section_label": "Chapter 20: Single-Phase Induction Motors", "section_title": "Single-Phase Induction Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 21538-22301", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-20/", "snippets": [ "CHAPTER XX SINGLE-PHASE INDUCTION MOTORS 177. The magnetic circuit of the induction motor at or near synchronism consists of two magnetic fluxes superimposed upon each other in quadrature, in time, and in position. In the polyphase motor these fluxes are produced by e.m.fs. displaced in phase. In the monocyclic motor one of the fluxes is due to the primary power cir ...", "... mary circuit, the other by the currents produced in the secondary or armature, which are carried into quadrature posi- tion by the rotation of the armature. In consequence thereof, while in all these motors the magnetic distribution is the same at or near synchronism, and can be represented by a rotating field of uniform intensity and uniform velocity, it remains such in polyphase and monocyclic motors; but in the single-phase motor, with increasing slip — that is, decreasing speed — the quadrature field decreases, si ...", "... ngle-phase motor is equal to that of the same motor under the same condition of operation on a polyphase circuit, multiplied with the speed; hence equal to zero at standstill. Thus, while single-phase induction motors are quite satisfac- tory at or near synchronism, their torque decreases proportionally with the speed, and becomes zero at standstill. That is, they are not self-starting, but some starting device has to be used. Such a starting device may either be mechanical or electrical. All the electrical startin ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-22", "section_label": "Apparatus Section 1: Synchronous Machines: General", "section_title": "Synchronous Machines: General", "kind": "apparatus-section", "sequence": 22, "number": 1, "location": "lines 8518-8657", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-22/", "snippets": [ "I. General 3. The most important class of alternating-current apparatus consists of the synchronous machines. They comprise the alternating-current generators, single-phase and polyphase, the synchronous motors, the phase compensators, the phase con- verters, the phase balancers, the synchronous boosters and the exciters of indu ...", "I. General 3. The most important class of alternating-current apparatus consists of the synchronous machines. They comprise the alternating-current generators, single-phase and polyphase, the synchronous motors, the phase compensators, the phase con- verters, the phase balancers, the synchronous boosters and the exciters of induction generators, that is, synchronous machines producing wattless lagging or leading currents, and th ...", "... -current apparatus consists of the synchronous machines. They comprise the alternating-current generators, single-phase and polyphase, the synchronous motors, the phase compensators, the phase con- verters, the phase balancers, the synchronous boosters and the exciters of induction generators, that is, synchronous machines producing wattless lagging or leading currents, and the con- verters. Since the latter combine features of the commutating machines with those of ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-35", "section_label": "Chapter 35: Balanced Symmetrical Polyphase Systems", "section_title": "Balanced Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 35, "number": 35, "location": "lines 37453-37957", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-35/", "snippets": [ "... voltage, eo = 52,100 X \\/3 = 90,000 volts; voltage drop in line, = 11.1 per cent. 305. Balanced polyphase systems thus can be calculated as single-phase systems, and this has been done in man}^ preceding chapters, as in those on the induction machines, synchronous machines, etc., that is, apparatus which is usually operated on polyphase circuits. BALANCED SYMMETRICAL POLYPHASE SYSTEMS 453 Only in dealing with those phenomena which are resultants of all the phases of the polyphase system, in the resolution of th ...", "... lue of the constant has to be used, which corresponds to the resultant effect. This, for instance, is the case in calcu- lating the magnetic field of the induction machine — which is energized by the combination of all phases — or the armature reaction of synchronous machines, etc. For instance, in the induction machine, from the generated e.m.f., e — in Chapter XVIII — the magnetic flux of the machine is calculated, and from the magnetic flux and the dimensions of the magnetic circuit: length and section of air-gap, ...", "... rent per phase required to produce the resulting m.m.f,, Fo, therefore, is 1 = > nm hence, for a three-phase system, 1 = 5 ' 6 n and for a quarter-phase system, with two coils in quadrature, n V2 In the investigation of the armature reaction of synchronous machines. Chapter XXII, the armature reaction of an 7«-phase machine is, by §271, Worn/ . 454 ALTERNATING-CURRENT PHENOMENA where m = number of phases, no = number of turns per phase, effective, that is, allow- ing for the spread of turns over a ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-15", "section_label": "Chapter 15: The General Alternating-Current Transformer Or Frequency Converter", "section_title": "The General Alternating-Current Transformer Or Frequency Converter", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 12683-13648", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "snippets": [ "... primary frequency, or frequency of impressed E.M.F., s JV = secondary frequency ; 222 ALTERNATING-CURRENT PHENOMENA. and the E.M.F. induced per secondary turn by the mutual flux has to the E.M.F. induced per primary turn the ratio s, s = 0 represents synchronous motion of the secondary ; s < 0 represents motion above synchronism — driven by external mechanical power, as will be seen ; s = 1 represents standstill ; s > 1 represents backward motion of the secondary that is, motion against the mechanical force a ...", "... frequency ; 222 ALTERNATING-CURRENT PHENOMENA. and the E.M.F. induced per secondary turn by the mutual flux has to the E.M.F. induced per primary turn the ratio s, s = 0 represents synchronous motion of the secondary ; s < 0 represents motion above synchronism — driven by external mechanical power, as will be seen ; s = 1 represents standstill ; s > 1 represents backward motion of the secondary that is, motion against the mechanical force acting between primary and secondary (thus representing driving by ex- ...", "... minal voltage * This applies to the case where the secondary contains inductive reac- tance only ; or, rather, that kind of reactance which is proportional to the fre- quency. In a condenser the reactance is inversely proportional to the frequency, in a synchronous motor under circumstances independent of the frequency. Thus, in general, we have to set, x = x' + x\" -\\ x\"\\ where x' is that part of the reactance which is proportional to the frequency, x\" that part of the reac- tance independent of the frequency, and x' ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-15", "section_label": "Chapter 17: Inductor Machines", "section_title": "Inductor Machines", "kind": "chapter", "sequence": 15, "number": 17, "location": "lines 20294-20974", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-15/", "snippets": [ "CHAPTER XVII INDUCTOR MACHINES Inductor Alternators, Etc. 156. Synchronous machines may be built with stationary field and revolving armature, as shown diagrammatically in Fig. 134, or with revolving field and stationary armature, Fig. 135, or with stationary field and stationary armature, but revolving magnetic circuit. The r ...", "... ing magnetic circuit. The revolving-armature type was the most frequent in the early days, but has practically gone out of use except for special Fia. 134. — Revolving armature alternator Fig. 135.— Revolving field al ternator. purposes, and for synchronous commutating machines, as the revolving-armature type of structure is almost exclusively used for commutating machines. The revolving-field type is now almost exclusively used, as the standard construction of alter- nators, synchronous motors, etc. The ind ...", "... purposes, and for synchronous commutating machines, as the revolving-armature type of structure is almost exclusively used for commutating machines. The revolving-field type is now almost exclusively used, as the standard construction of alter- nators, synchronous motors, etc. The inductor type had been used to a considerable extent, and had a high reputation in the Stanley alternator. It has practically gone out of use for standard frequencies, due to its lower economy in the use of materials, but has remained a v ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-91", "section_label": "Apparatus Section 13: Synchronous Converters: Direct-current Converter", "section_title": "Synchronous Converters: Direct-current Converter", "kind": "apparatus-section", "sequence": 91, "number": 13, "location": "lines 16065-16540", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-91/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-91/", "snippets": [ "... to a neutral point as shown diagrammatically in Fig. 140 for n = 3, this neutral is equidis- tant in potential from the two sets of commutator brushes, and such a machine can be used as continuous current converter, to SYNCHRONOUS CONVERTERS 263 transform in the ratio of potentials 1 :2 or 2 : 1 or 1 : 1, in the latter case transforming power from one side of a three- wire system to the other side. Obviously either the n autotransformers can ...", "... the generator side of the converter is equal but opposite to the armature reaction of the corresponding currents entering the motor side, and the motor and generator armature reactions thus neutralize each other, as in the synchronous converter; that is, the resultant SYNCHRONOUS CONVERTERS 265 armature reaction of the continuous-current converter is prac- tically zero, or the only remaining armature reaction is that corresponding to the relatively small ...", "... but opposite to the armature reaction of the corresponding currents entering the motor side, and the motor and generator armature reactions thus neutralize each other, as in the synchronous converter; that is, the resultant SYNCHRONOUS CONVERTERS 265 armature reaction of the continuous-current converter is prac- tically zero, or the only remaining armature reaction is that corresponding to the relatively small current required to rotate the machine, that ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-14", "section_label": "Chapter 14: The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "section_title": "The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14089-14918", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "snippets": [ "... quency, or frequency of impressed E.M.F., s JV=i secondary frequency ; 196 AL TERN A TING-CURRENT PHENOMENA. [f 1 36 and the E.M.F. induced per secondary turn by the mutual flux has to the E.M.F. induced per primary turn the ratio s^ J =r represents synchronous motion of the secondary ; J < represents motion above synchronism — driven by external mechanical power, as will be seen ; J = 1 represents standstill ; J > 1 represents backward- motion of the secondary that is, motion against the mechanical force ac ...", "... cy ; 196 AL TERN A TING-CURRENT PHENOMENA. [f 1 36 and the E.M.F. induced per secondary turn by the mutual flux has to the E.M.F. induced per primary turn the ratio s^ J =r represents synchronous motion of the secondary ; J < represents motion above synchronism — driven by external mechanical power, as will be seen ; J = 1 represents standstill ; J > 1 represents backward- motion of the secondary that is, motion against the mechanical force acting between primary and secondary (thus representing driving by ex ...", "... +r) ^js{xi + x) ♦ This applies to the case where the secondary contains inductive reac- tance only : or, rather, that kind of reactance which is proportional to the fre- quency. In a condenser the reactance is inversely proportional to the frequency in a synchronous motor under circumstances independent of the frequency. Thus, in general, we have to set, x = x' -^ x\" -^ x''\\ where x' is that part of the reactance which is proportional to the frequency, jt\" that part of the reac- tance independent of the frequency, and ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-04", "section_label": "Chapter 5: Single-Phase Induction Motor", "section_title": "Single-Phase Induction Motor", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 8555-10582", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-04/", "snippets": [ "... ic flux. A component of the armature currents then magnetizes in the direction at right angles (electrically) to the main magnetic flux, and the armature currents thus produce a quadrature magnetic flux, increasing from zero at standstill, to a maximum at synchronism, and approximately proportional to the quadrature component of the armature polarization, P: P sin (1 — s) • 93 ill ELECTRICAL APPARATUS The torque of the single-phase motor then is produced by the action of the quadrature flux on the energy cu ...", "... ion, P: P sin (1 — s) • 93 ill ELECTRICAL APPARATUS The torque of the single-phase motor then is produced by the action of the quadrature flux on the energy currents induced by the main flux, and thus is proportional to the quadrature flux. At synchronism, the quadrature magnetic flux produced by the armature currents becomes equal to the main magnetic flux produced by the impressed single-phase voltage (approximately, in reality it is less by the impedance drop of the exciting current in the armature cond ...", "... n magnetic flux produced by the impressed single-phase voltage (approximately, in reality it is less by the impedance drop of the exciting current in the armature conductors) and the magnetic disposition of the single-phase induction motor thus becomes at synchronism iden- tical with that of the polyphase induction motor, and approxi- mately so near synchronism. The magnetic field of the single-phase induction motor thus may be said to change from a single-phase alternating field at standstill, over an unsymmetrical ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-35", "section_label": "Chapter 13: Transient Term Of The Rotating Field", "section_title": "Transient Term Of The Rotating Field", "kind": "chapter", "sequence": 35, "number": 13, "location": "lines 13936-14548", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-35/", "snippets": [ "CHAPTER XIII. TRANSIENT TERM OF THE ROTATING FIELD. 106. The resultant of np equal m.m.fs. equally displaced from each other in space angle and in time-phase is constant in intensity, and revolves at constant synchronous velocity. When acting upon a magnetic circuit of constant reluctance in all directions, such a polyphase system of m.m.fs. produces a revolving magnetic flux, or a rotating field. (\" Theory and Calculation of Alternating Current Phenomena,\" 4th edition, ...", "... and as the sums containing - - i equal zero, we have np os(0-00) -cos00, (8) and for 6 = oo f that is as permanent term, this gives /0=^SFcos(0-00); (9) ft hence, a maximum, and equal to -~ &, that is, constant, for 00 = 0, that is, uniform synchronous rotation. That is, the resultant of a polyphase system of m.m.fs., in permanent con- dition, rotates at constant intensity and constant synchronous velocity. Before permanent condition is reached, however, the resultant m.m.f. in the direction #0 = 6, t ...", "... Fcos(0-00); (9) ft hence, a maximum, and equal to -~ &, that is, constant, for 00 = 0, that is, uniform synchronous rotation. That is, the resultant of a polyphase system of m.m.fs., in permanent con- dition, rotates at constant intensity and constant synchronous velocity. Before permanent condition is reached, however, the resultant m.m.f. in the direction #0 = 6, that is, in the direction of the synchronously rotating vector, in which in permanent condition 194 TRANSIENT PHENOMENA the m.m.f . is maximu ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-27", "section_label": "Apparatus Section 6: Synchronous Machines: Characteristic Curves of Alternating-current Generator", "section_title": "Synchronous Machines: Characteristic Curves of Alternating-current Generator", "kind": "apparatus-section", "sequence": 27, "number": 6, "location": "lines 9170-9291", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-27/", "snippets": [ "... abscissas and for the three conditions, 1. Non-inductive load, p = 1, q = 0. 2. Inductive load of 0 = 60 degrees lag, p = 0.5, q = 0.866. 3. Anti-inductive load of — 6 = 60 degrees lead, p = 0.5, q = -0.866. SYNCHRONOUS MACHINES 139 The values r = 0.1, XQ = 5, E = 1000, are assumed. These curves are called the compounding curves of the synchronous generator. In Fig. 60 are shown, at constant nominal generated e.m.f. EQ, that is, a ...", "... = 0.866. 3. Anti-inductive load of — 6 = 60 degrees lead, p = 0.5, q = -0.866. SYNCHRONOUS MACHINES 139 The values r = 0.1, XQ = 5, E = 1000, are assumed. These curves are called the compounding curves of the synchronous generator. In Fig. 60 are shown, at constant nominal generated e.m.f. EQ, that is, at constant field excitation F0, the values of terminal vol- E = 000 £=5, '•*& z EO.F, 500 20 10 00 80 100 12 ...", "... nstant nominal generated e.m.f. EQ, that is, at constant field excitation F0, the values of terminal vol- E = 000 £=5, '•*& z EO.F, 500 20 10 00 80 100 120 UO 160 180 200AMP. FIG. 59. — Synchronous generator compounding curves. tage E with the current I as abscissas and for the same resistance and synchronous reactance r = 0.1, XQ = 5, for the three different conditions, 1. Non-inductive load, p = 1, q = 0, EQ ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-80", "section_label": "Apparatus Subsection 80: Direct-current Commutating Machines: C. Commutating Machines 221", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 221", "kind": "apparatus-subsection", "sequence": 80, "number": null, "location": "lines 13120-13188", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-80/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-80/", "snippets": [ "... le-phase motors. For this purpose, com- binations of repulsion and induction type or of series and in- duction type are used. 3. As adjustable speed, alternating-current motor of single- phase and of polyphase type. The synchronous motor and the induction motor both are constant and fixed speed, the former synchronous, the latter near synchronous. Operating the induction motor materially below synchronism, by arma- ture resistance, is inefficient and g ...", "... series and in- duction type are used. 3. As adjustable speed, alternating-current motor of single- phase and of polyphase type. The synchronous motor and the induction motor both are constant and fixed speed, the former synchronous, the latter near synchronous. Operating the induction motor materially below synchronism, by arma- ture resistance, is inefficient and gives a speed which varies with the load. By changing the number of poles, or by con ...", "... are used. 3. As adjustable speed, alternating-current motor of single- phase and of polyphase type. The synchronous motor and the induction motor both are constant and fixed speed, the former synchronous, the latter near synchronous. Operating the induction motor materially below synchronism, by arma- ture resistance, is inefficient and gives a speed which varies with the load. By changing the number of poles, or by concatena- tion, multi-speed ind ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-84", "section_label": "Apparatus Section 5: Synchronous Converters: Armature Reaction", "section_title": "Synchronous Converters: Armature Reaction", "kind": "apparatus-section", "sequence": 84, "number": 5, "location": "lines 15161-15475", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-84/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-84/", "snippets": [ "V. Armature Reaction 93. The armature reaction of the polyphase converter is the resultant of the armature reactions of the machine as direct- current generator and as synchronous motor. If the com- mutator brushes are set at right angles to the field poles or without lead or lag, as is usually done in converters, the direct- current armature reaction consists in a polarization in quadra- ture behin ...", "... n irn = resultant polarization, in effective ampere-turns of one phase of the converter. The resultant m.m.f. of n equal m.m.fs. of effective value of FI, thus maximum value of FI \\/2, acting under equal angles SYNCHRONOUS CONVERTERS 247 — , and displaced in phase from each other by - of a period, or 71 71 phase angle — , is found thus: = Fi\\/2sin (0 -- — j = one of the m.m.fs. of phase 2iir angle 0 = -- , where i = 0, 1 ...", "... I 2 ir - — )COB(T-— we have that is, the resultant m.m.f. in any direction T has the phase 6 = r, and the intensity, rcFiA/2 ~^~ thus revolves in space with uniform velocity and constant in- tensity, in synchronism with the frequency of the alternating current. 248 ELEMENTS OF ELECTRICAL ENGINEERING Since in the converter, Fl = ^M, TTU we have the resultant m.m.f. of the power component of the alternating current in the n-ph ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-06", "section_label": "Lecture 6: Higher Harmonics Of The Generator Wave", "section_title": "Higher Harmonics Of The Generator Wave", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3133-3507", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-06/", "snippets": [ "... ccur between the line capacity and the circuit inductance. The origin and existence of higher harmonics therefore bears investigation in transformers, transmlission lines and cable systems. ORIGIN OF HIGHER HARMONICS Higher harmonics may originate in synchronous machines, as generators, synchronous motors and converters, and in transformers. These two classes of higher harmonics are very different. The former have constant potential character; the latter, con- stant current character; their cure and prevention ...", "... e circuit inductance. The origin and existence of higher harmonics therefore bears investigation in transformers, transmlission lines and cable systems. ORIGIN OF HIGHER HARMONICS Higher harmonics may originate in synchronous machines, as generators, synchronous motors and converters, and in transformers. These two classes of higher harmonics are very different. The former have constant potential character; the latter, con- stant current character; their cure and prevention there- fore must be different, and th ...", "... coming from a transformer is eliminated by short circuit Short circuiting a generator harmonic, however, gives large 8o GENERAL LECTURES short circuit currents, due to the constant potential character, and is therefore dangerous. HIGHER HARMONICS OF SYNCHRONOUS MACHINES In synchronous machines, as alternating current genera- tors, the higher harmonics are : At No Load I St. The distribution of magnetism in the air gap depends on the shape of the field poles; it is not a sine wave; neither is the e. m. f . ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-16", "section_label": "Theory Section 16: Phase Control of Transmission Lines", "section_title": "Phase Control of Transmission Lines", "kind": "theory-section", "sequence": 16, "number": 16, "location": "lines 6222-6813", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-16/", "snippets": [ "... . PHASE CONTROL OF TRANSMISSION LINES 97 u ti e 0 50 10,000 50 25 10,105 100 0 10,XKX) 150 -25 9,658 81. (3) In a circuit whose voltage e0 fluctuates by 20 per cent, between 1800 and 2200 volts, a synchronous motor of internal impedance Z0 = r0 + jx0 = 0.5 + 5 j is connected through a reactive coil of impedance Z\\ = r\\ + jx\\ = 0.5 -f- 10 j and run light, as compensator (that is, generator of reactive currents). How will ...", "... pedance Z0 = r0 + jx0 = 0.5 + 5 j is connected through a reactive coil of impedance Z\\ = r\\ + jx\\ = 0.5 -f- 10 j and run light, as compensator (that is, generator of reactive currents). How will the voltage at the synchronous motor terminals e\\, at constant excitation, that is, constant counter e.m.f. e = 2000, vary as function of e$ at no load and at a load of i = 100 amp. power current, and what will be the reactive current in the synch ...", "... onous motor terminals e\\, at constant excitation, that is, constant counter e.m.f. e = 2000, vary as function of e$ at no load and at a load of i = 100 amp. power current, and what will be the reactive current in the synchronous motor? Let I = ii — jiz = current in receiving circuit of voltage e\\. Of this current 1,—jiz is taken by the synchronous motor of counter e.m.f. 'e, and thus EI = e — Zoji2 = e + X0i2 - jr0i2'} or, reduced, e^= ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-23", "section_label": "Apparatus Section 2: Synchronous Machines: Electromotive Forces", "section_title": "Synchronous Machines: Electromotive Forces", "kind": "apparatus-section", "sequence": 23, "number": 2, "location": "lines 8658-8740", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-23/", "snippets": [ "II. Electromotive Forces 6. In a synchronous machine we have to distinguish between terminal voltage E, real generated e.m.f. #1, virtual generated e.m.f. EZ, and nominal generated e.m.f. EQ. The real generated e.m.f. EI is the e.m.f. generated in the alter- nator arm ...", "... , r = effective resistance. The virtual generated e.m.f. E2 is the e.m.f. which would be generated by the flux produced by the field poles, or flux corre- sponding to the resultant m.m.f., that is, the resultant of the SYNCHRONOUS MACHINES 129 m.m.fs. of field excitation and of armature reaction. Since the magnetic flux produced by the armature, or flux of armature self-inductance, combines with the field flux to the resultant flux, the flux produced ...", "... s merely a fictitious quantity, which, however, is very useful for the investigation of alternators by allowing the combination of armature reaction and self-inductance into a single effect by a (fictitious) self-inductance or synchronous reactance XQ. The nominal generated e.m.f. would be the terminal voltage with open circuit and load excitation if the saturation curve were a straight line. The synchronous reactance XQ is thus a quantity combining armature ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-24", "section_label": "Apparatus Section 3: Synchronous Machines: Armature Reaction", "section_title": "Synchronous Machines: Armature Reaction", "kind": "apparatus-section", "sequence": 24, "number": 3, "location": "lines 8741-8906", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-24/", "snippets": [ "... m.f., and thus magnetizes the preceding, demagnetizes the following magnet pole (in the di- rection of rotation) in an. alternating-current generator A] magnetizes the following and demagnetizes the preceding mag- net pole in a synchronous motor A' (since in a generator the rotation is against, in a synchronous motor with the magnetic attractions and repulsions between field and armature). In this case the armature current neither magnetizes nor demag- netizes ...", "... ole (in the di- rection of rotation) in an. alternating-current generator A] magnetizes the following and demagnetizes the preceding mag- net pole in a synchronous motor A' (since in a generator the rotation is against, in a synchronous motor with the magnetic attractions and repulsions between field and armature). In this case the armature current neither magnetizes nor demag- netizes the field as a whole, but magnetizes the one side, demag- SYNCHRONOUS M ...", "... a synchronous motor with the magnetic attractions and repulsions between field and armature). In this case the armature current neither magnetizes nor demag- netizes the field as a whole, but magnetizes the one side, demag- SYNCHRONOUS MACHINES 131 netizes the other side of each field pole, and thus merely distorts the magnetic field. 9. If the armature current lags behind the nominal generated e.m.f., it reaches its maximum in a position where the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-38", "section_label": "Apparatus Section 17: Synchronous Machines: Short-circuit Currents of Alternators", "section_title": "Synchronous Machines: Short-circuit Currents of Alternators", "kind": "apparatus-section", "sequence": 38, "number": 17, "location": "lines 10190-10429", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-38/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-38/", "snippets": [ "... cuit current of an alternator at full-load excitation usually is from two to five times full-load current, and even less in very large high-speed steam turbine alternators. It is where EQ = nominal generated e.m.f., ZQ = synchronous impe- dance of alternator, representing the combined effect of arma- ture reaction and armature self-inductance. In the first moment after short circuiting, however, the current frequently is many times larger than the permanen ...", "... time — occasionally several seconds — elapses before the armature reaction becomes effective. At short circuit, the magnetic field flux is greatly reduced by the demagnetizing action of the armature current, and the gen- SYNCHRONOUS MACHINES 161 erated e.m.f. thereby reduced from the nominal value EQ to the virtual value Ez; the latter is consumed by the armature self- inductive impedance z, or self-inductive reactance, which is practically the same i ...", "... neously start from zero in all phases and gradually approach their symmetrical appear- ance, i.e., in a three-phase machine three currents displaced by 120 degrees. Hereby the field current is made pulsating, with nor- mal or synchronous frequency, that is, with the same frequency as the armature current. This full frequency pulsation gradually dies out and the field current becomes constant with a polyphase short circuit, while with a single-phase short cir ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-85", "section_label": "Apparatus Section 6: Synchronous Converters: Reactive Currents and Compounding", "section_title": "Synchronous Converters: Reactive Currents and Compounding", "kind": "apparatus-section", "sequence": 85, "number": 6, "location": "lines 15476-15585", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-85/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-85/", "snippets": [ "VI. Reactive Currents and Compounding 96. Since the polarization due to the power component of the alternating current as synchronous motor is in quadrature ahead of the field magnetization, the polarization or magnetizing effect of the lagging component of alternating current is in phase, that of the leading component of alternating current in oppositon t ...", "... lagging, the field excitation at the same impressed e.m.f. has to be lower, and if the alter- nating current is leading, the field excitation has to be higher, than required with the alternating current in phase with the SYNCHRONOUS CONVERTERS 251 e.m.f. Inversely, by raising the field excitation a leading current, or by lowering it a lagging current, can be produced in a converter (and in a synchronous motor). Since the alternating current can ...", "... he alternating current in phase with the SYNCHRONOUS CONVERTERS 251 e.m.f. Inversely, by raising the field excitation a leading current, or by lowering it a lagging current, can be produced in a converter (and in a synchronous motor). Since the alternating current can be made magnetizing or demagnetizing according to the field excitation, at constant impressed alternating voltage, the field excitation of the con- verter can be varied through a wide ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-08", "section_label": "Lecture 8: Generation", "section_title": "Generation", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 3781-4217", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-08/", "snippets": [ "... eriority of the steam turbine in efficiency, while marked at rated load, is still far greater at partial load, light load and overload. b. Smaller size, weight and space occupied. c. Uniform rate of rotation, therefore decreased liability of hunting of synchronous machines, and decreased necessity of heavy foundations to withstand reciprocating strains. d. Greater reliability of operation and far less attend- ance required. The steam turbine reaps a far greater benefit in economy than the steam engine from super ...", "... ements. Where the power cannot be generated in the form in which it is used, and that is the case in all larger systems, three- phase alternators are almost universally used. The single-phase system has the disadvantage that single- phase induction and synchronous motors and converters are inferior to polyphase machines, and single-phase alternators larger and less efficient, and for lighting, where single-phase is preferable, single-phase lighting circuits can be operated from polyphase alternators. Two-phase al ...", "... n both be considered, which makes the calculation more complicated; or the armature reaction may be neglected and the self-induction made so much larger as to allow for the armature reaction. This self-induction is then no GENERAL LECTURES called the \"synchronous reactance\" and, combined with the armature resistance, the \"synchronous impedance\" of the ma- chine. Or the self-induction may be neglected and only the armature reaction considered, but which is increased to allow for the self-induction. The last way ( ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-32", "section_label": "Apparatus Section 11: Synchronous Machines: Unbalancing of Polyphase Synchronous Machines", "section_title": "Synchronous Machines: Unbalancing of Polyphase Synchronous Machines", "kind": "apparatus-section", "sequence": 32, "number": 11, "location": "lines 9719-9748", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-32/", "snippets": [ "XI. Unbalancing of Polyphase Synchronous Machines 23. The preceding discussion applies to polyphase as well as single-phase machines. In polyphase machines the nominal generated e.m.fs. or nominal counter-generated e.m.fs. are neces- sarily the same in all phases (or ...", "... lyphase machines the nominal generated e.m.fs. or nominal counter-generated e.m.fs. are neces- sarily the same in all phases (or bear a constant relation to each other). Thus in a polyphase generator, if the current or the SYNCHRONOUS MACHINES 151 phase relation of the current is different in the different branches, the terminal voltage must become different also, more or less. This is called the unbalancing of the polyphase generator. It is due to dif ...", "... must become different also, more or less. This is called the unbalancing of the polyphase generator. It is due to different load or load of different inductance factor in the different branches. Inversely, in a polyphase synchronous motor, if the terminal voltages of the different branches are unequal, due to an unbal- ancing of the polyphase circuit, the synchronous motor takes more current or lagging current from the branch of higher vol- tage, and t ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-90", "section_label": "Apparatus Section 12: Synchronous Converters: Conclusion", "section_title": "Synchronous Converters: Conclusion", "kind": "apparatus-section", "sequence": 90, "number": 12, "location": "lines 15983-16064", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-90/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-90/", "snippets": [ "XII. Conclusion 103. Of the types of machines, converter, inverted converter, and double-current generator, sundry combinations can be de- devised with each other and with synchronous motors, alternators, direct-current motors and generators. Thus, for instance, a converter can be used to supply a certain amount of mechanical power as synchronous motor. In this case the alternating current is ...", "... binations can be de- devised with each other and with synchronous motors, alternators, direct-current motors and generators. Thus, for instance, a converter can be used to supply a certain amount of mechanical power as synchronous motor. In this case the alternating current is increased beyond the value corresponding to the direct current by the amount of current giving the mechanical power, and the armature reactions do not neutralize each ot ...", "... rator is represented by the so-called \"motor converter,\" which consists of the concatenation of a commutating machine with an induction machine. If the secondary of an induction machine is connected to a second induction or synchronous machine on the same shaft, and of the same number of poles, the combination runs at half synchronous speed, and the first induction machine as frequency converter supplies half of its power as electric power of half frequ ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-10", "section_label": "Chapter 11: Rotary Terminal Single-Phase Induction Motor", "section_title": "Rotary Terminal Single-Phase Induction Motor", "kind": "chapter", "sequence": 10, "number": 11, "location": "lines 14762-14896", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-10/", "snippets": [ "... they can be revolved. With the brushes, B, at standstill on the stationary commutator, C, the rotor, S, has no torque, and the current in the stator, P, is the usual large standstill current of the induction motor. If now the brushes, B, are revolved at synchronous speed, /, in the direc- tion shown by the arrow, the rotor, S, again has no torque, but the stator, P, carries only the small exciting current of the motor, and the electrical conditions in the motor are the same, as would be with stationary brushes, B, a ...", "... peed, /, in the direc- tion shown by the arrow, the rotor, S, again has no torque, but the stator, P, carries only the small exciting current of the motor, and the electrical conditions in the motor are the same, as would be with stationary brushes, B, at synchronous speed of the rotor, S. If now the brushes, B, are slowed down below synchronism, /, to speed, /i, the rotor, S, begins to turn, in reverse direction, as shown by the arrow, at a speed, /2, and a torque corresponding to the slip, 8 = / — (/i + /2). Thus, ...", "... e, but the stator, P, carries only the small exciting current of the motor, and the electrical conditions in the motor are the same, as would be with stationary brushes, B, at synchronous speed of the rotor, S. If now the brushes, B, are slowed down below synchronism, /, to speed, /i, the rotor, S, begins to turn, in reverse direction, as shown by the arrow, at a speed, /2, and a torque corresponding to the slip, 8 = / — (/i + /2). Thus, if the load on the motor is such as to require the torque given at the slip, s, ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "section_label": "Lecture 10: Continual And Cumulative Oscillations", "section_title": "Continual And Cumulative Oscillations", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... issler tube con- duction passes the current through the residual vapor stream. Other hysteresis cycles than those of the arc are instrumental in the energy supply to other systems of continual oscillation. Thus, for instance, the hysteresis cycle between synchronizing force and position displacement supplies the energy of the con- tinual or cumulative oscillation, called hunting, in synchronous machines, as alternators, synchronous motors and converters. The mechanism, by which the hysteresis cycle supplies the energy ...", "... nstrumental in the energy supply to other systems of continual oscillation. Thus, for instance, the hysteresis cycle between synchronizing force and position displacement supplies the energy of the con- tinual or cumulative oscillation, called hunting, in synchronous machines, as alternators, synchronous motors and converters. The mechanism, by which the hysteresis cycle supplies the energy of continual oscillations, has been investigated in the case of the hunting of synchronous machines,* but is still practically un ...", "... her systems of continual oscillation. Thus, for instance, the hysteresis cycle between synchronizing force and position displacement supplies the energy of the con- tinual or cumulative oscillation, called hunting, in synchronous machines, as alternators, synchronous motors and converters. The mechanism, by which the hysteresis cycle supplies the energy of continual oscillations, has been investigated in the case of the hunting of synchronous machines,* but is still practically un- known in the case of continual oscil ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-04", "section_label": "Chapter 5: Methods Of Approximation", "section_title": "Methods Of Approximation", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 15156-16482", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-04/", "snippets": [ "... the form, h b _b/ s\\ (14) QTj^wli^ a greater exactness is required, by taking in the second term, ■^V T±s--ai}^-a^-^ '15) 128. Example. AVhat is the current input to an induction motor, at impressed voltage eo and slip s (given as fraction of synchronous speed) if ro — jxo is the impedance of the primary circuit of the motor, and ri — jxi the impedance of the secondary circuit of the motor at full frequency, and the exciting current of the motor is neglected; assuming s to be a small quantity; that is, th ...", "... <^-w, (28) Example 2. How does the short-circuit current of an alternator vary with the speed, at constant field excitation? When an alternator is short circuited, the total voltage generated in its armature is consumed by the resistance and the synchronous reactance of the armature. The voltage generated in the armature at constant field excitation is proportional to its speed. Therefore, if eo is the voltage generated in the armature at some given speed So, for instance, the rated speed of the machine, th ...", "... MATICS. S or, if for convenience, the fraction -^ is denoted by a, then a = -^ and e = aeo, oo where a is the ratio of the actual speed, to that speed at which the generated voltage is eo- If r is the resistance of the alternator armature, xq the synchronous reactance at speed So, the synchronous reactance at speed Sh x = axo, and the current at short circuit then is i=^^=^ , \"■\"> (29) Usually r and xo are of such magnitude that r consumes at full load about 1 per cent or less of the generated voltage, whi ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-11", "section_label": "Lecture 11: Lightning Protection", "section_title": "Lightning Protection", "kind": "lecture", "sequence": 11, "number": 11, "location": "lines 4931-5294", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-11/", "snippets": [ "... arresters became insufificient : the machine cur- rent following the lightning discharge frequently was so enor- mous that the circuit did not open at the end of the half wave, but the arrester held an arc and burned up. Furthermore, the introduction of synchronous motors, and of parallel operation of generators, made it essential that the lightning arrester should open again instantly after dis- charge. For, if the short circuit current over the arrester lasted for any appreciable time: a few seconds, synchronous ...", "... f synchronous motors, and of parallel operation of generators, made it essential that the lightning arrester should open again instantly after dis- charge. For, if the short circuit current over the arrester lasted for any appreciable time: a few seconds, synchronous motors and converters dropped out of step, the generators broke their S3mchronism, and the system in this way would be shut down. The horn gap arrester, in which the arc rises between horn-shaped terminals, and by lengthening, blows itself out, therefore ...", "... shut down. The horn gap arrester, in which the arc rises between horn-shaped terminals, and by lengthening, blows itself out, therefore became unsuitable for general service ; since without series resistance, the short circuiting arc lasted too long for synchronous apparatus to remain in step, and with series resist- ance reducing the current so as not to affect synchronous ma- chines, it failed to protect under severe conditions. Thus it has been relegated for use as an emergency arrester on some over- head lines, ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-111", "section_label": "Apparatus Section 5: Induction Machines: Induction Booster", "section_title": "Induction Machines: Induction Booster", "kind": "apparatus-section", "sequence": 111, "number": 5, "location": "lines 21589-21646", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-111/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-111/", "snippets": [ "... acts like a constant impedance. 350 ELEMENTS OF ELECTRICAL ENGINEERING The apparent impedance and its components, the apparent resistance and apparent reactance represented by the induction machine, vary with the slip. At synchronism apparent impe- dance, resistance, and reactance are a maximum. They decrease with increasing positive slip. With increasing negative slip the apparent impedance and reactance decrease also, the apparent FIG. 191. — Effective im ...", "... gives the apparent impe- dance, resistance, and reactance of the machine shown in Figs, 176 and 177, etc., with the speed as abscissas. The cause is that the power current is in opposition to the ter- minal voltage above synchronism, and thereby the induction INDUCTION MACHINES 351 machine behaves as an impedance of negative resistance, that is, adding a power e.m.f. into the circuit proportional to the current. As may be seen herefrom, the inductio ...", "... to generate and insert in the circuit an e.m.f. proportional to the current, and the amount of the boosting effect can be varied by varying the speed, that is, the slip at which the induction machine is revolving. Above synchronism the induction machine boosts, that is, raises the voltage; below synchronism it lowers the voltage; in either case also adding an out-of-phas.e e.m.f. due to its reactance. The greater the slip, either positive or negative, ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-31", "section_label": "Apparatus Section 10: Synchronous Machines: Efficiency and Losses", "section_title": "Synchronous Machines: Efficiency and Losses", "kind": "apparatus-section", "sequence": 31, "number": 10, "location": "lines 9651-9718", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-31/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-31/", "snippets": [ "X. Efficiency and Losses 22. Besides the above described curves the efficiency curves are of interest. The efficiency of alternators and synchronous motors is usually so high that a direct determination by measuring the mechanical power and the electric power is less reliable than 10 20 30 4ff 50 60 TO 80 90 100 UO 120 130 140 150 ...", "... ermination by measuring the mechanical power and the electric power is less reliable than 10 20 30 4ff 50 60 TO 80 90 100 UO 120 130 140 150 160 170 ISO 150 200 KW. FIG. 70. — Synchronous generator, efficiency and losses. the method of adding the losses, and the latter is therefore com- monly used. The losses consist of the following: the resistance loss in the armature; the resistance loss in the field ci ...", "... uming in the preceding example a friction loss of 2000 watts; an iron loss of 3000 watts, at the generated e.m.f. EI = 1000; a 10 30 30 40 50 60 70 1.00 UO 120 130 140 150 100 170 ISO 190 200 K.W, FIG. 71. — Synchronous motor efficiency and losses. resistance loss in the field circuit of 800 watts, at EQ = 1000, and a load loss at full load of 600 watts. The loss curves and efficiency curves are plotted in Fig. 70 for the generator, ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-37", "section_label": "Apparatus Section 16: Synchronous Machines: Higher Frequency Cross Currents Between Synchronous Machines", "section_title": "Synchronous Machines: Higher Frequency Cross Currents Between Synchronous Machines", "kind": "apparatus-section", "sequence": 37, "number": 16, "location": "lines 10124-10189", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-37/", "snippets": [ "XVI. Higher Frequency Cross Currents between Synchronous Machines 30. If several synchronous machines of different wave shapes are connected into the same circuit, cross currents exist between the machines of frequencies which are odd multiples of the circuit frequency, that is, ...", "XVI. Higher Frequency Cross Currents between Synchronous Machines 30. If several synchronous machines of different wave shapes are connected into the same circuit, cross currents exist between the machines of frequencies which are odd multiples of the circuit frequency, that is, higher harmonics thereof. The machines ...", "... e circuit frequency, that is, higher harmonics thereof. The machines may be two or more generators, in the same or in different stations, of wave shapes containing higher harmonics of different order, intensity or phase, or synchronous motors or converters of wave shapes different from that of the system to which they are connected. The intensity of these cross currents is the difference of the corresponding harmonics of the machines divided by the impe ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-92", "section_label": "Apparatus Section 14: Synchronous Converters: Three-wire Generator and Converter", "section_title": "Synchronous Converters: Three-wire Generator and Converter", "kind": "apparatus-section", "sequence": 92, "number": 14, "location": "lines 16541-16617", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-92/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-92/", "snippets": [ "... and Converter 107. A machine based upon the principle of the direct-current converter is frequently used to supply a three- wire direct-current distribution system (Edison system). This machine may be a single generator or synchronous converter, which is designed for the voltage between the outside conductors of the circuit (the positive and the negative conductor), 220 to 280 volts, while the middle conductor of the system, or neutral conductor, is con- ...", "... nverter, which is designed for the voltage between the outside conductors of the circuit (the positive and the negative conductor), 220 to 280 volts, while the middle conductor of the system, or neutral conductor, is con- SYNCHRONOUS CONVERTERS 271 nected to the generator by autotransformer and collector rings, or, in the case of a synchronous converter, is connected to the neutral of the step-up transformers, and the latter thus used as autotransfor ...", "... ive conductor), 220 to 280 volts, while the middle conductor of the system, or neutral conductor, is con- SYNCHRONOUS CONVERTERS 271 nected to the generator by autotransformer and collector rings, or, in the case of a synchronous converter, is connected to the neutral of the step-up transformers, and the latter thus used as autotransformers. -*; to v 2 \"* n C, 2 0 1 , o )T ' k ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-10", "section_label": "Chapter 10: Resistance And Reactance Of Transmission", "section_title": "Resistance And Reactance Of Transmission", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6993-9766", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-10/", "snippets": [ "... ENT PHENOMENA use of shunted reactance, so that a much larger output can be transmitted over the Hne with no drop, or even with a rise, of voltage. Shunted susceptance, therefore, is extensively used for voltage control of transmission lines, by means of synchronous condensers, or by synchronous converters with compound field winding. 5. Maximum Rise of Voltage at Receiver Circuit 78. Since, under certain circumstances, the voltage at the receiver circuit may be higher than at the generator, it is of interest to ...", "... reactance, so that a much larger output can be transmitted over the Hne with no drop, or even with a rise, of voltage. Shunted susceptance, therefore, is extensively used for voltage control of transmission lines, by means of synchronous condensers, or by synchronous converters with compound field winding. 5. Maximum Rise of Voltage at Receiver Circuit 78. Since, under certain circumstances, the voltage at the receiver circuit may be higher than at the generator, it is of interest to determine what is the maximum v ...", "... be remarked here that of the sources of susceptance, or reactance, a choking coil or reactive coil corresponds to an inductive reactance; a condenser corresponds to a condensive reactance; a polarization cell corresponds to a condensive reactance; a synchronous machine (motor, generator or converter) cor- responds to an inductive or a condensive reactance at will ; an induction motor or generator corresponds to an inductive reactance. The reactive coil and the polarization cell are specially suited for series ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-21", "section_label": "Chapter 21: Dibtobtiox Of Wavs-Shafe And Its Causes", "section_title": "Dibtobtiox Of Wavs-Shafe And Its Causes", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 23274-24559", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "snippets": [ "... ) + 51 [f cos {{2 y + 1) hence, the E.M.F. [,,sin((2y + l)^-a,) + .,^,siii((2y+l)^-V)]! §§216,217] DISTORTIOiV OF WAVE-SHAPE. 327 Pulsation of Reactance. 216. The main causes of a pulsation of reactance are : magnetic saturation and hysteresis, and synchronous motion. Since in an ironclad magnetic circuit the magnetism is not proportional to the M.M.F., the wave of magnetism and thus the wave of E.M.F. will differ from the wave of cur- rent. As far as this distortion is due to the variation of permeability, th ...", "... ne wave, the mag- netism and the E.M.F. will differ from sine shape. For further discussion of this distortion of wave-shape by hysteresis, Chapter X. may be consulted. 217. Distortion of wave-shape takes place also by the pulsation of reactance due to synchronous rotation, as dis- cussed in chapter on Reaction Machines. In Figs. 148 and 149, at a sine wave of impressed E.M.F., the distorted current waves have been constructed. Inversely, if a sine wave of current, / = /cos P, 328 ALTERNATING-CURRENT PHENOMEN ...", "... urrent waves have been constructed. Inversely, if a sine wave of current, / = /cos P, 328 ALTERNATING-CURRENT PHENOMENA. [§217 passes through a circuit of synchronously varying reac- tance; as for instance, the armature of a unitooth alterna- tor or synchronous motor — or, more general, an alternator whose armature reluctance is different in different positions with regard to the field poles — and the reactance is ex- pressed by Ar=jr{l + ccos(2)3-a>)}; or, more general, ^=^|l+^€,cos(2y)3-cu,)|; the wave ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-22", "section_label": "Chapter 22: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 21190-21982", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "snippets": [ "... etic flux is : 00 = $ cos 13 ey cos (2 y ff - cos((2y+l) hence, the E.M.F. 2 ; sm(P — DISTORTION OF WAVE-SHAPE. 391 Pulsation of Reactance. 237. The main causes of a pulsation of reactance are : magnetic saturation and hysteresis, and synchronous motion. Since in an ironclad magnetic circuit the magnetism is not proportional to the M.M.F., the wave of magnetism and thus the wave of E.M.F. will differ from the wave of cur- rent. As far as this distortion is due to the variation of permeability, th ...", "... ne wave, the mag- netism and the E.M.F. will differ from sine shape. For further discussion of this distortion of wave-shape by hysteresis, Chapter X. may be consulted. 238. Distortion of wave-shape takes place also by the pulsation of reactance due to synchronous rotation, as dis- cussed in chapter on Reaction Machines. In Figs. 148 and 149, at a sine wave of impressed E.M.F., the distorted current waves have been constructed. Inversely, if a sine wave of current, / = / cos B, 392 ALTERNATING-CURRENT PHENOME ...", "... ed current waves have been constructed. Inversely, if a sine wave of current, / = / cos B, 392 ALTERNATING-CURRENT PHENOMENA. passes through a circuit of synchronously varying reac- tance ; as for instance, the armature of a unitooth alterna- tor or synchronous motor — or, more general, an alternator whose armature reluctance is different in different positions with regard to the field poles — and the reactance is ex- pressed by or, more general, X = the wave of magnetism is X = x 1 + yr ^ cos (2 y ft- ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-07", "section_label": "Chapter 7: Shaping Of Waves : General", "section_title": "Shaping Of Waves : General", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 12222-12961", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-07/", "snippets": [ "... imum dux density, the hysteresis loss may be increased. Therefore, in alternating-current engineering, the aim gener- 114 ELECTRIC CIRCUITS ally is to produce and use a wave which is a sine wave or nearly so. 60. In an alternating-current generator, synchronous or in- duction machine, commutating machine, etc., the wave of voltage induced in a single armature conductor or \"face conductor\" equals the wave of field flux distribution around the periphery of the magnet field, modified, however, by the reluctance pul ...", "... en, curve III as well as V are approximately sine waves, but the one of twice the frequency of the other. Thus, such a machine, by reversing connections between the two wind- ings A and B, could be made to give two frequencies, one double the other, or as synchronous motor could run at two speeds, one one-half the other. Fig. 53. 61. Distribution of the winding over an arc of the periphery^ o^ the armature eliminates or reduces the higher harmonics, so tti^^t the terminal voltage wave of an alternator with distri ...", "... = — sm -^r- no) 2 ncu r, 2r/i . ?ia) -Bn = — en Sin -TT- nco 2 (3) and ^ = — { ei sin TT sin + \"TT sin -^ sin 3(0 — as) 0) [ 2, 6 2 + -g Sin -2\" sin 5(0 - as) + . } (4) Thus, in a three-phase winding like that of the three-phase synchronous converter, in which each phase covers an arc of 120° 2x .^ . 0) TT , = -0-, It is 2 = Q, nence, E = 3m\\/3 2x Ci sin ^ = sin 5{ — as) + ^ sin 7(0 — ay) h . . . . | (5) that is, the third harmonic and all its multiples, the ninth, f ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-10", "section_label": "Chapter 10: Instability Of Circuits : The Arc", "section_title": "Instability Of Circuits : The Arc", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 17632-21381", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-10/", "snippets": [ "... made themselves felt as disturbances or troubles in electric circuits, they either remained imunderstood or the theo- retical study was limited to the specific phenomenon, as in the case of lightning, dropping out of step of induction motors, hunt- ing of synchronous machines, etc., or, as in the design of arc lamps and arc-lighting machinery, the opinion prevailed that theoretical calculations are impossible and only design by trying, based on practical experience, feasible. The first class of imstable phenomena, wh ...", "... y voltage, however, starts it again, and so periodically the arc starts and extinguishes, aa an \"oscillating arc.\" 84. There are certain circuit elements which tend to produce instability, such as arcs, pyroelectric conductors, condensers, induction and synchronous motors, etc., and their recognition therefore is of great importance to the engineer, in guarding \\^ 1 [<^ INSTABILITY OF CIRCUITS 165 s^ainst instability. Whether instability results, and what form it assumes, depends, however, not only on th ...", "... he form of high- frequency disturbances or abrupt changes of current or voltage, such as is shown for instance in the oscillograms. Figs. 80 and 81. Somewhat similar effects of instability are produced by pyro- electric conductors. Induction motors and synchronous motors may show instability of speed: dropping out of step, etc. III. Permanent instability 86. If the constants of an electric circuit, as resistance, in- ductance, capacity, disruptive strength, voltage, speed, etc., have values, which can not coexis ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-36", "section_label": "Chapter 14: Short-Circuit Currents Of Alternators", "section_title": "Short-Circuit Currents Of Alternators", "kind": "chapter", "sequence": 36, "number": 14, "location": "lines 14549-15353", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "snippets": [ "... ting Current Phenomena,\" the armature reaction can be represented by an equivalent, or effective reactance, z2, and the self-inductive reactance, xv and the effective reactance of 199 200 TRANSIENT PHENOMENA armature reaction, x2J combine to form the synchronous react- ance, XQ = xl + x2, and the short-circuit current of the alterna- tor, in permanent condition, therefore can be expressed by where e0 = nominal generated e.m.f. 113. The effective reactance of armature reaction, xv differs, however, essentially ...", "... ment of the field flux to a change of m.m.f., is the transient term of armature reaction. In a polyphase alternator, the resultant m.m.f. of the .armature in permanent conditions is constant in intensity and revolves with regard to the armature at uniform synchronous speed, hence is stationary 202 TRANSIENT PHENOMENA with regard to the field. In the first moment, however, the resultant armature m.m.f . is changing in intensity and in velocity, approaching its constant value by a series of oscillations, as disc ...", "... ent as (18) i = ktl{ cos (6 -.*)>-« ** cos V , (19) X. (X. + £,) 1 v 1 ' 2' and by equation (10) of Chapter XIII, the armature reaction as f -*9\\ . + xjs x° )( . -^e n) ? ?-r L < I - e *' cos 0 f , (20) where x^ + x2 = x0 is the synchronous reactance of the alter- nator. For 6 = oo, or in permanent condition, equations (18), (19), (20) assume the usual form: and i = kt!0 -2 cos (0 x f f (21) 117. As an example is shown, in Fig. 53, the instantaneous value of the transient ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-37", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 37, "number": 1, "location": "lines 15354-15625", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "snippets": [ "... ent in the receiver circuit is made unidirectional (though more or less pulsating) and there- fore rectified. In rectifying alternating voltages, either both half waves of voltage can be taken from the same source, as the same trans- former coil, and by synchronous reversal of connections sent in the same direction into the receiver circuit, or two sources of voltage, as the two secondary coils of a transformer, may be used, and the one half wave taken from the one source, and sent into the receiver circuit, the oth ...", "... acter of the alternating supply voltage, into single phase, quarter phase and three phase, and by the character of the electric circuit, into constant potential and constant current rectifiers. Mechanical rectification by a commutator driven by a separate synchronous motor has not yet found any industrial application. Rectification by a commuta- tor driven by the generator of the alternating voltage has found very extended and important industrial use in the excitation of the field, or a part of the field (the series ...", "... ny industrial application. Rectification by a commuta- tor driven by the generator of the alternating voltage has found very extended and important industrial use in the excitation of the field, or a part of the field (the series field) of alternators and synchronous motors, and especially in the constant-current arc machine. The Brush arc machine is a quarter-phase alternator connected to a rectifying commutator on the armature shaft, and the Thomson-Houston arc machine is a star-connected three-phase alternator conn ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... tems, calculating the discharge capacity of lightning arres- ters, etc., the magnitude of the quantity is often sufficient. In 254 ^ ENGINEERING MATHEMATICS. calculating the critical speed of turbine alternators, or the natural period of oscillation of synchronous machines, the same applies, since it is of importance only to see that these speeds are sufficiently^ remote from the normal operating speed to give no trouble in operation. (b) Approximate calculation, requiring an accuracy of one or a few per cent onl ...", "... onstant and an exact calculation of the motion of the pendulum by elliptic functions becomes necessary. In electrical engineering, one has frequently to deal w^ith oscillations similar to those of the pendulum, for instance, in the hunting or surging of synchronous machines. In general, the frequency of oscillation is assumed as constant, but where, as in cumulative hunting of synchronous machines, the amplitude of the swing reaches large values, an appreciable change of the period must be expected, and where the hu ...", "... ering, one has frequently to deal w^ith oscillations similar to those of the pendulum, for instance, in the hunting or surging of synchronous machines. In general, the frequency of oscillation is assumed as constant, but where, as in cumulative hunting of synchronous machines, the amplitude of the swing reaches large values, an appreciable change of the period must be expected, and where the hunting is a resonance effect with some other periodic motion, as the engine rotation, the change of frequency with increase of ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-10", "section_label": "Lecture 10: Regulation And Control", "section_title": "Regulation And Control", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 4595-4930", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-10/", "snippets": [ "... when all the load was lighting load, but are unsuited at present for mixed load. 3rd. Form D alternator or compensated alternator with compensating exciter. Exciter is connected direct and has the same number of poles as the alternator so as to be in synchronism. The main current passes by collector rings through the exciter armature, usually with interposition of a transformer to keep the high voltage away from the exciter. The main current is sent through the exciter in such direc- tion that with non-inducti ...", "... used but hand control of the field rheostat, since in such large machines the load only varies slowly and never changes much, as for reasons of economy the machines are run near full load ; with the change of load, machines are shut down or started up. Synchronous Motors and Converters. In an alternating current system or part of the system containing large synchronous motors or converters the voltage can be controlled by varying the motor or converter field in the same way as with alternators, that is, by Tirrill ...", "... ever changes much, as for reasons of economy the machines are run near full load ; with the change of load, machines are shut down or started up. Synchronous Motors and Converters. In an alternating current system or part of the system containing large synchronous motors or converters the voltage can be controlled by varying the motor or converter field in the same way as with alternators, that is, by Tirrill Regulator or commutator and series field, etc. POTENTIAI. REGUIvATORS. I. Compensator regulator. With ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-09", "section_label": "Theory Section 9: Vector Diagrams", "section_title": "Vector Diagrams", "kind": "theory-section", "sequence": 9, "number": 9, "location": "lines 2865-3233", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-09/", "snippets": [ "... f e.m.fs. are considered in a circuit of the same current, or for the e.m.f., if a number of currents are produced by the same e.m.f., or for the generated e.m.f. in apparatus such as transform- ers and induction motors, synchronous apparatus, etc. With the current as zero vector, all horizontal components of e.m.f. are power components, all vertical components are reac- tive components. With the e.m.f. as zero vector, all horizontal components of curre ...", "... iagram of e.m.f. and current in transmission line. Cur- rent leading. e.m.f. of the generator shall be maintained constant at all loads, and the voltage regulation effected by producing lagging or leading currents with a synchronous motor in the receiving cir- cuit. The line has a resistance rx = 7.6 ohms and a reactance Xi = 4.35 ohms per wire, the generator is star connected, the resistance per circuit being r2 = 0.71, and the (synchronous) react ...", "... ith a synchronous motor in the receiving cir- cuit. The line has a resistance rx = 7.6 ohms and a reactance Xi = 4.35 ohms per wire, the generator is star connected, the resistance per circuit being r2 = 0.71, and the (synchronous) reactance is x2 = 25 ohms. ^ What must be the wattless or re- active component of the current, and therefore the total current and its phase relation at no load, one-quarter load, one-half load, three-quarters load, and ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-35", "section_label": "Apparatus Section 14: Synchronous Machines: Division of Load in Parallel Operation", "section_title": "Synchronous Machines: Division of Load in Parallel Operation", "kind": "apparatus-section", "sequence": 35, "number": 14, "location": "lines 9879-9917", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-35/", "snippets": [ "XIV. Division of Load in Parallel Operation 26. Much more important than equality of terminal voltage before synchronizing is equality of frequency. Inequality of frequency, or rather a tendency to inequality of frequency (since by necessity the machines hold each other in step or at equal frequency), causes cross currents which transfer'energy ...", "... riving power tends to slow down, and thus relieves the latter by increasing the load on the former. Thus these cross currents are power currents, and cause at no load or light load the one machine to drive the other as synchronous motor, while under load the result is that the machines do not share the load in proportion to their respective capacities. The speed of the prime mover, as steam engine or turbine, changes with the load. The frequency ...", "... is not the same, the load is not divided proportionally between the alternators, but the alternator connected to the prime mover of closer speed regula- tion takes more than its share of the load under heavy loads, and SYNCHRONOUS MACHINES 155 less under light loads. Thus, too close speed regulation of prime movers is not desirable in parallel operation of alternators." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-04", "section_label": "Chapter 4: Vector Representation", "section_title": "Vector Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2149-2759", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-04/", "snippets": [ "... ltage consumed l:)y inductive reactance, OE'2 = counter e.m.f. of inductive reactance, OE3 = voltage consumed by impedance, OE'i = counter e.m.f. of impedance. Obviously, these counter e.m.fs. are different from, for instance, the counter e.m.f. of a synchronous motor, in so far as they have no independent existence, but exist only through, and as long as the current exists. In this respect they are analogous to the opposing force of friction in mechanics. 21. Coming back to the equation found for the voltage at ...", "... ceiving circuit is inductive than if it is non-inductive. From Fig. 16, Ea = V{E COS 6 4- /r)2 + (E sin 6 + Ixy. If, however, the current in the receiving circuit is leading, as 26 ALTERNATING-CURRENT PHENOMENA is the case when feeding condensers or synchronous motors whose counter e.m.f. is larger than the impressed voltage, then the voltage will be. represented, in Fig. 17, by a vector, OE, lagging behind the current, 01, by the angle of lead, d'; and in this case we get, by combining OE with OEi, in phase wit ...", "... m.f., with an inductive load the potential difference at the alternator terminals will be lower than with a non-inductive load, and that with a non-inductive load it will be lower than when feeding into a cir- cuit with leading current, as for instance, a synchronous motor circuit under the circumstances stated above. 23. As a further example, we may consider the diagram of an alternating-current transformer, feeding through its secondary circuit an inductive load. For simplicity, we may neglect here the magnetic h ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-09", "section_label": "Chapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "section_title": "Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 4674-6992", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-09/", "snippets": [ "... , / and E change very little for small values of Xo; but if X is large, that is, if the receiver circuit is of large re- actance, / and E change considerably with a change of Xq. (b) If X is negative, that is, if the receiver circuit contains condensers, synchronous motors, or other apparatus which produce leading currents, below a certain value of Xq the de- nominator in the expression of E becomes Eo', that is, the reactance, Xo, raises the voltage. (c) E = Eo, or the insertion of a series reactance, Xo ...", "... ) = r = 0.6, x -{- Xo = 0, and tan do = 0; that 4 Eo Ex / E ^^ r Er 0 Fig. 55. Fig. 56. Fig. 57. is, the current and e.m.f. in the supply circuit are in phase with each other, or the circuit is in electrical resonance. Since a synchronous motor in the condition of efficient work- ing acts as a condensive reactance, we get the remarkable result that, in synchronous motor circuits, choking coils, or reactive coils, can be used for raising |he voltage. In Figs. 55 to 57, the vector diagrams ...", "... the current and e.m.f. in the supply circuit are in phase with each other, or the circuit is in electrical resonance. Since a synchronous motor in the condition of efficient work- ing acts as a condensive reactance, we get the remarkable result that, in synchronous motor circuits, choking coils, or reactive coils, can be used for raising |he voltage. In Figs. 55 to 57, the vector diagrams are shown for the conditions Eo = 100, Xo = 0.6, X = 0 a; = + 0.8 a; = - 0.8 (Fig. 48) E = 85.7 (Fig. 49) E = 65.7 (Fi ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-16", "section_label": "Chapter 16: Power, And Double-Frequency Quantities In", "section_title": "Power, And Double-Frequency Quantities In", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 16077-16520", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-16/", "snippets": [ "... ^ = secondary current in the quadrature direction in space, the torque is „ ri-rrT n-i ,-ii ^ D =- [EI]' = e^V - eVK By this equation the torque is given in watts, the meaning being that D = [EI]' is the power which would be exerted by the torque at synchronous speed, or the torque in synchronous watts. The torque proper is then D --^ ^°- 27r/p' where p = number of pairs of poles of the motor. / = frequency. In the polyphase induction motor, if I2 = i^ + ji^^ is the secondary current in quadrature pos ...", "... ure direction in space, the torque is „ ri-rrT n-i ,-ii ^ D =- [EI]' = e^V - eVK By this equation the torque is given in watts, the meaning being that D = [EI]' is the power which would be exerted by the torque at synchronous speed, or the torque in synchronous watts. The torque proper is then D --^ ^°- 27r/p' where p = number of pairs of poles of the motor. / = frequency. In the polyphase induction motor, if I2 = i^ + ji^^ is the secondary current in quadrature position, in space, to e.m.f. Ei, the ...", "... ge, that is, force times length in quadrature position with force; while energy is defined as force times length in the direction of the force. Ex- pressing quadrature position by ''imaginary,\" thus gives torque of the dimension of imaginary energy; and ''synchronous watts,\" which is torque times frequency, or torque divided by time, thus becomes of the dimension of imaginary power. Thus, in its complex imaginary form, the vector product of force and length contains two quadrature components, of which the one is energ ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-25", "section_label": "Chapter 25: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 29375-32539", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-25/", "snippets": [ "... windings, such pronounced wave shape distortions as shown by the unitooth alternators shown as illustrations, have become infrequent. Pulsation of Reactance 236. The main causes of a pulsation of reactance are mag- netic saturation and hysteresis, and synchronous motion. Since in an iron-clad magnetic circuit the magnetism is not propor- tional to the m.m.f., the wave of magnetism and thus the wave of e.m.f. will differ from the wave of current. As far as this distortion is due to the variation of permeability, th ...", "... e wave, the magnetism and the e.m.f. will differ from sine-shape. For further discussion of this distortion of wave-shape by hysteresis. Chapter XII may be consulted. 237. Distortion of wave-shape takes place also by the pul- sation of reactance due to synchronous rotation, as discussed in the chapter on Reaction Machines, in \"Theory and Calculation of Electrical Apparatus.\" With a sine wave of e.m.f., distorted current waves result. Inversely, if a sine wave of current, i = I cos jS, exists through a circuit ...", "... impressed voltage, a distor- tion of the capacity current wave occurs, which is largely effect- ive, but partly reactive due to the increase of capacity under corona. Pulsation of Resistance 239. To a certain extent the investigation of the effect of synchronous pulsation of the resistance coincides with that of reactance; since a pulsation of reactance, when unsymmetrical with regard to the current wave, introduces a power component which can be represented by an \"effective resistance.\" Inversely, an unsymmetri ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-08", "section_label": "Chapter 8: Capacity", "section_title": "Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3872-6370", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "snippets": [ "... non-inductive, / and £ change very little for small values of x^ ; but if x is large, that is, if the receiver circuit is of large reactance, / and £ change much with a change b.) If X is negative, that is, if the receiver circuit con- tains condensers, synchronous motors, or other apparatus which produce leading currents — above a certain value of x^ the denominator in the expression of E^ becomes < ;?, or E > E^\\ that is, the reactance, x^ , raises the potential. c.) E = E^f or the insertion of a series inductanc ...", "... , ;r = ^ .8, the total impedance of the circuit is r - y (.r + ;r^) = r = .6, x + x^ = 0, and tan w^ = ; that is, the current and E.M.F. in the supply circuit are in phase with each other, or the circuit is in electrical resofiafice. Fig. 43. Since a synchronous motor in the condition of efficient working acts as a condensance, we get the remarkable result that, in synchronous motor circuits, choking coils, or reactive coils, can be used for raising the voltage. In Figs. 42 to 44, the polar diagrams are shown fo ...", "... current and E.M.F. in the supply circuit are in phase with each other, or the circuit is in electrical resofiafice. Fig. 43. Since a synchronous motor in the condition of efficient working acts as a condensance, we get the remarkable result that, in synchronous motor circuits, choking coils, or reactive coils, can be used for raising the voltage. In Figs. 42 to 44, the polar diagrams are shown for the conditions — £, = 100, ^. = .6, ^ = (Fig. 42) £ = 85.7 a: = + .4 (Fig. 43) £ = 73.7 x= -A (Fig. 44) ^ = 1 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-08", "section_label": "Chapter 8: Circuits Containing Resistance, Inductance, And Capacity", "section_title": "Circuits Containing Resistance, Inductance, And Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3577-5333", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "snippets": [ "... uctive, / and E change very little for small values of x0 ; but if x is large, that is, if the receiver circuit is of large reactance, / and E change much with a change of x0. b.} If x is negative, that is, if the receiver circuit con- tains condensers, synchronous motors, or other apparatus which produce leading currents — above a certain value of x the denominator in the expression of E, becomes < z, or E > E0 ; that is, the reactance, x0 , raises the potential. c.) E = E0 , or the insertion of a series inductanc ...", "... =f .8, the total impedance of the circuit is r — j (x -f x0} = r = .6, x + x0 = 0, and tan S>0 = 0 ; that is, the current and E.M.F. in the supply circuit are in phase with each other, or the circuit is in electrical resonance. \\ Fig. 43. Since a synchronous motor in the condition of efficient working acts as a condensance, we get the remarkable result that, in synchronous motor circuits, choking coils, or reactive coils, can be used for raising the voltage. In Figs. 42 to 44, the polar diagrams are shown fo ...", "... rrent and E.M.F. in the supply circuit are in phase with each other, or the circuit is in electrical resonance. \\ Fig. 43. Since a synchronous motor in the condition of efficient working acts as a condensance, we get the remarkable result that, in synchronous motor circuits, choking coils, or reactive coils, can be used for raising the voltage. In Figs. 42 to 44, the polar diagrams are shown for the conditions — E0 = 100, x0 = .6, x = 0 . (Fig. 42) E = 85.7 x = + .8 (Fig. 43) E = 65.7 (Fig. 44) E = 158.1 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-20", "section_label": "Chapter 20: Commutator Motors", "section_title": "Commutator Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 19458-20501", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "snippets": [ "... rs — that is, motors in which the current enters or leaves the armature over brushes through a segmental commutator — have been built of various types, but have not found any extensive appli- cation, in consequence of the superiority of the induction and synchronous motors, due to the absence of commu- tators. The main subdivisions of commutator motcrs are the repulsion motor, the series motor, and the shunt motor. REPULSION MOTOR. 214. The repulsion motor -is an induction motor or transformer motor ; that is, a ...", "... ^ cos2 x) hence the difference, or the mechanical power developed by the motor armature, COMMUTATOR MOTORS. 361 and substituting for e, egk cos X (x^ sin X + r^k cos X) ~ fa + r sin X + kx cos X)2 + (xl + x sin \\ — kr cos X)2 ' and the torque in synchronous watts, P sin X 7X cos A]' = [^/! cos X}> _ ^ cos X (xl sin X + r^k cos X) r2 + x2 The stationary torque is, k = 0, _ ifo2^ si ...", "... t, or at least causes vicious sparking when interrupted by the motion of the arm'ature. To overcome this difficulty various arrangements have been proposed, but have not found an application. 370 ALTERNATING-CURRENT PHENOMENA. 224. Compared with the synchronous motor which has practically no lagging currents, and the induction motor which reaches very high power factors, the power factor of the series motor is low, as seen from Fig. 163, which repre- sents about the best possible design of such motors. In the ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-19", "section_label": "Chapter 21: Regulating Pole Converters", "section_title": "Regulating Pole Converters", "kind": "chapter", "sequence": 19, "number": 21, "location": "lines 30088-31715", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-19/", "snippets": [ "... ses it — with lagging cur- rent in Fig. 203, leading current in Fig. 202 — anil with lag of the alternating current, by phase angle, 6 = t, under the conditions of Fig. 203, the total resultant armature reaction vanishes, that is, the lagging component of synchronous-motor armature reaction compensates for the component of the direct -current reaction, 430 ELECTRICAL APPARATUS which is not compensated by the armature reaction of the power component of the alternating current. It is interesting t<> note that in ...", "... -1.17, e = c,-2.34e2 = 0.322^jcos 3 0-0.227 cos 5 0. | It is interesling tn note that in the last case the fundamental frequency disappears and the machine is a generator of triple frequency, that is, produces or consumes a frequency equal to three times synchronous frequency. In this ease the sevmUl harmonic also disappears, and only the fifth is appreciable. Iiut could be greatly reduced by a different kind of pole inc. From above table follows: (1) (2) (3) (4) (5) (6) normal MilMIIIHII: fuuiln- rocntal alter- ...", "... 0i 00 — 01, 446 ELECTRICAL APPARATUS and equations (19) and (20) assume the form: Three-phase: Six-phase : r = i^f -0.621. COS2 0i r = **» - 0.621. COS2 0i The equation (18) is the most general equation of the relative heating of the synchronous converter, including phase displace- ment, 0i, losses, pi} shift of brushes, ny shift of the resultant mag- netic flux, t0, and the third harmonic, t. While in a converter of standard or normal ratio the armature heating is a minimum for unity power-fact ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... tion at the receiving end becomes seriously impaired 314 TRANSIENT PHENOMENA hereby, even if the line resistance is moderate, and the operation of apparatus which require approximate constancy of voltage but do not operate on constant current — as most synchronous apparatus — becomes difficult. Hence, at the end of very long transmission lines the voltage regulation becomes poor, and synchronous machines tend to instability and have to be provided with powerful steadying devices, giving induction motor features, ...", "... operation of apparatus which require approximate constancy of voltage but do not operate on constant current — as most synchronous apparatus — becomes difficult. Hence, at the end of very long transmission lines the voltage regulation becomes poor, and synchronous machines tend to instability and have to be provided with powerful steadying devices, giving induction motor features, and with a line approaching quarter-wave length, voltage regulation at the receiving end ceases. In this case the constant potential-c ...", "... -current input, the output voltage would drop off, from no load to full load, by about 8 per cent. This, with a line of 15 per cent resistance drop, is a far closer voltage regulation than can be produced by constant potential supply, except by the use of synchronous machines for phase control." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-03", "section_label": "Lecture 3: Light And Power Distribution", "section_title": "Light And Power Distribution", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 983-1526", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-03/", "snippets": [ "... ut separate transformers and frequently separate feeders are used for the motors, and very large motors commonly built for the primary distribution voltage of 2200, are connected to these mains. For use in an alternating current distribution system, the synchronous motor hardly comes into consideration, since the synchronous type is suitable mainly for large powers, where it is operated on a separate circuit. 38 GENERAL LECTURES The alternating current motor mostly used in small and moderate sizes — such as come ...", "... used for the motors, and very large motors commonly built for the primary distribution voltage of 2200, are connected to these mains. For use in an alternating current distribution system, the synchronous motor hardly comes into consideration, since the synchronous type is suitable mainly for large powers, where it is operated on a separate circuit. 38 GENERAL LECTURES The alternating current motor mostly used in small and moderate sizes — such as come into consideration for power distribution from a general sup ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... park gap is set, it discharges, and the system is short circuited to ground, until the arc rises and gradually blows itself out. As this requires an appreciable time, motors and converters have usually dropped out of step, and the gen- erators have broken synchronism, that is, the system is shut down and has to be started up again. This type of protection therefore is not particularly favored in systems which require reasonable continuity of service, but if used, it is considered rather as an emergency device in addit ...", "... occurs. At the end of the half-wave, the current falls to zero, and the reverse current cannot start, that is, the circuit of the arrester is opened. A short circuit on the system, for a fraction of a half- wave, does not interfere with the operation of synchronous apparatus, that is, the operation of the system is not affected by a discharge over the multi-gap arrester. In a large system, the short circuit current is very consid- erable ; its power, and thus the heating effect produced by it, is enormous. The ene ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-107", "section_label": "Apparatus Section 1: Induction Machines: General", "section_title": "Induction Machines: General", "kind": "apparatus-section", "sequence": 107, "number": 1, "location": "lines 18949-19165", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-107/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-107/", "snippets": [ "... oduces currents in the short-circuited armature or secondary winding, usually the rotor, and by its action on these currents drags along the secondary conductors, and thus speeds up the armature and tends to bring it up to synchronism, that is, to the same speed as the rotating field, at which speed the secondary currents would disappear by the armature conductors moving together with the rotating field, and thus cutting no lines of force. The secondary ...", "... he two superimposed mag- netic quadrature fields is excited by the primary electric circuit, the other by the . secondary currents carried into quadrature position by the rotation of the secondary. In either case, at or near synchronism the magnetic fields are practically identical. The transformer feature being predominant, in theoretical investigations of induction motors it is generally preferable to start therefrom. The characteristics of the transformer a ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-112", "section_label": "Apparatus Section 6: Induction Machines: Phase Converter", "section_title": "Induction Machines: Phase Converter", "kind": "apparatus-section", "sequence": 112, "number": 6, "location": "lines 21647-21812", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-112/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-112/", "snippets": [ "VI. Phase Converter 158. It may be seen from the preceding that the induction machine can operate equally well as motor, below synchronism, and as generator, above synchronism. In the single-phase induction machine the motor or generator action occurs in one primary circuit only, but in the direction in quadrature to the primary circuit there is a mere magnet ...", "VI. Phase Converter 158. It may be seen from the preceding that the induction machine can operate equally well as motor, below synchronism, and as generator, above synchronism. In the single-phase induction machine the motor or generator action occurs in one primary circuit only, but in the direction in quadrature to the primary circuit there is a mere magnetizing current either in the secondary ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-39", "section_label": "Apparatus Section 1: Direct-current Commutating Machines: General", "section_title": "Direct-current Commutating Machines: General", "kind": "apparatus-section", "sequence": 39, "number": 1, "location": "lines 10430-10474", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-39/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-39/", "snippets": [ "... current motors which transform electric power into mechanical power, and direct-current con- verters which transform electric power into a different form of electric power. Since the most important class of the latter are the synchronous converters, which combine features of the synchronous machines with those of the commutating machines, they shall be treated in a sepa- rate chapter. By the excitation of their mag- net fields, commutating machines are divid ...", "... hanical power, and direct-current con- verters which transform electric power into a different form of electric power. Since the most important class of the latter are the synchronous converters, which combine features of the synchronous machines with those of the commutating machines, they shall be treated in a sepa- rate chapter. By the excitation of their mag- net fields, commutating machines are divided into magneto machines, in which the field consists ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-42", "section_label": "Apparatus Subsection 42: Direct-current Commutating Machines: C. Commutating Machines", "section_title": "Direct-current Commutating Machines: C. Commutating Machines", "kind": "apparatus-subsection", "sequence": 42, "number": null, "location": "lines 10586-10645", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-42/", "snippets": [ "... e. Thus such FIG. 85. — Multiple double spiral ring winding. windings are mostly used for large low-voltage machines, but as very few large direct-current generators are built nowadays, and alternating-current generation with synchronous converters usu- ally preferred, and as multiple spiral or reentrant windings are inconvenient in synchronous converters, their use has greatly decreased. 39. A distinction is frequently made between lap winding and wave windin ...", "... ge machines, but as very few large direct-current generators are built nowadays, and alternating-current generation with synchronous converters usu- ally preferred, and as multiple spiral or reentrant windings are inconvenient in synchronous converters, their use has greatly decreased. 39. A distinction is frequently made between lap winding and wave winding. These are, however, not different types; but the wave winding is merely a constructive modification of ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-87", "section_label": "Apparatus Section 9: Synchronous Converters: Inverted Converters", "section_title": "Synchronous Converters: Inverted Converters", "kind": "apparatus-section", "sequence": 87, "number": 9, "location": "lines 15735-15810", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-87/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-87/", "snippets": [ "... device is necessary to cut the in- verted converter off the circuit entirely as soon as its speed ex- ceeds the danger limit. The relatively safest arrangement is separate excitation of the inverted converter by an exciter SYNCHRONOUS CONVERTERS 257 mechanically driven thereby, since an increase of speed in- creases the exciter voltage at a still higher rate, and thereby the excitation of the converter, and thus tends to check its speed. This dang ...", "... er into the alter- nating-current system but at the same time receives wattless current from the alternating system, lagging at under-excitation, leading at over-excitation, and can in the same way as an ordinary converter or synchronous motor be used to compensate for watt- less currents in other parts of the alternating system, or to regu- late the voltage by phase control." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-88", "section_label": "Apparatus Section 10: Synchronous Converters: Frequency", "section_title": "Synchronous Converters: Frequency", "kind": "apparatus-section", "sequence": 88, "number": 10, "location": "lines 15811-15892", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-88/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-88/", "snippets": [ "... hallower slots are necessary. The 60-cycle converter cannot be built with anything like the same armature reaction as is feasible at lower frequency. On the armature reaction, however, very largely depends the stability of a synchronous motor or converter, and machines of low armature reaction tend far more to surging and pulsation of current and voltage than machines of high armature reaction. The 60-cycle converter therefore cannot be made quite as stab ...", "... ycle con- verters give excellent service. It is this inherent inferiority of the 60-cycle converter which has largely been instrumental in introducing 25 cycles as the frequency of electric power generation and distribution. SYNCHRONOUS CONVERTERS 259 At 25 cycles, converters are used on railway load — the most fluctuating and therefore most severe service — built for 1200 volts, and even still much higher voltages are available." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-95", "section_label": "Apparatus Section 1: Alternating-current Transformer: General", "section_title": "Alternating-current Transformer: General", "kind": "apparatus-section", "sequence": 95, "number": 1, "location": "lines 16804-16911", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-95/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-95/", "snippets": [ "... primary distribution voltage (2300) to the low secondary consumer voltage (110, 220). From the high transmission (30 to 150 kilovolts) to the primary distribution voltage (2300) or the voltage required by syn- chronous motor, synchronous converter, etc. From the low or medium high generator voltage to the high transmission voltage. Other occasional uses of transformers are: To electrically tie systems together, so as to permit exchange of power between th ...", "... r, etc. From the low or medium high generator voltage to the high transmission voltage. Other occasional uses of transformers are: To electrically tie systems together, so as to permit exchange of power between them, and synchronous operation. In this case, depending on the distribution of the load in the system, either transformer winding may be primary or secondary. To break up electrically a very large system, so that a ground in one part does n ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-28", "section_label": "Chapter 28: General Polyphase Systems", "section_title": "General Polyphase Systems", "kind": "chapter", "sequence": 28, "number": 28, "location": "lines 34777-34928", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-28/", "snippets": [ "... nches of the polyphase sys- tem, which may be more or less interlinked with each other. In general the investigation of a polyphase system is carried out by treating the single-phase branch circuits independently. Thus all the discussions on generators, synchronous motors, induction motors, etc., in the preceding chapters, apply to single- phase systems as well as polyphase systems, in the latter case the total power being the sum of the powers of the individual or branch circuits. If the polyphase system consists ...", "... an independent system. The six-phase system, consisting of two three-phase systems in opposition to each other, and derived by transformation from + .E —E nmTswusvsvrno- Fig. 195. a three-phase system, in the alternating supply circuit of large synchronous converters. The inverted three-phase system, consisting of two e.m.fs. dis- placed from each other by 60°, and derived from two phases of a three-phase system by transformation with two transformers, of which the secondary of one is reversed with regard ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-29", "section_label": "Chapter 29: Symmetrical Polyphase Systems", "section_title": "Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 29, "number": 29, "location": "lines 34929-35255", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-29/", "snippets": [ "... tem. Higher systems than the quarter-phase or four-phase system have not been very extensively used, and are thus of less practical interest. A symmetrical six-phase system, derived by trans- formation from a three-phase system, has found application in synchronous converters, as offering a higher output from these machines, and a symmetrical eight-phase system proposed for the same purpose. 271. A characteristic feature of the symmetrical n-phase sys- tem is that under certain conditions it can produce a rotating ...", "... of each coil. The phase of the resultant m.m.f. at the time represented by the angle /3 is tan d ^ — cot jS; hence d = ~ ^ o' That is, the m.m.f. produced by a symmetrical ?i-phase system revolves with constant intensity, V2 and constant speed, in synchronism with the frequency of the system; and, if the reluctance of the magnetic circuit is constant, the magnetism revolves with constant intensity and constant speed also, at the point acted upon symmetrically by the n m.m.fs. of the n-phase system. This is a ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... ensance proper, and an energy com- ponent, the dielectric hysteresis. The condensance of a polarization cell, however, begins to decrease at very low potentials, as soon as the counter E.M.F. of chemical dissociation is approached. The condensance of a synchronizing alternator is of the nature of a variable quantity ; that is, the- synchronous reactance changes gradually, according to the relation of impressed and of counter E.M.F., from inductance over zero to condensance. Besides the phenomena discussed in the fo ...", "... nsance of a polarization cell, however, begins to decrease at very low potentials, as soon as the counter E.M.F. of chemical dissociation is approached. The condensance of a synchronizing alternator is of the nature of a variable quantity ; that is, the- synchronous reactance changes gradually, according to the relation of impressed and of counter E.M.F., from inductance over zero to condensance. Besides the phenomena discussed in the foregoing as terms of the energy components and the wattless compo- nents of cur ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-19", "section_label": "Chapter 19: Commutatob Motobs", "section_title": "Commutatob Motobs", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 21339-22387", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "snippets": [ "... rs — that is, motors in which the current enters or leaves the armature over brushes through a segmental commutator — have been built of various types, but have not found any extensive appli- cation, in consequence of the superiority of the induction and synchronous motors, due to the absence of commu- tators. The main subdivisions of commutator motors are the repulsion motor, the series motor, and the shunt motor. REPULSION MOTOR. 193. The repulsion motor is an induction motor or transformer motor ; that is, a ...", "... troys it, or at least causes vicious sparking when interrupted by the motion of the armature. To overcome this difficulty various arrangements have been proposed, but have not found an application. §203] COMMUTATOR MOTORS. 307 203. Compared with the synchronous motor which has practically no lagging currents, and the induction motor which reaches very high power factors, the power factor of the series motor is low, as seen from Fig. 147, which repre- sents about the best possible design of such motors. In the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-22", "section_label": "Chapter 20: Ri", "section_title": "Ri", "kind": "chapter", "sequence": 22, "number": 20, "location": "lines 24560-25119", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "snippets": [ "... cs. Thus if upon a sine wave of alter- nating E.M.F. higher harmonic waves are superposed, the effective E.M.F., and the power produced by this wave in a given circuit or with a given effective current, are increased. In consequence hereof alternators and synchronous motors of ironclad unitooth construction — that is, machines giving waves with pronounced higher harmonics — give with the same number of turns on the armature, and the same mag- netic flux per field pole at the same frequency, a higher output than machi ...", "... ds upon the maximum value of magnetism, it follows that the hysteretic loss in a transformer is less with a dis- torted wave of a unitooth alternator than with a sine wave. Thus with the distorted waves of unitooth machines, generators, transformers, and synchronous motors — and induction motors in so far as they are transformers — operate more efficiently. 229. From another side the same problem can be approached. If upon a transformer a sine wave of E.M.F. is im- pressed, the wave of magnetism will be a sine wa ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-12", "section_label": "Chapter 12: Power, And Double Frequency Quantities In General", "section_title": "Power, And Double Frequency Quantities In General", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 9381-9740", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "snippets": [ "... dary current in the quadrature di- rection in space, POWER, AND DOUBLE FREQUENCY QUANTITIES. 157 the torque is By this equation the torque is given in watts, the mean- ing being that T = \\E /]•>' is the power which would be exerted by the torque at synchronous speed, or the torque in synchronous watts. The torque proper is then where / = number of pairs of poles of the motor. In the polyphase induction motor, if 72 = il +/zu is the secondary current in quadrature position, in space, to E.M.F. Ej. The ...", "... ection in space, POWER, AND DOUBLE FREQUENCY QUANTITIES. 157 the torque is By this equation the torque is given in watts, the mean- ing being that T = \\E /]•>' is the power which would be exerted by the torque at synchronous speed, or the torque in synchronous watts. The torque proper is then where / = number of pairs of poles of the motor. In the polyphase induction motor, if 72 = il +/zu is the secondary current in quadrature position, in space, to E.M.F. Ej. The current in the same direction in spac ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-23", "section_label": "Chapter 23: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 21983-22448", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "snippets": [ "... cs. Thus if upon a sine wave of alter- nating E.M.F. higher harmonic waves are superposed, the effective E.M.F., and the power produced by this wave in a given circuit or with a given effective current, are increased. In consequence hereof alternators and synchronous motors of ironclad unitooth construction — that is, machines giving waves with pronounced higher harmonics — give with the same number of turns on the armature, and the same mag- netic flux per field pole at the same frequency, a higher output than machi ...", "... ds upon the maximum value of magnetism, it follows that the hysteretic loss in a transformer is less with a dis- torted wave of a unitooth alternator than with a sine wave. Thus with the distorted waves of unitooth machines, generators, transformers, and synchronous motors — and induction motors in so far as they are transformers — operate more efficiently. 250. From another side the same problem can be approached. If upon a transformer a sine wave of E.M.F. is im- pressed, the wave of magnetism will be a sine wa ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-25", "section_label": "Chapter 25: General Polyphase Systems", "section_title": "General Polyphase Systems", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 23643-23780", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-25/", "snippets": [ "... nches of the polyphase system, which may be more or less interlinked with each other. In general the investigation of a polyphase system is carried out by treating the single-phase branch circuits independently. Thus all the discussions on generators, synchronous motors, induction motors, etc., in the preceding chapters, apply to single-phase systems as well as polyphase systems, in the latter case the total power being the sum of the powers of the individual or branch circuits. If the polyphase system consists ...", "... be either an interlinked system or an indepen- dent system. The six-phase system, consisting of two three-phase sys- tems in opposition to each other, and derived by transforma- tion from a three-phase system, in the alternating supply circuit of large synchronous converters. The inverted three-phase system, consisting of two E.M.F.'s displaced from each other by 60°, and derived from two phases of a three-phase system by transformation with two transformers, of which the secondary of one is reversed with regard ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-26", "section_label": "Chapter 26: Symmetrical Polyphase Systems", "section_title": "Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 23781-24053", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-26/", "snippets": [ "... tem. Higher systems, than the quarter-phase or four-phase system, have not been very extensively used, and are thus of less practical interest. A symmetrical six-phase system, derived by transformation from a three-phase system, has found application in synchronous converters, as offering a higher output from these machines, and a symmetrical eight- phase system proposed for the same purpose. 265. A characteristic feature of the symmetrical »- phase system is that under certain conditions it can pro- duce a M.M.F. ...", "... the time repre- sented by the angle ft is : tan w = — cot /8 ; hence w = /? — ^ That is, the M.M.F. produced by a symmetrical «-phase system revolves with constant intensity : SYMMETRICAL POLYPHASE SYSTEMS. 439 F= — • V25 and constant speed, in synchronism with the frequency of the system ; and, if the reluctance of the magnetic circuit is constant, the magnetism revolves with constant intensity and constant speed also, at the point acted upon symmetri- cally by the n M.M.Fs. of the w-phase system. This i ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 557-1002", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-01/", "snippets": [ "... ic stored energy. This for instance is the case in the charge or discharge of a condenser through an inductive circuit. If energy can be stored in more than two different forms, still more complex phenomena may occur, as for instance in the hunt- ing of synchronous machines at the end of long transmission lines, where energy can be stored as magnetic energy in the line and apparatus, as dielectric energy in the line, and as mechanical energy in the m_omentum of the motor. 6. The study and calculation of the permane ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 460-882", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "snippets": [ "... ic stored energy. This for instance is the case in the charge or discharge of a condenser through an inductive circuit. If energy can be stored in more than two different forms, still more complex phenomena may occur, as for instance in the hunt- ing of synchronous machines at the end of long transmission lines, where energy can be stored as magnetic energy in the line and apparatus, as dielectric energy in the line, and as mechanical energy in the momentum of the motor. 6. The study and calculation of the permanen ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... wo limits of the engineering range of the quantity give extremes. Thus r = 0 gives the maximum, r = oo the minimum of current. io6. Example lo. An alternating-current generator, of generated e.m.f. e = 2500 volts, internal resistance ro = 0.25 ohms, and synchronous reactance a:o = 10 ohms, is loaded by a circuit comprising a resistor of constant resistance r = 20 ohms, and a reactor of reactance x in series with the resistor r. What value of reactance x gives maximum output? If i = current of the alternator, its po ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-05", "section_label": "Chapter 6: Empirical Curves", "section_title": "Empirical Curves", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 16483-21988", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-05/", "snippets": [ "... the thirteenth harmonics. This method of determining two similar harmonics, with a little practice, becomes very convenient and useful, and may 248 ENGINEERING MATHEMATICS. frequently be used visually also, in determining the frequency of hunting of synchronous machines, etc. In the phenomenon of hunting, frequently two periods are superimposed, forced frequency, resulting from the speed of generator, etc., and the natural frequency of the machine. Counting the number of impulses, /, per minute, and the number o ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-12", "section_label": "Lecture 12: Electric Railway", "section_title": "Electric Railway", "kind": "lecture", "sequence": 12, "number": 12, "location": "lines 5295-7123", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-12/", "snippets": [ "... therefore not much used in this country, where the highest speed which the motor equipment can give is desired. ' With induction motors, feeding back in the line is simplest, because induction motors become generators above l62 GENERAL LECTURES synchronism, and so feed back when running down a long hill. Therefore on mountain railways, induction motors have the advantage. In an induction motor there is no running on the motor curve, and so the efficiency of acceleration is lower. Objection to the series ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-106", "section_label": "Apparatus Section 9: Alternating-current Transformer: Reactors", "section_title": "Alternating-current Transformer: Reactors", "kind": "apparatus-section", "sequence": 106, "number": 9, "location": "lines 18813-18948", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-106/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-106/", "snippets": [ "... circuit is still below saturation. Industrially, reactors are often denoted in per cent. Thus for Volt- REACTOR Ampere Characteristic Rec Vo ts e FIG. 175. — Volt-ampere characteristic of reactor. phase control in synchronous converter circuits, 15 per cent, re- actances are used. This means, at full-load current, the voltage consumed by these reactances is 15 per cent, of the circuit voltage. 131. With the increasing size and increasing voltage ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-12", "section_label": "Theory Section 12: Impedance of Transmission Lines", "section_title": "Impedance of Transmission Lines", "kind": "theory-section", "sequence": 12, "number": 12, "location": "lines 3761-4464", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-12/", "snippets": [ "... ed for different values of the current 7 by varying the phase angle. / Thus, if means are provided to vary the phase angle of the receiving circuit, by producing lagging and leading currents at will (as can be done by synchronous motors or converters) , the voltage at the receiving circuit can be maintained constant IMPEDANCE OF TRANSMISSION LINES 61 within a certain range irrespective of the load and generator voltage. In Fig. 30 let OE = E ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-14", "section_label": "Theory Section 14: Rectangular Coordinates", "section_title": "Rectangular Coordinates", "kind": "theory-section", "sequence": 14, "number": 14, "location": "lines 5264-5831", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-14/", "snippets": [ "... transmission line of impedance Z = r -}- jx = 20 + 50 j ohms feeds a receiving circuit. At the receiving end an apparatus is connected which produces reactive lagging or leading currents at will (synchronous machine) ; 12,000 volts are impressed upon the line. How much lagging and leading currents respectively must be produced at the receiving end of the line to get 10,000 volts (a) at no load, (6) at 50 ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-17", "section_label": "Theory Section 17: Impedance and Admittance", "section_title": "Impedance and Admittance", "kind": "theory-section", "sequence": 17, "number": 17, "location": "lines 6814-7380", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-17/", "snippets": [ "... d = 3327. P )WER CURRENT REC'D AMP V *OLT8 5000 3000 5000 3000 2000 10 20 JO 40 50 DO 70 80 90 100 110 120 130 140 150 FIG. 40. — Reactive load characteristics of a transmission line fed by synchronous generator with constant field excitation. Substituting different values for i gives i ' ei i e ei 0 15,133 14,700 100 10,050 11,100 25 14,488 14,400 125 7,188 8,800 50 13,525 13,800 150 2,325 4,840 ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-25", "section_label": "Apparatus Section 4: Synchronous Machines: Self-inductance", "section_title": "Synchronous Machines: Self-inductance", "kind": "apparatus-section", "sequence": 25, "number": 4, "location": "lines 8907-9034", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-25/", "snippets": [ "... gle EOI = 0. _The e.m.f. consumed by resistance is OE \\ = Ir in phase with 01. The e-m-i^ consumed by reactance is OEfz — Ix, 90 degrees ahead of 01. The real generated e.m.f. is found by combining OE and OE\\ to SYNCHRONOUS MACHINES 135 The virtual generated e.m.f. is OEi and OE'Z combined to = E2. The m.m.f. required to produce -this e.m.f. Ez is OF = F, Fa I E, FIG. 52. — Diagram of generator e.m.fs. and m.m.fs. for non-r ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-34", "section_label": "Apparatus Section 13: Synchronous Machines: Parallel Operation", "section_title": "Synchronous Machines: Parallel Operation", "kind": "apparatus-section", "sequence": 34, "number": 13, "location": "lines 9821-9878", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-34/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-34/", "snippets": [ "... rated in parallel, or synchronized with any other alternator. A single-phase machine can be syn- chronized with one phase of a polyphase machine, or a quarter- phase machine operated in parallel with a three-phase machine by synchronizing one phase of the former with one phase of the latter. Since alternators in parallel must be in step with each other and have the same terminal voltage, the condition of satis- factory parallel operation is that the freque ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-45", "section_label": "Apparatus Subsection 45: Direct-current Commutating Machines: C. Commutating Machines 177", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 177", "kind": "apparatus-subsection", "sequence": 45, "number": null, "location": "lines 10737-10777", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-45/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-45/", "snippets": [ "... e side of the coil enters or leaves the field before the other. Therefore, in commutating machines it is seldom that a pitch is used that falls short of full pitch by more than one or two teeth, while in induction and synchronous machines occasionally as low a pitch as 50 per cent, is used, and two-thirds pitch is frequently employed. For special purposes, as in single-phase commutator motors fractional-pitch windings are sometimes used. 41. Series ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-59", "section_label": "Apparatus Section 8: Direct-current Commutating Machines: Armature Reaction", "section_title": "Direct-current Commutating Machines: Armature Reaction", "kind": "apparatus-section", "sequence": 59, "number": 8, "location": "lines 11616-11694", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-59/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-59/", "snippets": [ "... F ELECTRICAL ENGINEERING C -j- go 2 Fa with the average cos = — , and is thus — yu ^\" Fao 2 Fa 2 ni When comparing the armature reaction of commutating ma- chines with other types of machines, as synchronous machines 2 Fa etc., the resultant armature reaction Fao = - - has to be used. In discussing commutating machines proper, however, the value Fa = ni is usually considered as the armature reaction. 56. The armature re ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-63", "section_label": "Apparatus Subsection 63: Direct-current Commutating Machines: C. Commutating Machines 197", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 197", "kind": "apparatus-subsection", "sequence": 63, "number": null, "location": "lines 11795-11863", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-63/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-63/", "snippets": [ "... istic Curves 60. The field characteristic or regulation curve, that is, curve giving the terminal voltage as function of the current output at constant field excitation, is of less importance in commutating machines than in synchronous machines, since commutating machines are usually not operated with separate and constant excitation, and the use of the series field affords a convenient means of changing the field excitation proportionally to the load. Th ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-65", "section_label": "Apparatus Section 13: Direct-current Commutating Machines: Commutation", "section_title": "Direct-current Commutating Machines: Commutation", "kind": "apparatus-section", "sequence": 65, "number": 13, "location": "lines 11905-11980", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-65/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-65/", "snippets": [ "... armature coil during commutation is eo = 2irfoLiot where io = current reversed, and the energy which has to be dissipated during commutation is i = cot P ; That is, the M.M.F. produced by a symmetrical «-phase system revolves with constant intensity : F = ,— » V2 and constant speed, in synchronism with the frequency of the system ; and, if the reluctance of the magnetic circuit §238] SYMMETRICAL POLYPHASE SYSTEMS. 355 is constant, the magnetism revolves with constant intensity and constant speed also, at the point acted upon symmetri- cally by ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-04", "section_label": "Chapter 4: Graphic Representation", "section_title": "Graphic Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 1743-2321", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "snippets": [ "... by inductance, OEX' = counter E.M.F. of inductance, OEZ = E.M.F. consumed by impedance, OEt ' = counter E.M.F. of impedance. 26 ALTERNATING-CURRENT PHENOMENA. Obviously, these counter E.M.Fs. are different from, for instance, the counter E.M.F. of a synchronous motor, in so far as they have no independent existence, but exist only through, and as long as, the current flows. In this respect they are analogous to the opposing force of friction in mechanics. if. \\f —X« Fig. 15. 19. Coming back to the eq ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-09", "section_label": "Chapter 9: Resistance And Reactance Of Transmission Lines", "section_title": "Resistance And Reactance Of Transmission Lines", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 5334-6956", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "snippets": [ "... . In conclusion, it may be remarked here that of the sources of susceptance, or reactance, a choking coil or reactive coil corresponds to an inductance ; a condenser corresponds to a condensance ; a polarization cell corresponds to a condensance ; a synchronizing alternator (motor or generator) corresponds to an inductance or a condensance, at will; an induction motor or generator corresponds to an inductance. The choking coil and the polarization cell are specially suited for series reactance, and the condenser ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "... ensance proper, and an energy com- ponent, the dielectric hysteresis. The condensance of a polarization cell, however, begins to decrease at very low potentials, as soon as the counter E.M.F. of chemical dissociation is approached. The condensance of a synchronizing alternator is of the nature of a variable quantity ; that is, the effective reactance changes gradually, according to the relation of impressed and of counter E.M.F., from inductance over zero to condensance. Besides the phenomena discussed in the foreg ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-16", "section_label": "Chapter 16: Load Balance Of Polyphase Systems", "section_title": "Load Balance Of Polyphase Systems", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 29302-30428", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-16/", "snippets": [ "... o balance an unbalanced polyphase system thus requires a storage of energy, hence can not be done by any method of connection or transformation. Thus mechanical momentum acts as energy-storing device in the use as phase bal- ancer, of the induction or the synchronous machine. Electrically, energy is stored by inductance and by capacity. The question then arises, whether by the use of a reactor, or a condenser, con- nected to a suitable phase of the system, an unequally loaded polyphase system can be balanced, so as to ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... TS, 44. The charge and discharge of a condenser through an inductive circuit produces periodic currents of a frequency depending upon the circuit constants. The range of frequencies which can be produced by electro- dynamic machinery is rather limited: synchronous machines or ordinary alternators can give economically and in units of larger size frequencies from 10 to 125 cycles. Frequencies below 10 cycles are available by commutating machines with low frequency excitation. Above 125 cycles the difficulties rapid ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... NDEX 571 PAGE Stored energy of complex circuit 515 Stranded conductor, effective resistance of current distribution 370 Stray field and starting current of transformer 184 Suppression of pulsations of direct current by capacity and inductance. 134 Synchronous reactance and short-circuit current 200 rectifier 221 Telegraph, wireless 388 cable, submarine, standing waves 454 Telephone 281 circuit, long distance, standing waves 454 Terminal conditions of condenser equations 50 Tesla transformer and oscil ..." ] } ] }, { "id": "light", "label": "Light", "aliases": [ "Light", "light", "luminous", "visible light" ], "total_occurrences": 2196, "matching_section_count": 85, "matching_source_count": 13, "source_totals": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 1600, "section_count": 13 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 322, "section_count": 13 }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 154, "section_count": 4 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 24, "section_count": 9 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 17, "section_count": 4 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 16, "section_count": 8 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 15, "section_count": 10 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 15, "section_count": 7 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 8, "section_count": 5 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 7, "section_count": 4 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 6, "section_count": 2 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 6, "section_count": 4 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 6, "section_count": 2 } ], "section_hits": [ { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 274, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... e circuit. With the exception of a few of the larger cities, all the street lighting by arc lamps in this country is done by constant current systems, either direct current or alternating current. For direct current constant current supply, separate arc light machines have been built, and are still largely used. In these machines, inherent regulation for constant current is produced by using a very high armature reaction and relatively weak field excitation; that is, the armature ampere turns are nearly equal ...", "... into the arc circuit supplied from the constant potential source, and by separating or coming together, vary in reactance with the load, and thereby maintain constant current. While the alternating current arc lamp is less efficient, that is, gives less light for the same power, than the direct cur- rent arc lamp, the disadvantages of the use of numerous arc machines have led to the extended adoption of alternating cur- rent series arc lighting before the development of the mercury 224 GENERAL LECTURES arc ...", "... efficiency for all sizes except such small sizes where mechanical difficulties appear in the filament production, the efficiency of the arc decreases greatly with decrease of current ; that is, the arc is at the greatest efficiency only for large units of light, but rather inefficient and not so well suited for small units of light. Even in large units, the efficiency of light production of the direct current carbon arc lamp is not superior to that of the tungsten incandescent lamp ; that of the alternating cur ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-12", "section_label": "Lecture 12: Illumination And Illuminating Engineering", "section_title": "Illumination And Illuminating Engineering", "kind": "lecture", "sequence": 12, "number": 12, "location": "lines 16485-17445", "status": "candidate", "occurrence_count": 257, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-12/", "snippets": [ "LECTURE XII. ILLUMINATION AND ILLUMINATING ENGINEERING. 110. Artificial light is used for the purpose of seeing and distinguishing objects clearly and comfortably when the day- light fails. The problem of artificial lighting thus comprises con- sideration of the source of light or the illuminant; the flux of light issuing from it; ...", "LECTURE XII. ILLUMINATION AND ILLUMINATING ENGINEERING. 110. Artificial light is used for the purpose of seeing and distinguishing objects clearly and comfortably when the day- light fails. The problem of artificial lighting thus comprises con- sideration of the source of light or the illuminant; the flux of light issuing from it; the distribution of the light flux in space, that is, the light flux density in space and more particularl ...", "... INATION AND ILLUMINATING ENGINEERING. 110. Artificial light is used for the purpose of seeing and distinguishing objects clearly and comfortably when the day- light fails. The problem of artificial lighting thus comprises con- sideration of the source of light or the illuminant; the flux of light issuing from it; the distribution of the light flux in space, that is, the light flux density in space and more particularly at the illuminated objects; the illumination, that is, the light flux density reflected from ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-10", "section_label": "Lecture 10: Light Flux And Distribution", "section_title": "Light Flux And Distribution", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 9389-12573", "status": "candidate", "occurrence_count": 226, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-10/", "snippets": [ "LECTURE X. LIGHT FLUX AND DISTRIBUTION. 86. The light flux of an illuminant is its total radiation power, in physiological measure. It therefore is the useful output of the illuminant, and the efficiency of an illuminant thus is the ratio of the total light flux divided ...", "LECTURE X. LIGHT FLUX AND DISTRIBUTION. 86. The light flux of an illuminant is its total radiation power, in physiological measure. It therefore is the useful output of the illuminant, and the efficiency of an illuminant thus is the ratio of the total light flux divided by the power input. In general, the ...", "LECTURE X. LIGHT FLUX AND DISTRIBUTION. 86. The light flux of an illuminant is its total radiation power, in physiological measure. It therefore is the useful output of the illuminant, and the efficiency of an illuminant thus is the ratio of the total light flux divided by the power input. In general, the distribution of the light flux throughout space is not uniform, but the light-flux density is different in different directions from an illuminant. Unit light-flux density is the light-flux density which ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-03", "section_label": "Lecture 3: Physiological Effects Of Radiation", "section_title": "Physiological Effects Of Radiation", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2366-3638", "status": "candidate", "occurrence_count": 171, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-03/", "snippets": [ "... fferences in intensity without measuring them. The photo- graphic camera realizes it. An exposure taken in T^ second with TV opening of the diaphragm in full sunlight usually gives a better photograph than an exposure of 10 minutes at full opening, in the light of the full moon. The ratio of time of exposure in the two cases, however, is about 1 to 1,000,000, thus showing the difference in the intensity of illumination. Also, the disk of the moon, when seen in daylight, has about the same intensity as the sky — ...", "... loudless sky, less than white reflecting clouds. As the surface of the moon's disk, of one-half degree diameter, is about TffsWtf the surface of the sky, it thus follows that the daylight reflected from the sky is about 100,000 times more intense than the light of the full moon. The organ by which we perceive the radiation, the human eye (Fig. 20), contains all the elements of a modern photographic camera — an achromatic lense: the lense L, of high refractive power, enclosed between the two transparent liquids ...", "... ween the two transparent liquids A and B which correct the color dispersion, that is, give the achromatic property; a diaphragm: the iris 7, which allows the increase or decrease of the opening P, the pupil; a shutter: the eyelids and 87 38 RADIATION, LIGHT, AND ILLUMINATION the sensitive plate or retina R. The nerves of vision end at the back of the retina, and in the center of the retina is a spot F, the \"sensitive spot \" or \" fova,\" at which the retina is very thin, and the nerve ends specially plentif ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-11", "section_label": "Lecture 11: Light Intensity And Illumination", "section_title": "Light Intensity And Illumination", "kind": "lecture", "sequence": 11, "number": 11, "location": "lines 12574-16484", "status": "candidate", "occurrence_count": 140, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-11/", "snippets": [ "LECTURE XI. LIGHT INTENSITY AND ILLUMINATION. A. INTENSITY CURVES FOR UNIFORM ILLUMINATION. 102. The distribution of the light flux in space, and thus the illumination, depends on the location of the light sources, and on their distribution curves. The character of the ...", "LECTURE XI. LIGHT INTENSITY AND ILLUMINATION. A. INTENSITY CURVES FOR UNIFORM ILLUMINATION. 102. The distribution of the light flux in space, and thus the illumination, depends on the location of the light sources, and on their distribution curves. The character of the required illumi- nation depends on the purpose for which it is used: a general illumination of low and approxima ...", "LECTURE XI. LIGHT INTENSITY AND ILLUMINATION. A. INTENSITY CURVES FOR UNIFORM ILLUMINATION. 102. The distribution of the light flux in space, and thus the illumination, depends on the location of the light sources, and on their distribution curves. The character of the required illumi- nation depends on the purpose for which it is used: a general illumination of low and approximately uniform intensity for street lighting; a general illumination of uniform h ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-13", "section_label": "Lecture 13: Physiological Problems Of Illuminating Engineering", "section_title": "Physiological Problems Of Illuminating Engineering", "kind": "lecture", "sequence": 13, "number": 13, "location": "lines 17446-17956", "status": "candidate", "occurrence_count": 132, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-13/", "snippets": [ "LECTURE XIII. PHYSIOLOGICAL PROBLEMS OF ILLUMINATING ENGINEERING. 123. The design of an illumination requires the solution of physiological as well as physical problems. Physical considera- tions, for instance, are the distribution of light-flux intensity throughout the illuminated space, as related to size, location and number of light sources, while the relation, to the satisfac- tory character of the illumination, of the direction of the light, its subdivision and diffusion, etc., are phy ...", "... sign of an illumination requires the solution of physiological as well as physical problems. Physical considera- tions, for instance, are the distribution of light-flux intensity throughout the illuminated space, as related to size, location and number of light sources, while the relation, to the satisfac- tory character of the illumination, of the direction of the light, its subdivision and diffusion, etc., are physiological questions. Very little, however, is known on the latter, although the entire field of t ...", "... tions, for instance, are the distribution of light-flux intensity throughout the illuminated space, as related to size, location and number of light sources, while the relation, to the satisfac- tory character of the illumination, of the direction of the light, its subdivision and diffusion, etc., are physiological questions. Very little, however, is known on the latter, although the entire field of the physiological effects of the physical methods of illumination is still largely unexplored. As result thereof, ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-09", "section_label": "Lecture 9: Measurement Of Light And Radiation", "section_title": "Measurement Of Light And Radiation", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 8511-9388", "status": "candidate", "occurrence_count": 125, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-09/", "snippets": [ "LECTURE IX. MEASUREMENT OF LIGHT AND RADIATION. 74. Since radiation is energy, it can be measured as such by converting the energy of radiation into some other form of energy, as, for instance, into heat, and measuring the latter. Thus a beam of radiation may be measured by having it ...", "... ut 0.4 per cent, a change of one millionth corresponds to a temperature rise °f ?tfW deg. cent. Thus, by the bolometer, extremely small amounts of radiation can be measured, as, for instance, the power of the moon's radiation, etc. 166 MEASUREMENT OF LIGHT AND RADIATION. 167 The total radiation energy of a body for a given time can be measured by absorbing it and measuring the heat produced by it, as; for instance, the amount of ice melted in a calorimeter. Any particular range of the total radiation, as, ...", "... tely the power in the visible, the ultra-red, and the ultra-violet range, the method of input and losses can be used to give the total radiation power, and, by bolometer or other means, the relative powers of the component radiations measured in a beam of light. From the total radiation and the ratio of its components, then, follows the values of radiation power of the components. 75. Light, however, cannot be measured by any of the pre- ceding methods, since light, in the sense in which it is con- sidered pho ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 110, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... energy of the latter is very much greater; a sufficiently sensitive heat-measuring instrument, as a bolometer, shows the heat produced by the interception of the rays of the mercury lamp or the rays of the moon. The most conspicuous form of radiation is light, and, therefore, it was in connection with this form that the laws of radiation were first studied. 1 2 RADIATION, LIGHT, AND ILLUMINATION. 2. The first calculations of the velocity of light were made by astronomers in the middle of the eighteenth c ...", "... produced by the interception of the rays of the mercury lamp or the rays of the moon. The most conspicuous form of radiation is light, and, therefore, it was in connection with this form that the laws of radiation were first studied. 1 2 RADIATION, LIGHT, AND ILLUMINATION. 2. The first calculations of the velocity of light were made by astronomers in the middle of the eighteenth century, from the observations of the eclipses of the moons of Jupiter. A number of moons revolve around the planet Jupiter, so ...", "... ys of the moon. The most conspicuous form of radiation is light, and, therefore, it was in connection with this form that the laws of radiation were first studied. 1 2 RADIATION, LIGHT, AND ILLUMINATION. 2. The first calculations of the velocity of light were made by astronomers in the middle of the eighteenth century, from the observations of the eclipses of the moons of Jupiter. A number of moons revolve around the planet Jupiter, some of them so close that seen from the earth they pass behind Jupiter a ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 107, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "LECTURE II. RELATION OF BODIES TO RADIATION. 9. For convenience, the total range of known radiations can be divided into two classes, the electric waves and the light waves, which are separated from each other by the blank space in the middle of the spectrum of radiation (Fig. 14). Under light waves we here include also the invisible ultra-red radiation and the ultra-violet radiation and the non-refrangible radiations, ...", "... RADIATION. 9. For convenience, the total range of known radiations can be divided into two classes, the electric waves and the light waves, which are separated from each other by the blank space in the middle of the spectrum of radiation (Fig. 14). Under light waves we here include also the invisible ultra-red radiation and the ultra-violet radiation and the non-refrangible radiations, as X-rays, etc., separated from the latter by the second blank space of the radiation spectrum. In the following, mainly the ...", "... waves we here include also the invisible ultra-red radiation and the ultra-violet radiation and the non-refrangible radiations, as X-rays, etc., separated from the latter by the second blank space of the radiation spectrum. In the following, mainly the light waves, that is, the second or high frequency range of radiation, will be discussed. The elec- tric waves are usually of importance only in their relation to the radiator or oscillator which produces them, or to the receiver on which they impinge, and thus ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 90, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "LECTURE VI. LUMINESCENCE. 43. All methods of producing radiation, and more particularly light, other than the temperature radiation or incandescence, are generally comprised by the name luminescence. Some special cases of luminescence have already been discussed in the phe- nomena of fluorescence and phosphorescence, represented by the conversion ...", "... phorescence is the production of radiation from the energy stored in the phosphorescent body. This energy may be derived from internal changes in the body, as slow combustion, or may have been received by the body at some previous time — as by exposure to light a calcium sulphide screen absorbs the energy of incident radiation, stores it in some form, and afterwards radiates it. Fluorescence and phosphorescence usually occur simulta- neously : the energy supplied to such a luminescent body brings about certain ...", "... Thermo-luminescence is exhibited by some materials, as the violet colored crystals of fluorite (CaFl2), which, when slightly warmed, luminesce — it is this which gave the name \"fluores- cence\" to the phenomenon. Some solutions, when crystallizing, show light during the formation of crystals, and thus may be said to exhibit a physical phosphorescence. Chemical phosphorescence is exhibited by yellow phosphorus and its solutions, which in the air glow by slow combustion, at ordinary atmospheric temperature. As ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-02", "section_label": "Lecture 2: Conclusions From The Relativity Theory", "section_title": "Conclusions From The Relativity Theory", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 736-2388", "status": "candidate", "occurrence_count": 75, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... new conceptions are so small that they usually cannot be observed even by the most accurate scientific investigation, and in the few instances where the differences have been measured, as in the disturbances of Mercury's orbit, the bending of the beam of light in the gravitational field, etc., they are close to the limits of observation. 12 CONCLUSIONS FROM RELATIVITY THEORY 13 We have seen that the length of a body and the time on it change with the relative velocity of the observer. The highest velociti ...", "... s and 5000 millions respectively. The highest cosmic velocity probably is that of a comet passing the sun at grazing distance, 200 kilometers per second. The shortening of the length even then would be only one in four millions. The bending of a beam of light in the gravitational field of the sun is only a fraction of a thousandth of a degree. The overrunning of the perihelium of the planet Mercury is only about 20 miles out of more than a hundred million miles. Therefore the principal value of the relativi ...", "... theory thus far consists in the better conception of nature and its laws which it affords. Some of the most interesting illustra- tions of this will be discussed in the following pages. B. THE ETHER AND THE FIELD OF FORCE Newton's corpuscular theory of light explained radiation as a bombardment by minute particles projected at extremely high velocities, in much the same way as the alpha and the beta rays are explained today. This corpuscular theory was disproven by the phenomenon of interference, in the foll ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-07", "section_label": "Lecture 7: Flames As Illuminants", "section_title": "Flames As Illuminants", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 6609-7140", "status": "candidate", "occurrence_count": 72, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-07/", "snippets": [ "... n by the conversion of the chemical energy of com- bustion— the flames — and those deriving the energy of radia- tion from electric energy — the incandescent lamp and the arc lamp, and other less frequently used electric illuminants. Flames. To produce light from the chemical energy of combustion, almost exclusively hydrocarbon flames are used, as the gas flame, the candle, the oil lamp, the gasolene and kerosene lamp, etc.; that is, compounds of hydrogen and carbon or of hydrogen, carbon and some oxygen are ...", "... if the air supply is insufficient, to carbon monoxide, CO, a very poisonous, combustible, odorless gas (coal gas), which thus appears in all incomplete combustions and is present, also, as intermediary stage, in complete combustion. The mechanism of the light production by the hydrocarbon flame I illustrate here on the luminous gas flame : where the gas issues from the burner into the air, it burns at the surface of the gas jet. By the heat of combustion the gas is raised to a high temperature. Most hydrocarbo ...", "... poisonous, combustible, odorless gas (coal gas), which thus appears in all incomplete combustions and is present, also, as intermediary stage, in complete combustion. The mechanism of the light production by the hydrocarbon flame I illustrate here on the luminous gas flame : where the gas issues from the burner into the air, it burns at the surface of the gas jet. By the heat of combustion the gas is raised to a high temperature. Most hydrocarbons, however, cannot stand high temperatures, but split up, dissociate ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-08", "section_label": "Lecture 8: Arc Lamps And Arc Lighting", "section_title": "Arc Lamps And Arc Lighting", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 7141-8510", "status": "candidate", "occurrence_count": 69, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-08/", "snippets": [ "... fi6 0[5 25 1 0 FIG. 45. arc length, I, we get tor every value of current, i, a practically straight line, as shown for the magnetite arc in Fig. 45, for values of current of 1, 2, 4 and 8 amperes. These lines are steeper 137 138 RADIATION, LIGHT, AND ILLUMINATION. for smaller currents, that is, low-current arcs consume a higher voltage for the same length than high-current arcs, the in- crease being greater the longer the arc. These lines in Fig. 45 intersect in a point which lies at I = — 0.12 ...", "... i\\ and, as the power is p0 = eQi, it follows that the voltage, e0, consumed at the arc terminals is constant. The power consumed in the arc stream : pl = ej,, is given off, by heat conduction, convection, and by radiation, from the sur- 140 RADIATION, LIGHT, AND ILLUMINATION. face of the arc stream, and thus, as the temperature of the arc stream is constant, and is that of the boiling point of the arc vapor, the power pl consumed in the arc stream is proportional to its surface, that is, to the product of a ...", "... occurs, the arc meets only a part of this ter- minal drop e\", and, for very short arc length, only the terminal drop e0' occurs. Possibly the voltage e0' = 28 is consumed at the negative terminal in producing the conducting vapor stream, 142 RADIATION, LIGHT, AND ILLUMINATION. while the voltage e\" = 8 is consumed by the moving vapor stream in penetrating a layer of dead carbon vapor formed by heat evaporation from the positive terminal, and surrounding this terminal. Stability Curves of the Arc. 64. From ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-05", "section_label": "Lecture 5: Temperature Radiation", "section_title": "Temperature Radiation", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3946-5076", "status": "candidate", "occurrence_count": 59, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-05/", "snippets": [ "... TURE V. TEMPERATURE RADIATION. 34. The most common method of producing radiation is by impressing heat energy upon a body and thereby raising its tem- perature. Up to a short time ago this was the only method avail- able for the production of artificial light. The temperature is raised by heating a body by the transformation of chemical energy, that is, by combustion, and in later years by the trans- formation of electric energy, as in the arc and incandescent lamp. With increasing temperature of a body the ...", "... the radiator and thus increasing radiation power, its temperature first rises proportional to the power input and then slower and ultimately approaches proportionality with the fourth root of the power output: 4/p- T =V — • ll V kA 72 RADIATION, LIGHT, AND ILLUMINATION. In Fig. 27 is shown the radiation curve, with the temperatures T as ordinates and the radiated power Pr as abscissas, the upper curve with 100 times the scale of abscissas. Thus, to double the temperature rise from 10 deg. cent, to 2 ...", "... frequency of radiation also increases, that is, the higher frequen- cies increase more rapidly than the lower frequencies and higher and higher frequencies appear, until ultimately frequencies are reached where the radiation becomes visible to the eye, as light. When with increasing temperature the radiation just begins to be visible, it appears as a faint colorless grey, \"gespenster grau\" exhibiting the same weird and indistinct appearance as are seen at higher intensities in the monochrome blue and violet radi ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-04", "section_label": "Lecture 4: Chemical And Physical Effects Of Radiation", "section_title": "Chemical And Physical Effects Of Radiation", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3639-3945", "status": "candidate", "occurrence_count": 42, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-04/", "snippets": [ "... ody which is responsive to them. The chemical action of radiation is specific to its frequency and seems to be some kind of a resonance effect. We may picture to ourselves that the frequency of vibration of a silver atom is that of violet or ultra-violet light, and therefore, when struck by a wave of this frequency, is set in vibration by resonance, just as a tuning fork is set in vibration by a sound wave of the frequency with which it can vibrate, and if the vibration of the silver atom, in response to the fr ...", "... ibration by a sound wave of the frequency with which it can vibrate, and if the vibration of the silver atom, in response to the frequency of radiation, becomes sufficiently intense, it breaks away from the atom with which it is chemically 64 RADIATION, LIGHT, AND ILLUMINATION. combined in the compound, the silver bromide, etc., and this compound thus splits up, dissociates. The phenomenon, how- ever, must be more complex, as a simple resonance vibration would be especially pronounced at one definite frequenc ...", "... higher and for lower frequencies. The chemical action of radiation on silver compounds, however, does not show such a response to any definite frequency, but, while strongest in the ultra-violet, ex- tends over the entire range from the frequency of green light beyond the ultra-violet and up to the highest frequencies of X-rays. That the chemical activity of radiation is some form of resonance, is, however, made very probable by the relation which exists between the active frequency range and the weight of the ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-03", "section_label": "Lecture 3: Gravitation And The Gravitational Fleld", "section_title": "Gravitation And The Gravitational Fleld", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2389-3594", "status": "candidate", "occurrence_count": 38, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-03/", "snippets": [ "... field. The energy field is a storage of energy in space, character- ized by the property of exerting a force on any body susceptible to this energy — that is, a magnetic field on a magnetizable body, a gravitational field on a gravitational mass, etc. Light, or, in general, radiation, is an electromagnetic wave — ^that is, an alternation or periodic variation of the electromagnetic field^ — and the difference between the alternating fields of our transmission lines, the electro- magnetic waves of our radio s ...", "... ation, is an electromagnetic wave — ^that is, an alternation or periodic variation of the electromagnetic field^ — and the difference between the alternating fields of our transmission lines, the electro- magnetic waves of our radio stations, the waves of visible light and the X-rays are merely those due to the differences of frequency or wave length. The energy field at any point of space is determined by two constants, the intensity and the direction, and the force exerted by the field on a susceptible body is propor ...", "... motion to an accelerated system. The law of gravitation thus appears here as such a mathematical transformation to an acceler- ated system and has been derived in this manner by Einstein. For all velocities which are small compared with the velocity of light Einstein's law of gravitation and Newton's law give the same results, and a difference appears only when the velocity of the moving bodies approaches in magnitude the velocity of light, as is the case, for instance, with ionic motions. Thus the gravitat ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-04", "section_label": "Lecture 4: The Characteristics Of Space A. The Geometry Of The Gravitational Field", "section_title": "The Characteristics Of Space A. The Geometry Of The Gravitational Field", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3595-6820", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-04/", "snippets": [ "LECTURE IV THE CHARACTERISTICS OF SPACE A. THE GEOMETRY OF THE GRAVITATIONAL FIELD The starting point of the relativity theory is that the laws of nature, including the velocity of light in empty space, are the same everywhere and with regard to any system to which they may be referred — whether on the revolving platform of the earth or in the speeding railway train or in the space between the fixed stars. From this it follows that the l ...", "... triangle which we can meas- ure is limited to a few hundred million miles. ^ The mathe- maticians therefore used to speculate whether such a departure would be discovered if we could measure a tri- angle between some distant fixed stars with some hundred light-years as sides. The answer has now been given indirectly by the rela- tivity theory, showing that physical space varies between ^ Some of these properties will be explained later on. ^ The diameter of the orbit of the earth. 74 RELATIVITY AND SPAC ...", "... tained in and as a part of a four-dimensional Euclidean space (and mathematically there is no difficulty in this), then from this four-dimensional Euclidean space we would see that the straight lines of our space are really circles with about 100,000,000 light-years' radius. But the center of the circle and its curvature are outside of our 3-space, in the fourth dimension, exactly as the straight line of the elliptic 2-space is a circle seen from the Euclidean 3-space containing the elliptic 2-space as sphere, ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-01", "section_label": "Lecture 1: General", "section_title": "General", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 275-735", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-01/", "snippets": [ "... me laws of nature apply everywhere. If the laws of nature are the same in the railway train moving at constant speed on straight, level track as they are on the \"rigid\" platform of the earth or in the empty space among the fixed stars, then the speed of light must also be the same, 186,000 miles per second, and so must be the speed with which the electric current travels in its circuit, which is the speed of light. This is important because all observations depend on it. Any event is either observed by seeing ...", "... the \"rigid\" platform of the earth or in the empty space among the fixed stars, then the speed of light must also be the same, 186,000 miles per second, and so must be the speed with which the electric current travels in its circuit, which is the speed of light. This is important because all observations depend on it. Any event is either observed by seeing it or recorded by some electrical arrange- ment, and in either case we do not get the exact time when the event occurs but a time later by the time it takes t ...", "... is is important because all observations depend on it. Any event is either observed by seeing it or recorded by some electrical arrange- ment, and in either case we do not get the exact time when the event occurs but a time later by the time it takes the light to reach our eye or the electric current to flow from the event to the recording device, and to get the exact time of the event, we therefore have to allow for the time taken by the light or the electric current. Owing to the enormous speed of the light, ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-16", "section_label": "Lecture 16: The Incandescent Lamp", "section_title": "The Incandescent Lamp", "kind": "lecture", "sequence": 16, "number": 16, "location": "lines 9687-9919", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-16/", "snippets": [ "... es of electric illuminants are the in- candescent lamp and the arc. In the incandescent lamp the current flows through a solid conductor, usually in a vacuum, and the heat produced in the resistance of the conductor makes it incandescent, thus giving the light. Incandescent lamps in an electric circuit therefore act as non-inductive ohmic resistance and can there- fore be operated equally well on constant potential as on con- stant current. As electric distribution systems are always constant potential, most in ...", "... . As electric distribution systems are always constant potential, most incandescent lamps are operated on constant potential ; and only for outdoor lighting, that is, for street lighting in cases where the arc lamp is too large and too expensive a unit of light for the requirements, incandescent lamps are used on a constant, direct or alternating current cir- cuit; they are then usually built for the standard arc circuits, and thus for low voltage. For general convenience the efficiency of incandescent lamps i ...", "... l life ; since experience has shown, that after a decrease of candle power of 20%, with the carbon filament lamp, under average conditions, it is more economical to replace the lamp with a new lamp, than to continue its use ; as then the increased cost of light due to the lower efficiency is greater than the cost of the lamp, when distributed over 500 hours. 2IO GENERAL LECTURES In discussing incandescent lamp efficiencies, it is therefore essential to make sure that the efficiency is given at the useful li ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "CHAPTER II. LONG-DISTANCE TRANSMISSION LINE. 3. If an electric impulse is sent into a conductor, as a trans- mission line, this impulse travels along the line at the velocity of light (approximately), or 188,000 miles per second. If the line is open at the other end, the impulse there is reflected and returns at the same velocity. If now at the moment when the impulse arrives at the starting point a second impulse, of opposite directio ...", "... enomenon of electrical resonance thus is that alternating impulses occur at time intervals equal to the time required for the impulse to travel the length of the line and back; that is, the time of one half wave of impressed e.m.f. is the time required by light to travel twice the length of the line, or the time of one complete period is the time light requires to travel four times the length of the line; in other words, the number of periods, or frequency of the impressed alternating e.m.fs., in resonance condi ...", "... ual to the time required for the impulse to travel the length of the line and back; that is, the time of one half wave of impressed e.m.f. is the time required by light to travel twice the length of the line, or the time of one complete period is the time light requires to travel four times the length of the line; in other words, the number of periods, or frequency of the impressed alternating e.m.fs., in resonance condition, is the velocity of light divided by four times the length of the line; or, in free osc ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-01", "section_label": "Lecture 1: General Review", "section_title": "General Review", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 154-565", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-01/", "snippets": [ "... apidly disappear- ing, as it is somewhat low for general distribution, and higher than desirable for conversion to direct current. It was largely used also for power distribution in mills and factories as the lowest frequency at which arc and incandescent light- ing is still feasible; for the reason that 40 cycle generators driven by slow speed reciprocating engines are more easily operated in parallel, due to the lower number of poles. With the development of the steam turbine as high speed prime mover, the co ...", "... and correspondingly higher candle power with the more efficient metallized carbon and metal filaments, the 220 volt lamp is from 10 to 15^ less efficient, that is, requires from 10 to 15% more power than the no volt lamp, when producing the same amount of light at the same useful life. This differ- ence is inherent in the incandescent lamp, and is due to the far greater length and smaller section of the 220 volt filament, compared with the no volt filament, and therefore no possibil- ity of overcoming it exists ...", "... loss of efficiency of 10 to 15%, resulting from the use of the 220 volt lamp, is far greater than the saving in power and in cost of investment in the supply mains ; and the 220 volt system with no volt lamps is therefore more efficient, in the amount of light produced in the customer's lamps, than the 440 volt system with 220 volt lamps. In this country, since the early days, the illuminating companies have accepted the responsibility up to the output in light at the customer's lamps, by supplying and renewing ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-03", "section_label": "Lecture 3: Light And Power Distribution", "section_title": "Light And Power Distribution", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 983-1526", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-03/", "snippets": [ "THIRD LECTURE LIGHT AND POWER DISTRIBUTION 1\"^ N A DIRECT current distribution system, the motor load is connected to the outside mains at 220 volts, \"^\"^ and only very small motors, as fan motors, between outside mains and neutral ; since the latter connection, with a la ...", "... that which the motor actually gives, and that which it would give, with the same torque, at full speed, is consumed in the rheostat. Where therefore different motor speeds are required, pro- visions are made in the induction motor to change the number LIGHT AND POWER DISTRIBUTION 39 of poles; thereby a number of different definite speeds are available, at which the motor operates economically as \"multi- speed\" motor. The starting torque of the polyphase induction motor with starting rheostat in the ar ...", "... laces where motors are used and three-phase motors are operated by separate step-down transformers. In the lighting feeders, the voltage is then controlled by feeder regulators, or, in a smaller system, the generator excitation is varied so as to main- LIGHT AND POWER DISTRIBUTION 41 tain the proper voltage on the lighting phase. At load, the three-phase triangle then more or less unbalances, but induction motors are very little sensitive to unbalancing of the voltage, and by their regulation — ^by taking mo ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-09", "section_label": "Lecture 9: Hunting Of Synchronous Machines", "section_title": "Hunting Of Synchronous Machines", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 4218-4594", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-09/", "snippets": [ "... oo much and too little steam. HUNTING OF SYNCHRONOUS MACHINES 119 In this case the frequency of hunting does not depend on the engine speed and does not vary much with the field exci- tation, but the hunting is usually much less at heavy load than at light load. The reason is that at load, when the engfines take much steam, a little change in the steam supply does not make so much difference as at light load, where the engines take very little steam, and so a small change of the governor has a great effect. ...", "... oes not vary much with the field exci- tation, but the hunting is usually much less at heavy load than at light load. The reason is that at load, when the engfines take much steam, a little change in the steam supply does not make so much difference as at light load, where the engines take very little steam, and so a small change of the governor has a great effect. 4th. To run in parallel, the speed of the engines driving the alternators must decrease with the load so that the alter- nators divide the load. ...", "... be no division of the load; the one engine could take all the load, the other nothing. If the speed curve of the engine is such that the speed does not fall off much between no load and moderate load, then the alternators will not well divide the load at light loads, and hunt while running in parallel at light load, but steady down at heavier loads. To distinguish between different kinds of hunting: 1st. Change of frequency with change of field excita- tion points to magnetic hunting, especially if very mark ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-01", "section_label": "Chapter 1: Electric Conduction. Soled And Liquid", "section_title": "Electric Conduction. Soled And Liquid", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 959-3894", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-01/", "snippets": [ "... ch the conduction of the electric current converts energy into no other form but heat. That is, a consumption of power takes place in the metallic con- 1 2 ELECTRIC CIRCUITS ductors by conversion into heat, and into beat only. Indirectly, we may get light, if the heat produced raises the temperature high enough to get visible radiation as in the incandescent lamp filament, but this radiation is produced from heat, and directly the conversion of electric energy takes place into beat. Most of the metaUic con ...", "... volt-ampere characteristic in some pyroelectric conductors, especially those of high resistance, of very high negative temperature coefficient and of considerable cross-section, results the tendency to unequal current distribution and the formation of a \"luminous streak,\" at a sudden applica- tion of high voltage. Thus, if the current passing through a graphite-clay rod of a few hundred ohms resistance is gradually increased, the temperature rises, the voltage first increases and then decreases, while the rod pass ...", "... of low resistance, high current and high temperature, while most of the section is still in the high-resistance range (2) and never passes beyond this range, as it is practically short-circuited. Thus, practically all the cur- rent passes by an irregular luminous streak through a small sec- tion of the rod, while most of the section is relatively cold and practically does not participate in the conduction. Gradually, by heat conduction the temperature and the current density may become more imiform, if before this ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-02", "section_label": "Chapter 2: Electric Conduction. Gas And Vapor", "section_title": "Electric Conduction. Gas And Vapor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3895-5444", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-02/", "snippets": [ "... por, gas and vacuum conduction. Typical of this is, that the volt-ampere characteristic is dropping, that is, the voltage decreases with in- crease of current, and that luminescence accompanies the con- duction, that is, conversion of electric energy into light. Thus, gas and vapor conductors are unstable on constant- potential supply, but stable on constant current. On constant potential they require a series resistance or reactance, to produce stability. Such conduction may be divided into three distinct ty ...", "... to produce stability. Such conduction may be divided into three distinct types: spark conduction, arc conduction, and true electronic conduction. In spark conduction, the gas or vapor which fills the space be- tween the electrodes is the conductor. The light given by the gaseous conductor thus shows the spectrum of the gas or vapor which fills the space, but the material of the electrodes is imma- terial, that is, affects neither the light nor the electric behavior of the gaseous conductor, except indirectly, ...", "... r which fills the space be- tween the electrodes is the conductor. The light given by the gaseous conductor thus shows the spectrum of the gas or vapor which fills the space, but the material of the electrodes is imma- terial, that is, affects neither the light nor the electric behavior of the gaseous conductor, except indirectly, in so far as the section of the conductor at the terminals depends upon the terminal sur- face. In arc conduction, the conductor is a vapor stream issuing from the negative terminal ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-11", "section_label": "Lecture 11: Lightning Protection", "section_title": "Lightning Protection", "kind": "lecture", "sequence": 11, "number": 11, "location": "lines 4931-5294", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-11/", "snippets": [ "... W\"~l HEN the first telegraph circuits were strung across the country, lightning protection became necessary, and ■^ was given to these circuits at the station by connecting spark gaps between the circuit conductors and the ground. When, however, electric light and power circuits made their appearance, this protection against lightning by a simple small spark gap to ground became insufficient, and this addi- tional problem arose : to open the short circuit of the machine current, which resulted from and followed ...", "... ct synchronous ma- chines, it failed to protect under severe conditions. Thus it has been relegated for use as an emergency arrester on some over- head lines, to operate only when a shutdown is unavoidable. To limit the machine current which followed the light- ning discharge, and so enable the lightning arrester to open the discharge circuit, series resistance was introduced in the arrester. Series resistance, however, also limited the discharge current, and with very heavy discharges, such lightning arrester ...", "... first discharge, therefore is deflected over the resistances, limited thereby ; and the circuit so finally opened by the unshunted spark gaps. With the change in the character, size and power of electric circuits, the problem of their protection against light- ning thus also changed and became far more serious and difficult. Other forms of lightning, which did not exist in the small electric circuits of early days, also made their appear- ance, and protection now is required not only against the damage threat ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-109", "section_label": "Apparatus Section 3: Induction Machines: Single -phase Induction Motor", "section_title": "Induction Machines: Single -phase Induction Motor", "kind": "apparatus-section", "sequence": 109, "number": 3, "location": "lines 20428-21157", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-109/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-109/", "snippets": [ "... ase motor running synchronously, that is, doing no work whatever, the secondary becomes current- less, and the primary current is the exciting current of the motor only. In the single-phase induction motor, even when running light, the secondary still carries the exciting current of the mag- netic flux in quadrature with the axis of the primary exciting coil. Since, this flux has essentially the same intensity as the flux in the direction of the ax ...", "... he primary exciting coil. Since, this flux has essentially the same intensity as the flux in the direction of the axis of the primary exciting coil, the current in the armature of the single-phase induction motor run- ning light, and therefore also the primary current corresponding thereto, has the same m.m.f., that is, the same intensity, as the primary exciting current, and the total primary current of the single-phase induction motor running light ...", "... light, and therefore also the primary current corresponding thereto, has the same m.m.f., that is, the same intensity, as the primary exciting current, and the total primary current of the single-phase induction motor running light is thus twice the exciting current, that is, it is the exciting current of the main magnetic flux plus the current producing in the secondary the exciting current of the cross magnetic flux. In reality it is slightly les ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-24", "section_label": "Chapter 24: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 25682-29374", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-24/", "snippets": [ "... ei < eo; that is, motor e.m.f. < generator e.m.f. If 2 = 2 r, ei = eo; that is, motor e.m.f. = generator e.m.f. If 2 > 2 r, ei > go; that is, motor e.m.f. > generator e.m.f. In either case, the current in the synchronous motor is leading. 221. B. Running Light, p = 0. When running light, or for p = 0, we get, by substituting in (19) and (20), eoz /l ^^ = TV2 ?o /r z-\\2 ^ j 1 + ^ cos 2 r, ei > go; that is, motor e.m.f. > generator e.m.f. In either case, the current in the synchronous motor is leading. 221. B. Running Light, p = 0. When running light, or for p = 0, we get, by substituting in (19) and (20), eoz /l ^^ = TV2 ?o /r z-\\2 ^ j 1 + ^ cos ) Vl6.4Xl0-«p}. Maximum output, p = 156.25 kw. (21) at ei = 2795 volts i = 125 amp. Running light, (22) ei2 + 500 i^ - 6.25 X 10* + 40 iei = 0 ei = 20i ± V6.25 X 10^ - 100 i^ (28) SYNCHRONOUS MOTOR 325 At the minimum value of counter e.m.f., ei= 0 is z = 112 (29) At the minimum value of current, i= 0 is ei = 2500 (30) At the maximum ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "section_label": "Lecture 10: Continual And Cumulative Oscillations", "section_title": "Continual And Cumulative Oscillations", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... ng force, (27) ROUND PARALLEL CONDUCTORS. 137 G e and K = - — -„ = - — -, = dielectric field intensity, (28) where v- is the reduction factor from the electrostatic to the electromagnetic system of units, and y = 3 X 10^0 cm. sec. = velocity of light; (29) the dielectric density then is D = kK = -^j, (30) 4 TTVH where k = specific capacity of medium, = 1 in air. The dielectric flux then is where A = section of dielectric flux. Or inversely: e = i^^^. (32) If then \"^ = dielectric flux, in Fi ...", "... follows: the external inductance was, by (9), Li = 2 log - 10~^ h per cm., and multiplying this with (38) gives (39) CLi — — : ^2 or V\"Li that is, the capacity equals the reciprocal of the external inductance Li times the velocity square of light. The external inductance Li would be the inductance of a conductor which had perfect con- ductivity, or zero losses of power. It is Vlc = velocity of propagation of the electric field, and this velocity is less than the velocity of light, due to the re ...", "... city square of light. The external inductance Li would be the inductance of a conductor which had perfect con- ductivity, or zero losses of power. It is Vlc = velocity of propagation of the electric field, and this velocity is less than the velocity of light, due to the retardacion by the power dissipation in the conductor, and becomes equal to the velocity of light V if there is no power dissipation, and, in the latter case, L would be equal to Li, the external inductance. The equation (39) is the most conv ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-10", "section_label": "Lecture 10: Inductance And Capacity Of Round Parallel Conductors", "section_title": "Inductance And Capacity Of Round Parallel Conductors", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6089-7274", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "snippets": [ "... 28 ELECTRIC DISCHARGES, WAVES AND IMPULSES. and K = - — 2 = - — ^ = dielectric field intensity, (28) 4 Trf 4 irV L where v2 is the reduction factor from the electrostatic to the electromagnetic system of units, and v = 3 X 1010 cm. sec. = velocity of light; (29) the dielectric density then is where K = specific capacity of medium, = 1 in air. The dielectric flux then is where A = section of dielectric flux. Or inversely: -IS?* : || (32) If then ^ = dielectric flux, in Fig. 60, at a distance x from ...", "... mediately it follows: the external inductance was, by (9), Li = 2 log- 10~9 h per cm., and multiplying this with (38) gives or CL> = £' (39) that is, the capacity equals the reciprocal of the external inductance LI times the velocity square of light. The external inductance LI would be the inductance of a conductor which had perfect con- ductivity, or zero losses of power. It is VLC = velocity of propagation of the electric field, and this velocity is less than the velocity of light, due to the r ...", "... ity square of light. The external inductance LI would be the inductance of a conductor which had perfect con- ductivity, or zero losses of power. It is VLC = velocity of propagation of the electric field, and this velocity is less than the velocity of light, due to the retardation by the power dissipation in the conductor, and becomes equal to the velocity of light v if there is no power dissipation, and, in the latter case, L would be equal to LI, the external inductance. The equation (39) is the most conv ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... 6000 kw. are to be transmitted over a long distance transmis- sion line at 44,000 volts. The transmission line has a length of 60 miles, and consists of three wires No. 0 B. & S. with 5 ft. between the wires. The question arises, whether during times of light load the old 750-kw. generators can be used economically on the trans- mission line. These old machines give an electromotive force wave, which, like that of most earlier machines, differs con- vsiderably from a sine wave, and it is to be investigated, wh ...", "... ently necessary also in engineering, to get from a limited number of observations the highest accuracy of the constants. 123. As instance, the method of least squares may be applied in separating from the observations of an induction motor, when running light, the component losses, as friction, hysteresis, etc. MAXIMA AND MINIMA. 183 In a 440-volt 50-h.p. induction motor, when running light, that is, without load, at various voltages, let the terminal voltage e, the current input i, and the power input ...", "... he method of least squares may be applied in separating from the observations of an induction motor, when running light, the component losses, as friction, hysteresis, etc. MAXIMA AND MINIMA. 183 In a 440-volt 50-h.p. induction motor, when running light, that is, without load, at various voltages, let the terminal voltage e, the current input i, and the power input p be observed as given in the first three colunms of Table I: Table I e i p ih- Vn PO calc. J 148 220 320 8 11 19 ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-02", "section_label": "Lecture 2: General Distribution", "section_title": "General Distribution", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 566-982", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-02/", "snippets": [ "... tion may have, in addition to the neutral bus bar zero, three positive GENERAL DISTRIBUTION 25 bus bars i, i', i\", and three negative bus bars 2, 2', 2\", differing respectively from the neutral bus by 120, 130 and 140 volts, as shown in Fig. 3. At light load, when the drop of voltage in the feeders is negligible, the feeders connect to the busses I, o, 2 of 120 volts. When the load increases, some of the feeders are shifted over, by transfer bus bars, to the 130 volt busbars i' and 2'; with still further ...", "... ferent bus bars are operated through boosters, or by connection with the storage battery reserve, etc. In addition to feeders and mains, tie feeders usually con- nect the generating station or substation with adjacent stations, so that during periods of light load, or in case of breakdown, a station may be shut down altogether and supplied from adjacent stations by tie feeders. Such tie feeders also permit most stations to operate without storage battery reserve, that is, to concentrate the storage batteries i ...", "... t is, a system using secondary distribution mains as far as feasible, the all year efficiency is about the same as with the direct current system. In such an alternating current system, 34 GENERAL LECTURES the efficiency at heavy load is higher, and at light load lower, than in the direct current system ; in this respect the alternating current system has the advantage over the direct current system, since at the time of heavy load the power is more valuable than at light load." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-19", "section_label": "Chapter 19: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 18053-19457", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "snippets": [ "... 0; that is, motor E.M.F. < generator E.M.F. If z = 2 r, el = e0 ; that is, motor E.M.F. = generator E.M.F. If z > 2 r, r0; that is, motor E.M.F. > generator E.M.F. In either case, the current in the synchronous motor is leading. 207. B. Running Light, p = 0. When running light, or for / = 0, we get, by substitut- ing in (19) and (20), (26) Obviously this condition cannot well be fulfilled, since p must at least equal the power consumed by friction, etc. ; and thus the true no-load curve merely ...", "... nerator E.M.F. If z = 2 r, el = e0 ; that is, motor E.M.F. = generator E.M.F. If z > 2 r, r0; that is, motor E.M.F. > generator E.M.F. In either case, the current in the synchronous motor is leading. 207. B. Running Light, p = 0. When running light, or for / = 0, we get, by substitut- ing in (19) and (20), (26) Obviously this condition cannot well be fulfilled, since p must at least equal the power consumed by friction, etc. ; and thus the true no-load curve merely approaches the curve / = 0, ...", "... — = 0, as del (32) If, as abscissas, elt and as ordinates, zi, are chosen, the axis of these ellipses pass through the points of maximum power given by equation (22). It is obvious thus, that in the V-shaped curves of syn- chronous motors running light, the two sides of the curves are not straight lines, as usually assumed, but arcs of ellipses, the one of concave, the other of convex, curvature. These two ellipses are shown in Fig. 154, and divide the whole space into six parts — the two parts A and A ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-01", "section_label": "Chapter 1: Speed Control Of Induction Motors", "section_title": "Speed Control Of Induction Motors", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1368-3542", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-01/", "snippets": [ "... - 0.1 j; Zo = r„+ j\"j:0 =0.1 +0.3j; Z, = rl+jxl = 0.1 -f 0.3j; the speed-torque curve of this motor is shown as A in Fig. 1 SPEED CONTROL 3 Suppose now a resistance, r, i8 inserted in series into the sec- ondary circuit, which when cold — that is, at light-load — equals the internal secondary resistance: but increases so as to double with 100 amp. passing through it. This resistance can then be represented by: r = r° (1 + i,« 10-*) = 0.1 (1 +»i,10-4), NDUCTION MOTOR -110 I ^ z,=r, + .3i SPE ...", "... , rlT were made as low as possible, tx = 0.05, and the rest added as externa] resistance of high temperature coefficient: r\" = 0.05, giving the total resistance: = 0.1 (1 + 0.5 ir 10\"4). (4) This gives the same resistance as curve A ; r\\ = 0.1, at light- load, where iL is small and the external part of the resistance cold. But with increasing load the resistance, r'i, increases, and the motor gives the curve shown as C in Fig. 1. As seen, curve C is the same near synchronism as A, but in starting gives ...", "... , r + r, & = 8, where s = slip at torque, T, with short-circuited armature, or resistance, rt. As seen from Fig. 7, very close constant-speed regulation is produced by the use of the pyro-electric resistance, over a wide range of load, and only at light-load the motor speeds up. Thus, good constant. -a peed regulation at any speed below synchronism, down to very low speeds, would be produced— at a corresponding sacrifice of efficiency, however — by the use of suitable pyro-electric conductors in the mot ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "... - 0.2 (1 - s)]. The load curves of this motor couple are shown in Fig. 31. As 84 ELECTRICAL APPARATUS Bent, power-factor and apparent efficiency rise to high values, and even the efficiency is higher than in the straight induction motor. However, at light-load the power-factor and thus the apparent efficiency falls off, very much in the same manner as in the con- catenation with a synchronous motor. It is interesting to note the relatively great drop of speed at light-load, while at heavier load the speed ...", "... traight induction motor. However, at light-load the power-factor and thus the apparent efficiency falls off, very much in the same manner as in the con- catenation with a synchronous motor. It is interesting to note the relatively great drop of speed at light-load, while at heavier load the speed remains more nearly constant. This is a general characteristic of anti-inductive im- pedance in the induction-motor secondary, and shared by the use of an electrostatic condenser in the secondary. For comparison, on ...", "... ndenser of capacity impedance: Z, = - 0.012 j, thus giving: 0.04> Z' = 0.1 + 0.3j(s-^p) Fig. 33 shows the load curves of this motor with condenser in the secondary. As seen, power-factor and apparent effi- ciency are high at load, but fall off at light-load, being similar in character as with a commutating machine concatenated to the induction machine, or with the secondary excited by direct current, that is, with conversion of the induction into a synchro- nous motor. Interesting is the speed charact ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-14", "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "section_title": "Constant-Potential Constant-Current Trans Formation", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "... circuits, and to a lim- ited extent also for electric furnaces, a constant, or approximately constant alternating current is required. While constant alter- nating-current arcs have largely come out of use and their place taken by constant direct-current luminous arc circuits, or incan- descent lamps, the constant direct current is usually derived by rectification of constant alternating-current supply circuits. Such constant alternating currents are usually produced from constant- voltage supply circuits by mean ...", "... ensive or inductive, when inserted in a constant-potential circuit, tends toward a constant-current r^ulation, at least within a certain range of load. That is, at varying resistance, r, and therefore varying load, the current is approximately constant at light load, and drops off only gradu- ally with increasing load. 256 ELECTRIC CIRCUITS This constant-current regulation, and the power-factor of the circuit, are best if the reactance of the receiver circuit is of oppo- site sign to the series reactance ...", "... nces, that is, by combinations of inductive and condensive reactances, the constant alternating current is in quadrature with the constant e.m.f. Even in constant-current control by series inductive reactances, the constancy of current is most perfect for light loads, where the reactance voltage is large and thus the constantr current voltage almost in quadrature, and the constant-current control is impaired in direct proportion to the shift of phase of the constant current from quadrature relation. 13 ^ ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-48", "section_label": "Chapter 8: Velocity Of Propagation Of Electric Field", "section_title": "Velocity Of Propagation Of Electric Field", "kind": "chapter", "sequence": 48, "number": 8, "location": "lines 26095-27002", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "snippets": [ "... ered as in phase with the current, the electrostatic component as in phase with the voltage. In reality, however, the electric field starts at the conductor and propa- gates from there through space with a finite though very high velocity, the velocity of light; that is, at any point in space the electric field at any moment corresponds not to the condi- tion of the electric energy flow at that moment but to that at a moment earlier by the time of propagation from the conductor to the point under consideration, ...", "... tic field is neglected. With alternating currents traversing the conductor this is permissible when the distance to the return conductor is a negligible fraction of the wave length; that is, if Z' is § negligible compared with -, where S = the speed of light and VELOCITY OF PROPAGATION OF ELECTRIC FIELD 391 / = the frequency of alternating current. It obviously is not permissible in a conductor having no return conductor. If a conductor conveying an alternating current has no return conductor, its circui ...", "... r. The magnetic field at a distance I from the conductor and at time t corresponds to the current in the conductor at the time t - t', where if is the time required for the electric field to travel the distance I, that is, t' = -, where $ = the speed of light; o or, the magnetic field at distance I and time t corresponds to the current in the conductor at the time t — - . 71. Representing the time t by angle 6 = 2 nft, where /== the frequency of the alternating current in the conductor, and denoting 2f ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-04", "section_label": "Lecture 4: Load Factor And Cost Of Power", "section_title": "Load Factor And Cost Of Power", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 1527-2561", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-04/", "snippets": [ "... fixed cost, A ; labor, attendance and inspection are partly fixed cost A, partly proportional cost B, — economy of operation requires therefore a shifting of as large a part thereof over into class B, by shutting down smaller substations during periods of light load, etc. Incandescent lamp renewals, arc lamp trimming, etc., are essentially proportional costs, B. The reserve capacity of a plant, the steam reserve main- tained at the receiving end of a transmission line, the difference in cost between a duplica ...", "... ced to shut them down in winter with beginning darkness. It follows herefrom, that additional load on the station during the peak of the load curve is very expensive, since it increases the fixed cost A and C, while additional load during the periods of light station load, only increases the proportional cost B; it therefore is desirable to discriminate against peak loads in favor of day loads and night loads. For this purpose, two-rate meters have been developed, that is, meters which charge a higher price fo ...", "... nate against peak loads in favor of day loads and night loads. For this purpose, two-rate meters have been developed, that is, meters which charge a higher price for power consumed dur- ing the peak of the load curve, than for power consumed dur- ing the light station loads. To even out load curves, and cut down the peak load, maximum demand meters have been developed, that is, meters which charge for power somewhat in proportion to the load factor of the circuit controlled by the meter. Where the circuit is a ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-07", "section_label": "Lecture 7: High Frequency Oscillations And Surges", "section_title": "High Frequency Oscillations And Surges", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3508-3780", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-07/", "snippets": [ "... ete wave length would thus be two miles. Or, if a momentary discharge occurs over a lightning arrester to ground, the wave length may be only a few feet. The velocity with which the electric wave travels in an overhead line is practically the velocity of light, or about 188,000 miles per second: it would be exactly the velocity of light, except that by the resistance of the line conductor the velocity is very slightly reduced. In an underground cable, by the high capacity of the cable insulation, the velocity o ...", "... er a lightning arrester to ground, the wave length may be only a few feet. The velocity with which the electric wave travels in an overhead line is practically the velocity of light, or about 188,000 miles per second: it would be exactly the velocity of light, except that by the resistance of the line conductor the velocity is very slightly reduced. In an underground cable, by the high capacity of the cable insulation, the velocity of wave travel is greatly reduced, to about 50 to 70% of that ol light. From ...", "... city of light, except that by the resistance of the line conductor the velocity is very slightly reduced. In an underground cable, by the high capacity of the cable insulation, the velocity of wave travel is greatly reduced, to about 50 to 70% of that ol light. From the wave length and the velocity follows the dura- tion or time of one wave, and thereby the frequency of the oscillation. For instance, in the wave of two miles' length resulting from induction by a thunder cloud, as discussed above, the duration ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-12", "section_label": "Lecture 12: Electric Railway", "section_title": "Electric Railway", "kind": "lecture", "sequence": 12, "number": 12, "location": "lines 5295-7123", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-12/", "snippets": [ "... instance, a maximum acceleration and maxi- mum braking of two miles per hour per second, and assuming a retardation of one-quarter mile per hour per second by fric- tion (that is, assuming that the car slows down one-quarter mile per second, when running light on a level track) ; if then the time of one complete run between two stations is given equal to A B in Fig. 29, the simplest t)rpe of run consists of constant acceleration, from A to C, on the line A a, drawn 152 GENERAL LECTURES under a slope of two ...", "... refore on mountain railways, induction motors have the advantage. In an induction motor there is no running on the motor curve, and so the efficiency of acceleration is lower. Objection to the series motor is the unlimited speed ; that is, when running light, it runs away. In railroading this is no objection, because tlie motor is never running light and some- body is always in control. In elevator work the series motor is objectionable, due to the unlimited speed ; therefore a limited speed motor is neces- ...", "... e is no running on the motor curve, and so the efficiency of acceleration is lower. Objection to the series motor is the unlimited speed ; that is, when running light, it runs away. In railroading this is no objection, because tlie motor is never running light and some- body is always in control. In elevator work the series motor is objectionable, due to the unlimited speed ; therefore a limited speed motor is neces- sary. In elevators frequent stops, and so efficient acceleration are necessary; therefore a c ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-21", "section_label": "Apparatus Introduction 21: Introduction", "section_title": "Introduction", "kind": "apparatus-introduction", "sequence": 21, "number": null, "location": "lines 8292-8517", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-21/", "snippets": [ "... is unsatisfactory, since it includes in the same class apparatus of entirely different character, as the induction motor and the alternating-current generator, or the constant-potential commutating machine and the rectifying arc light machine. Thus the following classification, based on the characteristic features of the apparatus, as adopted by the A. I. E. E. Standard- izing Committee, is used in the following discussion. It refers only to the apparatu ...", "... half waves of an alternating single-phase or polyphase circuit in the same direction into the receiving circuit. The most impor- 124 ELEMENTS OF ELECTRICAL ENGINEERING tant class of such apparatus were the open-coil arc light ma- chines. They have been practically superseded by the mercury arc rectifier. (4) Induction machines are generally used as motors, poly- phase or single-phase. In this case they run at practically constant speed, ...", "... by the primary and secondary battery and the elec- trolytic cell; the transformation between electrical and heat energy by the thermopile and the electric heater or electric fur- nace; the transformation between electrical and light energy by the incandescent and arc lamps. In the following will be given a general discussion of the charac- teristics of the most frequently used and therefore most impor- tant classes of apparatus. A further discussion a ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-18", "section_label": "Chapter 16: Il", "section_title": "Il", "kind": "chapter", "sequence": 18, "number": 16, "location": "lines 19346-21338", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-18/", "snippets": [ "... generator E.M.F. If 2r = 2 r, ^1 = ^q; that is, motor E.M.F. = generator E.M.F. If ^ > 2 r, ^1 > ^o; that is, motor E.M.F. > generator E.M.F. In either case, the current in the synchronous motor is leading. 186. B. Running Lights / = 0. When running light, or for / = 0, we get, by substitut- ing in (19) and (20), (26) Obviously this condition can never be fulfilled absolutely, since/ must at least equal the power consumed by friction, etc. ; and thus the true no-load curve merely approaches the curve ...", "... 0, as -• '.= T'o-. (32) r r If, as abscissae, ^i, and as ordinates, zi, are chosen, the axis of these ellipses pass through the points of maximum power given by equation (22). It is obvious thus, that in the curves of synchronous motors running light, published by Mordey and others, the two sides of the V-shaped curves are not straight lines, as usually assumed, but arcs of ellipses, the one of concave, the other of convex, curvature. These two ellipses are shown in Fig. 138, and divide the whole sp ...", "... lOV. (17) ^1 = 5590 (19) VH(l-^-2xl0-«/) + (.894cos<^+.447sin<^)Vr^6.4xl0\"-«/}. i = 559 (20) Vi{(l-^-2xl0-V>) + (.894cos<^-.447sin<^)Vi^6.4xl0-«/}. (22) Maximum output, / = 156.25 kilowatts (21) at fi = 2,795 volts /■ =125 amperes Running light, ^j« + 500 /* - 6. 25 X 10* = F 40 /Vx = I ,^8^ ^1 = 20 /• i V6.25 X 10* - 100 n \\ ^ ^ At the minimum value of C.KM.F. ^i = is / = 112 (29) At the minimum value of current, / = is ^i = 2500 (30) At the maximum value of C.KM.F. lines of magnetic force. Dielectric flux: ^ = AD lines of dielectric force. v = 3 X 10 10 = velocity of light. The powers of 10, which appear in some expressions, are reduc- tion factors between the absolute or cgs. units which are used for $, 3C, CB, and the practical electrical units, and used for other constants. As the magnetic field and the dielectric fie ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-35", "section_label": "Apparatus Section 14: Synchronous Machines: Division of Load in Parallel Operation", "section_title": "Synchronous Machines: Division of Load in Parallel Operation", "kind": "apparatus-section", "sequence": 35, "number": 14, "location": "lines 9879-9917", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-35/", "snippets": [ "... g power tends to accelerate to the machine whose driving power tends to slow down, and thus relieves the latter by increasing the load on the former. Thus these cross currents are power currents, and cause at no load or light load the one machine to drive the other as synchronous motor, while under load the result is that the machines do not share the load in proportion to their respective capacities. The speed of the prime mover, as steam ...", "... divided proportionally between the alternators, but the alternator connected to the prime mover of closer speed regula- tion takes more than its share of the load under heavy loads, and SYNCHRONOUS MACHINES 155 less under light loads. Thus, too close speed regulation of prime movers is not desirable in parallel operation of alternators." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-74", "section_label": "Apparatus Subsection 74: Direct-current Commutating Machines: C. Commutating Machines", "section_title": "Direct-current Commutating Machines: C. Commutating Machines", "kind": "apparatus-subsection", "sequence": 74, "number": null, "location": "lines 12660-12763", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-74/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-74/", "snippets": [ "D. C. COMMUTATING MACHINES 213 proportionally to the load, gives curves C, D, and E, which are higher at light load, but fall off faster at high load. A still further shift of brushes near the maximum current value even overturns the curve as shown in F. Curves E and F correspond to a very great shift of brushes, and an armatu ...", "... mum current value even overturns the curve as shown in F. Curves E and F correspond to a very great shift of brushes, and an armature demagnetizing effect of the same magnitude as the field excitation, as realized in arc-light machines, in which the last part of the curve is used to secure inherent regulation for constant current. The resistance characteristic, that is, the dependence of the current and of the terminal voltage of the series gen ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "section_label": "Chapter 14: Dielectric Losses", "section_title": "Dielectric Losses", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "... alue of the current thus is: g^ i = ViTTi? = ^Vy' + (2x/A;)2 and the power consumption: or, since the dielectric density D is proportional to the voltage € ... gradient t and the permittivity: D= '^ 4.irvH (where y = 3 X 10^\" = velocity of light, see \"Theoretical Ele- ments of Electrical Engineering.\") Thus: ^ ~ k^ where V = Al = volume The power-factor then is: ^ ei Vy'-h (2 7r/A;)2 DIELECTRIC LOSSES 153 Or, if, as usually the case, the conductivity 7 is small compared with the su ...", "... A dielectric circuit, in which the power-factor decreases with increasing frequency, for instance, is that of the capacity of the transmission line; a dielectric circuit, in which the power-factor increases with the frequency, is that of the aluminum-cell light- ning arrester. 121. As seen, in the dielectric circuit, that is, in insulators in which the current is essentially a displacement current, the relations between voltage, current, power, phase angle and power- factor can be represented by the same sym ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-05", "section_label": "Chapter 6: Induction-Motor Regulation And Stability", "section_title": "Induction-Motor Regulation And Stability", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 10583-12397", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-05/", "snippets": [ "... of the constants c = 110 volts; Y = 0.01 - 0.1 j; Z0 - 0.1 -f- 0.3 j, Zi = 0.1 + 0.3 j, the stability curve is shown, together with speed, current, and torque, in Fig. 54, as function of the output. As seen, the stability coefficient, k„ is very high for light-load, decreases first rapidly and then slowly, until an output of 7000 watts is approached, and then rapidly drops below zero; that is, the motor becomes unstable and drops out of step, and speed, torque, and current change abruptly, as indicated by the a ...", "... down to about 0.01, and remains constant at this latter value, over a very wide range. The resultant stability coefficient, or stability coefficient of the system of motor and supply, A0 = kn + kn as shown in Fig. 54, thus drops from very high values at light-load down to zero at the load at which the curves, k, and fcr, in Fig. 54 intersect, or at 5800 kw., and there become negative; that is, the motor drops out of step, although still far below its maximum torque point, as indicated by the arrows in Fig. 54. ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-13", "section_label": "Chapter 15: Synchronous Rectifier", "section_title": "Synchronous Rectifier", "kind": "chapter", "sequence": 13, "number": 15, "location": "lines 18413-19373", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-13/", "snippets": [ "... rs, for storage-battery charging and for series arc lighting by constant direct current. For large powers, however, the rectifier does not appear applicable, but the synchronous converter takes its place. The two most important types of direct-current arc-light ma- chines, however, have in reality been mechanical rectifiers, and for compounding alternators, and for starting synchronous motors, rectifying commutators have been used to a considerable extent. Let, in Fig. 72, e be the alternating voltage wave of ...", "... currents, ih i2 and i0) as overlapped by the inductances, Xi, x* and x0, are shown in Fig. 103. Full description and discussion of the mercury-arc rectifier is contained in \"Theory and Calculation of Transient Phenomena,9' Section II, and in \"Radiation, Light and Illumination.\" 250 ELECTRICAL APPARATUS 143. To reduce the sparking at the rectifying commutator, the gap between the segments may be divided into a number of gaps, by small auxiliary segments, as shown in Fig. 104, and these then connected t ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-50", "section_label": "Chapter 1: General Equations", "section_title": "General Equations", "kind": "chapter", "sequence": 50, "number": 1, "location": "lines 27761-28694", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "snippets": [ "... circuit- may be chosen as is convenient, thus : the centimeters in the high- frequency oscillation over the multigap lightning arrester circuit, or a mile in a long-distance transmission circuit or high-potential cable, or the distance of the velocity of light, 300,000 km., etc. The permanent values of current and e.m.f. in such circuits of distributed constants have, for alternating-current circuits, been investigated in Section III, where it was shown that they can be treated as transient phenomena in space, ...", "... opagation of the electric phenomenon in the cir- cuit. (If no energy losses occur, r = 0, g = 0, in a straight con- ductor in a medium of unit magnetic and dielectric constant, that is, unit permeability and unit inductive capacity, S is the velocity of light.) 4. Since (11) is a quadratic equation, several pairs or corre- sponding values of a and b exist, which, in the most general case, are complex imaginary. The terms with conjugate complex imaginary values of a and b then have to be combined for the elim ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-52", "section_label": "Chapter 3: Standing Waves", "section_title": "Standing Waves", "kind": "chapter", "sequence": 52, "number": 3, "location": "lines 29316-30243", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "snippets": [ "... iven by (63) as 27T 2, (122) m Vie In an undamped wave, that is, in a circuit of zero r and zero g, in which no energy losses occur, the speed of propagation is and if the medium has unit permeability and unit inductivity, it is the speed of light, S0 = 3 X 1010. (124) In an undamped circuit, this wave length lWo would correspond to the frequency, STANDING WAVES 447 hence, from (62), '•-,Vr.- <125> The frequency at the wave length lWo is zero, since at this wave length the phenomenon cea ...", "... .7415 log ^ + 0.0805\\ in mh. per mile. (132) , For lr = 0.1825 inch and ld = 60 inches, L = 1.95 mh. per mile. The capacity of a conductor is given by C = I I - *—=\\ 109, in farads, (133) 450 TRANSIENT PHENOMENA where S0 = 3 X 1010 = the speed of light, and d = the allow- ance for capacity of insulation, tie wires, supports, etc., assumed as 5 per cent. Substituting £0, and reducing to one mile and common loga- rithm, gives mf.; (134) logf lr hence, in this instance, C = 0.0162 mf. Estima ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-02", "section_label": "Chapter 2: Potential Series And Exponential Function", "section_title": "Potential Series And Exponential Function", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3492-6063", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-02/", "snippets": [ "... ow To is small compared with r, it is 1-?^} (13) 1 r As; flic next ItM'm (»r the sorit>s woiiM In* ( -) . the errui \\/7 ' made by the simpler expression (13) is less than ( — ) . Thus, if To is 3 per cent of r, which is a fair average in interior light- ing circuits, {-) =0.032 = 0.0009, or less than 0.1 percent; hence, is usuall^^ negligible. 46. If an expression in its finite form is moi*e complicated and thereby less convenient for numerical calculation, as for instance if it contains roots, devel ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-05", "section_label": "Chapter 6: Empirical Curves", "section_title": "Empirical Curves", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 16483-21988", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-05/", "snippets": [ "... aturation would be used for deriving the theoretical equations, and the effect of magnetic saturation treated as secondary phenomenon. Or, for instance, when studying the excitation current of an induction motor, that is, the current consumed when running light, at low voltage the current may increase again with decreasing voltage, 212 ENGIN^EERING MATHEMATICS. instead of decreasing, as result of the friction load, when the voltage is so low that the mechanical friction constitutes an appreciable part of the ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... , lightning protection, etc., we get new functions. If ^=/(0 is the current in the conductor, as function of the time t, at a distance x from the conductor the magnetic field lags by the X time ti = -, where S is the speed of propagation (velocity of light). Since the field intensity decreases inversely propor- tional to the distance x, it thus is proportional to y= — - — ; (41) and the total magnetic flux then is / 2= j ydx A'-l) -j^T^'i' <*2) If the current is an alternating current, that is, f ( ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-05", "section_label": "Lecture 5: Long Distance Transmission", "section_title": "Long Distance Transmission", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2562-3132", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-05/", "snippets": [ "... orona effect is nothing up to a certain voltage, but at a certain voltage it begins and very rapidly increases. The voltage at which a loss by corona effect begins is where the air at the surface of the conductor breaks down, becomes conducting and thus luminous. This occurs at a potential gradient of 100,000 to 120,000 volts per inch. The potential gradient is highest at the surface of the conductor. e J? o ■>* c/ Fig. 18. In Fig. i8 let R = radius of conductor. 2 d = distance between con ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-08", "section_label": "Lecture 8: Generation", "section_title": "Generation", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 3781-4217", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-08/", "snippets": [ "... is, the turbine efficiency remains high at partial loads, and at overloads, where the steam engine efficiency falls off greatly; so that the superiority of the steam turbine in efficiency, while marked at rated load, is still far greater at partial load, light load and overload. b. Smaller size, weight and space occupied. c. Uniform rate of rotation, therefore decreased liability of hunting of synchronous machines, and decreased necessity of heavy foundations to withstand reciprocating strains. d. Greater r ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-13", "section_label": "Lecture 13: Electric Railway: Motor Characteristics", "section_title": "Electric Railway: Motor Characteristics", "kind": "lecture", "sequence": 13, "number": 13, "location": "lines 7124-8648", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-13/", "snippets": [ "... an therefore be assumed as approximately constant : somewhat higher at low and high speeds, as shown by curve F. The net torque then is given by the curve T. As seen, it is approximately a straight line, pass- ing through a point to, which is the \"running light current,\" and its corresponding speed, the \"free running speed\" of the motor. At this current io, the speed is highest; with increase of current it drops first very rapidly, and then more slowly; and the higher the saturation of the motor field is, the sl ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-110", "section_label": "Apparatus Section 4: Induction Machines: Induction Generator", "section_title": "Induction Machines: Induction Generator", "kind": "apparatus-section", "sequence": 110, "number": 4, "location": "lines 21158-21588", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-110/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-110/", "snippets": [ "... case the voltage 348 ELEMENTS OF ELECTRICAL ENGINEERING of the system is controlled by the field excitation of the syn- chronous machine, that is, its counter e.m.f. Either a synchro- nous motor of suitable size running light can be used herefor as exciter of the induction generator, or the exciting current of the induction generator may be derived from synchronous motors or converters in the same system, or from synchronous alternating- current ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-16", "section_label": "Theory Section 16: Phase Control of Transmission Lines", "section_title": "Phase Control of Transmission Lines", "kind": "theory-section", "sequence": 16, "number": 16, "location": "lines 6222-6813", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-16/", "snippets": [ "... 0 fluctuates by 20 per cent, between 1800 and 2200 volts, a synchronous motor of internal impedance Z0 = r0 + jx0 = 0.5 + 5 j is connected through a reactive coil of impedance Z\\ = r\\ + jx\\ = 0.5 -f- 10 j and run light, as compensator (that is, generator of reactive currents). How will the voltage at the synchronous motor terminals e\\, at constant excitation, that is, constant counter e.m.f. e = 2000, vary as function of e$ at no load a ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-19", "section_label": "Theory Section 19: Fields of Force", "section_title": "Fields of Force", "kind": "theory-section", "sequence": 19, "number": 19, "location": "lines 7737-7990", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-19/", "snippets": [ "... om the electric quantity \"gradient\" to the dielectric quantity \" field intensity,\" a numer- ical factor 4 irv2 enters, the one quantity being based on the volt as unit, the other on unit force action, v is the velocity of light, 3 X 1010, and the factor v2 the result of the convention of assum- ing the permittivity of empty space as unity. It is now easy to remember, where in the electromagnetic system of units the factor 4-Tr enters: it is ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-29", "section_label": "Apparatus Section 8: Synchronous Machines: Characteristic Curves of Synchronous Motor", "section_title": "Synchronous Machines: Characteristic Curves of Synchronous Motor", "kind": "apparatus-section", "sequence": 29, "number": 8, "location": "lines 9399-9553", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-29/", "snippets": [ "... for controlling the voltage in trans- mission lines, compensating for wattless currents of induction motors, etc. Synchronous machines used merely for supplying wattless currents, that is, synchronous motors or generators running light, with over-excited or under-excited field, are called synchronous condensers. They are used as exciters for induc- tion generators, as compensators for the reactive lagging currents SYNCHRONOUS MACHINES 147 of induction mot ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1120-1683", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-01/", "snippets": [ "... rmonic, since the inductive reactance is pro- portional to the frequency, and is thus greater with the higher harmonics, and thereby causes a general tendency toward simple sine shape, which has the effect that, in general, the alternating currents in our light and power circuits are sufficiently near sine waves to make the assumption of sine shape permissible. Hence, in the calculation of alternating-current phenomena, we can safely assume the alternating wave as a sine wave, with- out making any serious error ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-04", "section_label": "Chapter 4: Vector Representation", "section_title": "Vector Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2149-2759", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-04/", "snippets": [ "... econdary circuit, the lag in the primary circuit may be less than in the secondary. A conclusion from the foregoing is that the transformer is not suitable for producing currents of displaced phase, since primary and secondary current are, except at very light loads, very nearly in phase, or rather in opposition, to each other." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-11", "section_label": "Chapter 11: Phase Control", "section_title": "Phase Control", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 9767-10717", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-11/", "snippets": [ "... ircuit lagging or leading currents, the change of voltage, e, with a change of load in the circuit can be controlled. For instance, by changing the current from lagging at no-load to lead at heavy load the reactance, x, can be made to lower the voltage at light load and raise it at overload, and so make up for the increasing drop of voltage with increasing load, caused by the resistance, r, that is, to maintain constant voltage, or even a voltage, e, which rises with the load on the receiving circuit, at constan ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "... ides this, there is the increase of ohmic resistance due to unequal distribution of current, which, however, is usually not large enough to be noticeable. Furthermore, the electric field of the conductor progresses with a finite velocity, the velocity of light, hence lags behind 174 ALTERNATING-CURRENT PHENOMENA the flow of power in the conductor, and so also introduces power components, depending on current as well as on potential difference. 132. This gives, as the most general case, and per unit length ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-17", "section_label": "Chapter 17: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16521-17716", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-17/", "snippets": [ "... ndary condensive reactance. As shown in (a), the locus of the secondary terminal voltage, El, and thus of E^, etc., arc straight lines; and in (6) and (c), parts of one and the same circle; (a) is shown in full lines, {h) in heavy full lines, and (c) in light full lines. This diagram corre- sponds to constant maximum magnetic flux; that is, to constant secondary generated e.m.f. The diagrams representing constant ALTERNATING-CURRENT TRANSFORMER 197 primary impressed e.m.f. and constant secondary terminal v ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-23", "section_label": "Chapter 23: Synchronizing Alternators", "section_title": "Synchronizing Alternators", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 25135-25681", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-23/", "snippets": [ "... mp or other device, they are thrown in parallel. Equality of voltage is less important with moderate size alter- nators than equality of frequency, and perfect equality of phase is usually of importance only in avoiding an instantaneous flickering of the light of lamps connected to the system. When two alter- nators are thrown together, currents exist between the machines, which accelerate the one and retard the other machine until equal frequency and proper phase relation are reached. With modern ironclad alt ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-27", "section_label": "Chapter 27: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 33011-34776", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-27/", "snippets": [ "... nt, due to higher-frequency currents in the con- denser, is greater than the decrease, due to the compensation of lagging currents, and the power-factor is actually lowered by the condenser, over the total range of load up to overload, and espe- cially at light load. Where a compensator or transformer is used for feeding the condenser, due to the internal self-inductance of the compensa- tor, the higher harmonics of current are still more accentuated, that is, the power-factor still more lowered. In the prece ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-35", "section_label": "Chapter 35: Balanced Symmetrical Polyphase Systems", "section_title": "Balanced Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 35, "number": 35, "location": "lines 37453-37957", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-35/", "snippets": [ "... , the frequency which makes the length, I, of the line a quarter-wave length. Since the velocity of propagation of the electric field is the ve- ^ \"Theoretical Elements of Electrical Engineering.\" BALANCED SYMMETRICAL POLYPHASE SYSTEMS 451 locity of light, v, with a wave-length, 4 I, the number of waves per second, or frequency of oscillation of the line, is f - — and herefrom then follows: hence, for V I Vlc I = 100 miles, V = 186,000 miles per second, L = 0.23 henry, C = 1.26 mf. and ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1224-1727", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "snippets": [ "... lj. 3. Want ultti EatB suppress the higher harmonics of a complex harmonic wave more than the fundamental harmonic, and thereby causes a general tendency towards simple sine shape, which has the effect, that, in general, the alternating currents in our light and power circuits are sufficiently near sine waves to make the assumption of sine shape permissible. Hence, in the calculation of alternating-current phe- nomena, we can safely assume the alternating wave as a sine wave, without making any serious error ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-04", "section_label": "Chapter 4: Graphic Befrisxintation", "section_title": "Graphic Befrisxintation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2122-2743", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "snippets": [ "... condary circuit, the lag in the primary circuit may be less than in the secondary. A conclusion from the foregoing is that the transformer is not suitable for producing currents of displaced phase ; since primary and secondary current are, except at very light loads, very nearly in phase, or rather, in opposition,, to each other. i 23] SYMBOLIC METHOD. 88" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-13", "section_label": "Chapter 13: Ths Alternating^Cnrrent Traxsfobmer", "section_title": "Ths Alternating^Cnrrent Traxsfobmer", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 12673-14088", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "snippets": [ "... ocus of the secondary terminal vol- tage, ^j-, and thus of E^y etc., are straight lines; and in d.) and c), parts of one and the same circle a.) is shown i 123] ALTERNATING-CURRENT TRANSFORMER. 177 in full lines, b,) in heavy full lines, and c.) in light full lines. This diagram corresponds to constant maximum magnetic flux; that is, to constant secondary induced E.M.F. The diagrams representing constant primary impressed E.M.F. and constant secondary terminal voltage can be derived from the above by pro ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 963-1366", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "snippets": [ "... since the self-induc- tive reactance is proportional to the frequency, and is thus greater with the higher harmonics, and thereby causes a general tendency towards simple sine shape, which has the effect, that, in general, the alternating currents in our light and power circuits are sufficiently near sine waves to make the assumption of sine shape permissible. Hence, in the calculation of alternating-current phev nomena, we can safely assume the alternating wave as a sine wave, without making any serious erro ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-04", "section_label": "Chapter 4: Graphic Representation", "section_title": "Graphic Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 1743-2321", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "snippets": [ "... condary circuit, the lag in the primary circuit may be less than in the secondary. A conclusion from the foregoing is that the transformer is not suitable for producing currents of displaced phase ; since primary and secondary current are, except at very light loads, very nearly in phase, or rather, in opposition, to each other. SYMBOLIC METHOD." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-14", "section_label": "Chapter 14: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 11605-12682", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "snippets": [ "... he locus of the secondary terminal vol- tage, J5lt and thus of E0, etc., are straight lines; and in b.) and c.}, parts of one and the same circle a.} is shown AL TERNA TING-CURRENT TRANSFORMER. 203 in full lines, b.} in heavy full lines, and c.} in light full lines. This diagram corresponds to constant maximum magnetic flux ; that is, to constant secondary induced E.M.F. The diagrams representing constant primary impressed E.M.F. and constant secondary terminal voltage can be derived from the above by pr ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "... , due to higher frequency currents in the condenser, is greater than the decrease, due to the compensation of lagging cur- rents, and the power factor is actually lowered by the con- denser, over the total range of load up to overloads, and especially at light loads. Where a compensator or transformer is used for feeding- the condenser, due to the internal self-induction of the com- pensator, the higher harmonics of current are still more accentuated, that is the power factor still more lowered. In the prece ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-04", "section_label": "Chapter 5: Single-Phase Induction Motor", "section_title": "Single-Phase Induction Motor", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 8555-10582", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-04/", "snippets": [ "... is not neces- sary, as in a synchronous motor, to bring it up to full speed, but the motor begins to develop appreciable torque already at low speed, it is quite feasible to start small induction motors by hand, by a pull on the belt, etc.. especially at light-load and if«of high- resistance armature. (b) By converting the motor in starting into a shunt or series motor. This has the great objection of requiring a commutator, and a cwuttutating-machine rotor winding instead of the common iftd«c*iQ«i-n*otor s ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-12", "section_label": "Chapter 14: Phase Conversion And Single-Phase Generation", "section_title": "Phase Conversion And Single-Phase Generation", "kind": "chapter", "sequence": 12, "number": 14, "location": "lines 17125-18412", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-12/", "snippets": [ "... uarter- phase induction motor, this motor will not take power equally from both phases, e and e0, but takes power essentially only from phase, e. In starting, and at heavy load, a small amount of power is taken also from the quadrature voltage, eo, but at light- load, power may be returned into this voltage, so that in general the average power of e0 approximates zero, that is, the voltage, eo, is wattless. A monocyclic system thus may be defined as a system of poly- phase voltages, in which one of the power a ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-20", "section_label": "Chapter 22: Unipolar Machines", "section_title": "Unipolar Machines", "kind": "chapter", "sequence": 20, "number": 22, "location": "lines 31716-32137", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-20/", "snippets": [ "... e cylindrical gap be- tween N and 8. B, and B% are the two sets of brushes bearing on the collector rings at the end of the conductor, C, and F is the field exciting winding. The construction, Fig. 219, has the me- chanical disadvantage of a relatively light structure, (\", revolving at high speed between two stationary structures, N and S. As it is immaterial whether the magnet is stationary Of revolving, usually the inner core, iV, is re- volved with the conductor, as shown in Figs. 221 and 222. This short ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... uctor, 330, 332, 336 Load balance of polyphase system, 314 character determining stability in induction motor, 205 Loop of hysteresis, 56 Loss, percentage, in magnetic cycle, 60 Loxodromic spiral, 345 Luminescence in gas and vapor con- duction, 28 Luminous streak conduction in pyro- electric conductor, 18 M Magnetic circuits of induction motor, 228 elements, 77 friction, 56 mechanical forces, 107 Magnetism, 43 tables and data, 87, 88 wave distortion by saturation, 128 Magnetite arc, 36 hyst ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-38", "section_label": "Chapter 2: Circuit Control By Periodic Transient Phenomena", "section_title": "Circuit Control By Periodic Transient Phenomena", "kind": "chapter", "sequence": 38, "number": 2, "location": "lines 15626-15962", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-38/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-38/", "snippets": [ "... each of the two positions, however, varies: when requiring a high field excitation, the regulator remains a longer time in position r0, hence a shorter time in position (r0 + rt), before the rising potential throws it over into the next position; while at light load, requiring low field excitation, the duration of the period of high resistance, 223 224 TRANSIENT PHENOMENA (TO _|_ rj} is greater, and that of the period of low resistance, r0, less. 7. Let, ^ = the duration of the short circuit of resist ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-49", "section_label": "Chapter 9: High-Frequency Conductors", "section_title": "High-Frequency Conductors", "kind": "chapter", "sequence": 49, "number": 9, "location": "lines 27003-27760", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "snippets": [ "... ference without following its indentations, lr = the radius of the conductor, ld = the distance from the return conductor, X = the conductivity of conductor material, fi. = the permeability of conductor material, / = the frequency, S = the speed of light = 3 X 1010 cm., and (1) a = — — = the wave length constant, o the true ohmic resistance is the ohmic reactance, low frequency value is *o = 2 7r/70 1 2 loge f + ^l 10~9 ohms; (3) or, reduced to common logarithms by dividing by log e, x0 = 2 TT/ ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-51", "section_label": "Chapter 2: Discussion Of General Equations", "section_title": "Discussion Of General Equations", "kind": "chapter", "sequence": 51, "number": 2, "location": "lines 28695-29315", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "snippets": [ "... q VLC (m + s) - qs VLC q2LC r _m /L ~V' f __ k (m - s) + qh q VTC (m - s) + qs VTC h2 + k2 that is, and Writing q2LC \\/i Cl - C2 q ^ ~ rn ^ ^ m ^ 5- ^ y' ^ ^ ^ ^ ^ i: Fig. 79. . ia shunted by a condenser, the condenser nmkes the arc unstable and puts it out; the available supply voltage, however, starts it again, and so periodically the arc starts and extinguishes, aa an \"oscillating arc.\" 84. There are certain circuit elements which tend to produce ins ...", "... ■ 1.D ^ iin \\ C^ -' litn \\ V ^^ fn \\ in \\ \\ ■ ^ ■m ~- ^ .0 ■^ >^ ~ rn ^ ^ m ^ 5- ^ y' ^ ^ ^ ^ ^ i: Fig. 79. . ia shunted by a condenser, the condenser nmkes the arc unstable and puts it out; the available supply voltage, however, starts it again, and so periodically the arc starts and extinguishes, aa an \"oscillating arc.\" 84. There are certain circuit elements which tend to produce instability, such ...", "... it out; the available supply voltage, however, starts it again, and so periodically the arc starts and extinguishes, aa an \"oscillating arc.\" 84. There are certain circuit elements which tend to produce instability, such as arcs, pyroelectric conductors, condensers, induction and synchronous motors, etc., and their recognition therefore is of great importance to the engineer, in guarding \\^ 1 [<^ INSTABILITY OF CIRCUITS 165 s^ainst instability. Whether instability results, and what form it assumes, depe ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 73, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "CHAPTER XIII. DISTRIBUTED CAPACITY, INDUCTANCE, RESISTANCE, AND LEAKAGE. 107. As far as capacity has been considered in the foregoing chapters, the assumption has been made that the condenser or other source of negative reactance is shunted across the circuit at a definite point. In many ...", "CHAPTER XIII. DISTRIBUTED CAPACITY, INDUCTANCE, RESISTANCE, AND LEAKAGE. 107. As far as capacity has been considered in the foregoing chapters, the assumption has been made that the condenser or other source of negative reactance is shunted across the circuit at a definite point. In many cases, how- ever, the capacity is distributed over the whole le ...", "CHAPTER XIII. DISTRIBUTED CAPACITY, INDUCTANCE, RESISTANCE, AND LEAKAGE. 107. As far as capacity has been considered in the foregoing chapters, the assumption has been made that the condenser or other source of negative reactance is shunted across the circuit at a definite point. In many cases, how- ever, the capacity is distributed over the whole length of the conductor, so that the circuit can be considered as shunted by an infinite number o ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-27", "section_label": "Chapter 5: Resistance, Inductance, And Capacity In Series Condenser Charge And Discharge", "section_title": "Resistance, Inductance, And Capacity In Series Condenser Charge And Discharge", "kind": "chapter", "sequence": 27, "number": 5, "location": "lines 4072-5311", "status": "candidate", "occurrence_count": 72, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "snippets": [ "CHAPTER V. RESISTANCE, INDUCTANCE, AND CAPACITY IN SERIES. CONDENSER CHARGE AND DISCHARGE. 29. If a continuous e.m.f . e is impressed upon a circuit contain- ing resistance, inductance, and capacity in series, the stationary condition of the circuit is zero current, i = o, and the poten- tial differe ...", "CHAPTER V. RESISTANCE, INDUCTANCE, AND CAPACITY IN SERIES. CONDENSER CHARGE AND DISCHARGE. 29. If a continuous e.m.f . e is impressed upon a circuit contain- ing resistance, inductance, and capacity in series, the stationary condition of the circuit is zero current, i = o, and the poten- tial difference at the condenser e ...", "CHAPTER V. RESISTANCE, INDUCTANCE, AND CAPACITY IN SERIES. CONDENSER CHARGE AND DISCHARGE. 29. If a continuous e.m.f . e is impressed upon a circuit contain- ing resistance, inductance, and capacity in series, the stationary condition of the circuit is zero current, i = o, and the poten- tial difference at the condenser equals the impressed e.m.f., et =• e, no permanent current exists, but only the transient current of charge or discharge of the cond ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 56, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "... ement of the general wave by its equivalent sine wave, as before discussed, that is a sine wave of equal effective intensity and equal power, while sufficiently accu- rate in many cases, completely fails in other cases, espe- cially in circuits containing capacity, or in circuits containing periodically (and in synchronism with the wave) varying resistance or reactance (as alternating arcs, reaction ma- chines, synchronous induction motors, oversaturated mag- netic circuits, etc.). Since, however, the individual ...", "... roportional to the frequency (inductance, etc.). x0 is that part of the reactance which is independent of the frequency (mutual induction, synchronous motion, etc.). xc is that part of the reactance which is inversely pro- portional to the frequency (capacity, etc.). The impedance for the nth harmonic is, r —Jnn xm This term can be considered as the general symbolic expression of the impedance of a circuit of general wave shape. 412 ALTERNATING-CURRENT PHENOMENA. Ohm's law, in symbolic expression, a ...", "... ns of this symbolism will explain its mechanism and its usefulness more fully. \\st Instance : Let the E.M.F., be impressed upon a circuit of the impedance, 7 • ( *CN Z = *•—./„ \\nxm -- that is, containing resistance r, inductive reactance xm and capacity reactance xc in series. Let e? = 720 ef = 540 V = 283 4\" = - 283 e£ = - 104 *6\" = 138 or, ^ = 900 tan e^ = .75 *, = 400 tan o)3 = - 1 ^5 = 173 tan w5 = - 1.33 It is thus in symbolic expression, Zj = 10 + 80/; *! = 80.6 Z3 = 10 zz = 10 ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-29", "section_label": "Chapter 7: Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "section_title": "Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "kind": "chapter", "sequence": 29, "number": 7, "location": "lines 6798-7825", "status": "candidate", "occurrence_count": 55, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "snippets": [ "CHAPTER VII. RESISTANCE, INDUCTANCE, AND CAPACITY IN SERIES IN ALTERNATING-CURRENT CIRCUIT. 65. Let, at time t = 0 or 0 = 0, the e.m.f., e = E cos (0 - 00), (1) be impressed upon a circuit containing in series the resistance, r, the inductance, L, and the capacity, C. The inductive reactance is x = ...", "... R VII. RESISTANCE, INDUCTANCE, AND CAPACITY IN SERIES IN ALTERNATING-CURRENT CIRCUIT. 65. Let, at time t = 0 or 0 = 0, the e.m.f., e = E cos (0 - 00), (1) be impressed upon a circuit containing in series the resistance, r, the inductance, L, and the capacity, C. The inductive reactance is x = 2 TT/L 1 and the condensive reactance is xc = > 2 7T/C J where/ = frequency and 6 = 2 nft. (3) Then the e.m.f. consumed by resistance is ri\\ the e.m.f. consumed by inductance, is di di Ldt = xJe' and the e.m. ...", "... ctive reactance is x = 2 TT/L 1 and the condensive reactance is xc = > 2 7T/C J where/ = frequency and 6 = 2 nft. (3) Then the e.m.f. consumed by resistance is ri\\ the e.m.f. consumed by inductance, is di di Ldt = xJe' and the e.m.f. consumed by capacity is , (4) where i = instantaneous value of the current. di di C Hence, e = ri + x -- + xc I i dO, (5) da J di f* E cos (6 - 00) = ri + x — + xc li dO, (6) da J and hence, the difference. of potential at the condenser terminals is el = ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 51, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... uctance into a transmission line may be considered as an illustration of the phenomena in a complex circuit comprising sections of very different constants; that is, a combination of a circuit section of high inductance and small resistance and negligible capacity and conductance, as a generating station, with a circuit of distributed capacity and inductance, as a transmission line. The extreme case of such a discharge would occur if a short circuit at the busbars of a gen- erating station opens while the transmiss ...", "... omena in a complex circuit comprising sections of very different constants; that is, a combination of a circuit section of high inductance and small resistance and negligible capacity and conductance, as a generating station, with a circuit of distributed capacity and inductance, as a transmission line. The extreme case of such a discharge would occur if a short circuit at the busbars of a gen- erating station opens while the transmission line is connected to the generating station. Let r = the total resistance a ...", "... sbars of a gen- erating station opens while the transmission line is connected to the generating station. Let r = the total resistance and L = the total inductance of the inductive section of the circuit; also let g = 0, C= 0, and L0 = inductance, <70 = capacity, r0 = resistance, g0 = conduc- tance of the total transmission line connected to the inductive circuit. In either of the two circuit sections the total length of the section is chosen as unit distance, and, translated to the velocity measure, the length ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-27", "section_label": "Chapter 27: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 33011-34776", "status": "candidate", "occurrence_count": 50, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-27/", "snippets": [ "... cement of the general wave by its equivalent sine wave, as before discussed, that is, a sine wave of equal effective intensity and equal power, while sufficiently accurate in many cases, completely fails in other cases, especially in circuits con- taining capacity, or in circuits containing periodically (and in synchronism with the wave) varying resistance or reactance (as alternating arcs, reaction machines, synchronous induction motors, oversaturated magnetic circuits, etc.). Since, however, the individual harmo ...", "... oportional to the frequency (inductance, etc.), ^ Xo is that part of the reactance which is independent of the frequency (mutual inductance, synchronous motion, etc.). Xc is that part of the reactance which is inversely propor- tional to the frequency (capacity, etc.). The impedance for the nth harmonic is + jn (nxr^ + a^o + -^ ) This term can be considered as the general symbolic expression of the impedance of a circuit of general wave-shape. Ohm's law, in symbolic expression, assumes for the general al ...", "... ciation voltage of the electrolyte, etc. Such cir- cuits cannot correctly, and in many cases not even approximately, be treated by the theory of the equivalent sine waves, but re- quire the symbolism of the complex harmonic wave. 263. Second Example. — A condenser of capacity, Co = 20 mf. is connected into the circuit of a 60-cycle alternator giving a wave of the form, e = E{cos 4> - 0.10 cos 3 0 - 0.08 cos 5 0 + 0.06 cos 7 4>), or, in symbolic expression, E = e(li - O.IO3 - O.O85 + O.O67). The synchronous im ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-24", "section_label": "Chapter 2: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 24, "number": 2, "location": "lines 1993-2658", "status": "candidate", "occurrence_count": 50, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "snippets": [ "... an inductive circuit. continuous current in an inductive circuit: the exciting current of an alternator field, or a circuit having the constants r = 12 ohms; L = 6 henrys, and eQ = 240 volts; the abscissas being seconds of time. 13. If an electrostatic condenser of capacity C is connected to a continuous e.m.f. e0, no current exists, in stationary con- dition, in this direct-current circuit (except that a very small current may leak through the insulation or the dielectric of the condenser), but the condenser is ...", "... circuit. continuous current in an inductive circuit: the exciting current of an alternator field, or a circuit having the constants r = 12 ohms; L = 6 henrys, and eQ = 240 volts; the abscissas being seconds of time. 13. If an electrostatic condenser of capacity C is connected to a continuous e.m.f. e0, no current exists, in stationary con- dition, in this direct-current circuit (except that a very small current may leak through the insulation or the dielectric of the condenser), but the condenser is charged to t ...", "... 13. If an electrostatic condenser of capacity C is connected to a continuous e.m.f. e0, no current exists, in stationary con- dition, in this direct-current circuit (except that a very small current may leak through the insulation or the dielectric of the condenser), but the condenser is charged to the potential dif- ference eo; or contains the electrostatic charge Q = to0. In the moment of closing the circuit of e.m.f. e0 upon the capacity C, the condenser contains no charge, that is, zero potential difference e ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 49, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "... ber of poles large compared with the out- put, and the pole pitch thus must for economical reasons be kept small — as for instance a 100-hp. 60-cycle motor for 90 revolu- tions, that is, 80 poles— or where the requirement of an exutMrVV momentary overload capacity has to be met, etc. In such motors of necessity the exciting current or current at no-load — which is practically all magnetizing current — is a very large part of full-load current, and while fair efficiencies may nevertheless be secured, power-factor an ...", "... th the armature, in the circuit of the induction machine secondary, it generates voltage at the frequency of slip, whatever the latter may be. That is, the induction motor remains asynchronous, increases in slip with increase of load. 5. Excitation by a condenser in the secondary circuit of the induction motor. As the magnetizing current required by the induction motor is a reactive, that is, wattless lagging current, it does not require a generator for its production, but any apparatus consuming lead- ing, that ...", "... motor. As the magnetizing current required by the induction motor is a reactive, that is, wattless lagging current, it does not require a generator for its production, but any apparatus consuming lead- ing, that is, generating lagging currents, such as a condenser, can be used to supply the magnetizing current. 40, However, condenser, or synchronous or commutating machine, etc., in the secondary of the induction motor do not merely give the magnetizing current and thereby permit power- factor control, but they ma ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "section_title": "Dibtbisnted Capacity, Inductance, Besistance, And", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 47, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "CHAPTER XII. DIBTBISnTED CAPACITY, INDUCTANCE, BESISTANCE, AND liEAKAGE. 102. As far as capacity has been considered in the foregoing chapters, the assumption has been made that the condenser or other source of negative reactance is shunted across the circuit at a definite point. In ma ...", "CHAPTER XII. DIBTBISnTED CAPACITY, INDUCTANCE, BESISTANCE, AND liEAKAGE. 102. As far as capacity has been considered in the foregoing chapters, the assumption has been made that the condenser or other source of negative reactance is shunted across the circuit at a definite point. In many cases, how- ever, the capacity is distributed over the whole le ...", "CHAPTER XII. DIBTBISnTED CAPACITY, INDUCTANCE, BESISTANCE, AND liEAKAGE. 102. As far as capacity has been considered in the foregoing chapters, the assumption has been made that the condenser or other source of negative reactance is shunted across the circuit at a definite point. In many cases, how- ever, the capacity is distributed over the whole length of the conductor, so that the circuit can be considered as shunted by an infinite number o ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 40, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "CHAPTER XV DISTRIBUTED CAPACITY, INDUCTANCE, RESISTANCE, AND LEAKAGE 127. In the foregoing, the phenomena causing loss of energy in an alternating-current circuit have been discussed; and it has been shown that the mutual relation between current and e.m.f. can be expressed by two of ...", "... tance,\" etc., as discussed in the preceding chapter, the results apply also — within the range discussed in the preceding chapter — to circuits containing iron and other materials producing energy losses outside of the electric conductor. 128. As far as capacity has been considered in the foregoing chapters, the assumption has been made that the condenser or 168 DISTRIBUTED CAPACITY 169 other source of negative reactance is shunted across the circuit at a definite point. In many cases, however, the condensiv ...", "... discussed in the preceding chapter — to circuits containing iron and other materials producing energy losses outside of the electric conductor. 128. As far as capacity has been considered in the foregoing chapters, the assumption has been made that the condenser or 168 DISTRIBUTED CAPACITY 169 other source of negative reactance is shunted across the circuit at a definite point. In many cases, however, the condensive react- ance is distributed over the whole length of the conductor, so that the circuit can b ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-08", "section_label": "Chapter 8: Circuits Containing Resistance, Inductance, And Capacity", "section_title": "Circuits Containing Resistance, Inductance, And Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3577-5333", "status": "candidate", "occurrence_count": 39, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "snippets": [ "CHAPTER VIII. CIRCUITS CONTAINING RESISTANCE, INDUCTANCE, AND CAPACITY. 42. Having, in the foregoing, reestablished Ohm's law and Kirchhoff's laws as being also the fundamental laws of alternating-current circuits, when expressed in their com- plex form, E = ZS, or, / = YE, and *%E = 0 in a closed circuit, S/ = 0 at a ...", "... ion of these laws, and in the same manner as with continuous- current circuits, keeping in mind, however, that E, I, Z, Y, are complex quantities — calculate alternating-current cir- cuits and networks of circuits containing resistance, induc- tance, and capacity in any combination, without meeting with greater difficulties than when dealing with continuous- current circuits. It is obviously not possible to discuss with any com- pleteness all the infinite varieties of combinations of resis- tance, inductance, an ...", "... n any combination, without meeting with greater difficulties than when dealing with continuous- current circuits. It is obviously not possible to discuss with any com- pleteness all the infinite varieties of combinations of resis- tance, inductance, and capacity which can be imagined, and which may exist, in a system or network of circuits ; there- fore only some of the more common or more . interesting combinations will here be considered. 1.) Resistance in series with a circuit. 43. In a constant-potential s ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-31", "section_label": "Chapter 9: Divided Circuit", "section_title": "Divided Circuit", "kind": "chapter", "sequence": 31, "number": 9, "location": "lines 9228-10474", "status": "candidate", "occurrence_count": 39, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "snippets": [ "... 72. A circuit consisting of two branches or multiple circuits 1 and 2 may be supplied, over a line or circuit 3, with an impressed e.m.f., e0. Let, in such a circuit, shown diagrammatically in Fig 31, rv Lv Cl and r2, L2, Cz — resistance, inductance, and capacity, respectively, of the two branch circuits 1 and 2; r0, L0, C0 = Co Fig. 31. Divided circuit. resistance, inductance, and capacity of the undivided part of the circuit, 3. Furthermore let e = potential difference at terminals of branch circuits 1 and ...", "... ., e0. Let, in such a circuit, shown diagrammatically in Fig 31, rv Lv Cl and r2, L2, Cz — resistance, inductance, and capacity, respectively, of the two branch circuits 1 and 2; r0, L0, C0 = Co Fig. 31. Divided circuit. resistance, inductance, and capacity of the undivided part of the circuit, 3. Furthermore let e = potential difference at terminals of branch circuits 1 and 2, it and i2 respectively = currents in branch circuits 1 and 2, and i3 = current in undivided part of circuit, 3. Then ia = il + i2 ...", "... to a standard frequency, such as / = 60 cycles per second. Instead of the time t, then, an angle 0 = 2 nft (5) is introduced, and then we have di x di dd di ^ * (6) i/iift - 2 Kfo f Id0 - Xc/i dd, t since Hereby resistance, inductance, and capacity are expressed in the same units, ohms. Time is expressed by an angle 6 so that 360 degrees correspond to sV of a second, and the time effects thus are directly com- parable with the phenomena on a 60-cycle circuit. A better conception of the size or ma ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "section_label": "Lecture 10: Continual And Cumulative Oscillations", "section_title": "Continual And Cumulative Oscillations", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 36, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... ANDJMPULSES grams, Figs. 62 to 65, were taken on an artificial transmission line.* Oscillations of the type 64 and 65 are industrially used, as ''sing- ing arc, \" in wireless telegraphy, and are produced by shunting a suitable arc by a circuit containing capacity and inductance in series with each other. Fig. 62. — Semi -continuous Recurrent Oscillation of Arcing Ground in Transmission Line. Fig. 63. — Semi-continuous Hecurrent Oscillation of Arcing Ground in Transmission Lino. * \"Design, Construction and ...", "... of the oscilla- tion is insufficient to cause a discharge over the lightning arrester. The only effective protection seems to be a continuous dissipa- tion of the oscillating energy by a resistance closing the oscillat- ing circuit. In general, a moderate capacity would be connected in series with such damping resistance, and would be chosen so as to allow the high frequency to pass practically unobstructed, while practically stopping the passage of the machine frequency, and the waste of power, incident thereto. ...", "... d 60, while in high-potential trans- former windings, due to their much lesser damping, continuous oscillations seem to be more common, as in Fig. 46. Our knowl- edge of these phenomena is however still extremely incomplete. LECTUEE XI, INDUCTANCE AND CAPACITY OF ROUND PARALLEL CONDUCTORS. A. Inductance and capacity. 46. As inductance and capacity are the two circuit constants which represent the energy storage, and which therefore are of fundamental importance in the study of transients, their calcula- tio ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-08", "section_label": "Chapter 8: Capacity", "section_title": "Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3872-6370", "status": "candidate", "occurrence_count": 35, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "snippets": [ "CHAPTER VIII. . In this case, however, a reactance, +ja, would give fairly good starting-torque efficiency . In the same manner the effect of reactance or capacity inserted into one of the two motor coils can be calculated. As instances are given, in Fig. 37, the apparent torque efficiency, v, of the single-phase induction-motor starting device consisting of the insertion, in one of the two parallel motor circuits, ...", "... As instances are given, in Fig. 37, the apparent torque efficiency, v, of the single-phase induction-motor starting device consisting of the insertion, in one of the two parallel motor circuits, of various amounts of reactance, inductive or positive, and capacity 166 ELECTRICAL APPARATUS or negative, for a low secondary resistance motor of impedance: Z - 0.1 +0.3; and a high resistance armature, of the motor impedance: Z = 0.3 + 0.1 j resistance inserted into the one motor circuit, has the same effect .ft ...", "... rc 90° anc A 37.— Apparent starting-torque eflutenoei of phase-splitting de parallel cumieition uf motor cireuits. lie first motor, as positive reactance in the second motor, rsely. K Higher values of starting-torque efficiency are aecurec use of capacity in the one, and inductance in the other m nit. It is obvious that by resistance and inductance al phase displacement between the two component curre thus true quarter-phase relation, can not be reached. s resistance consumes energy, the use of resistance ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "LECTURE VII. LINE OSCILLATIONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy surges between magnetic — and dielectric — , and a transient component, by which the total stored energy decreases. Considering only the periodic component, the maximum value ...", "... (8) 7, eo, and io follow from the initial values e' and i' of the transient, 2bt t = 0 or (t> = 0: hence ^ = ^o cos 7 e' = —eo sin 7 tan 7 (9) (10) The preceding equations of the double-energy transient apply to the circuit in which capacity and inductance are massed, as, for instance, the discharge or charge of a condenser through an in- ductive circuit. Obviously, no material difference can exist, whether the capacity and the inductance are separately massed, or whether they are intermixe ...", "... 2bt t = 0 or (t> = 0: hence ^ = ^o cos 7 e' = —eo sin 7 tan 7 (9) (10) The preceding equations of the double-energy transient apply to the circuit in which capacity and inductance are massed, as, for instance, the discharge or charge of a condenser through an in- ductive circuit. Obviously, no material difference can exist, whether the capacity and the inductance are separately massed, or whether they are intermixed, a piece of inductance and piece of capacity alternating, or uniformly distributed ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3956-4744", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "snippets": [ "LECTURE VII. LINE OSCILLATIONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy 7\" /j'2 f^ r/>2 surges between magnetic -^- and dielectric — , and a transient £i A component, by which the total stored energy decreases. Considering only the periodic c ...", "... current and voltage is i = loe-^cos (0 - 7) 6 = eoe-^sinfa - 7) 7, e0, and i.Q follow from the initial values ef and i' of the transient, at £ = Oor 0 = 0: hence The preceding equations of the double-energy transient apply to the circuit in which capacity and inductance are massed, as, for instance, the discharge or charge of a condenser through an in- ductive circuit. Obviously, no material difference can exist, whether the capacity and the inductance are separately massed, or whether they are intermixe ...", "... follow from the initial values ef and i' of the transient, at £ = Oor 0 = 0: hence The preceding equations of the double-energy transient apply to the circuit in which capacity and inductance are massed, as, for instance, the discharge or charge of a condenser through an in- ductive circuit. Obviously, no material difference can exist, whether the capacity and the inductance are separately massed, or whether they are intermixed, a piece of inductance and piece of capacity alternating, or uniformly distributed ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "section_label": "Chapter 14: Dielectric Losses", "section_title": "Dielectric Losses", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "... equency and to the 1.6*^' power of the dielectric field: P = njD'-^ has been observed in rotating dielectric fields, but is so small, that it usually is overshadowed by the other losses. In alternating dielectric fields in solid materials, such as in condensers, coil insulation, etc., a loss is commonly observed which gives an approximately constant power-factor of the elec- tric energizing circuit, over a wide range of voltage and of fre- quency, from less than a fraction of 1 per cent, up to a few per cent. ...", "... the mag- netic flux distribution. As corresponding hereto in the dielectric field may be con- sidered the conduction loss through the resistance of the dielectric. In a homogeneous dielectric of electric conductivity 7 (usually very low) and specific capacity or permittivity k, if: I = thickness of the dielectric, A = area or cross-section, e = impressed alternating-current voltage, effective value, the dielectric capacity of the material is: JcA ^ ~~ I and the capacity susceptance: 152 ALTERNATING-C ...", "... n a homogeneous dielectric of electric conductivity 7 (usually very low) and specific capacity or permittivity k, if: I = thickness of the dielectric, A = area or cross-section, e = impressed alternating-current voltage, effective value, the dielectric capacity of the material is: JcA ^ ~~ I and the capacity susceptance: 152 ALTERNATING-CURRENT PHENOMENA hence the current passing through the dielectric as capacity- current or \"displacement current,\" is: ^ ^^ 2 7r//cA iQ = eo — 2 TTjCe = — -. — e The ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-01", "section_label": "Chapter 1: Speed Control Of Induction Motors", "section_title": "Speed Control Of Induction Motors", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1368-3542", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-01/", "snippets": [ "... ic, except that its speed is limited by synchronism. Series resistance in the armature thus is not suitable to produce steady running at low speeds. To a considerable extent, this disadvantage of inconstancy of speed can be overcome: (a) By the use of capacity or effective capacity in the motor secondary, which contracts the range of torque into that of approximate resonance of the capacity with the motor inductance, and thereby gives fairly constant speed, independent of the load, at various speed values deter ...", "... eed is limited by synchronism. Series resistance in the armature thus is not suitable to produce steady running at low speeds. To a considerable extent, this disadvantage of inconstancy of speed can be overcome: (a) By the use of capacity or effective capacity in the motor secondary, which contracts the range of torque into that of approximate resonance of the capacity with the motor inductance, and thereby gives fairly constant speed, independent of the load, at various speed values determined by the value of ...", "... g at low speeds. To a considerable extent, this disadvantage of inconstancy of speed can be overcome: (a) By the use of capacity or effective capacity in the motor secondary, which contracts the range of torque into that of approximate resonance of the capacity with the motor inductance, and thereby gives fairly constant speed, independent of the load, at various speed values determined by the value of the capacity. (6) By the use of a resistance of very high negative tempera- ture coefficient in the armature, ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-43", "section_label": "Chapter 3: The Natural Period Of The Transmission Line", "section_title": "The Natural Period Of The Transmission Line", "kind": "chapter", "sequence": 43, "number": 3, "location": "lines 21721-23178", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "snippets": [ "... h such a line discharges an accumulated charge of atmospheric electricity (lightning), or oscillates because of a sudden change of load, as a break of circuit, or in general a change of circuit conditions, as closing the circuit, etc. The discharge of a condenser through a circuit containing self- inductance and resistance is oscillating (provided the resistance does not exceed a certain critical value depending upon the capacity and the self-inductance) ; that is, the discharge current alternates with constantly ...", "... al a change of circuit conditions, as closing the circuit, etc. The discharge of a condenser through a circuit containing self- inductance and resistance is oscillating (provided the resistance does not exceed a certain critical value depending upon the capacity and the self-inductance) ; that is, the discharge current alternates with constantly decreasing intensity. The frequency of this oscillating discharge depends upon the capacity C and the self -inductance L of the circuit, and to a much lesser extent upon ...", "... ded the resistance does not exceed a certain critical value depending upon the capacity and the self-inductance) ; that is, the discharge current alternates with constantly decreasing intensity. The frequency of this oscillating discharge depends upon the capacity C and the self -inductance L of the circuit, and to a much lesser extent upon the resistance, so that, if the resistance of the circuit is not excessive, the frequency of oscillation can, by neglecting the resistance, be expressed with fair, or even close ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-45", "section_label": "Chapter 5: Distributed Series Capacity", "section_title": "Distributed Series Capacity", "kind": "chapter", "sequence": 45, "number": 5, "location": "lines 23586-23947", "status": "candidate", "occurrence_count": 23, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "snippets": [ "CHAPTER V. DISTRIBUTED SERIES CAPACITY. 43. The capacity of a transmission line, cable, or high-poten- tial transformer coil is shunted capacity, that is, capacity from conductor to ground, or from conductor to return conductor, or shunting across a section of the conductor, as from turn to t ...", "CHAPTER V. DISTRIBUTED SERIES CAPACITY. 43. The capacity of a transmission line, cable, or high-poten- tial transformer coil is shunted capacity, that is, capacity from conductor to ground, or from conductor to return conductor, or shunting across a section of the conductor, as from turn to turn or layer to lay ...", "CHAPTER V. DISTRIBUTED SERIES CAPACITY. 43. The capacity of a transmission line, cable, or high-poten- tial transformer coil is shunted capacity, that is, capacity from conductor to ground, or from conductor to return conductor, or shunting across a section of the conductor, as from turn to turn or layer to layer of a transformer coil. In some circuits, in addition to this shunted capacity, dis- ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-14", "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "section_title": "Constant-Potential Constant-Current Trans Formation", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "... es a good application of the terms \"impedance,\" admittance,\" etc., and offers a large number of problems or examples for the symbolic method of dealing with alternating-current phenomena. Even outside of arc lighting, such combinations of inductance and capacity which t«nd toward constant-voltage constant-cur- rent transformation are of considerable importance as a poffsiblo source of danger to the system. In a constant-current circuit, the load is taken off by short-circuiting, while opc;n-circuiting causes the ...", "... = r{l + jk) where k = tangent of the angle of lag = -; H Fig 116. CONSTANT'CURRENT TRANSFORMATION 257 let the receiver circuit be shunted by a constant condensive react- ance, Xe'f let then: ^ = potential difference of receiver circuit or the condenser terminals, / = current in the receiver circuit, or the \"secondary current,'' /i = current in the condenser, /o = total supply current, or \"primary current.'' Then /o = / + /i (26) and the e.m.f. at receiver circuit is ^ = Z/ (27) at the condens ...", "... 7 let the receiver circuit be shunted by a constant condensive react- ance, Xe'f let then: ^ = potential difference of receiver circuit or the condenser terminals, / = current in the receiver circuit, or the \"secondary current,'' /i = current in the condenser, /o = total supply current, or \"primary current.'' Then /o = / + /i (26) and the e.m.f. at receiver circuit is ^ = Z/ (27) at the condenser, ^ = - jxch (28) hence, /i=if/ (29) and, in the main circuit, the impressed e.m.f. is ^0 = eo = ^ + ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... 7 (a — j) dec a. Hence the apparent reactance of the oscillating-current cir- cuit is, in symbolic expression, X = x{a — j) dec a. Hence it contains a power component, ax, and the impedance is Z = (r—X) dec a= {r—x{a—j)] dec a = {r —ax +jx) dec a. Capacity 186. Let r = resistance, C = capacity, and Xc = o~~7?t = con- ZtJkj densive reactance. In a circuit excited by the oscillating current, 7, the e.m.f. consumed due to the capacity, C, is Ere = ^(idt = 2^ J /d« = fc fld4>; 348 ELECTRIC CIRCUITS or, ...", "... eactance of the oscillating-current cir- cuit is, in symbolic expression, X = x{a — j) dec a. Hence it contains a power component, ax, and the impedance is Z = (r—X) dec a= {r—x{a—j)] dec a = {r —ax +jx) dec a. Capacity 186. Let r = resistance, C = capacity, and Xc = o~~7?t = con- ZtJkj densive reactance. In a circuit excited by the oscillating current, 7, the e.m.f. consumed due to the capacity, C, is Ere = ^(idt = 2^ J /d« = fc fld4>; 348 ELECTRIC CIRCUITS or, by substitution, Es^ = xl i€-*»* cos ...", "... e impedance is Z = (r—X) dec a= {r—x{a—j)] dec a = {r —ax +jx) dec a. Capacity 186. Let r = resistance, C = capacity, and Xc = o~~7?t = con- ZtJkj densive reactance. In a circuit excited by the oscillating current, 7, the e.m.f. consumed due to the capacity, C, is Ere = ^(idt = 2^ J /d« = fc fld4>; 348 ELECTRIC CIRCUITS or, by substitution, Es^ = xl i€-*»* cos (0 — e) d4> X i€\"\"<** {sin (0 — «) — a cos (0 — ^)} 1 + a2 (1 + a^) cos a ^ ^' hence, in symbolic expression, (a — j) (cos ^ — i sin ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "section_label": "Chapter 30: Quartbr-Fhase System", "section_title": "Quartbr-Fhase System", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... +j) dec a. Hence the apparent reactance of the oscillating current circuit is, in symbolic expression, X == X (a +y) dec a. Hence it contains an energy component ax, and the impedance is Z ={r — X) dec a = {r — x (a +j)) dec a = {r—ax —jx) dec a. Capacity, 285. Let r = resistance, C= capacity, and x^ = 1/ 2 «• C = capacity reactance. In a circuit excited by the oscillating §286] OSCILLATING CURRENTS. 415 current /, the electromotive force consumed by the capacity C is or, by substitution, Ej,^x Cu ...", "... ce of the oscillating current circuit is, in symbolic expression, X == X (a +y) dec a. Hence it contains an energy component ax, and the impedance is Z ={r — X) dec a = {r — x (a +j)) dec a = {r—ax —jx) dec a. Capacity, 285. Let r = resistance, C= capacity, and x^ = 1/ 2 «• C = capacity reactance. In a circuit excited by the oscillating §286] OSCILLATING CURRENTS. 415 current /, the electromotive force consumed by the capacity C is or, by substitution, Ej,^x Cu-^* cos (<^ — «) // — w)} (1 + ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-32", "section_label": "Chapter 32: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 25904-27405", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "snippets": [ "... dec a . Hence the apparent reactance of the oscillating current circuit is, in symbolic expression, X = x (a +y') dec a. Hence it contains an energy component ax, and the impedance is Z = (r — X) dec a = {r — x (a +/')} dec a = (r — ax —jx) dec a. Capacity. 314. Let r = resistance, C = capacity, and xc = 1 /2-n-JVC = capacity reactance. In a circuit excited by the oscillating OSCILLATING CURRENTS. 503 current /, the electromotive force consumed by the capacity Cis or, by substitution, Ex = x I * e ...", "... the oscillating current circuit is, in symbolic expression, X = x (a +y') dec a. Hence it contains an energy component ax, and the impedance is Z = (r — X) dec a = {r — x (a +/')} dec a = (r — ax —jx) dec a. Capacity. 314. Let r = resistance, C = capacity, and xc = 1 /2-n-JVC = capacity reactance. In a circuit excited by the oscillating OSCILLATING CURRENTS. 503 current /, the electromotive force consumed by the capacity Cis or, by substitution, Ex = x I * e~a* cos (<£ {sin (<£ — w) — a COS (<£ — ...", "... is, in symbolic expression, X = x (a +y') dec a. Hence it contains an energy component ax, and the impedance is Z = (r — X) dec a = {r — x (a +/')} dec a = (r — ax —jx) dec a. Capacity. 314. Let r = resistance, C = capacity, and xc = 1 /2-n-JVC = capacity reactance. In a circuit excited by the oscillating OSCILLATING CURRENTS. 503 current /, the electromotive force consumed by the capacity Cis or, by substitution, Ex = x I * e~a* cos (<£ {sin (<£ — w) — a COS (<£ — oi 2 (1 + 02) COS a henc ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-21", "section_label": "Chapter 23: Review", "section_title": "Review", "kind": "chapter", "sequence": 21, "number": 23, "location": "lines 32138-32819", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-21/", "snippets": [ "... Leblanc to oppose the hunt- ing tendency, and extensively used. Amplifier. — 161. An apparatus to intensify telephone and radio telephone currents. High-frequency inductor alternator excited by the telephone current, usually by armature reaction through capacity. The generated current is then rectified, be- fore transmission in long-distance telephony, after transmission in radio telephony. Arc Machines. — 138. Constant-current generators, usually direct-current, with rectifying commutators. The last and most e ...", "... d winding by the rectified current. The limitation of l he power, which can be rectified, and the need of readjusting the brushes with a change of the inductivity of the load, hasmade njGfl compounding unsuitahie for the modern high-power altcrnu- ton. Condenser Motor. — 77. Single-phase induction motor with condenser in tertiary circuit on stator, for producing shirting torque and high power-factor. The space angle between pri- mary and tertiary stator circuit usually is 45° to 60°, and often a three-phase motor ...", "... e power, which can be rectified, and the need of readjusting the brushes with a change of the inductivity of the load, hasmade njGfl compounding unsuitahie for the modern high-power altcrnu- ton. Condenser Motor. — 77. Single-phase induction motor with condenser in tertiary circuit on stator, for producing shirting torque and high power-factor. The space angle between pri- mary and tertiary stator circuit usually is 45° to 60°, and often a three-phase motor is used, with single-phase supply on one phase. and cond ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-23", "section_label": "Chapter 1: The Constants Of The Electric Circuit", "section_title": "The Constants Of The Electric Circuit", "kind": "chapter", "sequence": 23, "number": 1, "location": "lines 1317-1992", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "snippets": [ "... rom generator to receiver circuit, as is usually the case, or may increase, as in an alternating-current circuit with leading current, and while the current may remain constant throughout the circuit, or decrease, as in a transmission line of considerable capacity with a leading or non-inductive receiver circuit, the flow of energy always decreases from generating to receiving circuit, and the power gradient therefore is characteristic of the direc- tion of the flow of energy.) In the space outside of the conduct ...", "... ltage e and measuring this current i by its magnetic action, in the usual voltmeter. The coefficients L and (7, which are the proportionality factors of the magnetic and of the dielectric component of the electric field, are called the inductance and the capacity of the circuit, respectively. As electric power P is resolved into the product of current i and voltage e, the power loss in the conductor, Ph therefore can also be resolved into a product of current i and voltage et which is consumed in the conductor. ...", "... constant representing the intensity of the electro- magnetic component of the electric field of the circuit, called inductance. C = circuit constant representing the intensity of the electro- static component of the electric field of the circuit, called capacity. 3. A change of the magnetic field of the conductor, that is, of the number of lines of magnetic force surrounding the conductor, generates an e.m.f. '-3 <•> in the conductor and thus absorbs a power *\"-*-<£ (6) or, by equation (2) : = Li ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3721-4369", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-06/", "snippets": [ "... - rent, r = resistance = coefficient of power dissipation by the current. If the energy is stored by the voltage e, as dielectric field, the duration of the transient would be TV - -, (3) g 59 60 ELECTRIC DISCHARGES, WAVES AND IMPULSES. where C = capacity = coefficient of energy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power consumption by the voltage, as leakage conductance by the voltage, corona, dielectric hysteresis, etc. Thus the transient of the spontan ...", "... ergy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power consumption by the voltage, as leakage conductance by the voltage, corona, dielectric hysteresis, etc. Thus the transient of the spontaneous discharge of a condenser would be represented by e = eoe~'^\\ (4) Similar single-energy transients may occur in other systems. For instance, the transient by which a water jet approaches con- stant velocity when falling under gravitation through a resisting medium would have t ...", "... Vq = limiting velocity, g = acceleration of gravity, and would be given by v = Vo[l-e~'^). (6) In a system in which energy can be stored in two different forms, as for instance as magnetic and as dielectric energy in a circuit containing inductance and capacity, in addition to the gradual decrease of stored energy similar to that represented by the single-energy transient, a transfer of energy can occur between its two different forms. Thus, if i = transient current, e = transient voltage (that is, the differe ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3287-3955", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "snippets": [ "... rent, r = resistance = coefficient of power dissipation by the current. If the energy is stored by the voltage e, as dielectric field, the duration of the transient would be TJ = -, (3) s/ 59 60 ELECTRIC DISCHARGES, WAVES AND IMPULSES. where C = capacity = coefficient of energy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power consumption by the voltage, as leakage conductance by the voltage, corona, dielectric hysteresis, etc. Thus the transient of the spontan ...", "... ergy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power consumption by the voltage, as leakage conductance by the voltage, corona, dielectric hysteresis, etc. Thus the transient of the spontaneous discharge of a condenser would be represented by e = e0e~£ct. (4) Similar single-energy transients may occur in other systems. For instance, the transient by which a water jet approaches con- stant velocity when falling under gravitation through a resisting medium would have ...", "... VQ = limiting velocity, g = acceleration of gravity, and would be given by v = v0(l-6~r}. (6) In a system in which energy can be stored in two different forms, as for instance as magnetic and as dielectric energy in a circuit containing inductance and capacity, in addition to the gradual decrease of stored energy similar to that represented by the single-energy transient, a transfer of energy can occur between its two different forms. Thus, if i = transient current, e = transient voltage (that is, the differe ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-20", "section_label": "Chapter 20: Single-Phase Induction Motors", "section_title": "Single-Phase Induction Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 21538-22301", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-20/", "snippets": [ "... y other way related, as by transformation. The impedances of these circuits are made different from each other as much as possible to produce a phase displacement between them. This can be done either by inserting external impedances in the circuits, as a condenser and a reactive coil, or by making the internal impedances of the motor circuits different, as by making one coil of high and the other of low resistance. 2. Inductive Devices. The different primary circuits of the motor are inductively related to each o ...", "... e at standstill is: Do =vDi= aie^v, and the single-phase motor torque at slip s is: D = aieHl - {I - v) s]. 180. In the single-phase motor considerably more advan- tage is gained by compensating for the wattless magnetizing component of current by capacity than in the polyphase motor, where this wattless component of the current is relatively small. The use of shunted capacity, however, has the dis- advantage of requiring a wave of impressed e.m.f. very close to sine shape, since even with a moderate variat ...", "... the single-phase motor considerably more advan- tage is gained by compensating for the wattless magnetizing component of current by capacity than in the polyphase motor, where this wattless component of the current is relatively small. The use of shunted capacity, however, has the dis- advantage of requiring a wave of impressed e.m.f. very close to sine shape, since even with a moderate variation from sine shape the wattless charging current of the condenser of higher frequency may lower the power-factor more than ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-07", "section_label": "Chapter 7: Shaping Of Waves : General", "section_title": "Shaping Of Waves : General", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 12222-12961", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-07/", "snippets": [ "... rts of the circuit, it may change to a shape which is undesirable or even Figs. 46 to 49. dangerous. Voltage, e, and current, i, are related to each other \\>y proportionality, by differentiation and by integration, with sistance, r, inductance, L, and capacity, C, as factors, e = n, r di e = cl idt, and as the differentials and integrals of sines are sines, as long SB r, L and C are constant — which is mostly the case — sine waves of SHAPING OF WAVES 113 voltage produce sine waves of current and i ...", "... however, would by differentiation give a self-inductive voltage wave, which is peakedj like Fig. 48, A voltage wave like Fig. 48, which is more efficient in transformation, may by further distortion, as by intensifica- tion of the triple harmonic by line capacity, assume the shape, Fig. 49, and the latter then would give, when impressed upon a transformer, a double-peaked wave of magnetism, Fig. 50, and such wave of magnetism gives a magnetic cycle with two small i secondary loops at high density, as shown ...", "... e relatively harm- less, except where very excessive and causing appreciable increase of the maximiun voltage, or the maximum magnetic flux ahd thus hysteresis loss. The very high harmonics as a rule are rela- tively harmless in all circuits containing no capacity, since they are necessarily fairly small and still further suppressed by the inductance of the circuit. They may become serious and even dangerous, however, if capacity is present in the circuit, as the current taken by capacity is proportional to the fre ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... MATHEMATICS. f ■ . Theoretically, obviously this condition can never be perfectly attained, and frequently the deviation from sine shape is suffi- cient to require practical consideration/ especially in those cases, where the electric circuit contains electrostatic capacity, as is for instance, the case with long-distance transmission lines, underground cable systems, high potential transformers, etc. (However, no matter how much the alternating or other periodic wave differs from simple sine shape — ^that is, however much ...", "... idual harmonic can be calculated, without calculating the preceding harmonics. For instance, let the generator e.m.f. wave, Fig. 44, Table II, column 2, be impressed upon an underground cable system Fig. 44. Generator e.m.f. wave. of such constants (capacity and inductance), that the natural frequency of the system is 670 cycles per second, while the generator frequency is 60 cycles. The natural frequency of the TRIGONOMETRIC SERIES. 115 circuit is then close to that of the 11th harmonic of the generat ...", "... ric series, give for the voltage between each terminal and the neutral, or the Y voltage of the three-phase system, the equa- tion : e = eo{sin ^-0.12 sin (3<9- 2. 3°) -0.23 sin (5^-1.5°) +0.13 sin (7^-6. 2°)1. . (1) In first approximation, the line capacity may be considered as a condenser shunted across the middle of the line; that is, half the line resistance and half the line reactance is in series with the line capacity. As the receiving apparatus do not utilize the higher har- monics of the generator ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-09", "section_label": "Chapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "section_title": "Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 4674-6992", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-09/", "snippets": [ "... idity. In the general equations, x appears in the expressions for / and E only as x^, so that / and E assume the same value when X is negative as when x is positive; or, in other words, series resistance acts upon a circuit with leading current, or in a condenser circuit, in the same way as upon a circuit with lag- ging current, or an inductive circuit. For a given impedance, z, of the receiver circuit, the current, /, and e.m.f., E, are smaller the larger the value of r; that is, the less the difference of phase ...", "... on-inductive, / and E change very little for small values of Xo; but if X is large, that is, if the receiver circuit is of large re- actance, / and E change considerably with a change of Xq. (b) If X is negative, that is, if the receiver circuit contains condensers, synchronous motors, or other apparatus which produce leading currents, below a certain value of Xq the de- nominator in the expression of E becomes Eo', that is, the reactance, Xo, raises the voltage. (c) E = Eo, or the insertion of a series ...", "... III). 66 ALTERNATING-CURRENT PHENOMENA As seen, curve I is symmetrical, and with increasing Xo the voltage E remains first almost constant, and then drops off with increasing rapiditj^ In the inductive circuit series inductive reactance, or in a condenser circuit series condensive reactance, causes the voltage to drop off very much faster than in a non-inductive circuit. Series inductive reactance in a condenser circuit, and series condensive reactance in an inductive circuit, cause a rise of potential. T ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "section_label": "Chapter 16: Induction Motor", "section_title": "Induction Motor", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "... her way related, as by transformation. The impedances of these circuits are made different from each other as much as possible, to produce a phase displacement between them. This can be done either by inserting external impedances into the circuits, as a condenser and a reactive coil, or by making the internal impedances of the motor circuits differ- ent, as by making one coil of high and the other of low resistance. 2. Inductive Devices. The different primary circuits of the motor are inductively related to each ...", "... e-phase motor torque at standstill is : and the single-phase motor torque at slip s is : T = of [1 - (1 - v) s] 178. In the single-phase motor considerably more advantage is gained by compensating for the wattless mag- netizing component of current by capacity than in the polyphase motor, where this wattless current is relatively small. The use of shunted capacity, however, has the dis- advantage of requiring a wave of impressed E.M.F. very close to sine shape ; since even with a moderate variation from sine s ...", "... - v) s] 178. In the single-phase motor considerably more advantage is gained by compensating for the wattless mag- netizing component of current by capacity than in the polyphase motor, where this wattless current is relatively small. The use of shunted capacity, however, has the dis- advantage of requiring a wave of impressed E.M.F. very close to sine shape ; since even with a moderate variation from sine shape the wattless charging current of the con- denser of higher frequency may lower the power factor more ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-01", "section_label": "Chapter 1: Electric Conduction. Soled And Liquid", "section_title": "Electric Conduction. Soled And Liquid", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 959-3894", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-01/", "snippets": [ "... which are called the electric field, the two main components of the electric field being the electromagnetic component, characterized by the cir- cuit constant inductance, L, and the electrostatic component, characterized by the electric circuit constant capacity, C. Inside of the conductor we find a conversion of energy into heat; that is, electric power is consumed in the conductor by what may be considered as a kind of resistance of the conductor to the flow of electric power, and so we speak of resistance of t ...", "... cell, which produces the hydrogen and oxygen films which hold back the current flow by their counter e.m.f. The current thus flows ahead of the voltage or counter e.m.f. which it produces, as a leading current, and the polarization cell thus acts like a condenser, and is called an \"electrolytic condenser.\" It has an enormous electrostatic capacity, or \"effective capacity,\" but can stand low voltage only — 1 volt or less — and therefore is of limited industrial value. As chemical action requires appreciable time, s ...", "... ygen films which hold back the current flow by their counter e.m.f. The current thus flows ahead of the voltage or counter e.m.f. which it produces, as a leading current, and the polarization cell thus acts like a condenser, and is called an \"electrolytic condenser.\" It has an enormous electrostatic capacity, or \"effective capacity,\" but can stand low voltage only — 1 volt or less — and therefore is of limited industrial value. As chemical action requires appreciable time, such electrolytic condensers show at commer ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-33", "section_label": "Chapter 40: General System Of Circuits", "section_title": "General System Of Circuits", "kind": "chapter", "sequence": 33, "number": 40, "location": "lines 12217-12884", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-33/", "snippets": [ "CHAPTER XL GENERAL SYSTEM OF CIRCUITS. (A) Circuits containing resistance and inductance only. 95. Let, upon a general system or network of circuits con- nected with each other directly or inductively, and containing resistance and inductance, but no capacity, a system of e.m.fs., ey be impressed. These e.m.fs. may be of any frequency or wave shape, or may be continuous or anything else, but are supposed to be given by their equations. They may be free of transient terms, or may contain transient terms dependi ...", "... The sixteen coefficients, A?, i = 1, 2, 3, 4, ft = 1, 2, 3, 4, are now determined by the 16 independent linear equations (12) and (13). (27) 1T4 TRANSIENT PHENOMENA (B) Circuits containing resistance, self -inductance, mutual in- ductance and capacity. 97. The general method of dealing with such a system is the same as in (A). Kirchhoff's equation (1) is of the form i dt = 0. (28) Eliminating now all the currents which can be expressed in terms of other currents, by means of equation (2), leave ...", "... (28) gives n inde- pendent equations of the form n n 7 • n eq - X\" &A - X\" c«'-ir - X\" &ff / *« dt = °- (29) i i i Resolving these equations for / iK dt gives e/ = i fi*= 2> + I>- + 2;c^ (so) as the equations of the potential differences at the condensers. Differentiating (29) gives where q = 1, 2, . . . n. By the same reasoning as before, the solution of these equa- tions (31) can be split into two components, a permanent term, (32) and a transient term, which disappears for t = oo , and is given ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-24", "section_label": "Chapter 24: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 25682-29374", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-24/", "snippets": [ "... imum efficiency of the synchronous motor system is the same as in a system containing resistance and condensive reactance, fed over an inductive line, the lead of the current against the generated e.m.f., Ei, here acting in the same way as the con- denser capacity in Chapter XI. 218. D. Eo = constant; Pi = constant. If the power of a synchronous motor remains constant, we have (Fig. 154) I X OEi^ = constant, or, since OE^ = Ir, I = ^^^ and OE' X OE^^ = OE' X E'E,' = constant, r Hence we get the diagram for an ...", "... This is the same v-alue which represents the maximum power transmissible by e.m.f., eo, over a non-inductive line of resistance, r; or, more generally, the maximum power which can be trans- mitted over a line of impedance. into any circuit, shunted by a condenser of suitable capacity. Substituting (21) in (19) and (20), we get, Co 2r (22) SYNCHRONOUS MOTOR 319 and the displacement of phase in the synchronous motor, hence, cos (ei, i) =-:— = -; lei z tan (ei, i) = - -, (23) that is, the angle ...", "... e which represents the maximum power transmissible by e.m.f., eo, over a non-inductive line of resistance, r; or, more generally, the maximum power which can be trans- mitted over a line of impedance. into any circuit, shunted by a condenser of suitable capacity. Substituting (21) in (19) and (20), we get, Co 2r (22) SYNCHRONOUS MOTOR 319 and the displacement of phase in the synchronous motor, hence, cos (ei, i) =-:— = -; lei z tan (ei, i) = - -, (23) that is, the angle of internal displacem ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-23", "section_label": "Chapter 23: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 21983-22448", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "snippets": [ "... non-inductive part of the circuit shows the higher harmonics in a reduced amplitude. That is, self-induction in series to a non-induc- tive circuit reduces the higher harmonics or smooths out the wave to a closer resemblance with sine shape. In- versely, capacity in series to a non-inductive circuit con- sumes less E.M.F. at higher than at lower frequency, and thus makes the higher harmonics of current and of poten- tial difference in the non-inductive part of the circuit more pronounced — intensifies the harmonic ...", "... ctive circuit con- sumes less E.M.F. at higher than at lower frequency, and thus makes the higher harmonics of current and of poten- tial difference in the non-inductive part of the circuit more pronounced — intensifies the harmonics. Self-induction and capacity in series may cause an in- crease of voltage due to complete or partial resonance with higher harmonics, and a discrepancy between volt-amperes and watts, without corresponding phase displacement, as will be shown hereafter. 246. In long-distance transm ...", "... to complete or partial resonance with higher harmonics, and a discrepancy between volt-amperes and watts, without corresponding phase displacement, as will be shown hereafter. 246. In long-distance transmission over lines of notice- able inductance and capacity, rise of voltage due to reso- nance may occur with higher harmonics, as waves of higher frequency, while the fundamental wave is usually of too low a frequency to cause resonance. An approximate estimate of the possible rise by reso- nance with various ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... arge against ground. These moisture particles conglomer- ate with each other to larger moisture particles and ultimately 264 GENERAL LECTURES rain drops. By the collection of n* particles into one, the diameter of the particle has increased n fold. Its capacity has also increased n fold (the capacity of a sphere being pro- portional to the diameter). The particle contains, however, the accumulated charges of n* smaller particles, and n' times the charge, with n times the capacity, gives ii^ times the poten- tia ...", "... cles conglomer- ate with each other to larger moisture particles and ultimately 264 GENERAL LECTURES rain drops. By the collection of n* particles into one, the diameter of the particle has increased n fold. Its capacity has also increased n fold (the capacity of a sphere being pro- portional to the diameter). The particle contains, however, the accumulated charges of n* smaller particles, and n' times the charge, with n times the capacity, gives ii^ times the poten- tial. It follows herefrom that with the cong ...", "... rticle has increased n fold. Its capacity has also increased n fold (the capacity of a sphere being pro- portional to the diameter). The particle contains, however, the accumulated charges of n* smaller particles, and n' times the charge, with n times the capacity, gives ii^ times the poten- tial. It follows herefrom that with the conglomeration of the water particles, their potential must increase rapidly, propor- tionately to the square of their diameter. The conglomeration of moisture particles in the clouds is, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1120-1683", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-01/", "snippets": [ "... active component of e.m.f., or the e.m.f. in phase with the current, the re- actance, X, refers to the wattless or reactive component of e.m.f., or the e.m.f. in quadrature with the current. 3. The principal sources of reactance are electromagnetism and capacity. Electromagnetism An electric current, i, in a circuit produces a magnetic flux surrounding the conductor in lines of magnetic force (or more correctly, lines of magnetic induction), of closed, circular, or other form, which alternate with the alternat ...", "... 62 = iXm', and, since both e.m.fs. are in quadrature to each other, the total e.m.f. is e = Ver + 62^ = i Vr^ + x„,^ = iz; that is, the impedance, z, takes in alternating-current circuits the place of the resistance, r, in continuous-current circuits. Capacity 4. If upon a condenser of capacity C an e.m.f., e, is impressed, the condenser receives the electrostatic charge, Ce. If the e.m.f., e, alternates with the frequency, /, the average rate of charge and discharge is 4 /, and 2 irf the maximum rate of cha ...", "... oth e.m.fs. are in quadrature to each other, the total e.m.f. is e = Ver + 62^ = i Vr^ + x„,^ = iz; that is, the impedance, z, takes in alternating-current circuits the place of the resistance, r, in continuous-current circuits. Capacity 4. If upon a condenser of capacity C an e.m.f., e, is impressed, the condenser receives the electrostatic charge, Ce. If the e.m.f., e, alternates with the frequency, /, the average rate of charge and discharge is 4 /, and 2 irf the maximum rate of charge and discharge, sinuso ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... ctual generated e.m.f., alternator, 272 Admittance, 55 of dielectric, 154 due to eddy currents, 137 to hysteresis, 129 Admittivity of dielectric circuit, 160 Air-gap in magnetic circuit, 119, 132 Ambiguity of vectors, 39 Amplitude, 6, 20 Apparent capacity of distorted wave, 386 efficiency of induction motor, 234 impedance of transformer, 201 torque efficiency of induction motor, 234 Arc causing harmonics, 353 as pulsating resistance, 352 volt-ampere characteristic, 354 wave constrtiction, 355 Arma ...", "... characteristic, 354 wave constrtiction, 355 Armature reaction of alternator, 260, 272 Average value of wave, 11 Balanced polyphase system, 397 Balance factor of polyphase system, 406 Brush discharge, 112 Cable, topographical characteristic, 42 Capacity, 4, 9 of line, 174 Choking coil, 96 Circuit characteristic of line and cable, 44 dielectric and dynamic, 159 factor of general wave, 383 Coefficient of eddy currents, 138 of hysteresis, 123 Combination of sine waves, 31 Compensation for laggi ...", "... cable, 44 dielectric and dynamic, 159 factor of general wave, 383 Coefficient of eddy currents, 138 of hysteresis, 123 Combination of sine waves, 31 Compensation for lagging currents by condensance, 72 Condensance in symbolic expression, 36 Condenser as reactance and suscep- tance, 96 with distorted wave, 384 motor on distorted wave, 392 motor, single-phase induction, 249, 257 synchronous, 339 Conductance of circuit with induc- tive line, 84 direct current, 55 due to eddy currents, 137 effecti ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... e same law as the magnetic hysteresis, This loss, probably true dielectric static hysteresis, was observed under conditions such that a loss proportional to the square of density and frequency must be small, while at high densities and frequencies, as in condensers, the true dielectric hysteresis may be entirely obscured by a viscous loss, represented by W-^ = ciVcB*. 99. If the loss of power by electrostatic hysteresis is proportional to the square of the frequency and of the field intensity, — as it probably nea ...", "... . 99. If the loss of power by electrostatic hysteresis is proportional to the square of the frequency and of the field intensity, — as it probably nearly is under the working con- 140 ALTERNATING-CURRENT PHENOMENA. [§9& ditions of alternating-current condensers, — then it is pro- portional to the square of the E.M.F., that is, the effective conductance, gy due to dielectric hysteresis is a constant ; and, since the condenser susceptance, — b =b\\ is a constant also, — unlike the magnetic inductance, — the ratio o ...", "... working con- 140 ALTERNATING-CURRENT PHENOMENA. [§9& ditions of alternating-current condensers, — then it is pro- portional to the square of the E.M.F., that is, the effective conductance, gy due to dielectric hysteresis is a constant ; and, since the condenser susceptance, — b =b\\ is a constant also, — unlike the magnetic inductance, — the ratio of con- ductance and susceptance, that is, the angle of difference of phase due to dielectric hysteresis, is a constant. This I found proved by experiment. This would ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-22", "section_label": "Chapter 20: Ri", "section_title": "Ri", "kind": "chapter", "sequence": 22, "number": 20, "location": "lines 24560-25119", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "snippets": [ "... non-inductive part of the circuit shows the higher harmonics in a reduced amplitude. That is, self-induction in series to a non-induc- tive circuit reduces the higher harmonics or smooths out the wave to a closer resemblance with sine shape. In- versely, capacity in series to a non-inductive circuit con- sumes less E.M.F. at higher than at lower frequency, and thus makes the higher harmonics of current and of poten- tial difference in the non-inductive part of the circuit more pronounced — intensifies the harmonic ...", "... ctive circuit con- sumes less E.M.F. at higher than at lower frequency, and thus makes the higher harmonics of current and of poten- tial difference in the non-inductive part of the circuit more pronounced — intensifies the harmonics. Self-induction and capacity in series may cause an in- crease of voltage due to complete or partial resonance. 225. In long-distance transmission over lines of notice- able inductance and capacity, rise of voltage due to reso- nance may under circumstances be expected with higher ...", "... part of the circuit more pronounced — intensifies the harmonics. Self-induction and capacity in series may cause an in- crease of voltage due to complete or partial resonance. 225. In long-distance transmission over lines of notice- able inductance and capacity, rise of voltage due to reso- nance may under circumstances be expected with higher harmonics, as waves of higher frequency, while the funda- mental wave is usually of too low a frequency to cause resonance. An approximate estimate of the possible rise ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "... the magnetic hysteresis, ^ = ^(B'-6. This loss, probably true dielectric static hysteresis, was observed under conditions such that a loss proportional to the square of density and frequency must be small, while at high densities and frequencies, as in condensers, the true dielectric hysteresis may be entirely obscured by a viscous loss, represented by W^ = e7V(B2. 99. If the loss of power by electrostatic hysteresis is proportional to the square of the frequency and of the field intensity, — as it probably near ...", "... (B2. 99. If the loss of power by electrostatic hysteresis is proportional to the square of the frequency and of the field intensity, — as it probably nearly is under the working con- 146 AL TERNA TING-CURRENT PHENOMENA. ditions of alternating-current condensers, — then it is pro- portional to the square of the E.M.F., that is, the effective conductance, g, due to dielectric hysteresis is a constant ; and, since the condenser susceptance, — b= b', is a constant also, — unlike the magnetic inductance, — the ratio ...", "... he working con- 146 AL TERNA TING-CURRENT PHENOMENA. ditions of alternating-current condensers, — then it is pro- portional to the square of the E.M.F., that is, the effective conductance, g, due to dielectric hysteresis is a constant ; and, since the condenser susceptance, — b= b', is a constant also, — unlike the magnetic inductance, — the ratio of con- ductance and susceptance, that is, the angle of difference of phase due to dielectric hysteresis, is a constant. This I found proved by experiment. This would ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-16", "section_label": "Chapter 16: Load Balance Of Polyphase Systems", "section_title": "Load Balance Of Polyphase Systems", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 29302-30428", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-16/", "snippets": [ "... y, hence can not be done by any method of connection or transformation. Thus mechanical momentum acts as energy-storing device in the use as phase bal- ancer, of the induction or the synchronous machine. Electrically, energy is stored by inductance and by capacity. The question then arises, whether by the use of a reactor, or a condenser, con- nected to a suitable phase of the system, an unequally loaded polyphase system can be balanced, so as to give constant power during the cycle. In interlinked polyphase circ ...", "... us mechanical momentum acts as energy-storing device in the use as phase bal- ancer, of the induction or the synchronous machine. Electrically, energy is stored by inductance and by capacity. The question then arises, whether by the use of a reactor, or a condenser, con- nected to a suitable phase of the system, an unequally loaded polyphase system can be balanced, so as to give constant power during the cycle. In interlinked polyphase circuits, such as the three-phase sys- tem, with unbalanced load carried over l ...", "... es become unequal. This makes voltage regulation more complicated than in a balanced system. A great unbalancing of the load, such as produced by operating a heavy single-phase load, as a single-phase railway or electric furnace, greatly reduces the power capacity of lines, trans- formers and generators. Unbalanced load on the generators causes a pulsating armature reaction: at single-phase load, the armature reaction pulsates between more than twice the average value, and a small reversed value, between f (cos a + ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-48", "section_label": "Chapter 8: Velocity Of Propagation Of Electric Field", "section_title": "Velocity Of Propagation Of Electric Field", "kind": "chapter", "sequence": 48, "number": 8, "location": "lines 26095-27002", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "snippets": [ "... here, as in wireless teleg- raphy, action at great distance is required, only conductors without return conductor can be used. To establish consider- able currents in such open conductors requires high frequen- cies, so that the current is absorbed by the capacity of the conductor or the capacity attached to its end. No conductor f parallel to the ground can be treated as conductor without : return conductor, since secondary currents in the ground and ! also in the higher strata of the atmosphere act as return con- ...", "... , action at great distance is required, only conductors without return conductor can be used. To establish consider- able currents in such open conductors requires high frequen- cies, so that the current is absorbed by the capacity of the conductor or the capacity attached to its end. No conductor f parallel to the ground can be treated as conductor without : return conductor, since secondary currents in the ground and ! also in the higher strata of the atmosphere act as return con- ductor with regard to the electr ...", "... be discussed : (A) The inductance of a finite section of an infinitely long con- ductor without return conductor. (B) The mutual inductance between two finite conductors without return conductors, at considerable distance from each other. ((7) The capacity of a sphere in free space. (D) The capacity of a sphere against ground, in space. Cases A and B deal with the electromagnetic, C and D with the electrostatic component of the electric field. A. Inductance of a length I of an infinitely long conductor wi ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1003-1658", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-02/", "snippets": [ "... e energy of the magnetic field $ = Li of the circuit. 9. Exactly analogous relations exist in the dielectric field. The dielectric field, or dielectric flux-, ^, is proportional to the voltage e, with a proportionality factor, C, which is called the capacity of the circuit: ^ = Ce. (6) The dielectric field represents stored energy, w. To produce it, power, p, must, therefore, be supplied by the circuit. Since power is current times voltage: p = i'e, (7) to produce the dielectric field ^¥ of the voltage ...", "... roduce the dielectric field ^¥ of the voltage e, a current i^ must be consumed in the circuit, which with the voltage e gives THE ELECTRIC FIELD. V6 the power p, which suppHes the stored energy w of the dielectric field ^. This current i' is called the capacity current, or, wrongly, charging current or condenser current. Since no power is required to maintain the field, but power is required to produce it, the capacity current must be proportional to the rate of increase of the dielectric field: ■• = y or b ...", "... urrent i^ must be consumed in the circuit, which with the voltage e gives THE ELECTRIC FIELD. V6 the power p, which suppHes the stored energy w of the dielectric field ^. This current i' is called the capacity current, or, wrongly, charging current or condenser current. Since no power is required to maintain the field, but power is required to produce it, the capacity current must be proportional to the rate of increase of the dielectric field: ■• = y or by (6), i' = C* (9) de If e and therefore ^ decre ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 883-1530", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "snippets": [ "... e energy of the magnetic field $ = Li of the circuit. 9. Exactly analogous relations exist in the dielectric field. The dielectric field, or dielectric flux, ty} is proportional to the voltage 6, with a proportionality factor, C, which is called the capacity of the circuit: f = Ce. (6) The dielectric field represents stored energy, w. To produce it, power, p, must, therefore, be supplied by the circuit. Since power is current times voltage, p = i'e. (7) To produce the dielectric field ty of the voltage ...", "... oduce the dielectric field ty of the voltage e, a current ir must be consumed in the circuit, which with the voltage e gives THE ELECTRIC FIELD. 13 the power p, which supplies the stored energy w of the dielectric field ^. This current i' is called the capacity current, or, wrongly, charging current or condenser current. Since no power is required to maintain the field, but power is required to produce it, the capacity current must be proportional to the increase of the dielectric field: or by (6), i' = C^ ...", "... rrent ir must be consumed in the circuit, which with the voltage e gives THE ELECTRIC FIELD. 13 the power p, which supplies the stored energy w of the dielectric field ^. This current i' is called the capacity current, or, wrongly, charging current or condenser current. Since no power is required to maintain the field, but power is required to produce it, the capacity current must be proportional to the increase of the dielectric field: or by (6), i' = C^. (9) de If e and therefore ^ decrease, -j- and th ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-09", "section_label": "Chapter 9: Wave Screens. Even Harmonics", "section_title": "Wave Screens. Even Harmonics", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 16964-17631", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-09/", "snippets": [ "... duced in propor- tion to their order, n. Even if r is large compared with x, and thus c^>lj iSnally c^ becomes negligible with n^, and the harmonics decrease with their order. 77. The screening effect of the series reactance is increased by shunting a capacity, C, beyond the inductance, L, that is, across the resistance, r, as shown in Fig. 73. By consuming current jTRRRRRTl e 1 rmmM Fig. 73. r e Fig. 74. proportional to frequency and voltage, the condenser shimts the more of the current p ...", "... ctance is increased by shunting a capacity, C, beyond the inductance, L, that is, across the resistance, r, as shown in Fig. 73. By consuming current jTRRRRRTl e 1 rmmM Fig. 73. r e Fig. 74. proportional to frequency and voltage, the condenser shimts the more of the current passing through the reactance, the higher the frequency, and thereby still further reduces the higher harmonies of current in the resistance, r, and thus of voltage across this re- sistance. Its effect is limited, however, b ...", "... ance, the higher the frequency, and thereby still further reduces the higher harmonies of current in the resistance, r, and thus of voltage across this re- sistance. Its effect is limited, however, by the decreasing voltage distortion at r and thus at the condenser, C. Thus the screening effect is still further increased by inserting a second inductance, L, beyond the condenser, C, in series to the resistance, r, as shown in Fig. 74. By making the second induct- ance equal to the first one, and making the condenser ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-32", "section_label": "Chapter 10: Mutual Inductance", "section_title": "Mutual Inductance", "kind": "chapter", "sequence": 32, "number": 10, "location": "lines 10475-12216", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "snippets": [ "CHAPTER X. MUTUAL INDUCTANCE. 82. In the preceding chapters, circuits have been considered containing resistance, self-inductance, and capacity, but no mutual inductance; that is, the phenomena which take place in the circuit have been assumed as depending upon the impressed e.m.f. and the constants of the circuit, but not upon the phenomena taking place in any other circuit. Of the magnetic fl ...", "... as factors, it is preferable to eliminate nl and n2 by reducing one circuit to the other by the ratio of turns M a = — , and then use the simpler equations (1), (2). ni 84. (A) Circuits containing resistance, inductance, and mutual inductance but no capacity. In such a circuit, shown diagrammatically in Fig. 38, we have di. di~ ~ * and e2 = r2i2 + x2— 2 + xm ^ • (6) Differentiating (6) gives de2 _ di2 d?i2 d2il ~dd~~T2dd^ x*~dF~VXm^] * See the chapters on induction machines, etc., in \" Theory and ...", "... 2 ' rr _r2 *^W *t/1*x/2 *°W MUTUAL INDUCTANCE 147 The exponent a is given by a quadratic equation (18). This quadratic equation (18) always has two real roots, and in this respect differs from the quadratic equation appearing in a circuit containing capacity, which latter may have two imaginary roots and so give rise to an oscillation. Mutual induction in the absence of capacity thus always gives a logarithmic transient term; thus, a = (r^2 + T^} \\ ; (T^ rf + * T^Xm • (19) •>//y«/y» /y» * \\ Z/ ^jU/2 .t ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-26", "section_label": "Chapter 26: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 32540-33010", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-26/", "snippets": [ "... ductive part of the circuit show the higher harmonics in a reduced amplitude. That is, self-inductive react- ance in series with a non-inductive circuit reduces the higher harmonics or smooths out the wave to a closer resemblance to sine-shape. Inversely, capacity in series to a non-inductive circuit consumes less e.m.f. at higher than at lower frequency, and thus makes the higher harmonics of current and of potential EFFECTS OF HIGHER HARMONICS 373 difference in the non-inductive part of the circuit more pro- ...", "... f. at higher than at lower frequency, and thus makes the higher harmonics of current and of potential EFFECTS OF HIGHER HARMONICS 373 difference in the non-inductive part of the circuit more pro- nounced— intensifies the harmonics. Self-induction and capacity in series may cause an increase of voltage due to complete or partial resonance with higher har- monics, and a discrepancy between volt-amperes and watts, without corresponding phase displacement, as will be shown hereafter. 253. In long-distance transm ...", "... t. The reactance voltage in the transformers at full-load = 5 per cent, with the fundamental wave. The resistance drop in the line at full-load = 10 per cent. The reactance voltage in the line at full-load = 20 per cent, with the fundamental wave. The capacity or charging current of the line = 20 per cent, of the full-load current, /, at the frequency of the fundamental. The line capacity may approximately be represented by a condenser shunted across the middle of the line. The e.m.f. at the generator terminal ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 557-1002", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-01/", "snippets": [ "... t a different current i\\ and possibly different voltages e' ', but again i' and e' are per- manent, that is, remain the same as long as the circuit remains unchanged. Let, however, in Fig. 2, a direct-current generator G be connected to an electrostatic condenser C. Before the switch S is closed, and therefore also in the moment of closing the switch, no current flows in the line A. Immediately after the switch S is closed, current begins to flow over line A into the condenser C, charging this condenser up to the ...", "... or G be connected to an electrostatic condenser C. Before the switch S is closed, and therefore also in the moment of closing the switch, no current flows in the line A. Immediately after the switch S is closed, current begins to flow over line A into the condenser C, charging this condenser up to the voltage given by the generator. When the \"A ELECTRIC DISCHARGES, WAVES AND IMPULSES. condenser C is charged, the current in the Hne A and the condenser C is zero again. That is, the permanent condition before closin ...", "... ctrostatic condenser C. Before the switch S is closed, and therefore also in the moment of closing the switch, no current flows in the line A. Immediately after the switch S is closed, current begins to flow over line A into the condenser C, charging this condenser up to the voltage given by the generator. When the \"A ELECTRIC DISCHARGES, WAVES AND IMPULSES. condenser C is charged, the current in the Hne A and the condenser C is zero again. That is, the permanent condition before closing the switch S, and also so ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 460-882", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "snippets": [ "... a different current i', and possibly different voltages e1 '; but again i' and e' are per- manent, that is, remain the same as long as the circuit remains unchanged. Let, however, in Fig. 2, a direct-current generator G be connected to an electrostatic condenser C. Before the switch S is closed, and therefore also in the moment of closing the switch, no current flows in the line A. Immediately after the switch S is closed, current begins to flow over line A into the condenser C, charging this condenser up to the ...", "... or G be connected to an electrostatic condenser C. Before the switch S is closed, and therefore also in the moment of closing the switch, no current flows in the line A. Immediately after the switch S is closed, current begins to flow over line A into the condenser C, charging this condenser up to the voltage given by the generator. When the 1 DISCHARGES, WAVES AND IMPULSES. condenser C is charged, the current in the line A and the condenser C is zero again. That is, the permanent condition before closing the ...", "... ctrostatic condenser C. Before the switch S is closed, and therefore also in the moment of closing the switch, no current flows in the line A. Immediately after the switch S is closed, current begins to flow over line A into the condenser C, charging this condenser up to the voltage given by the generator. When the 1 DISCHARGES, WAVES AND IMPULSES. condenser C is charged, the current in the line A and the condenser C is zero again. That is, the permanent condition before closing the switch S, and also some time ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-06", "section_label": "Lecture 6: Higher Harmonics Of The Generator Wave", "section_title": "Higher Harmonics Of The Generator Wave", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3133-3507", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-06/", "snippets": [ "SIXTH LECTURE HIGHER HARMONICS OF THE GENERATOR WAVE mHE open circuit reactance of the transformer is the only reactance high enough to give resonance with the line capacity at fundamental frequency. All other reactances are too low for this. Since, however, the inductive reactance increases and the capacity reactance decreases proportionally to the frequency, the two reactances come nearer together for higher frequency; tha ...", "... WAVE mHE open circuit reactance of the transformer is the only reactance high enough to give resonance with the line capacity at fundamental frequency. All other reactances are too low for this. Since, however, the inductive reactance increases and the capacity reactance decreases proportionally to the frequency, the two reactances come nearer together for higher frequency; that is, for the higher harmonics of the generator wave, and for some of the higher harmonics of the generator wave resonance rise of voltag ...", "... ly to the frequency, the two reactances come nearer together for higher frequency; that is, for the higher harmonics of the generator wave, and for some of the higher harmonics of the generator wave resonance rise of voltage so may occur between the line capacity and the circuit inductance. The origin and existence of higher harmonics therefore bears investigation in transformers, transmlission lines and cable systems. ORIGIN OF HIGHER HARMONICS Higher harmonics may originate in synchronous machines, as gener ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... moderate temperatures were invisible because of too low frequency and are thus called \" ultra-red rays,\" or \" infra-red rays/' as they are outside of and below the red end of the range of visible radiation. To produce powerful ultra-violet rays, I use a condenser dis- charge between iron terminals, a so-called ultra-violet arc lamp. Three iron spheres, 7 in Fig. 11, of about f in. diameter, are mounted on an insulator B. The middle sphere is fixed, the NATURE AND DIFFERENT FORMS OF RADIATION. 13 outer ones adj ...", "... in Fig. 11, of about f in. diameter, are mounted on an insulator B. The middle sphere is fixed, the NATURE AND DIFFERENT FORMS OF RADIATION. 13 outer ones adjustable and set for about ^ in. gap. This lamp is connected across a high voltage 0.2-mf. mica condenser C, which is connected to the high voltage terminal of a small step-up trans- former T giving about 15,000 volts (200 watts, 110 •*- 13,200 volts). The low tension side of the transformer is connected to the 240-volt 60-cycle circuit through a rheostat R t ...", "... al of a small step-up trans- former T giving about 15,000 volts (200 watts, 110 •*- 13,200 volts). The low tension side of the transformer is connected to the 240-volt 60-cycle circuit through a rheostat R to limit the current. The transformer charges the condenser, and when the voltage of the condenser has risen sufficiently high it discharges through the spark gaps I by an oscillation of high frequency (about 500,000 cycles), then charges again from the transformer, discharges through the gap, etc. As several such ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-04", "section_label": "Lecture 4: Load Factor And Cost Of Power", "section_title": "Load Factor And Cost Of Power", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 1527-2561", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-04/", "snippets": [ "... dis- tribution. Since of the three parts of the cost, only one, B, is propor- tional to the power used, hence constant per kilowatt output, — the other two parts being independent of the output, — hence the higher per kilowatt, the smaller a part of the capacity of the plant the output is ; it follows that the cost of power delivered is a function of the ratio of the actual output of the plant, to the available capacity. Interest on the investment of developing the water power or building the steam plant, the t ...", "... ts being independent of the output, — hence the higher per kilowatt, the smaller a part of the capacity of the plant the output is ; it follows that the cost of power delivered is a function of the ratio of the actual output of the plant, to the available capacity. Interest on the investment of developing the water power or building the steam plant, the transmission lines, cables and distribution circuits, and depreciation are items of the character A, or fixed cost, since they are practically independent of the ...", "... requires therefore a shifting of as large a part thereof over into class B, by shutting down smaller substations during periods of light load, etc. Incandescent lamp renewals, arc lamp trimming, etc., are essentially proportional costs, B. The reserve capacity of a plant, the steam reserve main- tained at the receiving end of a transmission line, the difference in cost between a duplicate pole line and a single pole line with two circuits, the storage battery reserve of the distribution system, the tie feeders ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-17", "section_label": "Theory Section 17: Impedance and Admittance", "section_title": "Impedance and Admittance", "kind": "theory-section", "sequence": 17, "number": 17, "location": "lines 6814-7380", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-17/", "snippets": [ "... AND ADMITTANCE ' 99 total e.m.f. resulting from the impressed e.m.f. and all e.m.fs. produced by the current i in the circuit. Such counter e.m.fs. may be due to inductance, as self-induc- tance, or mutual inductance, to capacity, chemical polarization, etc. The counter e.m.f. of self-induction, or e.m.f. generated by the magnetic field produced by the alternating current i, is repre- sented by a quantity of the same dimensions as resistance, and mea ...", "... = 110 volts per phase, the current is /0 = ii — jiz = 100 — 100 j at standstill, the torque = D0. The two phases are connected in series in a single-phase cir- cuit of e.m.f. e = 220, and one phase shunted by a condenser of 1 ohm capacity reactance. What is the starting torque D of the motor under these con- ditions, compared with Z>0, the torque on a quarter-phase cir- IMPEDANCE AND ADMITTANCE 103 cuit, and what the relative torque pe ...", "... hase, the current is /0 = ii — jiz = 100 — 100 j at standstill, the torque = D0. The two phases are connected in series in a single-phase cir- cuit of e.m.f. e = 220, and one phase shunted by a condenser of 1 ohm capacity reactance. What is the starting torque D of the motor under these con- ditions, compared with Z>0, the torque on a quarter-phase cir- IMPEDANCE AND ADMITTANCE 103 cuit, and what the relative torque per volt-ampere input, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1224-1727", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "snippets": [ "... rs to the energy component of E.M.F., or the E.M.F. in phase with the current, the reactance, ;r, refers to the wattless component of E.M.F., or the E.M.F. in quadrature with the current. 3. The principal sources of reactance are electro-mag- netism and capacity. ELECTRO-MAGNETISM, An electric current, /, flowing through a circuit, produces a magnetic flux surrounding the conductor in lines of magnetic force (or more correctly, lines of magnetic induc- tion), of closed, circular, or other form, which alternate ...", "... is : t\\ = Lv ; 1 4] INTRODUCTION, 5 and, since both E.M.Fs. are in quadrature to each other, the total E.M.F. is — that is, the impedance, ^, takes in alternating-current cir- cuits the place of the resistance, r, in continuous-current •circuits. CAPACITY. 4. If upon a condenser of capacity, C, an E.M.F., e, is impressed, the condenser receives the electrostatic charge, Ce. If the E.M.F., e, alternates with the frequency, iV, the average rate of charge and discharge is 4 A^, and 2w JV the maximum rate o ...", "... TRODUCTION, 5 and, since both E.M.Fs. are in quadrature to each other, the total E.M.F. is — that is, the impedance, ^, takes in alternating-current cir- cuits the place of the resistance, r, in continuous-current •circuits. CAPACITY. 4. If upon a condenser of capacity, C, an E.M.F., e, is impressed, the condenser receives the electrostatic charge, Ce. If the E.M.F., e, alternates with the frequency, iV, the average rate of charge and discharge is 4 A^, and 2w JV the maximum rate of charge and discharge, si ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-05", "section_label": "Chapter 5: Symbouc Mbthod", "section_title": "Symbouc Mbthod", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2744-3229", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "snippets": [ "... ^ er — /x , . /r + ') O'-./*'') «'+^*'' . ' ~ ei' ' 40 ALTERNATING-CURRENT PHENOMENA. 30. If C is the capacity of a condenser in series in a circuit of current I = i + //', the E.M.F. impressed upon the terminals of the condenser is E = - - , 90° behind the current ; and may be represented by — - - , or jx^ /, where x^ = - is the capacity reactance or condensati ...", "... nator, we have — T _ or, if E = e -\\-je' is the impressed E.M.F., and 7 = i ' -\\- ji' the current flowing in the circuit, its impedance is — 0 +./>') O'-./*'') «'+^*'' . ' ~ ei' ' 40 ALTERNATING-CURRENT PHENOMENA. 30. If C is the capacity of a condenser in series in a circuit of current I = i + //', the E.M.F. impressed upon the terminals of the condenser is E = - - , 90° behind the current ; and may be represented by — - - , or jx^ /, where x^ = - is the capacity reactance or condensatice 2 TT NC o ...", "... owing in the circuit, its impedance is — 0 +./>') O'-./*'') «'+^*'' . ' ~ ei' ' 40 ALTERNATING-CURRENT PHENOMENA. 30. If C is the capacity of a condenser in series in a circuit of current I = i + //', the E.M.F. impressed upon the terminals of the condenser is E = - - , 90° behind the current ; and may be represented by — - - , or jx^ /, where x^ = - is the capacity reactance or condensatice 2 TT NC of the condenser. Capacity reactance is of opposite sign to magnetic re- actance ; both may be combined i ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 2774-3131", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-06/", "snippets": [ "... he diagram is shown for 45° lag, in Fig. 30 for noninductive load, and in Fig. 31 for 45° lead of the currents with regard to their E.M.Fs. BALANCED THREE -PHASE SYSTEM 45° LEAD THREE-PHASE CIRCUIT 80°LA» TRANSMISSION LINE' WITH DISTRIBUTED CAPACITY, INDUCTANCB RESISTANCE AUD LEAKAQB •I, Fig. 31. Fig. 32. As seen, the induced generator E.M.F. and thus the generator excitation with lagging current must be higher, with leading current lower, than at non-inductive load, or conversely with th ...", "... Ev Ez, E9 fall off more with lagging, less with leading current, than with non- inductive load. 36. As further instance may be considered the case of a single phase alternating current circuit supplied over a cable containing resistance and distributed capacity. 48 ALTERNATING-CURRENT PHENOMENA. Let in Fig. 33 the potential midway between the two terminals be assumed as zero point 0. The two terminal voltages at the receiver circuit are then represented by the points E and El equidistant from 0 and opposite ...", "... ctively. Considering first an element of the line or cable next to the receiver circuit. In this an E.M.F. EEl is consumed by the resistance of the line element, in phase with the current OI, and proportional thereto, and a current //x con- sumed by the capacity, as charging current of the line element, 90° ahead in phase of the E.M.F. OE and propor- tional thereto, so that at the generator end of this cable element current and E.M.F. are OI^ and OEl respectively. Passing now to the next cable element we have ag ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-19", "section_label": "Chapter 19: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 18053-19457", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "snippets": [ "... e of the impressed SYNCHRONOUS MOTOR. 329 E.M.F., or self-induction of the circuit compensated by the effect of the lead of the motor current. This condition of maximum efficiency of a circuit we have found already in the Chapter on Inductance and Capacity. 202. B. EQ and El constant, I variable. Obviously EQ lies again on the circle eQ with EQ as radius and O as center. Fig. 143. E lies on a straight line e, passing throtigh the origin; Since in the parallelogram OE E0 Ev EEQ = E^ we derive EQ b ...", "... iency, into a non- inductive circuit. -334 ALTERNATING-CURRENT PHENOMENA. In this case, In general, it is, taken from the diagram, at the condi- tion of maximum efficiency : Comparing these results with those in Chapter IX. on Self-induction and Capacity, we see that the condition of maximum efficiency of the synchronous motor system is the same as in a system containing only inductance and •capacity, the lead of the current against the induced E.M.F. El here acting in the same way as the condenser capaci ...", "... - tion of maximum efficiency : Comparing these results with those in Chapter IX. on Self-induction and Capacity, we see that the condition of maximum efficiency of the synchronous motor system is the same as in a system containing only inductance and •capacity, the lead of the current against the induced E.M.F. El here acting in the same way as the condenser capacity in Chapter IX. 204. Fig. 147. D. En = constant ; P = constant. If the power of a synchronous motor remains constant, we have (Fig. 147) ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-52", "section_label": "Chapter 3: Standing Waves", "section_title": "Standing Waves", "kind": "chapter", "sequence": 52, "number": 3, "location": "lines 29316-30243", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "snippets": [ "... = §J (127) that is, the ratio of the energy coefficients is equal to the ratio of the reactive coefficients of the circuit. The standing wave can never be oscillatory, but is always exponential, or gradually dying out, if either the inductance L or the capacity 0 vanishes ; that is, the circuit contains no capacity or contains no inductance. In all other cases the standing wave is oscillatory for waves shorter than the critical value L = -— , where 0 V - 9 V §} > (128) and is exponential or gradual for st ...", "... nts is equal to the ratio of the reactive coefficients of the circuit. The standing wave can never be oscillatory, but is always exponential, or gradually dying out, if either the inductance L or the capacity 0 vanishes ; that is, the circuit contains no capacity or contains no inductance. In all other cases the standing wave is oscillatory for waves shorter than the critical value L = -— , where 0 V - 9 V §} > (128) and is exponential or gradual for standing waves longer than the critical wave length lWo; ...", "... al for standing waves longer than the critical wave length lWo; or for k < ko the standing wave is exponential, for k > ka it is oscillatory.0 The value kQ = m VLC thus takes a similar part in the theory of standing waves as the value r02 = 4 L0C0 in the condenser discharge through an inductive circuit; that is, it separates the exponential or gradual from trigonometric or oscillatory conditions. The difference is that the condenser discharge through an inductive circuit is gradual, or oscillatory, depending on t ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 6125-6803", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-09/", "snippets": [ "... -up transformer, the two lines, and the load. Let then Xi = length of line, X2 = length of transformer circuit, and X3 = length of load circuit, in velocity measure.* If then * If Zi = length of circuit section in any measure, and Lo = inductance, Co = capacity per unit of length U, then the length of the circuit in velocity measure is Xi = aoh, where o-q = v LoCo. Thus, if L = inductance, C = capacity per transformer coil, n = number of transformer coils, for the transformer the unit of length is the coil; henc ...", "... , in velocity measure.* If then * If Zi = length of circuit section in any measure, and Lo = inductance, Co = capacity per unit of length U, then the length of the circuit in velocity measure is Xi = aoh, where o-q = v LoCo. Thus, if L = inductance, C = capacity per transformer coil, n = number of transformer coils, for the transformer the unit of length is the coil; hence the 110 ELECTRIC DISCHARGES, WAVES AND IMPULSES. Ui = 900 = power- dissipation constant of the line, W2 = 100 = power-dissipation constant ...", "... at is, in the line: p = 79ie\"2oox^ the energy of the wave decreases slowly; in the transformer: p = p2€+^''°°^, the energy of the wave increases rapidly; length li = n, and the length in velocity measure, X = aou = n ^ LC. Or, if L = inductance, C = capacity of the entire transformer, its length in velocity measure is \\ = ^ LC. Thus, the reduction to velocity measure of distance is very simple. Oscillations of the compound circuit. Ill in the load: p = pse~^^^^^, the energy of the wave decreases rap ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 5521-6088", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "snippets": [ "... -up transformer, the two lines, and the load. Let then Xi = length of line, X2 = length of transformer circuit, and Xs = length of load circuit, in velocity measure.* If then * If Zi = length of circuit section in any measure, and L0 = inductance, Co = capacity per unit of length Zi, then the length of the circuit in velocity measure is Xi = o-oZi, where l)vi(iit 1, that is, when passing from ci a section of low inductance and high capacity into a section of high inductance and low capacity, as from a transmission line into a transformer or a reactive coil, the voltage of the wave is s* increased; if — < 1, that is, when passing from a section of high ci inductance and low capacity in ...", "... assing from one section C2 of a circuit to another section, the voltage of the wave may ^ . decrease or may increase. If — > 1, that is, when passing from ci a section of low inductance and high capacity into a section of high inductance and low capacity, as from a transmission line into a transformer or a reactive coil, the voltage of the wave is s* increased; if — < 1, that is, when passing from a section of high ci inductance and low capacity into a section of low inductance and high capacity, as ...", "... gh capacity into a section of high inductance and low capacity, as from a transmission line into a transformer or a reactive coil, the voltage of the wave is s* increased; if — < 1, that is, when passing from a section of high ci inductance and low capacity into a section of low inductance and high capacity, as from a transformer to a transmission line, the voltage of the wave is decreased. This explains the frequent increase to destructive voltages, when entering a station from the transmission line or cab ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-04", "section_label": "Chapter 3: The Individualistic Era: From Competition to Co-operation", "section_title": "The Individualistic Era: From Competition to Co-operation", "kind": "chapter", "sequence": 4, "number": 3, "location": "lines 874-1745", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-04/", "snippets": [ "... e take out as crops, then under the present industrial organization of our country we will not be able to maintain our present standard of living. All these features together have created an abnormal increase of consuming capacity of our nation, and so it was only in the last decades that the means of possible production have be- gun to increase beyond the possible demand for consumption and the industrial problem has become urgent. This problem h ...", "... epresents that part of the cost which is proportional to the amount of commodity produced. Fixed cost, for instance, 25 AMERICA AND THE NEW EPOCH is the interest on the investment. Whether the factory is working full capacity, or only part of its capacity, or standing entirely idle, the interest charges continue the same. Proportionate cost, for instance, is that of raw materials; if we produce twice as much, twice as much material is needed. ...", "... which is proportional to the amount of commodity produced. Fixed cost, for instance, 25 AMERICA AND THE NEW EPOCH is the interest on the investment. Whether the factory is working full capacity, or only part of its capacity, or standing entirely idle, the interest charges continue the same. Proportionate cost, for instance, is that of raw materials; if we produce twice as much, twice as much material is needed. If the production ceases, the c ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... d frequently of an infinite number of waves. Electric radiation usually is of a single frequency, that is, of the frequency or wave length determined by the constants of the electric circuit which produces the radiation, mainly the induct- ance L and the capacity C. They may, however, have different wave shapes, that is, comprise, in adolition to the fundamental wave, higher harmonics or multiples thereof, just as the sound waves which represent the same tone with different musical instruments are of the same freq ...", "... ting to consider the corresponding relations in electric waves. In an electric circuit, the speed of propagation of an electric wave is, when neglecting the energy losses in and by the con- ductor: S = -L= , (5) VLC where L is the inductance, C the capacity of the conductor per unit length (the length measured in the same measure as the speed S). The inductance L is proportional to the permeability /*, and the capacity C proportional to the dielectric constant, or specific capacity K of the medium surround ...", "... sses in and by the con- ductor: S = -L= , (5) VLC where L is the inductance, C the capacity of the conductor per unit length (the length measured in the same measure as the speed S). The inductance L is proportional to the permeability /*, and the capacity C proportional to the dielectric constant, or specific capacity K of the medium surrounding the conductor, that is, the medium through which the electric wave propagates; that is, A V p* where A is a proportionality constant. The ratio of the speed o ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-21", "section_label": "Apparatus Introduction 21: Introduction", "section_title": "Introduction", "kind": "apparatus-introduction", "sequence": 21, "number": null, "location": "lines 8292-8517", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-21/", "snippets": [ "... its or sets of circuits moving with regard to each other. 5th. Stationary induction apparatus, consisting of a magnetic circuit interlinked with one or more electric circuits. 6th. Electrostatic and electrolytic apparatus as condensers and polarization cells. Apparatus changing from one to a different form of electric energy have been defined as: A. Transformers, when using magnetism, and as B. Converters, when using mechanical momentum as inter- media ...", "... apparatus, the synchronous motors, which are usually preferred for large powers, especially where frequent starting and considerable starting torque are not needed. Synchronous machines may be used as compensators or synchronous condensers, to produce wattless current, leading by over-excitation, lagging by under-excitation, or may be used as phase converters by operat- ing a polyphase synchronous motor by one pair of terminals from a single-phase circuit. The ...", "... n primary and secondary circuit, either elec- trically or magnetically. The stationary induction apparatus with one electric circuit are used for producing wattless lagging currents, as reactors, reactive or choke coils. (6) Condensers and polarization cells produce wattless leading currents, the latter, however, usually at a low efficiency, while the efficiency of the condenser is extremely high, frequently above 99 per cent. ; that is, the loss of powe ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-21", "section_label": "Chapter 21: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 22302-23970", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-21/", "snippets": [ "... trailing pole corner. Since the internal self-inductive reactance of the alternator itself causes a certain lag of the current behind the generated e.m.f., this condition of no displacement can exist only in a circuit with external negative reactance, as capacity, etc. ALTERNATING-CURRENT GENERATOR 2G1 If the armature current lags, it reaches the maximum later than the e.m.f.; that is, in a position where the armature-coil partly faces the field-pole which it approaches, as shown in dia- gram in Fig. 130. Sinc ...", "... .f. curve at non-inductive load is nearly horizontal at open-circuit, nearly vertical at short-circuit, and is similar to an arc of an ellipse. With reactive load the curves are more nearly straight lines. The voltage drops on inductive load and rises on capacity load. 26 24 22 20 3^u :10 \\ \\ \\ FIELD CHARACTERISTIC Eo=2500, Zo=1+10j,r=o. 90°LAG l2r=0 \\ \\, \\ \\ \\ \\, > \\ N •s_ / \\ \\% \\ ■. vV / ^w V. ft-:^ \\ / ^ \\ \\ / \\ K, N S, / ...", "... ^' / / / y ^^ ,-•' ■ / f /' , .-' ^k / / / y -'' / ^t M X ^ ,^ -\"' #' r 40 80 120 160 200 240 280 320 360 AMPERES Fig. 135. — Field characteristic of alternator at GO per cent, power-factor on condenser load. Every alternator does this near open-circuit, especially on non-inductive load. Even if the synchronous reactance, a^o, is not quite negli- gible, this regulation takes place, to a certain extent, on non- inductive circuit, since for a: = 0, £ ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-25", "section_label": "Chapter 25: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 29375-32539", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-25/", "snippets": [ "... r equivalent sine waves, and the investigation with sufficient exactness for most cases be carried out under the assumption of sine waves, as done in the preceding chapters. Similar phenomena take place in circuits containing polari- zation cells, leaky condensers, or other apparatus representing a synchronously varying negative reactance. Possibly dielectric hysteresis in condensers causes a distortion similar to that due to magnetic hysteresis. Inversely, at very high voltages, where corona appears on the condu ...", "... n of sine waves, as done in the preceding chapters. Similar phenomena take place in circuits containing polari- zation cells, leaky condensers, or other apparatus representing a synchronously varying negative reactance. Possibly dielectric hysteresis in condensers causes a distortion similar to that due to magnetic hysteresis. Inversely, at very high voltages, where corona appears on the conductors, with a sine wave of impressed voltage, a distor- tion of the capacity current wave occurs, which is largely effect- ...", "... eactance. Possibly dielectric hysteresis in condensers causes a distortion similar to that due to magnetic hysteresis. Inversely, at very high voltages, where corona appears on the conductors, with a sine wave of impressed voltage, a distor- tion of the capacity current wave occurs, which is largely effect- ive, but partly reactive due to the increase of capacity under corona. Pulsation of Resistance 239. To a certain extent the investigation of the effect of synchronous pulsation of the resistance coincides w ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-17", "section_label": "Chapter 17: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16362-17596", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "snippets": [ "... y at the trailing-pole corner. Since the internal self- inductance of the alternator itself causes a certain lag of the current behind the induced E.M.F., this condition of no displacement can exist only in a circuit with external nega- tive reactance, as capacity, etc. If the armature current lags, it reaches the maximum later than the E.M.F. ; that is, in a position where the armature coil partly faces the following-field pole, as shown in diagram in Fig. 127. Since the armature current flows Fig. 127. in ...", "... / j 800 f* . X / / / , 7 ,,*\" / / / m /- -*''\" A -n pe •M /y /x. **' ;-r *•\"' 1 B , £ I | 2 0^ **•!•• 0 • 0 m Fig. 732. Field Characteristic of Alternator, at 60% Power-factor on Condenser Load. 306 AL TERNA TING-CURRENT PHENOMENA. 1 I 1 1 '/ FIE LD CHARACTERISTIC / / i / f E0-2500, Zo-1-IOj, = o. 90°Leading Current / / I'R = O L / / / / / 7 / / r tu / / 2 / 1 / ? / / / ...", "... ?/ r / J / ^ *X / / 7 I* 11 ^ / / ^x / // / // / / // ! / / / I/ / / // / / / / / / g / ^-x ^ x'' xlO 3- A, nps. fig. 133. Field Characteristic of Alternator, on Wattless Condenser Load. With reactive load the curves are more nearly straight lines. The voltage drops on inductive, rises on capacity load. The output increases from zero at open circuit to a maxi- mum, and then decreases again to zero at short circuit. AL TERN A ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-11", "section_label": "Chapter 12: Frequency Converter Or General Alternating Current Transformer", "section_title": "Frequency Converter Or General Alternating Current Transformer", "kind": "chapter", "sequence": 11, "number": 12, "location": "lines 14897-17124", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-11/", "snippets": [ "... ; hence, secondary current: T E\\ _ snie /i ~ v T 7z - Zi + Z (n + r) + js (X! + x) 1 This applies to the case where the secondary contains inductive react- ance only; or, rather, that kind of reactance which is proportional to the frequency. In a condenser the reactance is inversely proportional to the frequency, in a synchronous motor under circumstances independent of the frequency. Thus, in general, we have to set, x = x' -f x\" + s'\", where x' is that part of the reactance which is proportional to the fre ...", "... he supply frequency, when motor, and for the generated or secondary frequency, when generator. Such a couple of frequency converter and driving motor and auxiliary generator has over a motor-generator set the advan- tage, that it requires a total machine capacity only equal to the output, while with a motor-generator set the total machine capacity equals twice the output. It has, however, the dis- advantage not to be as standard as the motor and the generator. If a synchronous machine is used, the frequency is co ...", "... erator. Such a couple of frequency converter and driving motor and auxiliary generator has over a motor-generator set the advan- tage, that it requires a total machine capacity only equal to the output, while with a motor-generator set the total machine capacity equals twice the output. It has, however, the dis- advantage not to be as standard as the motor and the generator. If a synchronous machine is used, the frequency is constant ; if an induction machine is used, there is a slip, increasing with the load, t ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-40", "section_label": "Chapter 4: Arc Rectification", "section_title": "Arc Rectification", "kind": "chapter", "sequence": 40, "number": 4, "location": "lines 17755-19259", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "snippets": [ "... , and in Figs. 67 to 76 oscillograms of this rectifier. Interesting to note is the high frequency oscillation at the ter- mination of the jump of the potential difference cC (Fig. 60) which represents the transient term resulting from the electro- static capacity of the transformer. At the end of the period of overlap of the two rectifying arcs one of the anode currents reaches 264 TRANSIENT PHENOMENA =£ 24 20 GO | 12 o 40 n 8 100 200 300 400 500 600 700 800 900 1000 1100 Volt Load Fig. 66. ...", "... ng arcs. Fig. 76. Rectified current in arc circuit. 266 TRANSIENT PHENOMENA zero and stops, and so its L — abruptly changes; that is, asud- ctt den change of voltage takes place in the circuit aACDc or bBCDc. Since this 'cuit contains distributed capacity, that of the transformer C' ^BC respectively, the line, etc., and inductance, an oscillatk ^.-.esults of a frequency depending upon the capacity and inductance, usually a few thousand cycles per second, and of a voltage depending upon the impressed e.m.f. ...", "... ctt den change of voltage takes place in the circuit aACDc or bBCDc. Since this 'cuit contains distributed capacity, that of the transformer C' ^BC respectively, the line, etc., and inductance, an oscillatk ^.-.esults of a frequency depending upon the capacity and inductance, usually a few thousand cycles per second, and of a voltage depending upon the impressed e.m.f.; that is, the L — of the circuit. An increase of inductance L dt di increases the angle of overlap and so decreases the — , hence does CLL ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1659-2484", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-03/", "snippets": [ "... ity is small, due to the limited extent of the circuit, resulting from the low voltage, and at the low voltage the dielectric energy thus is negligible, that is, the circuit stores appreciable energy only by the magnetic field. A circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectric field. The usual high-voltage capacity circuit, as that of an electrostatic machine, while of very small inductance, also is of very smal ...", "... t is, the circuit stores appreciable energy only by the magnetic field. A circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectric field. The usual high-voltage capacity circuit, as that of an electrostatic machine, while of very small inductance, also is of very small resistance, and the momentary discharge currents may be very consider- able, so that in spite of the very small inductance, considerable magnetic-energy ...", "... g. 10, a continuous voltage eo be im- pressed upon a wire coil of resistance r and inductance L (but A current Iq = — flows through the coil and % t 1 % io A C c c ..1. 1 Fig. 10. — Magnetic Single-energy Transient. negligible capacity), a magnetic field $0 10' Lio interlinks with the coil. Assuming now that the voltage eo is suddenly withdrawn, without changing 19 20 ELECTRIC DISCHARGES, WAVES AND IMPULSES. the constants of the coil circuit, as for instance by short- ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1531-2161", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "snippets": [ "... ity is small, due to the limited extent of the circuit, resulting from the low voltage, and at the low voltage the dielectric energy thus is negligible, that is, the circuit stores appreciable energy only by the magnetic field. A circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectric field. The usual high-voltage capacity circuit, as that of an electrostatic machine, while of very small inductance, also is of very smal ...", "... t is, the circuit stores appreciable energy only by the magnetic field. A circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectric field. The usual high-voltage capacity circuit, as that of an electrostatic machine, while of very small inductance, also is of very small resistance, and the momentary discharge currents may be very consider- able, so that in spite of the very small inductance, considerable __ magnetic-en ...", "... ^ oscillations appear, as in the dis- ' ~ charge of the Leyden jar. Fig 10._Magnetie Single.energy Let, as represented in Fig. 10, Transient, a continuous voltage e0 be im- pressed upon a wire coil of resistance r and inductance L (but negligible capacity). A current iQ = — flows through the coil and a magnetic field $0 10~8 = - - interlinks with the coil. Assuming now that the voltage e0 is suddenly withdrawn, without changing 19 20 ELECTRIC DISCHARGES, WAVES AND IMPULSES. the constants of the c ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-02", "section_label": "Lecture 2: Conclusions From The Relativity Theory", "section_title": "Conclusions From The Relativity Theory", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 736-2388", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... ght or two alternating currents) may be anything between their sum and their difference. Thus the two alternating currents consumed by two incandescent lamps add, being in phase; the two alternating currents consumed respectively by an inductance and by a capacity subtract, giving a resultant equal to their difference; that is, if they are equal, they extinguish each other. The phenomenon of interference thus leads to the wave theory of light. If light is a wave motion, there must be something to move, and this h ...", "... (permeability, or specific inductance, and permittivity, or specific capac- ity), and the velocity of propagation of the electromagnetic field — that is, the velocity of light — ^thus is: 1 c = ~7E=^ = 3 X IQio cm., where L is the inductance, C the capacity per unit space. As has been seen, the velocity of light has nothing to do with any rigidity and elasticity constants of matter, but is merely a function of the electromagnetic field constants of space. Lack of familiarity with the conception of the ene ...", "... 4^-% and thus becomes infinite, for y = c, the velocity of light. This energy, for y = 0, or the mass at rest, becomes: Eoo = wc^, which may be considered as the ''kinetic energy of mass,\" while m is a constant, similar to permeability or specific capacity. The kinetic energy required to give a mass m the relative velocity v then is given by: hi = — , — mc^. This expanded into a series gives: rp _ mv'^ . 3 my^ . _ mv\"^ fi i 3 y^ , | ^-\"^ + 8^+ • • • \"\"2\"r + 8c^+ • • •} The second term already is ne ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-108", "section_label": "Apparatus Section 2: Induction Machines: Polyphase Induction Motor", "section_title": "Induction Machines: Polyphase Induction Motor", "kind": "apparatus-section", "sequence": 108, "number": 2, "location": "lines 19166-20427", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-108/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-108/", "snippets": [ "... as the insertion of resistance in the primary circuit. 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 FIG. 180. — Induction motor starting torque with resistance secondary. in the Capacity inserted in the secondary very greatly increases the torque within the narrow range of capacity corresponding to resonance with the internal reactance of the motor, and the torque which can be produced in this way is far ...", "... 3.5 4.0 4.5 5.0 FIG. 180. — Induction motor starting torque with resistance secondary. in the Capacity inserted in the secondary very greatly increases the torque within the narrow range of capacity corresponding to resonance with the internal reactance of the motor, and the torque which can be produced in this way is far in excess of the maximum torque of the motor when running or when starting with resistance in ...", "... far in excess of the maximum torque of the motor when running or when starting with resistance in the secondary. 326 ELEMENTS OF ELECTRICAL ENGINEERING But even at its best value, the torque efficiency available with capacity in the secondary is below that available with resistance. For further discussion of the polyphase inductance motor, see \"Theory and Calculation of Alternating-current Phenomena.\"" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-29", "section_label": "Apparatus Section 8: Synchronous Machines: Characteristic Curves of Synchronous Motor", "section_title": "Synchronous Machines: Characteristic Curves of Synchronous Motor", "kind": "apparatus-section", "sequence": 29, "number": 8, "location": "lines 9399-9553", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-29/", "snippets": [ "... ttless currents of induction motors, etc. Synchronous machines used merely for supplying wattless currents, that is, synchronous motors or generators running light, with over-excited or under-excited field, are called synchronous condensers. They are used as exciters for induc- tion generators, as compensators for the reactive lagging currents SYNCHRONOUS MACHINES 147 of induction motors, for voltage control of transmission lines, etc. Sometimes they are cal ...", "... used as exciters for induc- tion generators, as compensators for the reactive lagging currents SYNCHRONOUS MACHINES 147 of induction motors, for voltage control of transmission lines, etc. Sometimes they are called \"rotary condensers\" or \"dynamic condensers\" when used only for producing lead- ing currents.", "... duc- tion generators, as compensators for the reactive lagging currents SYNCHRONOUS MACHINES 147 of induction motors, for voltage control of transmission lines, etc. Sometimes they are called \"rotary condensers\" or \"dynamic condensers\" when used only for producing lead- ing currents." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-19", "section_label": "Chapter 19: Commutatob Motobs", "section_title": "Commutatob Motobs", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 21339-22387", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "snippets": [ "... e magnetism of the field should be approxi- mately in phase with the impressed E.M.F., that is, the field reactance negligible. Since the self-induction of the field is far in excess to its resistance, this requires the insertion of negative reactance, or capacity, in the field. If the self-induction of the field circuit is balanced by capacity, the motor will operate, provided that the armature reactance is low, and that in starting sufficient resistance is inserted in the armature circuit to keep the armature c ...", "... ., that is, the field reactance negligible. Since the self-induction of the field is far in excess to its resistance, this requires the insertion of negative reactance, or capacity, in the field. If the self-induction of the field circuit is balanced by capacity, the motor will operate, provided that the armature reactance is low, and that in starting sufficient resistance is inserted in the armature circuit to keep the armature current approximately in phase with the E.M.F. Under these conditions the equations o ...", "... mature current approximately in phase with the E.M.F. Under these conditions the equations of the motor will be similar to those of the series motor. However, such motors have not been introduced, due to the difficulty of maintaining the balance between capacity and self-induction in the field circuit, which depends upon the square of the frequency, and thus is disturbed by the least change of frequency. The main objection to both series and shunt motors is the destructive sparking at the commutator due to the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-20", "section_label": "Chapter 20: Commutator Motors", "section_title": "Commutator Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 19458-20501", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "snippets": [ "... e magnetism of the field should be approxi- mately in phase with the impressed E.M.F., that is, the field reactance negligible. Since the self-induction of the field is far in excess to its resistance, this requires the insertion of negative reactance, or capacity, in the field. If the self-induction of the field circuit is balanced by capacity, the motor will operate, provided that the armature reactance is low, and that in starting sufficient resistance is inserted in the armature circuit to keep the armature c ...", "... ., that is, the field reactance negligible. Since the self-induction of the field is far in excess to its resistance, this requires the insertion of negative reactance, or capacity, in the field. If the self-induction of the field circuit is balanced by capacity, the motor will operate, provided that the armature reactance is low, and that in starting sufficient resistance is inserted in the armature circuit to keep the armature current approximately in phase with the E.M.F. Under these conditions the equations o ...", "... mature current approximately in phase with the E.M.F. Under these conditions the equations of the motor will be similar to those of the series motor. However, such motors have not been introduced, due to the difficulty of maintaining the balance between capacity and self-induction in the field circuit, which depends upon the square of the frequency, and thus is disturbed by the least change of frequency. The main objection to both series and shunt motors is the destructive sparking at the commutator due to the ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-08", "section_label": "Chapter 4: Distributed Capacity Of High-Potential Trans Former. 342", "section_title": "Distributed Capacity Of High-Potential Trans Former. 342", "kind": "chapter", "sequence": 8, "number": 4, "location": "lines 875-887", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-08/", "snippets": [ "CHAPTER IV. DISTRIBUTED CAPACITY OF HIGH-POTENTIAL TRANS- FORMER. 342 40. The transformer coil as circuit of distributed capacity, and the character of its capacity. 342 41. The differential equations of the transformer coil, and their integral equations. 344 42. Terminal conditio ...", "CHAPTER IV. DISTRIBUTED CAPACITY OF HIGH-POTENTIAL TRANS- FORMER. 342 40. The transformer coil as circuit of distributed capacity, and the character of its capacity. 342 41. The differential equations of the transformer coil, and their integral equations. 344 42. Terminal conditions and final approximate equations. 346" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-55", "section_label": "Chapter 6: Transition Points And The Complex Circuit", "section_title": "Transition Points And The Complex Circuit", "kind": "chapter", "sequence": 55, "number": 6, "location": "lines 32709-33527", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "snippets": [ "... uit, and across transition points, at which the circuit constants change, and the same equations (266) and (267) apply throughout the entire circuit. In this case, however, in any section of the circuit, (268) where Lt and Ct are the inductance and the capacity, respect- ively, of the section i of the circuit, per unit length, for instance, per mile, in a line, per turn in a transformer coil, etc. In a complex circuit the time variable t is the same throughout the entire circuit, or, in other words, the frequen ...", "... conductor may be unknown. For instance, choosing the total length of conductor in the high-potential transformer as unit length, then the length of the transformer winding in the velocity measure ^ is >10 = \\/L0C0, where L0 — total inductance, C0 = total capacity of transformer. The introduction of the distance variable ^ thus permits the representation in the circuit of apparatus as reactive coils, etc., in which one of the constants is very small compared with the other and therefore is usually neglected and t ...", "... tus as reactive coils, etc., in which one of the constants is very small compared with the other and therefore is usually neglected and the apparatus considered as \"massed inductance,'7 etc., and allows the investi- gation of the effect of the distributed capacity of reactive coils and similar matters, by representing the reactive coil as a finite (frequently quite long) section ^0 of the circuit. 43. Let y*0, Av >^2, ... kn be a number of transition points at which the circuit constants change and the quantities ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-05", "section_label": "Chapter 6: Empirical Curves", "section_title": "Empirical Curves", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 16483-21988", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-05/", "snippets": [ "... ditions on which the rational law is based are rarely perfectly fulfilled. For instance, the representation of a decaying current by an exponential fimction is based on the assumption that the resistance and the inductance of the cu'cuit are constant, and capacity absent, and none of these conditions can ever be perfectly satisfied, and thus a deviation occurs from the theoretical condition, by what is called \" secondary effects.\" 143. To derive an equation, which represents an empirical curve, careful considerati ...", "... \\% EMPIRICAL CURVES, 239 which is the equation of the magnetite arc volt-ampere charac- teristic. 155. Example 3. The change of current resulting from a change of the conditions of an electric circuit containing resist- ance, inductance, and capacity is recorded by oscillograph and gives the curve reproduced as I in Fig. 81. From this curve log ■\\ \"^ _^ ^ H V i \\ \\ s 0 A 1 \\ \\^ N \\ \\ \\ \\ \\, \\ \\ N \\^ ] r \\ V \\ II \\ 1 n —) V*- \\ N ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... 3 or 4 times normal current, or whether it is 40 to 50 times normal current, but it is immaterial whether it is 45 to 46 or 50 times normal. In studying lightning phenomena, and, in general, abnormal voltages in electric systems, calculating the discharge capacity of lightning arres- ters, etc., the magnitude of the quantity is often sufficient. In 254 ^ ENGINEERING MATHEMATICS. calculating the critical speed of turbine alternators, or the natural period of oscillation of synchronous machines, the same applies, ...", "... th curve. If the entire curve is irregular, the calculation should be thrown away, and the entire work done anew, and if this happens repeatedly with the same calculator, the calculator is advised to find another position more in agreement with his mental capacity. If a single point of the curve appears irregular, this points to an error in its calculation, and the calculation of the point is checked; it the error is not found, this point is calculated entirely separately, since it is much more difficult to find an ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-08", "section_label": "Lecture 8: Generation", "section_title": "Generation", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 3781-4217", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-08/", "snippets": [ "... ations to withstand reciprocating strains. d. Greater reliability of operation and far less attend- ance required. The steam turbine reaps a far greater benefit in economy than the steam engine from superheat of the steam, and from a high vacuum in the condenser. Some of the disadvantages of the steam turbine are : a. It is a new type of machine, developed only within the last ten years, and operating engineers and attendants are therefore less familiar with it than with the reciprocating engine ; and the stea ...", "... he boilers of the most efficient steam turbine. The cause is that the gas engine works over a far greater temperature range than the steam engine and even the steam turbine — although the latter, by its ability to economic- ally utilize superheat and high condenser vacuum, gets the benefit of a larger temperature range over the steam engine. If therefore the gas engine were not so very greatly handi- capped in every other respect, it would long have superseded the steam engine and the steam turbine. The disadvant ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-107", "section_label": "Apparatus Section 1: Induction Machines: General", "section_title": "Induction Machines: General", "kind": "apparatus-section", "sequence": 107, "number": 1, "location": "lines 18949-19165", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-107/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-107/", "snippets": [ "... winding the current is lagging nearly 90 deg., as magnetizing current. Thus field and armature would be out of phase with each other. To overcome this objection either there is inserted in series with the field circuit a condenser of such capacity as to bring the current back into p>hase with the voltage, or the field may be excited from a separate e.m.f. differing 90 deg. in phase from that supplied to the armature. The former arrange- ment has ...", "... t is lagging nearly 90 deg., as magnetizing current. Thus field and armature would be out of phase with each other. To overcome this objection either there is inserted in series with the field circuit a condenser of such capacity as to bring the current back into p>hase with the voltage, or the field may be excited from a separate e.m.f. differing 90 deg. in phase from that supplied to the armature. The former arrange- ment has the disadvantage o ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-110", "section_label": "Apparatus Section 4: Induction Machines: Induction Generator", "section_title": "Induction Machines: Induction Generator", "kind": "apparatus-section", "sequence": 110, "number": 4, "location": "lines 21158-21588", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-110/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-110/", "snippets": [ "... ynchronous alternating- current generators operated in parallel with the induction gen- erator, in which latter case, however, these currents can be said to come from the synchronous alternator as lagging currents. Electrostatic condensers, as an underground cable system, may also be used for excitation, but in this case besides the condensers a synchronous machine or other means is required to secure stability. The induction machine may thus be considered ...", "... case, however, these currents can be said to come from the synchronous alternator as lagging currents. Electrostatic condensers, as an underground cable system, may also be used for excitation, but in this case besides the condensers a synchronous machine or other means is required to secure stability. The induction machine may thus be considered as consuming a lagging reactive magnetizing current at all speeds, and con- suming a power current below syn ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-12", "section_label": "Theory Section 12: Impedance of Transmission Lines", "section_title": "Impedance of Transmission Lines", "kind": "theory-section", "sequence": 12, "number": 12, "location": "lines 3761-4464", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-12/", "snippets": [ "... ne current; E = the e.m.f. at receiving end of the line, and 6 = the angle of lag of current 7 behind e.m.f. E. B < 0 thus denotes leading, 0 > 0 lagging current, and 6 = 0 a non-in- ductive receiver circuit. The capacity of the transmission 0 line shall be considered as negligible. FIG. 27.— Vector diagram ,1 i f , v i. of current and e.m.fs. in a _Assummg the phase of the current transmission line assuming QI ...", "... sidered as negligible. FIG. 27.— Vector diagram ,1 i f , v i. of current and e.m.fs. in a _Assummg the phase of the current transmission line assuming QI = / as zero in the polar diagram, zero capacity. Fig. 27, the e.m.f. E is represented by vector OE, ahead of 07 by angle 0. The e.m.f. consumed by re- sistance r is OEi = Ei = Ir in phase with the current, and the e.m.f. consumed by reactance x is OE% = Ez = I ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-19", "section_label": "Theory Section 19: Fields of Force", "section_title": "Fields of Force", "kind": "theory-section", "sequence": 19, "number": 19, "location": "lines 7737-7990", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-19/", "snippets": [ "... that is, the forces greater. FIG. 46. — A mathematical plot of fields shown in C. Magnetic fields may be demonstrated by iron filings brought into the field; dielectric fields by particles of a material of high specific capacity, such as mica. Fig. 45 shows the dielectric field of a pair of parallel conductors, the magnetic field between these conductors, and their combination. Fig. 46 shows the same as calculated. As further illustration, Fig. 47 ...", "... quantity. Proportional thereto by a numerical factor is the dielectric quantity: dielectric field intensity K = . 2, and if k is the dielectric conductivity of the medium in the dielectric field, called specific capacity or permittivity, the dielectric flux density is D = kK, and the total dielectric flux ^ is flux density times area. Here again, at the transition from the electric quantity \"gradient\" to the dielectric quantity \" field in ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-20", "section_label": "Theory Section 20: Nomenclature", "section_title": "Nomenclature", "kind": "theory-section", "sequence": 20, "number": 20, "location": "lines 7991-8291", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-20/", "snippets": [ "... quantity or charge Dielectric density Dielectric field inten- Lines of dielectric force Coulombs Dielectric lines per cm.2 Coulombs per cm.2 Dielectric Dielectric Dielectric k sity Permittivity Dielectric Specific capacity 120 ELEMENTS OF ELECTRICAL ENGINEERING TABLE OF SYMBOLS. Continued Symbol Name Unit Character 9 Dielectric gradient Volts per centimeter Electrical Voltage gradient Electrifying force C Capacity Farad; micro ...", "... ric Specific capacity 120 ELEMENTS OF ELECTRICAL ENGINEERING TABLE OF SYMBOLS. Continued Symbol Name Unit Character 9 Dielectric gradient Volts per centimeter Electrical Voltage gradient Electrifying force C Capacity Farad; microfarad Dielectric P,P Power, effect Watt; kilowatt General W,w.... Energy, work Joule; kilo joule General T,# Temperature Degrees Centigrade General t Time Seconds General $,$,0... Time angle Deg ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-11", "section_label": "Chapter 11: Phase Control", "section_title": "Phase Control", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 9767-10717", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-11/", "snippets": [ "... g for the impedance of the motor). Phase control of transmission lines is especially suited for circuits supplying synchronous motors or converters; since such machines, in addition to their mechanical or electrical load, can with a moderate increase of capacity carry or produce con- siderable values of wattless current. For instance, a quadrature component of current equal to 50 per cent, of the power com- ponent of current consumed by a synchronous motor would increase the total current only to VI 4- 0.5^ = 1.1 ...", "... ue of i^, and where very great overload capacities are required, i„i may not be sufficient, and ii may have to be chosen corresponding to full-load and a higher value of i'o permitted, that is, some sacrifice made in the power-factor, in favor of overload capacity. So, for instance, the values may be chosen ii, corresponding to full-load, and required that i'o does not exceed half of full-load current; i'o < 0.5ii, and that the synchronous converter or motor can carry at least 100 per cent, overload, that is, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-32", "section_label": "Chapter 32: Transformation Of Polyphase Systems", "section_title": "Transformation Of Polyphase Systems", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 36062-36514", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-32/", "snippets": [ "... ransformers is frequently used in long-distance transmissions, to allow grounding of the high-potential neutral. Under certain conditions — which there- fore have to be guarded against — it is liable to induce excessive voltages by resonance with the line capacity. J_I_i P^^lIM nm Fig. 210. The reverse thereof, or the Y-delta connection, is undesirable on unbalanced load, since it gives what has been called a \"float- ing neutral;\" the three primary Y voltages do not remain even approximately constant, ...", "... erate inequality of load, and the system thus loses all ability to maintain constant voltage at unequal distribution of load, that is, becomes inoperative. In high-potential systems in this case excessive voltages may be induced by resonance with the line capacity. For instance, if only one phase of the secondary triangle is 426 ALTERNATING-CURRENT PHENOMENA loaded, the other two unloaded, the primary current of the loaded phase must return over the other two transformers, which, at open secondaries, act as ve ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-04", "section_label": "Chapter 4: Graphic Befrisxintation", "section_title": "Graphic Befrisxintation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2122-2743", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "snippets": [ "... nductive line is greater, if the receiving circuit is inductive, than if it is non-inductive. From ¥\\g, 16, — Eo = V(^ cos a> + Jry + {E^m u> -f Jx)\\ Fig. 16. If, however, the current in the receiving circuit is leading, as is the case when feeding condensers or syn- chronous motors whose counter E.M.F. is larger than the -impressed E.M.F., then the E.M.F. will be represented, in Fig. 17, by a vector, OEy lagging behind the current, Oly by the angle of lead w; and in this case we get, by combining OE with OE^ ...", "... current and primary E.M.F. required to produce in the secondary circuit the ^ame E.M.F. and current ; or conversely, at a given primary >A Flq, 20. impressed E.M.F., E^^ the secondary E.M.F., E^, will be smaller with an inductive, and larger with a condenser (leading current) load, than with a non-inductive load. At the same time we see that a difference of phase existing in the secondary circuit of a transformer reappears / V 82 AL TERNA TING-CURRENT PHENOMENA, [§ 22 in the primary circuit, somewh ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-09", "section_label": "Chapter 9: Kbsistanci: And Kbactance Of Transmission Iine8", "section_title": "Kbsistanci: And Kbactance Of Transmission Iine8", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 6371-8268", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "snippets": [ "... nd non- inductive receiver circuit, or a non-inductive receiver circuit and a non-inductive line. In conclusion, it may be remarked here that of the sources of susceptance, or reactance, a choking coil or reactive coil corresponds to an inductance ; a condenser corresponds to a condensance ; a polarization cell corresponds to a condensance ; a synchronizing alternator (motor or generator) corresponds to an inductance or a condensance, at will ; an induction motor or generator corresponds to an inductance or ...", "... or generator) corresponds to an inductance or a condensance, at will ; an induction motor or generator corresponds to an inductance or condensance, at will. The choking coil and the. polarization cell are specially suited for series reactance, and the condenser and syn- chronizer for shunted susceptance. 104 ALTERNATING-CURRENT PHENOMENA. . [§ 72" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-13", "section_label": "Chapter 13: Ths Alternating^Cnrrent Traxsfobmer", "section_title": "Ths Alternating^Cnrrent Traxsfobmer", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 12673-14088", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "snippets": [ "... en the load is changed from full load, /j = 60 amperes in a non-inductive secondary external circuit to no load or open circuit. a.) By increase of secondary resistance ; 6.) by increase of secondary inductive reactance ; c.) by increase of sec- ondary capacity reactance. As shown in a.), the locus of the secondary terminal vol- tage, ^j-, and thus of E^y etc., are straight lines; and in d.) and c), parts of one and the same circle a.) is shown i 123] ALTERNATING-CURRENT TRANSFORMER. 177 in full lines, ...", "... here are now directly appli- cable to the transformer, giving the variation and the con- trol of secondary terminal voltage, resonance phenomena, etc. Thus, for instance, if Z( = Z^, and the transformer con- tains a secondary coil, constantly closed by a condenser reactance of such size that this auxiliary circuit, together with the exciting circuit, gives the reactance —x^y with a non-inductive secondary circuit Z^ = /-p we get the condi- tion of transformation from constant primary potential to constant secondar ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-16", "section_label": "Chapter 16: Aiitebnatingh-Current Osnebator", "section_title": "Aiitebnatingh-Current Osnebator", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 17025-18828", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "snippets": [ "... ty at the trailing-pole corner. Since the internal self- inductance of the alternator alone causes a certain lag of the current behind the induced E.M.F., this condition of no displacement can exist only in a circuit with external nega- tive reactance, as capacity, etc. If the armature current lags, it reaches the maximum later than the E.M.F. ; that is, in a position where the armature coil partly faces the following-field pole, as shown in diagram in Fig. 111. Since the armature current flows Fiq. Ill, in ...", "... curve at non-inductive load is nearly horizontal at open circuit, nearly vertical at .short circuit, and is similar to an arc of an ellipsis. With reactive load the curves are more nearly straight lines. The voltage drops rapidly on inductive, rises on capacity The output increases from zero at open circuit to a max- imum, and then decreases again to zero at short circuit. 242 ALTERNATIXG-CURREKT PTIEKOMENA. [§164 1 ' i 1 1 1 s 0-2 ELD CMARACTERIS 50O. ZrMOj, r4o, B '^ N N s s \\ ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-21", "section_label": "Chapter 21: Dibtobtiox Of Wavs-Shafe And Its Causes", "section_title": "Dibtobtiox Of Wavs-Shafe And Its Causes", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 23274-24559", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "snippets": [ "... r equivalent sine waves, and the investigation with suffi- cient exactness for most cases be carried out under the assumption of sine waves, as done in the preceding chapters. Similar phenomena take place in circuits containing polarization cells, leaky condensers, or other apparatus representing a synchronously varying negative reactance. Possibly dielectric hysteresis in condensers causes a dis- tortion similar to that due to magnetic hysteresis. Pulsation of Resistance, 219. To'a certain extent the investigat ...", "... tion of sine waves, as done in the preceding chapters. Similar phenomena take place in circuits containing polarization cells, leaky condensers, or other apparatus representing a synchronously varying negative reactance. Possibly dielectric hysteresis in condensers causes a dis- tortion similar to that due to magnetic hysteresis. Pulsation of Resistance, 219. To'a certain extent the investigation of the effect of synchronous pulsation of the resistance coincides with that of reactance ; since a pulsation of react ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-04", "section_label": "Chapter 4: Graphic Representation", "section_title": "Graphic Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 1743-2321", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "snippets": [ "... ctive line is greater, if the receiving circuit is inductive, than if it is non-inductive. From Fig. 16, — E0 = V(^ cos w + Ir)2 -f- (E sin w + Ix)z. Fig. 18. If, however, the current in the receiving circuit is leading, as -is the case when feeding condensers or syn- chronous motors whose counter E.M.F. is larger than the impressed E.M.F., then the E.M.F. will be represented, in Fig. 17, by a vector, OE, lagging behind the current, Of, by the angle of lead £'; and in this case we get, by combining OE with OEr ...", "... rimary current and primary E.M.F. required to produce in the secondary circuit the same E.M.F. and current ; or conversely, at a given primary Fig. 20. impressed E.M.F., E0, the secondary E.M.F., E^ will be smaller with an inductive, and larger with a condenser (leading current) load, than with a non-inductive load. At the same time we see that a difference of phase existing in the secondary circuit of a transformer reappears 32 AL TERNA TING-CURRENT PHENOMENA. in the primary circuit, somewhat decreased if ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-09", "section_label": "Chapter 9: Resistance And Reactance Of Transmission Lines", "section_title": "Resistance And Reactance Of Transmission Lines", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 5334-6956", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "snippets": [ "... II.) ; the condition b = 0, b0 = 0, or a non-inductive line and non- inductive receiver circuit. In conclusion, it may be remarked here that of the sources of susceptance, or reactance, a choking coil or reactive coil corresponds to an inductance ; a condenser corresponds to a condensance ; a polarization cell corresponds to a condensance ; a synchronizing alternator (motor or generator) corresponds to an inductance or a condensance, at will; an induction motor or generator corresponds to an inductance. Th ...", "... hronizing alternator (motor or generator) corresponds to an inductance or a condensance, at will; an induction motor or generator corresponds to an inductance. The choking coil and the polarization cell are specially suited for series reactance, and the condenser and syn- chronizer for shunted susceptance. 104 ALTERNATING-CURRENT PHENOMENA." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-14", "section_label": "Chapter 14: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 11605-12682", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "snippets": [ "... en the load is changed from full load, /j = 60 amperes in a non-inductive secondary external circuit to no load or open circuit. a.) By increase of secondary resistance ; b.} by increase of secondary inductive reactance ; c.) by increase of sec- ondary capacity reactance. As shown in a.), the locus of the secondary terminal vol- tage, J5lt and thus of E0, etc., are straight lines; and in b.) and c.}, parts of one and the same circle a.} is shown AL TERNA TING-CURRENT TRANSFORMER. 203 in full lines, b.} ...", "... directly appli- cable to the transformer, giving the variation and the con- trol of secondary terminal voltage, resonance phenomena, etc. Thus, for instance, if Z/ = Z0, and the transformer con- tains an additional secondary coil, constantly closed by a condenser reactance of such size that this auxiliary circuit, together with the exciting circuit, gives the reactance — x0, . with a non-inductive secondary circuit Z^ = rv we get the • condition of transformation from constant primary potential to constant seconda ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-22", "section_label": "Chapter 22: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 21190-21982", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "snippets": [ "... r equivalent sine waves, and the investigation with suffi- cient exactness for most cases be carried out under the assumption of sine waves, as done in the preceding chapters. Similar phenomena take place in circuits containing polarization cells, leaky condensers, or other apparatus representing a synchronously varying negative reactance. Possibly dielectric hysteresis in condensers causes a dis- tortion similar to that due to magnetic hysteresis. Pulsation of Resistance. 240. To a certain extent the investigat ...", "... tion of sine waves, as done in the preceding chapters. Similar phenomena take place in circuits containing polarization cells, leaky condensers, or other apparatus representing a synchronously varying negative reactance. Possibly dielectric hysteresis in condensers causes a dis- tortion similar to that due to magnetic hysteresis. Pulsation of Resistance. 240. To a certain extent the investigation of the effect of synchronous pulsation of the resistance coincides with that of reactance ; since a pulsation of react ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-17", "section_label": "Chapter 19: Alternating- Current Motors In General", "section_title": "Alternating- Current Motors In General", "kind": "chapter", "sequence": 17, "number": 19, "location": "lines 21713-23905", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-17/", "snippets": [ "... ng the action of the motor at intermediate and at low speed, as for instance, when investigating the performance of a starting device, in bringing the motor up to speed, that is, during acceleration, this method so is more suited. An applica- tion to the \"condenser motor,\" that is, a single-phase induction motor using a condenser in a stationary tertiary circuit (under an angle, usually 60°, with the primary circuit) is given in the paper on \"Alternating-Current Motors,\" A. I. E. E. Transac- tions, 1904. P&D F ...", "... r instance, when investigating the performance of a starting device, in bringing the motor up to speed, that is, during acceleration, this method so is more suited. An applica- tion to the \"condenser motor,\" that is, a single-phase induction motor using a condenser in a stationary tertiary circuit (under an angle, usually 60°, with the primary circuit) is given in the paper on \"Alternating-Current Motors,\" A. I. E. E. Transac- tions, 1904. P&D Fig. 151. 180. As example are shown, in Fig. 151, with the speed a ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-22", "section_label": "Chapter 24: Conclusion", "section_title": "Conclusion", "kind": "chapter", "sequence": 22, "number": 24, "location": "lines 32820-33531", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-22/", "snippets": [ "... alternator, 279 Amplifier, 281 Arc rectifier, 248 Armature reaction of regulating pole converter, 426, 437 of unipolar machine, 457 B Balancer, phase, 228 Battery charging rectifier, 244 Brush arc machine as quarterphase rectifier, 244, 254 Capacity storing energy in phase conversion, 212 Cascade control, see Concatenation. Coil distribution giving harmonic torque in induction motor, 151 Commutating e.m.f. in rectifier, 239 field, singlephase commutator motor, 355, 359 machine, concatena ...", "... duction motor, 54, 89 induction generator, 200 leads, singlephase commutator motor, 351 motors, singlephase, 331 Compensated series motor, 372 Compensating winding, singlephase commutator motor, 336, 338 Concatenation of induction motors, 14, 40 Condenser excitation of induction motor secondary, 55, 84 singlephase induction motor, 120 speed control of induction motor, 13, 16 Contact making rectifier, 245 Cumulative oscillation of synchro- nous machine, 299 D Deep bar rotor of induction motor, 11 ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-08", "section_label": "Chapter 8: Shaping Of Waves By Magnetic Saturation", "section_title": "Shaping Of Waves By Magnetic Saturation", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 12962-16963", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-08/", "snippets": [ "... s, a sine wave of voltage impressed upon the reactance; or constant current, that is, a sine wave of current traversing the circuit; or any intermediate condition, such as brought about by the insertion of various amounts of resistance, or of reactance or capacity, in series to the closed magnetic cir- cuit reactance. The numerical values in Table III illustrate this. / gives the magnetic field intensity, and thus the direct current. SHAPING OF WAVES BY MAGNETIC SATURATION 133 which produces the magnetic dens ...", "... , / ^ N V B/ \\ ^ // \\t ^^=?rT\" / 1 a^ ^ \\ 5= \" 1 i / r*° U- ^ s // ^ ) // ^ V y ! frequencies with which the high-voltage coils of transformers, as circuits of distributed capacity, can resonate. 76. Magnetic saturation, and closed or partly closed magnetic circuits thus are a likely source of wave-shape distortion, resulting in high voltage peaks, and where they are liable to occur, as in 152 ELECTRIC CIRCUITS current transfor ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-35", "section_label": "Chapter 13: Transient Term Of The Rotating Field", "section_title": "Transient Term Of The Rotating Field", "kind": "chapter", "sequence": 35, "number": 13, "location": "lines 13936-14548", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-35/", "snippets": [ "... closed, and that this tran- sient term is oscillatory. In the preceding chapter, in circuits containing only resistance and inductance, the transient term has always been gradual or logarithmic, and oscillatory phenom- ena occurred only in the presence of capacity in addition to in- ductance. In the rotating field, or the polyphase m.m.f., we thus have a case where an oscillatory transient term occurs in a circuit containing only resistance and inductance but not capacity, and where this transient term is independe ...", "... enom- ena occurred only in the presence of capacity in addition to in- ductance. In the rotating field, or the polyphase m.m.f., we thus have a case where an oscillatory transient term occurs in a circuit containing only resistance and inductance but not capacity, and where this transient term is independent of the point of the wave at which the circuits were closed, that is, is always the same, regardless of the moment of start of the phe- nomenon. The transient term of the polyphase m.m.f. thus is independ- en ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-37", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 37, "number": 1, "location": "lines 15354-15625", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "snippets": [ "... thus be produced. On this principle, for instance, operated the controlling solenoid of the Thomson-Houston arc machine, and also numerous auto- matic potential regulators. 2. Production of high frequency oscillating currents by period- ically recurring condenser discharges has been discussed under \" oscillating current generator,\" in Section I, paragraph 44. Non-sinusoidal high frequency alternating currents are pro- duced by an arc, when made unstable by shunting it with a condenser, as discussed before. The ...", "... by period- ically recurring condenser discharges has been discussed under \" oscillating current generator,\" in Section I, paragraph 44. Non-sinusoidal high frequency alternating currents are pro- duced by an arc, when made unstable by shunting it with a condenser, as discussed before. The Ruhmkorff coil or inductorium also represents an appli- cation of periodically recurring transient phenomena, as also does Prof. E. Thomson's dynamostatic machine. 3. By reversing the connections between a source of alter- I ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-41", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 41, "number": 1, "location": "lines 19260-19338", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "snippets": [ "... method of treatment and the general form of the equations are the same as with transient functions of time. 2. Some of the cases in which transient phenomena in space are of importance in electrical engineering are : (a) Circuits containing distributed capacity and self-induc- tance, as long-distance energy transmission lines, long-distance telephone circuits, multiple spark-gaps, as used in some forms of high potential lightning arresters (multi-gap arrester), etc. (b) The distribution of alternating current i ...", "... of power consumption resulting therefrom. (d) The distribution of the electric field of a conductor through space, resulting from the finite velocity of propagation of the electric field, and the variation of self-inductance and mutual inductance and of capacity of a conductor without return, as function of the frequency, in its effect on wireless telegraphy. (e) Conductors conveying very high frequency currents, as lightning discharges." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-10", "section_label": "Chapter 9: America in the Individualistic Era", "section_title": "America in the Individualistic Era", "kind": "chapter", "sequence": 10, "number": 9, "location": "lines 4268-4715", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-10/", "snippets": [ "... Finally, in the 90's the end was reached; especially in those industries which had been organized into a few large corporations. The necessity of keeping the factories going, with the steadily increasing excess of productive capacity over the demand for the products, had made competition so vicious that it threatened with destruction the victor as well as the van- quished, in a universal v.Tcck of the industry. Thus co-operation had to come, of neces- ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-15", "section_label": "Chapter 14: Evolution: Inhibitory Power", "section_title": "Evolution: Inhibitory Power", "kind": "chapter", "sequence": 15, "number": 14, "location": "lines 6233-6597", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-15/", "snippets": [ "... ividualistic age. At least, so it appears. It might be called an aristocratic democracy, using the term aristocratic in its original mean- ing, that the influence of the individual on so- ciety should be proportional to his capacity — democratic; everybody has the same chance, the same right, and there is no discrimination — egalite; everybody is free to choose his ac- tivity, to develop his individuality — liberie; everybody is guaranteed in his standar ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-18", "section_label": "Chapter 17: Conclusion", "section_title": "Conclusion", "kind": "chapter", "sequence": 18, "number": 17, "location": "lines 7568-8027", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-18/", "snippets": [ "... our present political govern- ment, and commissions, made as competent and permanent as possible, would take over most of the work of industrial control and operation, the direct elective officials mainly acting in supervisory capacity, directing the policies of the commissions. Such organizations, if once created, would probably be as efficient and sat- isfactory as the industrial government devel- oped from the industrial corporation would be. However, it ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-03-record", "section_label": "Report Record 4: Record of Four Troubles", "section_title": "Record of Four Troubles", "kind": "report-record", "sequence": 4, "number": 4, "location": "PDF pages 16-27, lines 1139-2164", "status": "pdf-text-extracted-candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-03-record/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-03-record/", "snippets": [ "... e between the alternators reduces the synchroniz- ing power by limiting the synchronizing current; too small reactance may again reduce the maximum synchronizing power by lowering the EMF by the large voltage drop due to the large interchange currents. With a capacity of about 60,000 KW per station section and machines of the general characteristics of those involved (100% synchronous reactance, \\2^/^% true reactance, in average) , maximum synchronizing power would require a reactance between each station section and the r ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-05", "section_label": "Lecture 5: Single-Energy Tra.Nsient Of Ironclad Circuit", "section_title": "Single-Energy Tra.Nsient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3387-3720", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-05/", "snippets": [ "... he carrier of the field, etc.; and the proportionality between current or voltage and their respective fields, the magnetic and the dielectric, thus ceases, or, as it may be expressed, the inductance L is not constant, but varies w^ith the current, or the capacity is not constant, but varies with the voltage. The most important case is that of the ironclad magnetic cir- cuit, as it exists in one of the most important electrical apparatus, the alternating-current transformer. If the iron magnetic circuit contains a ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "LECTURE VIII. TRAVELING WAVES. 33. In a stationary oscillation of a circuit having uniformly distributed capacity and inductance, that is, the transient of a circuit storing energy in the dielectric and magnetic field, current and voltage are given by the expression i = ioe-\"^ cos ((/> T CO — 7), ^ . . e = eoe~\"' sin ((^ =F co — 7), where T co — 7), ) where 0 is the time angle, co the ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-04", "section_label": "Chapter 5: Methods Of Approximation", "section_title": "Methods Of Approximation", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 15156-16482", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-04/", "snippets": [ "... 2xa3/4(l+|il)x4(l-|82)xaV4x(l+2^)(l-2j) (1 _ \\4a2 a a J a3/2(l-3s2+2-- + S2--) \\ a a / \\ 4 a. a J 138. As further example may be considered the equations of an alternating-current electric circuit, containing distributed resistance, inductance, capacity, and shunted conductance, for instance, a long-distance transmission line or an underground high-potential cable. Equations of the Transmission Line. Let I be the distance along the line, from some starting point; E^ the voltage; 7, the current at poin ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-04", "section_label": "Lecture 4: The Characteristics Of Space A. The Geometry Of The Gravitational Field", "section_title": "The Characteristics Of Space A. The Geometry Of The Gravitational Field", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3595-6820", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-04/", "snippets": [ "... rnating current, 14 dielectric field, 20 Analogue, 2 dimensional, of uni- verse, 119 Axioms of mathematics, 70 metric, of space, 95, 110 B Beltrami's pseudosphere, 91 Bending of space, 88 Betel geuse, 67 Bolyai, 71 Bullet velocity, 13 C Capacity and wave velocity, 23 Centrifugal field, 47 force and inertia, 49 mass, 47 Characteristic of space, 69 constant of space, 81 Charge, electrostatic, 47 Circle, in centrifugal and gravita- tional field, 62 circumference and diameter, 61 Color, rel ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-01", "section_label": "Lecture 1: General Review", "section_title": "General Review", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 154-565", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-01/", "snippets": [ "... rrent must be supplied from a generating station or a converter substation, that is, a station containing revolv- ing machinery. As such a station requires continuous atterv- GENERAL REVIEW 17 tion, its operation would hardly be economical if not of a capacity of at least some hundred kilowatts. The direct cur- rent distribution system therefore can be used economically only if a sufficient demand exists, within a radius of i to 2 miles, to load a good sized generator or converter substation. The use of direct ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-03", "section_label": "Lecture 3: Light And Power Distribution", "section_title": "Light And Power Distribution", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 983-1526", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-03/", "snippets": [ "... ng current motor is lagging, the voltage drop caused by it in the reactance is therefore far greater than would be caused by the same current taken by a non-inductive load, as lamps. Furthermore, alternating current supply mains usually are of far smaller capacity, and therefore more affected in voltage. Large motors are therefore rarely connected to the lighting mains of an alternating current system, but separate transformers and frequently separate feeders are used for the motors, and very large motors commonly ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-11", "section_label": "Lecture 11: Lightning Protection", "section_title": "Lightning Protection", "kind": "lecture", "sequence": 11, "number": 11, "location": "lines 4931-5294", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-11/", "snippets": [ "... oltage to start a reverse arc. These lightning arresters operated satisfactorily with the smaller machines and circuits of limited power used in the earlier days, but when large machines of close regulation, and therefore of very large momentary overload capacity were in- 138 GENERAL LECTURES troduced, and a number of such machines operated in multiple, these lightning arresters became insufificient : the machine cur- rent following the lightning discharge frequently was so enor- mous that the circuit did not ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-04", "section_label": "Lecture 4: Chemical And Physical Effects Of Radiation", "section_title": "Chemical And Physical Effects Of Radiation", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3639-3945", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-04/", "snippets": [ "... s you see, none of them show any appreciable fluorescence in the mercury light. But if I turn off the mercury light, the calcium sulphide phosphoresces brightly in a blue glow, the others do not. Now I show you all three under the ultra-violet rays of the condenser discharge between iron terminals, or ultra-violet lamp (Fig. 11) and you see all three fluoresce brilliantly, in blue, green and red. Turning off the light all three continue to glow with about the same color, that is, phosphoresce, but the red fluorescen ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-103", "section_label": "Apparatus Section 6: Alternating-current Transformer: Heating and Ventilation", "section_title": "Alternating-current Transformer: Heating and Ventilation", "kind": "apparatus-section", "sequence": 103, "number": 6, "location": "lines 18461-18520", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-103/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-103/", "snippets": [ "... , by the natural ventilation of the air currents pro- duced by the centrifugal forces in rotating apparatus, and it is therefore fortunate that the transformer is the most efficient apparatus (except perhaps the electrostatic condenser) and thus has to dissipate less heat than any other apparatus of the same output. Thus in smaller transformers radiation and the natural convection from the surface are often sufficient to keep the tem- perature within safe ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-104", "section_label": "Apparatus Section 7: Alternating-current Transformer: Types of Transformers", "section_title": "Alternating-current Transformer: Types of Transformers", "kind": "apparatus-section", "sequence": 104, "number": 7, "location": "lines 18521-18665", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-104/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-104/", "snippets": [ "... ell-type three-phase transformer may produce triple frequency voltages, resulting from the triple frequency ALTERNATING-CURRENT TRANSFORMER 299 flux, and under unfavorable conditions, as when connecting to a system of high capacity — which intensifies these voltages — this may lead to destructive voltages, and YY connections with shell-type three-phase transformers thus lead to serious high voltage dangers. 125. The usual shell-type construction of three-p ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-106", "section_label": "Apparatus Section 9: Alternating-current Transformer: Reactors", "section_title": "Alternating-current Transformer: Reactors", "kind": "apparatus-section", "sequence": 106, "number": 9, "location": "lines 18813-18948", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-106/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-106/", "snippets": [ "... to eddy currents in the conductors. 130. A transformer of output P = e2iz has a size of winding space of ezi2 + #iii = 2 e2z*2, that is (with the air gap inserted into the magnetic circuit), gives a reactor of the capacity ei = 2 P. That is, a reactor has the size of a transformer of half its output. Reactors are frequently used in series to apparatus, and the vol- tage consumed by the reactance then varies with the current, and is, due ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-15", "section_label": "Theory Section 15: Load Characteristic of Transmission Line", "section_title": "Load Characteristic of Transmission Line", "kind": "theory-section", "sequence": 15, "number": 15, "location": "lines 5832-6221", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-15/", "snippets": [ "... as is to be expected. At short circuit, e = 0, 0 = \\/#o2 — xzi2 — ri, and ° ; (6) X' that is, the maximum line current which can be established with a non-inductive receiver circuit and negligible line capacity. 71. The condition of maximum 'power delivered over the line '• i| f-* on that is, substituting (3): '! V#o2 - x*i* = e + ri, and expanding, gives e* = (r2 + x2) i2 (8) = z2i2; hence, e — zi, a ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-53", "section_label": "Apparatus Subsection 53: Direct-current Commutating Machines: C. Commutating Machines 185", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 185", "kind": "apparatus-subsection", "sequence": 53, "number": null, "location": "lines 11132-11213", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-53/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-53/", "snippets": [ "... ted so as to produce a commutating flux proportional to the load, and thus giving the required commutating field at all loads. Such machines then give no inductive sparking, but regarding commutation are limited in overload capacity only by the current density under the brush. Such commutating poles are excited by series coils, that is, coils connected in series with the armature and having a number of effective turns higher than the number of effec ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-79", "section_label": "Apparatus Subsection 79: Direct-current Commutating Machines: C. Commutating Machines 219", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 219", "kind": "apparatus-subsection", "sequence": 79, "number": null, "location": "lines 13019-13119", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-79/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-79/", "snippets": [ "... to lag and thereby to be out of phase with the armature current which, to represent work, must essentially be an energy current, and thereby reduces output and efficiency and hence requires some method of compensation, as capacity in series with the field winding or excitation of the field from a quadrature phase of voltage. In the series motor the self-inductance of the field causes the main current to lag behind the impressed voltage and thereby ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-80", "section_label": "Apparatus Subsection 80: Direct-current Commutating Machines: C. Commutating Machines 221", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 221", "kind": "apparatus-subsection", "sequence": 80, "number": null, "location": "lines 13120-13188", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-80/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-80/", "snippets": [ "... In an inductive circuit, the current lags behind the voltage or, what is the same, the voltage leads the current, and the power-factor thus can be raised by compensation either by introducing a leading current, as from condenser or overexcited synchronous motor, or by in- troducing a lagging voltage. In the commutating machines, the voltage induced in the armature by its rotation is in phase with the field magnetism, and by lagging the field exc ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-82", "section_label": "Apparatus Section 3: Synchronous Converters: Variation of the Ratio of Electromotive Forces", "section_title": "Synchronous Converters: Variation of the Ratio of Electromotive Forces", "kind": "apparatus-section", "sequence": 82, "number": 3, "location": "lines 13796-13888", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-82/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-82/", "snippets": [ "... e.m.f. at the con- verter terminals, not only the wave of generator e.m.f., but also that of the converter counter e.m.f., may be instrumental. Thus, with a converter connected directly to a generating system of very large capacity, the impressed e.m.f. wave will be practically identical with the generator wave, while at the terminals of a converter connected to the generator over long lines with re- active coils or inductive regulators interposed, the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-84", "section_label": "Apparatus Section 5: Synchronous Converters: Armature Reaction", "section_title": "Synchronous Converters: Armature Reaction", "kind": "apparatus-section", "sequence": 84, "number": 5, "location": "lines 15161-15475", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-84/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-84/", "snippets": [ "... limitation does not exist in a converter; and a much greater armature reaction can be safely used in converters than in direct-current generators, the dis- tortion being absent in the former. The practical limit of overload capacity of a converter is usu- ally far higher than in a direct-current generator, since the arma- ture heating is relatively small, and since the distortion of field, which causes sparking on the commutator under overloads in a di ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-04", "section_label": "Chapter 4: Vector Representation", "section_title": "Vector Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2149-2759", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-04/", "snippets": [ "... ater if the receiving circuit is inductive than if it is non-inductive. From Fig. 16, Ea = V{E COS 6 4- /r)2 + (E sin 6 + Ixy. If, however, the current in the receiving circuit is leading, as 26 ALTERNATING-CURRENT PHENOMENA is the case when feeding condensers or synchronous motors whose counter e.m.f. is larger than the impressed voltage, then the voltage will be. represented, in Fig. 17, by a vector, OE, lagging behind the current, 01, by the angle of lead, d'; and in this case we get, by combining OE with OE ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-22", "section_label": "Chapter 22: Armature Reactions Of Alternators", "section_title": "Armature Reactions Of Alternators", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 23971-25134", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-22/", "snippets": [ "... t condition. Thus the momentary short- circuit current of an alternator is far greater than the perma- nent short-circuit current; many times in a machine of low self-induction and high armature reaction, as a low-frequency, high-speed alternator of large capacity; relatively little in a machine of low armature reaction and high self-induction, as a high-frequency unitooth alternator, 193. Graphically, the internal reactions of the alternating- current generator can be represented as follows: Let the impressed m ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-23", "section_label": "Chapter 23: Synchronizing Alternators", "section_title": "Synchronizing Alternators", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 25135-25681", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-23/", "snippets": [ "... ll pull, while the other is near the dead- point, and conversely. Consequently, alternately the one alter- nator will tend to speed up and the other slow down, then the other speed up and the first slow down. This effect, if not taken care of by fly-wheel capacity, causes a \"hunting\" or surging 292 SYNCHRONIZING ALTERNATORS 293 action; that is, a fluctuation of the voltage with the period of the engine revolution, due to the alternating transfer of the load from one engine to the other, which may even become s ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-33", "section_label": "Chapter 33: Efficiency Of Systems", "section_title": "Efficiency Of Systems", "kind": "chapter", "sequence": 33, "number": 33, "location": "lines 36515-37127", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-33/", "snippets": [ "... ground and back from ground to conductor. If the system is of considerable extent — as is the case where high voltages of serious disruptive strength have to be considered — • the neutral of the system is maintained at approximate ground potential by the capacity of the system, and the normal voltage stress from conductor to ground therefore is that from conductor to neutral, that is, the same as in a system with grounded neutral, and the basis of comparison then is the voltage from line to ground, and not between ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 3230-3545", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-06/", "snippets": [ "... which may be called the topographic circuit characteristic. Such a characteristic is, for instance, OE^E-IE^E^E^E^^ in Figs. 31 to 34, etc. ; further instances are shown in the following chapters, as curved characteristics in the chapter on distributed capacity, etc. 62 AL TERNA TJNG-CURRENT PHENOMENA. ^ [§ 38" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-14", "section_label": "Chapter 14: The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "section_title": "The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14089-14918", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "snippets": [ "... /yZ = snie \\ 1 ri-jsxi ) _ snie{r^jsx) ^ \\ {ri + r)-'js{xi + x)) (ri+r) ^js{xi + x) ♦ This applies to the case where the secondary contains inductive reac- tance only : or, rather, that kind of reactance which is proportional to the fre- quency. In a condenser the reactance is inversely proportional to the frequency in a synchronous motor under circumstances independent of the frequency. Thus, in general, we have to set, x = x' -^ x\" -^ x''\\ where x' is that part of the reactance which is proportional to the fre ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-17", "section_label": "Chapter 17: Synchbonizino Aiitebkatobs", "section_title": "Synchbonizino Aiitebkatobs", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 18829-19345", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-17/", "snippets": [ "... ll pull, while the other is near the dead-point, and conversely. Consequently, alter- nately the one alternator will tend to speed up and the other slow down, then the other speed up and the first slow down. This effect, if not taken care of by fly-wheel capacity, causes a \"hunting\" or pumping action; that is, a fluctuation of the lights with the period of the engine revo- lution, due to the alternating transfer of the load from one engine to the other, which may even become so excessive as to throw the machines o ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-20", "section_label": "Chapter 20: Beactiox Machines", "section_title": "Beactiox Machines", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 22388-23273", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "snippets": [ "... he current behind the impressed E.M.F. exists ; and an alternating generator will yield an E.M.F. without field excitation, only when closed by an external circuit of large negative reactance; that is, a circuit in which the current leads the E.M.F., as a condenser, or an over-excited synchronous motor, etc. Self-excitation, of the alternator by armature reaction can be explained by the fact that the counter E.M.F. of self-induction is not wattless or in quadrature with the cur- rent, but contains an energy compon ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "section_label": "Chapter 10: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "... mind, however, the existence of a higher harmonic as a possible disturbing factor which may become noticeable in those cases where the frequency of the higher harmonic is near the fre- quency of resonance of the circuit, that is, in circuits con- taining capacity besides the inductance. 79. The equivalent sine wave of exciting current leads the sine wave of magnetism by an angle a, which is called the angle of Jiysteretic advance of phase. Hence the cur- rent lags behind the E.M.F by ^ 90° — a, and the power i ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-15", "section_label": "Chapter 15: The General Alternating-Current Transformer Or Frequency Converter", "section_title": "The General Alternating-Current Transformer Or Frequency Converter", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 12683-13648", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "snippets": [ "... ry impedance Z, + Z= (r, + r) hence, secondary current Secondary terminal voltage * This applies to the case where the secondary contains inductive reac- tance only ; or, rather, that kind of reactance which is proportional to the fre- quency. In a condenser the reactance is inversely proportional to the frequency, in a synchronous motor under circumstances independent of the frequency. Thus, in general, we have to set, x = x' + x\" -\\ x\"\\ where x' is that part of the reactance which is proportional to the freq ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-18", "section_label": "Chapter 18: Synchronizing Alternators", "section_title": "Synchronizing Alternators", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17597-18052", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-18/", "snippets": [ "... ll pull, while the other is near the dead-point, and conversely. Consequently, alter- nately the one alternator will tend to speed up and the other slow down, then the other speed up and the first slow down. This effect, if not taken care of by fly-wheel capacity, causes a \"hunting\" or pumping action; that is, a fluctuation of the lights with the period of the engine revo- lution, due to the alternating transfer of the load from one engine to the other, which may even become so excessive as to throw the machines o ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-21", "section_label": "Chapter 21: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 20502-21189", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-21/", "snippets": [ "... he current behind the impressed E.M.F. exists; and an alternating generator will yield an E.M.F. without field excitation, only when closed by an external circuit of large negative reactance ; that is, a circuit in which the current leads the E.M.F., as a condenser, or an over-excited synchronous motor, etc. Self-excitation of the alternator by armature reaction can be explained by the fact that the counter E.M.F. of self-induction is not wattless or in quadrature with the cur- rent, but contains an energy compone ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-07", "section_label": "Chapter 8: Synchronizing Induction Motors", "section_title": "Synchronizing Induction Motors", "kind": "chapter", "sequence": 7, "number": 8, "location": "lines 13956-14465", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-07/", "snippets": [ "... by (14), (15), and (16): i), = ^6l~6. (20) As instances are shown, in Fig. 59, the motor torque, from equation (18), and the maximum synchronizing torque, from equation (20), for a motor of 5 per cent, drop of speed at full- load and very high overload capacity (a maximum power nearly two and a half times and a maximum torque somewhat over three times the rated value), that is, of low reactance, as can be produced at low frequency, and is desirable for intermittent service, hence of the constants : Zx = Zo = i ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-14", "section_label": "Chapter 16: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 14, "number": 16, "location": "lines 19374-20293", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-14/", "snippets": [ "... he current behind the impressed e.m.f. exists; and an alternating-current generator will yield an e.m.f. without field excitation only when closed by an external circuit of large negative reactance; that is, a circuit in which the current the e.m.f., as a condenser, or an overexcited synchronous iotor, etc. 14S. The usual explanation of the operation of the synchronous machine without field excitation is self-excitation by reactive armature currents. In a synchronous motor a lagging, in a generator a leading arma ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-15", "section_label": "Chapter 17: Inductor Machines", "section_title": "Inductor Machines", "kind": "chapter", "sequence": 15, "number": 17, "location": "lines 20294-20974", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-15/", "snippets": [ "... ance of the field coil, F, of the machine, Fig. 138, would make it impossible to force a tele- phone current through it, but the telephonic exciting current would be sent through the armature winding, which is of very low inductance, and by the use of the capacity the armature made self-exciting by leading current. Instead of sending the high-frequency machine current, which pulsates in amplitude with telephonic frequency, through radio transmission and rectifying the receiving current, we can rectify directly th ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-16", "section_label": "Chapter 18: Surging Of Synchronous Motors", "section_title": "Surging Of Synchronous Motors", "kind": "chapter", "sequence": 16, "number": 18, "location": "lines 20975-21712", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-16/", "snippets": [ "... b represents the consumption, a the oscilla- tion of energy by the pulsation of phase angle, p. b and a thus SURGING OF SYNCHRONOUS MOTORS 295 have a similar relation as resistance and reactance in alternating- current circuits, or in the discharge of condensers, a is the same term as in paragraph 167. Differential equation (19) is integrated by: 5 = Atc', (21) which, substituted in (19), gives: aAtc* + 2 bCAf + C2Aec* - 0, a + 2 bC + C2 = 0, which equation has the two roots: Ci - -6 + Vb*-a, C, = -6 ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-18", "section_label": "Chapter 20: Single-Phase Commutator Motors", "section_title": "Single-Phase Commutator Motors", "kind": "chapter", "sequence": 18, "number": 20, "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "... thus affords an easy means of producing the equivalent of a leading current. Therefore, the alternating-current commutator is one of the important methods of compensating for lagging: currents. Other methods are the use of electrostatic or electro- lytic condensers and of overexcited synchronous machines. Based on this principle, a number of designs of induction motors and other apparatus have been developed, using Qm commutator for neutralizing the lagging magnetizing current and the lag caused by self-inductance, ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-20", "section_label": "Chapter 22: Unipolar Machines", "section_title": "Unipolar Machines", "kind": "chapter", "sequence": 20, "number": 22, "location": "lines 31716-32137", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-20/", "snippets": [ "... nt converter, bj nut intermediary connections, from the collector rings 2, 3. 4. 250, As each conductor of the unipolar machine requires a separate pair of collector rings, with a reasonably moderate number of collector rings, unipolar machines of medium capacity are suited for low voltages only, such as for electrolytic machines, and have been built for this purpose to a limited extent, but in general it has been found more economical by series connection of the electrolytic cells to permit the use of higher volt ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-02", "section_label": "Chapter 2: Electric Conduction. Gas And Vapor", "section_title": "Electric Conduction. Gas And Vapor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3895-5444", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-02/", "snippets": [ "... covery of voltage, as with an electrostatic machine. Thus spark conduction also is called disruptive conduction and discon- tinuous conduction. Apparently continuous — though still interipittent — spark con- duction is produced at atmospheric pressure by capacity in series to the gaseous conductor, on an alternating-voltage supply, as corona, and as Geissler tube conduction at a partial vacuum, by an alternating-supply voltage with considerable reactance or resistance in series, or from a direct-current source of ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-13", "section_label": "Chapter 13: Reactance Of Synchronous Machines", "section_title": "Reactance Of Synchronous Machines", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 23466-24022", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-13/", "snippets": [ "CHAPTER XIII REACTANCE OF SYNCHRONOUS MACHINES 119. The synchronous machine — ^alternating-current generator, synchronous motor or synchronous condenser — consists of an armature containing one or more electric circuits traversed by alternating currents and synchronously revolving relative to a unidirectional magnetic field, excited by direct current. The armature circuit, like every electric circuit, has ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-07", "section_label": "Chapter 3: The Natural Period Of The Transmission Line. 320", "section_title": "The Natural Period Of The Transmission Line. 320", "kind": "chapter", "sequence": 7, "number": 3, "location": "lines 836-874", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-07/", "snippets": [ "CHAPTER III. THE NATURAL PERIOD OF THE TRANSMISSION LINE. 320 27. The oscillation of the transmission line as condenser. 320 28. The conditions of free oscillation. 321 29. Circuit open at one end, grounded at other end. 322 30. Quarter-wave oscillation of transmission line. 323 31. Frequencies of line discharges, and complex discharge wave. 327 32. Example of disc ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-09", "section_label": "Chapter 5: Distributed Series Capacity. 348", "section_title": "Distributed Series Capacity. 348", "kind": "chapter", "sequence": 9, "number": 5, "location": "lines 888-903", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-09/", "snippets": [ "CHAPTER V. DISTRIBUTED SERIES CAPACITY. 348 43. Potential distribution in multigap circuit. 348 44. Probable relation of the multigap circuit to the lightning flash in the clouds. 349 45. The differential equations of the multigap circuit, and their integral equations. 350 46. Terminal ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-12", "section_label": "Chapter 8: Velocity Of Propagation Op Electric Field. 387", "section_title": "Velocity Of Propagation Op Electric Field. 387", "kind": "chapter", "sequence": 12, "number": 8, "location": "lines 972-1013", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-12/", "snippets": [ "... al. 394 73. Self-inductive impedance, and numerical example. 395 74. Discussion of effective resistance and radiated power, as function of frequency. 396 75. Mutual inductance of two distant conductors of finite length. 398 76. Example. 399 77. Capacity of a sphere in space. 400 78. Example. 401 79. Sphere at a distance from ground. 402" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-49", "section_label": "Chapter 9: High-Frequency Conductors", "section_title": "High-Frequency Conductors", "kind": "chapter", "sequence": 49, "number": 9, "location": "lines 27003-27760", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "snippets": [ "... s upon the presence and location of other conductors, etc., in space, on the length of the conductor, and the distance from the return con- ductor. Since very high frequency currents, as lightning dis- charges, frequently have no return conductor, but the capacity at the end of the discharge path returns the current as \" dis- placement current,\" the extent and distribution of the magnetic field is indeterminate. If, however, the conductor under con- sideration is a small part of the total discharge — as the ground ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-53", "section_label": "Chapter 4: Traveling Waves", "section_title": "Traveling Waves", "kind": "chapter", "sequence": 53, "number": 4, "location": "lines 30244-31450", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "snippets": [ "... hich has the time decrement, that is, dies out at the rate In this decrement the factor 474 TRANSIENT PHENOMENA is the usual decrement of a circuit of resistance r and inductance Lj while the other factor, may be attributed to the conductance and capacity of the circuit, and the total decrement is the product, A further discussion of the equations (176) and (177) and the meaning of their transient term requires the consideration of the terminal conditions of the circuit. 27. The alternating components ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-54", "section_label": "Chapter 5: Free Oscillations", "section_title": "Free Oscillations", "kind": "chapter", "sequence": 54, "number": 5, "location": "lines 31451-32708", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "snippets": [ "... ibility of energy storage in more than one form so as to allow 478 FREE OSCILLATIONS 479 an interchange or surge of energy between its different forms, electromagnetic and electrostatic energy. Free oscillations occur only in circuits containing both capacity C and inductance, L. The absence of energy supply or abstraction defines the free oscillations by the condition that the power p = ei at the two ends of the circuit or section of the circuit must be zero at all times, or the circuit must be closed upon i ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-56", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit", "section_title": "Power And Energy Of The Complex Circuit", "kind": "chapter", "sequence": 56, "number": 7, "location": "lines 33528-34202", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "snippets": [ "... 17) and the total energy of the electromagnetic field of circuit element dX at time t is Aw'rr 1 /7 \"~ = V £~2\"\"'{ (4(7+BI)) cos 2 9' + (^0-JSC) sin 2 qt\\, dX d^ dl dX dX 52. The energy stored in the electrostatic field of the conductor or by the capacity C is given by CV dw2 = — dl\\ 518 TRANSIENT PHENOMENA or, substituting (310), and substituting in (319) the value of e from equation (290) gives the same expression as (311) except that the sign of the last two terms is reversed ; that is, the tot ..." ] } ] }, { "id": "magnetic-field", "label": "Magnetic Field", "aliases": [ "field of magnetism", "magnetic circuit", "magnetic field", "magnetic flux" ], "total_occurrences": 1922, "matching_section_count": 201, "matching_source_count": 14, "source_totals": [ { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 306, "section_count": 57 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 267, "section_count": 17 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 264, "section_count": 23 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 211, "section_count": 22 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 203, "section_count": 19 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 194, "section_count": 12 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 164, "section_count": 17 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 116, "section_count": 8 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 116, "section_count": 8 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 25, "section_count": 6 }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 25, "section_count": 3 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 24, "section_count": 6 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 5, "section_count": 2 }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 2, "section_count": 1 } ], "section_hits": [ { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-08", "section_label": "Chapter 8: Shaping Of Waves By Magnetic Saturation", "section_title": "Shaping Of Waves By Magnetic Saturation", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 12962-16963", "status": "candidate", "occurrence_count": 66, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-08/", "snippets": [ "CHAPTER VIII SHAPING OF WAVES BY MAGNETIC SATURATION 66. The wave shapes of current or volt^e produced by a closed magnetic circuit at moderate magnetic densities, such as are com- monly used in transformers and other induction apparatus, have 10 / ^ ^ 8- in.4 /' / -' f / '■ 1 i- 10 / 1 / 1 B- n.» / 1 / / / ...", "... - IB. 1 / 1 A / / .*=: W ■^-1 been discussed in \"Theory and Calculation of Alternating-cur- rent Phenomena. \" The characteristic of the wave-shape distortion by magnetic 126 ELECTRIC CIRCUITS BaturatioD in a closed magnetic circuit is the production of a high peak and fiat zero, of the current with a sine wave of impressed voltage, of the voltage with a sine wave of current traversing the circuit. k- ■^ ^^ MM ^ \\ \\ B - 1E,1 . E.0 I - 10. - B.0 1,- B.6 -J.8 ...", "... / ^ \\ \\ / / •si -^1 10. 57. B = 19.0, H = 50; and very high saturation: B = 19.7, H = 100. Figs. 56, 57, 58 and 59 show the four corresponding current waves /, at a sine wave of impressed voltage Coi and therefore sine wave of magnetic flux, B (neglecting ir drop in the winding, or rather, co is the voltage induced by the alternat- ing magnetic fiux density B). In these four figures, the maxi- SHAPING OF WAVES BY MAGNETIC SATURATION 127 mum Values of fio, B and / are chosen of the same sc ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-18", "section_label": "Chapter 20: Single-Phase Commutator Motors", "section_title": "Single-Phase Commutator Motors", "kind": "chapter", "sequence": 18, "number": 20, "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 53, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "... .m.f., as in this case the current in the armature circuit and the current in the field circuit and so the field magnetism both reverse. Theoretically, a direct-current motor therefore could be operated on an alternating impressed e.m.f. provided that the magnetic circuit of the motor is laminated, so as to fol- low the alternations of magnetism without serious loss of power, and that precautions are taken to have the field reverse simul- taneously with the armature. If the reversal of field magnetism should occur later th ...", "... gle-phase commutator motor has found an extensive use as railway motor, this type of motor will as an instance be treated in the following, and the other types discussed in the concluding paragraphs. II. Power-factor 190. In the commutating machine the magnetic field flux gen- erics the e.in.f. in the revolving armature conductors, which gives the motor output; the armature reaction, that is, the mag- net k Mux produced by the armature current, distorts and weakens the field, and requires a shifting of the brushes to ...", "... a shifting of the brushes to avoid Bparldag due to the short-circuit current under the commutator brushes, and where the brushes can not l>e shifted, as in a reversible motor. this necessitates the use of a strong field and weak armature to keep down the magnetic flux at the brushes. In the alternating- current motor the magnetic field flux generates in the armature conductors by their rotation the e.m.f. which does the work of the motor, but, as the field flux is alternating, it also generates SINGLE-PHASE COMMUTATO ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-34", "section_label": "Chapter 12: Magnetic Saturation And Hysteresis In Alternat Ing-Current Circuits", "section_title": "Magnetic Saturation And Hysteresis In Alternat Ing-Current Circuits", "kind": "chapter", "sequence": 34, "number": 12, "location": "lines 12885-13935", "status": "candidate", "occurrence_count": 46, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-34/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-34/", "snippets": [ "CHAPTER XII. MAGNETIC SATURATION AND HYSTERESIS IN ALTERNAT- ING-CURRENT CIRCUITS. 99. If an alternating e.m.f. is impressed upon a circuit con- taining resistance and inductance, the current and thereby the magnetic flux produced by the current immediately assume their final or permanent values only in case the circuit is closed at that point of the e.m:f. wave at which the permanent current is zero. Closing the circuit at any other point of the e.m.f. wave produces a tra ...", "... iately assume their final or permanent values only in case the circuit is closed at that point of the e.m:f. wave at which the permanent current is zero. Closing the circuit at any other point of the e.m.f. wave produces a transient term of current and of magnetic flux. So for instance, if the circuit is closed when the current i should have its negative maximum value - 70, and therefore the magnetic flux and the magnetic flux density also be at their negative maximum value - ^>0 and - (B0 — that is, in an inductive ci ...", "... rent is zero. Closing the circuit at any other point of the e.m.f. wave produces a transient term of current and of magnetic flux. So for instance, if the circuit is closed when the current i should have its negative maximum value - 70, and therefore the magnetic flux and the magnetic flux density also be at their negative maximum value - ^>0 and - (B0 — that is, in an inductive circuit, near the zero value of the decreasing e.m.f. wave — during the first half wave of e.m.f. the magnetic flux, which generates the count ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-01", "section_label": "Theory Section 1: Magnetism and Electric Current", "section_title": "Magnetism and Electric Current", "kind": "theory-section", "sequence": 1, "number": 1, "location": "lines 477-909", "status": "candidate", "occurrence_count": 43, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-01/", "snippets": [ "... ETISM AND ELECTRIC CURRENT 1. A magnet pole attracting (or repelling) another magnet pole of equal strength at unit distance with unit force1 is called a unit magnet pole. The space surrounding a magnet pole is called a magnetic field of force, or magnetic field. The magnetic field at unit distance from a unit magnet pole is called a unit magnetic field, and is represented by one line of magnetic force (or shortly \"one line\") per square centimeter, a ...", "... . A magnet pole attracting (or repelling) another magnet pole of equal strength at unit distance with unit force1 is called a unit magnet pole. The space surrounding a magnet pole is called a magnetic field of force, or magnetic field. The magnetic field at unit distance from a unit magnet pole is called a unit magnetic field, and is represented by one line of magnetic force (or shortly \"one line\") per square centimeter, and from a unit magnet pole ...", "... acting (or repelling) another magnet pole of equal strength at unit distance with unit force1 is called a unit magnet pole. The space surrounding a magnet pole is called a magnetic field of force, or magnetic field. The magnetic field at unit distance from a unit magnet pole is called a unit magnetic field, and is represented by one line of magnetic force (or shortly \"one line\") per square centimeter, and from a unit magnet pole thus issue a total o ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-46", "section_label": "Chapter 6: Alternating Magnetic Flux Distribution", "section_title": "Alternating Magnetic Flux Distribution", "kind": "chapter", "sequence": 46, "number": 6, "location": "lines 23948-24980", "status": "candidate", "occurrence_count": 42, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "snippets": [ "CHAPTER VI. ALTERNATING MAGNETIC FLUX DISTRIBUTION. 48. As carrier of magnetic flux iron is used, as far as possible, since it has the highest permeability or magnetic conductivity. If the magnetic flux is alternating or otherwise changing rapidly, an e.m.f. is generated by the change of mag ...", "CHAPTER VI. ALTERNATING MAGNETIC FLUX DISTRIBUTION. 48. As carrier of magnetic flux iron is used, as far as possible, since it has the highest permeability or magnetic conductivity. If the magnetic flux is alternating or otherwise changing rapidly, an e.m.f. is generated by the change of magnetic flux in the iron, and to avoid energy los ...", "CHAPTER VI. ALTERNATING MAGNETIC FLUX DISTRIBUTION. 48. As carrier of magnetic flux iron is used, as far as possible, since it has the highest permeability or magnetic conductivity. If the magnetic flux is alternating or otherwise changing rapidly, an e.m.f. is generated by the change of magnetic flux in the iron, and to avoid energy losses and demagnetization by the currents produced by these e.m.fs. the iron has to be subdivided in the direction in whi ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 883-1530", "status": "candidate", "occurrence_count": 40, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "snippets": [ "... heat, repre- sented by i?r. This, however, Fig. 7. is not all, but in the space surrounding the conductor cer- tain phenomena occur: magnetic and electrostatic forces appear. Fig. 8. — Electric Field of Conductor. The conductor is surrounded by a magnetic field, or a magnetic flux, which is measured by the number of lines of magnetic force . With a single conductor, the lines of magnetic force are concentric circles, as shown in Fig. 8. By the return conductor, the circles 10 THE ELECTRIC FIELD. 11 ...", "... d by i?r. This, however, Fig. 7. is not all, but in the space surrounding the conductor cer- tain phenomena occur: magnetic and electrostatic forces appear. Fig. 8. — Electric Field of Conductor. The conductor is surrounded by a magnetic field, or a magnetic flux, which is measured by the number of lines of magnetic force . With a single conductor, the lines of magnetic force are concentric circles, as shown in Fig. 8. By the return conductor, the circles 10 THE ELECTRIC FIELD. 11 are crowded together ...", "... r of lines of magnetic force . With a single conductor, the lines of magnetic force are concentric circles, as shown in Fig. 8. By the return conductor, the circles 10 THE ELECTRIC FIELD. 11 are crowded together between the conductors, and the magnetic field consists of eccentric circles surrounding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from the conductors, that is, a dielectric flux passes between the conductors, which ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1003-1658", "status": "candidate", "occurrence_count": 39, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-02/", "snippets": [ "... o heat, repre- sented by ^2r. This, however, Fig. 7. is not all, but in the space surrounding the conductor cer- tain phenomena occur: magnetic and electrostatic forces appear. Fig. 8. — Electric Field of Conductor. The conductor is surrounded by a magnetic field, or a magnetic flux, which is measured by the number of lines of magnetic force $. With a single conductor, the lines of magnetic force are concentric circles, as shown in Fig. 8. By the return conductor, the circles 10 THE ELECTRIC FIELD. 11 ar ...", "... d by ^2r. This, however, Fig. 7. is not all, but in the space surrounding the conductor cer- tain phenomena occur: magnetic and electrostatic forces appear. Fig. 8. — Electric Field of Conductor. The conductor is surrounded by a magnetic field, or a magnetic flux, which is measured by the number of lines of magnetic force $. With a single conductor, the lines of magnetic force are concentric circles, as shown in Fig. 8. By the return conductor, the circles 10 THE ELECTRIC FIELD. 11 are crowded together be ...", "... ber of lines of magnetic force $. With a single conductor, the lines of magnetic force are concentric circles, as shown in Fig. 8. By the return conductor, the circles 10 THE ELECTRIC FIELD. 11 are crowded together between the conductors, and the magnetic field consists of eccentric circles surrounding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from the conductors, that is, a dielectric flux passes between the conductors, which ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-12", "section_label": "Chapter 12: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 10718-13483", "status": "candidate", "occurrence_count": 37, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-12/", "snippets": [ "... unded by iron or other magnetic material, energy is expended outside of the con- ductor in the iron, by a kind of molecular friction, which, when the energy is supplied electrically, appears as magnetic hysteresis, and is caused by the cyclic reversals of magnetic flux in the iron in the alternating magnetic field. To examine this phenomenon, first a circuit may be con- sidered, of very high inductive reactance, but negligible true ohmic resistance; that is, a circuit entirely surrounded by iron, as, for instance, the ...", "... rgy is expended outside of the con- ductor in the iron, by a kind of molecular friction, which, when the energy is supplied electrically, appears as magnetic hysteresis, and is caused by the cyclic reversals of magnetic flux in the iron in the alternating magnetic field. To examine this phenomenon, first a circuit may be con- sidered, of very high inductive reactance, but negligible true ohmic resistance; that is, a circuit entirely surrounded by iron, as, for instance, the primary circuit of an alternating-current tra ...", "... nsuzned by the resist- ance, all the impressed e.m.f. must be consumed by the counter e.m.f. of self-induction, that is, the counter e.m.f. equals the impressed e.m.f.; hence, if the impressed e.m.f. is a sine wave, the counter e.m.f., and, therefore, the magnetic flux which generates the counter e.m.f., must follow a sine wave also. The alternating wave of current is not a sine wave in this case, but is distorted by hysteresis. It is possible, however, to plot the cur- rent wave in this case from the hysteretic cycle o ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "section_label": "Chapter 10: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 36, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "... ounded by iron or other magnetic material, energy is expended outside of the conductor in the iron, by a kind of molecular friction, which, when the energy is supplied electrically, appears as magnetic hysteresis, and is caused by the cyclic reversals of magnetic flux in the iron in the alternating magnetic field. To examine this phenomenon, first a circuit may be con- sidered, of very high inductance, but negligible true ohmic resistance ; that is, a circuit entirely surrounded by iron, as, for instance, the primary ...", "... nergy is expended outside of the conductor in the iron, by a kind of molecular friction, which, when the energy is supplied electrically, appears as magnetic hysteresis, and is caused by the cyclic reversals of magnetic flux in the iron in the alternating magnetic field. To examine this phenomenon, first a circuit may be con- sidered, of very high inductance, but negligible true ohmic resistance ; that is, a circuit entirely surrounded by iron, as, for instance, the primary circuit of an alternating-current transformer ...", "... ance, but negligible true ohmic resistance ; that is, a circuit entirely surrounded by iron, as, for instance, the primary circuit of an alternating-current transformer with open secondary circuit. The wave of current produces in the iron an alternating magnetic flux which induces in the electric circuit an E.M.F., — the counter E.M.F. of self-induction. If the ohmic re- sistance is negligible, that is, practically no E.M.F. con- sumed by the resistance, all the impressed E.M.F. must be consumed by the counter E.M.F. ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-25", "section_label": "Chapter 25: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 29375-32539", "status": "candidate", "occurrence_count": 35, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-25/", "snippets": [ "... ffect will cause distortion of the current wave, while with a sine wave of current passing through the circuit, a dis- torting effect will cause higher harmonics of e.m.f. 233. In a conductor revolving with uniform velocity through a uniform and constant magnetic field, a sine wave of e.m.f. is generated. In a circuit with constant resistance and constant reactance, this sine wave of e.m.f. produces a sine wave of current. Thus distortion of the wave-shape or higher har- monics may be due to lack of uniformity of the ve ...", "... and constant reactance, this sine wave of e.m.f. produces a sine wave of current. Thus distortion of the wave-shape or higher har- monics may be due to lack of uniformity of the velocity of the revolving conductor; lack of uniformity or pulsation of the magnetic field; pulsation of the resistance or pulsation of the reactance. 341 342 ALTERNATING-CURRENT PHENOMENA The first two cases, lack of uniformity of the rotation or of the magnetic field, cause higher harmonics of e.m.f. at open circuit. The last, pulsation ...", "... ty of the revolving conductor; lack of uniformity or pulsation of the magnetic field; pulsation of the resistance or pulsation of the reactance. 341 342 ALTERNATING-CURRENT PHENOMENA The first two cases, lack of uniformity of the rotation or of the magnetic field, cause higher harmonics of e.m.f. at open circuit. The last, pulsation of resistance and reactance, causes higher har- monics only when there is current in the circuit, that is, underload. Lack of uniformity of the rotation is hardly ever of practical in ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-10", "section_label": "Chapter 10: F", "section_title": "F", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 8269-10499", "status": "candidate", "occurrence_count": 32, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "snippets": [ "... ounded by iron or other magnetic material, energy is expended outside of the conductor in the iron, by a kind of molecular friction, which, when the energy is supplied electrically, appears as magnetic hysteresis, and is caused by the cyclic reversals of magnetic flux in the iron in the alternating magnetic field of force. To examine this phenomenon, first a circuit may be con- sidered, of very high inductance, but negligible true ohmic resistance ; that is, a circuit entirely surrounded by iron, as, for instance, th ...", "... nergy is expended outside of the conductor in the iron, by a kind of molecular friction, which, when the energy is supplied electrically, appears as magnetic hysteresis, and is caused by the cyclic reversals of magnetic flux in the iron in the alternating magnetic field of force. To examine this phenomenon, first a circuit may be con- sidered, of very high inductance, but negligible true ohmic resistance ; that is, a circuit entirely surrounded by iron, as, for instance, the primary circuit of an alternating-current t ...", "... ance, but negligible true ohmic resistance ; that is, a circuit entirely surrounded by iron, as, for instance, the primary circuit of an alternating-current transformer with open secondary circuit. The wave of current produces in the iron an alternating magnetic flux which induces in the electric circuit an E.M.F., — the counter E.M.F. of self-induction. If the ohmic resistance is negligible, the counter E.M.F. equals the impressed E.M.F. ; hence, if the impressed E.M.F. is §75] EFFECTIVE RESISTANCE AND REACTANCE, 1 ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-12", "section_label": "Chapter 12: Reactance Of Induction Apparatus", "section_title": "Reactance Of Induction Apparatus", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 22634-23465", "status": "candidate", "occurrence_count": 31, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-12/", "snippets": [ "CHAPTER XII REACTANCE OF INDUCTION APPARATUS 109. An electric current passing through a conductor is ac- companied by a magnetic field surrounding this conductor, and this magnetic field is as integral a part of the phenomenon, as is the energy dissipation by the resistance of the conductor. It is represented by the inductance, L, of the conductor, or the number of magnetic interlinkages ...", "CHAPTER XII REACTANCE OF INDUCTION APPARATUS 109. An electric current passing through a conductor is ac- companied by a magnetic field surrounding this conductor, and this magnetic field is as integral a part of the phenomenon, as is the energy dissipation by the resistance of the conductor. It is represented by the inductance, L, of the conductor, or the number of magnetic interlinkages with unit current in the conductor. Every circuit t ...", "... from the ohmic resistance, r, merely by being wattless or reactive, that is, representing not dissipation of energy, but surging of energy. Every alternating-current circuit thus has a resistance and a reactance, the latter representing the effect of the magnetic field of the current in the conductor. When dealing with alternating-current apparatus, especially those having several circuits, it must be realized, however, that the magnetic field of the circuit may have no independent exist- ence, but may merge into and ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-22", "section_label": "Chapter 22: Armature Reactions Of Alternators", "section_title": "Armature Reactions Of Alternators", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 23971-25134", "status": "candidate", "occurrence_count": 30, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-22/", "snippets": [ "... is due to the combined effect of armature reaction and armature self-induction. The counter m.m.f. of the armature current, or armature reaction, combines with the impressed m.m.f. or field excitation to the resultant m.m.f., which produces the resultant magnetic field in the field poles and generates in the armature an e.m.f. called the \"virtual generated e.m.f.,\" since it has no actual existence, but is merely a mathematical fiction. The counter e.m.f. of self-induction of the armature current, that is, e.m.f. generat ...", "... he armature an e.m.f. called the \"virtual generated e.m.f.,\" since it has no actual existence, but is merely a mathematical fiction. The counter e.m.f. of self-induction of the armature current, that is, e.m.f. generated by the armature current by a local magnetic flux, combines with the virtual generated e.m.f. to the actual generated e.m.f. of the armature, which corresponds to the magnetic flux in the armature core. This combined with the e.m.f. consumed by the armature resist- ance gives the terminal voltage. In m ...", "... . The counter e.m.f. of self-induction of the armature current, that is, e.m.f. generated by the armature current by a local magnetic flux, combines with the virtual generated e.m.f. to the actual generated e.m.f. of the armature, which corresponds to the magnetic flux in the armature core. This combined with the e.m.f. consumed by the armature resist- ance gives the terminal voltage. In most cases the effect of armature reaction and of self- induction are the same in character, and so both effects usually are contrac ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-15", "section_label": "Chapter 17: Inductor Machines", "section_title": "Inductor Machines", "kind": "chapter", "sequence": 15, "number": 17, "location": "lines 20294-20974", "status": "candidate", "occurrence_count": 30, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-15/", "snippets": [ "... , Etc. 156. Synchronous machines may be built with stationary field and revolving armature, as shown diagrammatically in Fig. 134, or with revolving field and stationary armature, Fig. 135, or with stationary field and stationary armature, but revolving magnetic circuit. The revolving-armature type was the most frequent in the early days, but has practically gone out of use except for special Fia. 134. — Revolving armature alternator Fig. 135.— Revolving field al ternator. purposes, and for synchronous commutat ...", "... in this field, its use is rapidly increasing. A typical inductor alternator is shown in Fig. 136. as eight- polar quarter-phase machine. 274 INDUCTOR MACHINES 275 Its armature coils, A, are stationary. One stationary field coil, F, surrounds the magnetic circuit of the machine, which consists of two sections, the stationary external one, B, which contains the armature, A, and a movable one, C, which contains the inductor, N. The inductor contains as many polar projec- tions, N, as there are cycles or pairs of pol ...", "... machine, which consists of two sections, the stationary external one, B, which contains the armature, A, and a movable one, C, which contains the inductor, N. The inductor contains as many polar projec- tions, N, as there are cycles or pairs of poles. The magnetic flux in the air gap and inductor does not reverse or alternate, as in the revolving-field type of alternator, Fig. 135, but is constant in direction, that is, all the inductor teeth are of the same polarity, but the flux density varies or pulsates, between a m ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-17", "section_label": "Chapter 17: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16521-17716", "status": "candidate", "occurrence_count": 29, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-17/", "snippets": [ "CHAPTER XVII THE ALTERNATING-CURRENT TRANSFORMER 141. The simplest alternating-current apparatus is the trans- former. It consists of a magnetic circuit interlinked with two electric circuits, a primary and a secondary. The primary circuit is excited by an impressed e.m.f., while in the secondary circuit an e.m.f. is generated. Thus, in the primary circuit power is consumed, and in the secondary a corresp ...", "... d a secondary. The primary circuit is excited by an impressed e.m.f., while in the secondary circuit an e.m.f. is generated. Thus, in the primary circuit power is consumed, and in the secondary a corresponding amount of power is produced. Since the same magnetic circuit is interlinked with both electric circuits, the e.m.f. generated per turn must be the same in the secondary as in the primary circuit; hence, the primary generated e.m.f. being approximately equal to the impressed e.m.f., the e.m.fs. at primary and at sec ...", "... approximately the ratio of their respective turns. Since the power produced in the secondary is approximately the same as that consumed in the primary, the primary and secondary currents are approximately in inverse ratio to the turns. 142. Besides the magnetic flux interlinked with both electric circuits — which flux, in a closed magnetic circuit transformer, has a circuit of low reluctance — a magnetic cross-flux passes between the primary and secondarj^ coils, surrounding one coil only, without being interlinked w ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-19", "section_label": "Chapter 21: Regulating Pole Converters", "section_title": "Regulating Pole Converters", "kind": "chapter", "sequence": 19, "number": 21, "location": "lines 30088-31715", "status": "candidate", "occurrence_count": 28, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-19/", "snippets": [ "CHAPTER XXI REGULATING POLE CONVERTERS 230. With a sine wave of alternating voltage, and the com- mutator brushes set at the magnetic neutral, that is, at right angles to the resultant magnetic flux, the direct voltage of a syn- chronous converter is constant at constant impressed alternating voltage. It equals the maximum value of the alternating voltaga between two diametrically opposite points of the commutator, or \"diametrical voltage,\" and the d ...", "... tral, or star or J voltage of the polyphase system. A change of the direct voltage, at constant, impressed alter- nating voltage (or inversely), can be produced: Either by changing the position angle between the eiuimjuia- tor brushes and the resultant magnetic flux, so that the direct voltage between the brushes is not the maximum diametrical alternating voltage but only a part thereof. Or by changing the maximum diametrical alternating voltage, at constant effective impressed voltage, by wave-shape distortion by ...", "... rease if the higher harmonies are in phase, and a reduction if the higher harmonics are in opposition to the fundamental wave of the dia- metrical or Y voltage. A. Variable Ratio by a Change of the Position Angle between Commutator Brushes and Resultant Magnetic Flux 231. Let, in the commutating maclane shown diagrammatic- ally in Fig. 195, the potential difference, or alternating voltage between one point, a, of the armature winding and the neutral, 0 (that is, the 1' voltage, or half the diametrical voltage) be rep ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 25, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "CHAPTER XI. FOUCAULT OR EDDY CURRENTS. 86. While magnetic hysteresis or molecular friction is a magnetic phenomenon, eddy currents are rather an elec- trical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric conductor, the magnetic field induces a current therein. The M.M.F. of this current reacts upon and affects the magnetic f ...", "... phenomenon, eddy currents are rather an elec- trical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric conductor, the magnetic field induces a current therein. The M.M.F. of this current reacts upon and affects the magnetic field, more or less ; consequently, an alternating magnetic field cannot penetrate deeply into a solid conductor, but a kind of screening effect is produced, which ...", "... tic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric conductor, the magnetic field induces a current therein. The M.M.F. of this current reacts upon and affects the magnetic field, more or less ; consequently, an alternating magnetic field cannot penetrate deeply into a solid conductor, but a kind of screening effect is produced, which makes solid masses of iron unsuitable for alternating fields, and necessitates the use of laminat ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "section_label": "Chapter 16: Induction Motor", "section_title": "Induction Motor", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 25, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "... d, but not the transfer of electrical energy, and thus the secondary circuits closed upon themselves. Transformer and induction motor thus are the two limiting cases of the general alternating- current transformer. Hence the induction motor consists of a magnetic circuit interlinked with two electric circuits or sets of circuits, the primary and the secondary circuit, which are movable with regard to each other. In general a num- ber of primary and a number of secondary circuits are used, angularly displaced around the pe ...", "... ndary quantities, the values reduced to the primary system shall be exclusively used, so that, to derive the true secondary values, these quantities have to be reduced backwards again by the factor a = ?*£-. «iA 153. Let $ = total maximum flux of the magnetic field per motor pole, We then have E— V2 77-72 TV^ 10 ~8 = effective E.M.F. induced by the mag- netic field per primary circuit. Counting the time from the moment where the rising magnetic flux of mutual induction & (flux interlinked with both electric circ ...", "... ctor a = ?*£-. «iA 153. Let $ = total maximum flux of the magnetic field per motor pole, We then have E— V2 77-72 TV^ 10 ~8 = effective E.M.F. induced by the mag- netic field per primary circuit. Counting the time from the moment where the rising magnetic flux of mutual induction & (flux interlinked with both electric circuits, primary and secondary) passes through zero, in complex quantities, the magnetic flux is denoted by and the primary induced E.M.F., 240 ALTERNATING-CURRENT PHENOMENA. where e= V2i ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-04", "section_label": "Chapter 4: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 6942-9061", "status": "candidate", "occurrence_count": 25, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-04/", "snippets": [ "CHAPTER IV MAGNETISM Hysteresis 36. Unlike the electric current, which requires power for its maintenance, the maintenance of a magnetic flux does not require energy expenditure (the energy consumed by the magnetizing current in the ohmic resistance of the magnetizing winding being an electrical and not a magnetic effect), but energy is required to produce a magnetic flux, is then stored as pot ...", "... , the maintenance of a magnetic flux does not require energy expenditure (the energy consumed by the magnetizing current in the ohmic resistance of the magnetizing winding being an electrical and not a magnetic effect), but energy is required to produce a magnetic flux, is then stored as potential energy in the magnetic flux, and is returned at the decrease or disappear- ance of the magnetic flux. However, the amount of energy re- turned at the decrease of magnetic flux is less than the energy consumed at the same incre ...", "... rgy expenditure (the energy consumed by the magnetizing current in the ohmic resistance of the magnetizing winding being an electrical and not a magnetic effect), but energy is required to produce a magnetic flux, is then stored as potential energy in the magnetic flux, and is returned at the decrease or disappear- ance of the magnetic flux. However, the amount of energy re- turned at the decrease of magnetic flux is less than the energy consumed at the same increase of magnetic flux, and energy is therefore dissipated ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-109", "section_label": "Apparatus Section 3: Induction Machines: Single -phase Induction Motor", "section_title": "Induction Machines: Single -phase Induction Motor", "kind": "apparatus-section", "sequence": 109, "number": 3, "location": "lines 20428-21157", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-109/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-109/", "snippets": [ "... reaction machines. A single-phase induction motor will not start from rest, but when started in either direction will accelerate with increasing torque and approach synchronism. When running at or very near synchronism, the magnetic field of the single-phase induction motor is practically identical with that of a polyphase motor, that is, can be represented by the theory of the rotating field. Thus, in a turn wound under angle r to the primary winding of ...", "... winding of the single-phase induction motor, at synchronism an e.m.f. is generated equal to that generated in a turn of the primary winding, but differing therefrom by angle 6 = T in time phase. In a polyphase motor the magnetic flux in any direction is due to the resultant m.m.f. of primary and of secondary currents, in the same way as in a transformer. The same is the case in the direction of the axis of the exciting coil of the single-phase ind ...", "... ame way as in a transformer. The same is the case in the direction of the axis of the exciting coil of the single-phase induc- tion motor. In the direction at right angles to the axis of the exciting coil, however, the magnetic flux is due to the m.m.f. of INDUCTION MACHINES 327 the secondary currents alone, no primary e.m.f. acting in this direction. Consequently, in the polyphase motor running synchronously, that is, doing no work whatever, the se ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "CHAPTER XI. FOUOAULT OR EDDY 0UBBENT8. • 86. While magnetic hysteresis or molecular friction is a magnetic phenomenon, eddy currents are rather an elec- trical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric conductor, the magnetic field induces a current therein. The M.M.F. of this current reacts upon and affects the magnetic f ...", "... phenomenon, eddy currents are rather an elec- trical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric conductor, the magnetic field induces a current therein. The M.M.F. of this current reacts upon and affects the magnetic field, more or less ; consequently, an alternating magnetic field cannot penetrate deeply into a solid conductor, but a kind of screening effect is produced, which ...", "... tic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric conductor, the magnetic field induces a current therein. The M.M.F. of this current reacts upon and affects the magnetic field, more or less ; consequently, an alternating magnetic field cannot penetrate deeply into a solid conductor, but a kind of screening effect is produced, which makes solid masses of iron unsuitable for alternating fields, and necessitates the use of laminat ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-13", "section_label": "Chapter 13: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 13484-14333", "status": "candidate", "occurrence_count": 23, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-13/", "snippets": [ "CHAPTER XIII FOUCAULT OR EDDY CURRENTS 105. While magnetic hysteresis due to molecular friction is a magnetic phenomenon, eddy currents are rather an electrical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric conductor, the magnetic field produces a current therein. The m.m.f. of this current reacts upon and affects the magnetic ...", "... ic phenomenon, eddy currents are rather an electrical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric conductor, the magnetic field produces a current therein. The m.m.f. of this current reacts upon and affects the magnetic field, more or less; consequently, an alternating magnetic field cannot penetrate deeply into a solid conductor, but a kind of screening effect is produced, which ...", "... tic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric conductor, the magnetic field produces a current therein. The m.m.f. of this current reacts upon and affects the magnetic field, more or less; consequently, an alternating magnetic field cannot penetrate deeply into a solid conductor, but a kind of screening effect is produced, which makes solid masses of iron unsuitable for alternating fields, and necessitates the use of laminate ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-04", "section_label": "Chapter 5: Single-Phase Induction Motor", "section_title": "Single-Phase Induction Motor", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 8555-10582", "status": "candidate", "occurrence_count": 23, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-04/", "snippets": [ "... ulation of Alternating-current Phenomena,\" the single-phase induction motor has inherently, no torque at standstill, that is, when used without special device to produce such torque by converting the motor into an unsym- metrical ployphase motor, etc. The magnetic flux at standstill is a single-phase alternating flux of constant direction, and the line of polarization of the armature or secondary currents, that is, the resultant m.m.f. of the armature currents, coincides with the axis of magnetic flux impressed by the p ...", "... se motor, etc. The magnetic flux at standstill is a single-phase alternating flux of constant direction, and the line of polarization of the armature or secondary currents, that is, the resultant m.m.f. of the armature currents, coincides with the axis of magnetic flux impressed by the primary circuit. When revolving, however, even at low speeds, torque appears in the single-phase induction motor, due to the axis of armature polarization being shifted against the axis of primary impressed magnetic flux, by the rotation. ...", "... with the axis of magnetic flux impressed by the primary circuit. When revolving, however, even at low speeds, torque appears in the single-phase induction motor, due to the axis of armature polarization being shifted against the axis of primary impressed magnetic flux, by the rotation. That is, the armature currents, lagging behind the magnetic flux which induces them, reach their maximum later than the magnetic flux, thus at a time when their conductors have already moved a distance or an angle away from coincidence w ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1659-2484", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-03/", "snippets": [ "... 0 volts, and 2200 volts. In them the capac- ity is small, due to the limited extent of the circuit, resulting from the low voltage, and at the low voltage the dielectric energy thus is negligible, that is, the circuit stores appreciable energy only by the magnetic field. A circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectric field. The usual high-voltage capacity circuit, as that of an electrostatic machine, while of very s ...", "... inuous voltage eo be im- pressed upon a wire coil of resistance r and inductance L (but A current Iq = — flows through the coil and % t 1 % io A C c c ..1. 1 Fig. 10. — Magnetic Single-energy Transient. negligible capacity), a magnetic field $0 10' Lio interlinks with the coil. Assuming now that the voltage eo is suddenly withdrawn, without changing 19 20 ELECTRIC DISCHARGES, WAVES AND IMPULSES. the constants of the coil circuit, as for instance by short- circuiting the termi ...", "... 20 ELECTRIC DISCHARGES, WAVES AND IMPULSES. the constants of the coil circuit, as for instance by short- circuiting the terminals of the coil, as indicated at A. With no voltage impressed upon the coil, and thus no power supplied to it, current i and magnetic flux $ of the coil must finally be zero. However, since the magnetic flux represents stored energy, it cannot instantly vanish, but the magnetic flux must gradually decrease from its initial value $0, by the dissipation of its stored energy in the resistance o ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1531-2161", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "snippets": [ "... 0 volts, and 2200 volts. In them the capac- ity is small, due to the limited extent of the circuit, resulting from the low voltage, and at the low voltage the dielectric energy thus is negligible, that is, the circuit stores appreciable energy only by the magnetic field. A circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectric field. The usual high-voltage capacity circuit, as that of an electrostatic machine, while of very s ...", "... eyden jar. Fig 10._Magnetie Single.energy Let, as represented in Fig. 10, Transient, a continuous voltage e0 be im- pressed upon a wire coil of resistance r and inductance L (but negligible capacity). A current iQ = — flows through the coil and a magnetic field $0 10~8 = - - interlinks with the coil. Assuming now that the voltage e0 is suddenly withdrawn, without changing 19 20 ELECTRIC DISCHARGES, WAVES AND IMPULSES. the constants of the coil circuit, as for instance by short- circuiting the terminals of ...", "... 20 ELECTRIC DISCHARGES, WAVES AND IMPULSES. the constants of the coil circuit, as for instance by short- circuiting the terminals of the coil, as indicated at A, with no voltage impressed upon the coil, and thus no power supplied to it, current i and magnetic flux <£ of the coil must finally be zero. However, since the magnetic flux represents stored energy, it cannot instantly vanish, but the magnetic flux must gradually decrease from its initial value 3>o, by the dissipation of its stored energy in the resistance ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-13", "section_label": "Chapter 13: Ths Alternating^Cnrrent Traxsfobmer", "section_title": "Ths Alternating^Cnrrent Traxsfobmer", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 12673-14088", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "snippets": [ "CHAPTER XIII. THS ALTERNATING^CnRRENT TRAXSFOBMER. 116. The simplest alternating-current apparatus is the transformer. It consists of a magnetic circuit interlinked with two electric circuits, a primary and a secondary. The primary circuit is excited by an impressed E.M.F., while in the secondary circuit an E.M.F. is induced. Thus, in the primary circuit power is consumed, and in the secondary a correspo ...", "... and a secondary. The primary circuit is excited by an impressed E.M.F., while in the secondary circuit an E.M.F. is induced. Thus, in the primary circuit power is consumed, and in the secondary a corresponding amount of power is produced. Since the same magnetic circuit is interlinked with both electric circuits, the E.M.F. induced per turn must be the same in the secondary as in the primary circuit ; hence, the primary induced E.M.F. being approximately equal to the impressed E.M.F., the E.M.Fs. at primary and at sec- ...", "... roximately the ratio of their respective turns. Since the power produced in the second- ary is approximately the same as that consumed in the primary, the primary and secondary currents are approxi- mately in inverse ratio to the turns. 117. Besides the magnetic flux interlinked with both electric circuits — which flux, in a closed magnetic circuit transformer, has a circuit of low reluctance — a magnetic cross-flux passes between the primary and secondary coils, surrounding one coil only, without being interlinked wi ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-22", "section_label": "Chapter 22: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 21190-21982", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "snippets": [ "... effect will cause distortion of the current wave, while with a sine wave of current passing through the circuit, a distorting effect will cause higher harmonics of E.M.F. 234. In a conductor revolving with uniform velocity through a uniform and constant magnetic field, a sine wave of E.M.F. is induced. In a circuit with constant resistance and constant reactance, this sine wave of E.M.F. produces 384 ALTERNATING-CURRENT PHENOMENA. a sine wave of current. Thus distortion of the wave-shape or higher harmonics may be ...", "... of E.M.F. produces 384 ALTERNATING-CURRENT PHENOMENA. a sine wave of current. Thus distortion of the wave-shape or higher harmonics may be due to : lack of uniformity of the velocity of the revolving conductor ; lack of uniformity or pulsation of the magnetic field ; pulsation of the resis- tance ; or pulsation of the reactance. The first two cases, lack of uniformity of the rotation or of the magnetic field, cause higher harmonics of E.M.F. at open circuit. The last, pulsation of resistance and reac- tance, cause ...", "... to : lack of uniformity of the velocity of the revolving conductor ; lack of uniformity or pulsation of the magnetic field ; pulsation of the resis- tance ; or pulsation of the reactance. The first two cases, lack of uniformity of the rotation or of the magnetic field, cause higher harmonics of E.M.F. at open circuit. The last, pulsation of resistance and reac- tance, causes higher harmonics only with a current flowing in the circuit, that is, under load. Lack of uniformity of the rotation is of no practical in- tere ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-19", "section_label": "Theory Section 19: Fields of Force", "section_title": "Fields of Force", "kind": "theory-section", "sequence": 19, "number": 19, "location": "lines 7737-7990", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-19/", "snippets": [ "... the mass, measures the intensity of the field: in the gravitational field of the earth 981 cm g sec. The force acting upon a mass m, then, is:F = gm, and is called the weight of the mass. In the same manner, in the magnetic field of a current as magnetomotive force, the intensity H of the magnetic field is measured by the force F which the field exerts on a magnetic mass or pole strength m: F = Hm; the intensity K of the di- electric field of ...", "... the earth 981 cm g sec. The force acting upon a mass m, then, is:F = gm, and is called the weight of the mass. In the same manner, in the magnetic field of a current as magnetomotive force, the intensity H of the magnetic field is measured by the force F which the field exerts on a magnetic mass or pole strength m: F = Hm; the intensity K of the di- electric field of a potential difference as electromotive force is measured by the force F ex ...", "... tive force, whereby the space is not neutral any more, but capable of exerting forces on anything susceptible to these forces: mechanical forces on masses in a gravitational field, magnetic forces on magnetic materials in a magnetic field, 114 ELEMENTS OF ELECTRICAL ENGINEERING A. — A photograph of a mica-filing map of the dielectric lines of force- between two cylinders. B. — A photograph of an iron-filing map of the magnetic lines of force about. t ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-14", "section_label": "Chapter 14: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 11605-12682", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "snippets": [ "CHAPTER XIV. THE ALTERNATING-CURRENT TRANSFORMER. 126. The simplest alternating-current apparatus is the transformer. It consists of a magnetic circuit interlinked with two electric circuits, a primary and a secondary. The primary circuit is excited by an impressed E.M.F., while in the secondary circuit an E.M.F. is induced. Thus, in the primary circuit power is consumed, and in the secondary a correspo ...", "... and a secondary. The primary circuit is excited by an impressed E.M.F., while in the secondary circuit an E.M.F. is induced. Thus, in the primary circuit power is consumed, and in the secondary a corresponding amount of power is produced. Since the same magnetic circuit is interlinked with both electric circuits, the E.M.F. induced per turn must be the same in the secondary as in the primary circuit ; hence, the primary induced E.M.F. being approximately equal to the impressed E.M.F., the E.M.Fs. at primary and at sec- ...", "... roximately the ratio of their respective turns. Since the power produced in the second- ary is approximately the same as that consumed in the primary, the primary and secondary currents are approxi- mately in inverse ratio to the turns. 127. Besides the magnetic flux interlinked with both electric circuits — which flux, in a closed magnetic circuit transformer, has a circuit of low reluctance — a magnetic cross-flux passes between the primary and secondary coils, surrounding one coil only, without being interlinked wi ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-01", "section_label": "Chapter 1: Speed Control Of Induction Motors", "section_title": "Speed Control Of Induction Motors", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1368-3542", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-01/", "snippets": [ "... s- ing slip, to get high torque at low speeds, the same result can be produced by the use of an effective resistance, such as the effect- ive or equivalent resistance of hysteresis, or of eddy currents. As the frequency of the secondary current varies, a magnetic circuit energized by the secondary current operates at the varying frequency of the slip, s. At a given current, i\\, the voltage required to send the current through the magnetic circuit is proportional to the frequency, that is, to 8. Hence, the suaceptance is ...", "... or of eddy currents. As the frequency of the secondary current varies, a magnetic circuit energized by the secondary current operates at the varying frequency of the slip, s. At a given current, i\\, the voltage required to send the current through the magnetic circuit is proportional to the frequency, that is, to 8. Hence, the suaceptance is inverse proportional to «: V = 6- (5) 8 The angle of hysteretic advance of phase, a, and the power- factor, in a closed magnetic circuit, are independent of the frequency, an ...", "... uired to send the current through the magnetic circuit is proportional to the frequency, that is, to 8. Hence, the suaceptance is inverse proportional to «: V = 6- (5) 8 The angle of hysteretic advance of phase, a, and the power- factor, in a closed magnetic circuit, are independent of the frequency, and vary relatively little with the magnetic density and thus the current, over a wide range,1 thus may approxi- mately be assumed as constant. That is, the hysteretic con- ductance is proportional to the susceptance : ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-03", "section_label": "Chapter 3: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 5445-6941", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-03/", "snippets": [ "CHAPTER III MAGNETISM Reluctivity 29. Considering magnetism as the phenomena of a \"magnetic circuit,\" the foremost differences between the characteristics of the magnetic circuit and the electric circuit are: (a) The maintenance of an electric circuit requires the ex- penditure of energy, while the maintenance of a magnetic circuit does not require the ...", "CHAPTER III MAGNETISM Reluctivity 29. Considering magnetism as the phenomena of a \"magnetic circuit,\" the foremost differences between the characteristics of the magnetic circuit and the electric circuit are: (a) The maintenance of an electric circuit requires the ex- penditure of energy, while the maintenance of a magnetic circuit does not require the expenditure of energy, though the starting of a magnetic circuit requires ener ...", "... the phenomena of a \"magnetic circuit,\" the foremost differences between the characteristics of the magnetic circuit and the electric circuit are: (a) The maintenance of an electric circuit requires the ex- penditure of energy, while the maintenance of a magnetic circuit does not require the expenditure of energy, though the starting of a magnetic circuit requires energy. A magnetic circuit, there- fore, can remain \"remanent\" or \"permanent.\" (6) All materials are fairly good carriers of magnetic flux, and the range of m ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-25", "section_label": "Chapter 3: Inductance And Resistance In Continuous Current Circuits", "section_title": "Inductance And Resistance In Continuous Current Circuits", "kind": "chapter", "sequence": 25, "number": 3, "location": "lines 2659-3514", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-25/", "snippets": [ "... in direct-current circuits to reduce the inductance than in alternating-current circuits, where the inductance usually causes a drop of voltage, and direct-current circuits as a rule have higher inductance, especially if the circuit is used for producing magnetic flux, as in solenoids, electro- magnets, machine-fields. Any change of the condition of a continuous-current circuit, as a change of e.m.f., of resistance, etc., which leads to a change of current from one value i0 to another value iv results in the appearan ...", "... ablished in the circuit in a practically inappre- ciable time, a fraction of a hundredth of a second. 22. Excitation of a motor field. Let, in a continuous-current shunt motor, e0 = 250 volts = impressed e.m.f., and the number of poles = 8. Assume the magnetic flux per pole, 0 = 12.5 megalines, and the ampere-turns per pole required to produce this magnetic flux as $ = 9000. Assume 1000 watts used for the excitation of the motor field gives an exciting current 1000 h =- = 4 amperes, and herefrom the resist ...", "... 22. Excitation of a motor field. Let, in a continuous-current shunt motor, e0 = 250 volts = impressed e.m.f., and the number of poles = 8. Assume the magnetic flux per pole, 0 = 12.5 megalines, and the ampere-turns per pole required to produce this magnetic flux as $ = 9000. Assume 1000 watts used for the excitation of the motor field gives an exciting current 1000 h =- = 4 amperes, and herefrom the resistance of the total motor field circuit is r = e-? = 62.5 ohms. 28 TRANSIENT PHENOMENA To produce JF ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "section_label": "Lecture 10: Continual And Cumulative Oscillations", "section_title": "Continual And Cumulative Oscillations", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... rgy storage, and which therefore are of fundamental importance in the study of transients, their calcula- tion is discussed in the following. The inductance is the ratio of the interlinkages of the mag- netic flux to the current, L^f, (1) v>^here $ = magnetic flux or number of lines of magnetic force, and n the number of times which each line of magnetic force interlinks with the current i. The capacity is the ratio of the dielectric flux to the voltage, C=l (2) where ^ is the dielectric flux, or number of line ...", "... ic materials, with the latter for all densities below the dielectric strength of the material, — the resultant field of any number of conductors at any point in space is the combination of the component fields of the individual conductors. ' Fig. 67. — Magnetic Field of Circuit. Thus the field of conductor A and return conductor B is the combination of the field of A, of the shape Fig. 8, and the field of B, of the same shape, but in opposite direction, as shown for the magnetic fields in Fig. 67. All the lines of ...", "... conductor A and return conductor B is the combination of the field of A, of the shape Fig. 8, and the field of B, of the same shape, but in opposite direction, as shown for the magnetic fields in Fig. 67. All the lines of magnetic force of the resultant magnetic field must pass between the two conductors, since a line of magnetic force, which surrounds both conductors, would have no m.m.f., and thus could not exist. That is, the lines of magnetic force of A beyond B, and those of B beyond A, shown dotted in Fig. 67, n ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-10", "section_label": "Lecture 10: Inductance And Capacity Of Round Parallel Conductors", "section_title": "Inductance And Capacity Of Round Parallel Conductors", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6089-7274", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "snippets": [ "... rage, and which therefore are of fundamental importance in the study of transients, their calcula- tion is discussed in the following. The inductance is the ratio of the interlinkages of the mag- netic flux to the current, £ = ?- (i) i/ where = magnetic flux or number of lines of magnetic force, and n the number of times which each line of magnetic force interlinks with the current i. The capacity is the ratio of the dielectric flux to the voltage, where \\f/ is the dielectric flux, or number of lines of di ...", "... netic materials, with the latter for all densities below the dielectric strength of the material,— the resultant field of any number of conductors at any point in space is the combination of the component fields of the individual conductors. Fig. 59. — Magnetic Field of Circuit. Thus the field of conductor A and return conductor B is the combination of the field of A, of the shape Fig. 8, and the field of B, of the same shape, but in opposite direction, as shown for the magnetic fields in Fig. 59. All the lines of ...", "... conductor A and return conductor B is the combination of the field of A, of the shape Fig. 8, and the field of B, of the same shape, but in opposite direction, as shown for the magnetic fields in Fig. 59. All the lines of magnetic force of the resultant magnetic field must pass between the two conductors, since a line of magnetic force, which surrounds both conductors, would have no m.m.f., and thus could not exist. That is, the lines of magnetic force of A beyond B, and those of B beyond A, shown dotted in Fig. 59, n ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-47", "section_label": "Chapter 7: Distribution Of Alternating-Current Density In Conductor", "section_title": "Distribution Of Alternating-Current Density In Conductor", "kind": "chapter", "sequence": 47, "number": 7, "location": "lines 24981-26094", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "snippets": [ "... vity or its magnetic per- meability high, the current density is not uniform throughout the conductor section, but decreases towards the interior of the conductor, due to the higher e.m.f. of self-inductance in the interior of the conductor, caused by the magnetic flux inside of the conductor. The phase of the current inside of the conductor also differs from that on the surface and lags behind it. In consequence of this unequal current distribution in a large conductor traversed by ^alternating currents, the effective ...", "... tning arrester connections, flat copper ribbon offers a very much smaller effective resistance than a round wire. Strand- ing the conductor, however, has no direct effect on this phenom- enon, since it is due to the magnetic action of the current, and the magnetic field in the stranded conductor is the same as in a solid conductor, other things being equal. That is, while eddy currents in the conductor, due to external magnetic fields, are eliminated by stranding the conductor, this is not the case with the increase of t ...", "... by unequal current dis- tribution. Stranding the conductor, however, may reduce unequal current distribution indirectly, especially with iron as conductor material, by reducing the effective or mean per- meability of the conductor, due to the break in the magnetic circuit between the iron strands, and also by the reduction of the mean conductivity of the conductor section. For instance, if in a stranded conductor 60 per cent of the conductor section DISTRIBUTION OF ALTERNATING CURRENT 871 is copper, 40 per cent space be ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2485-3386", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-04/", "snippets": [ "... ses in the manner as discussed in para- graph 13, that is, with a duration T = — - The permanent current 12 may be continuous, or alternating, or may be a changing current, as a transient of long duration, etc. The same reasoning applies to the voltage, magnetic flux, etc. Thus, let, in an alternating-current circuit traversed by current i'l, in Fig. 15 A, the conditions be changed, at the moment t = 0, so as to produce the current iV The instantaneous value of the current ii at the moment t = 0 can be considered as ...", "... e resultant currents (shown in drawn line) must be zero at any moment, not only during the permanent condition, but also dur- ing the transition period existing before the permanent condi- tion is reached. It is interesting to apply this to the resultant magnetic field produced by three equal three-phase magnetizing coils placed under equal angles, that is, to the starting of the three-phase rotating magnetic field, or in general any polyphase rotating magnetic field. Fig. 18. — Construction of Starting Transient of ...", "... d existing before the permanent condi- tion is reached. It is interesting to apply this to the resultant magnetic field produced by three equal three-phase magnetizing coils placed under equal angles, that is, to the starting of the three-phase rotating magnetic field, or in general any polyphase rotating magnetic field. Fig. 18. — Construction of Starting Transient of Rotating Field. As is well known, three equal magnetizing coils, placed under equal angles and excited by three-phase currents, produce a result- a ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-02", "section_label": "Lecture 2: Conclusions From The Relativity Theory", "section_title": "Conclusions From The Relativity Theory", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 736-2388", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... pose we have a permanent bar magnet M (Fig. 2) and bring a piece of iron / near it. It is attracted, or moved; that is, a force is exerted on it. We bring a piece of copper near the magnet, and nothing happens. We say the space surrounding the magnet is a magnetic field. A field, or field of force, we define as \"a condition in space exerting a force on a body susceptible to this field.\" Thus, a piece of iron being magnetizable — that is, susceptible to a magnetic field^ — ^will be acted upon; a piece of copper, not being ...", "... appens. We say the space surrounding the magnet is a magnetic field. A field, or field of force, we define as \"a condition in space exerting a force on a body susceptible to this field.\" Thus, a piece of iron being magnetizable — that is, susceptible to a magnetic field^ — ^will be acted upon; a piece of copper, not being magnetizable, shows no action. A field is completely defined and characterized at any point by its intensity and its direction, and in Faraday's pictorial representation of the field by the lines of for ...", "... quires energy, and this energy is stored in the space we call the field. Thus we can go further and define the field as ''a condition of energy storage in space exerting a force on a body susceptible to this energy.'' The space surrounding a magnet is a magnetic field. If we electrify a piece of sealing wax by rubbing it, it surrounds itself by a dielectric or electrostatic field, and bodies susceptible to electrostatic forces- — such as light pieces of paper — are attracted. The earth is surrounded by a gravitational ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-32", "section_label": "Chapter 10: Mutual Inductance", "section_title": "Mutual Inductance", "kind": "chapter", "sequence": 32, "number": 10, "location": "lines 10475-12216", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "snippets": [ "... nd capacity, but no mutual inductance; that is, the phenomena which take place in the circuit have been assumed as depending upon the impressed e.m.f. and the constants of the circuit, but not upon the phenomena taking place in any other circuit. Of the magnetic flux produced by the current in a circuit and interlinked with this circuit, a part may be interlinked with a second circuit also, and so by its change generate an e.m.f. in the second circuit, and part of the magnetic flux produced by Fig. 38. Mutual induct ...", "... place in any other circuit. Of the magnetic flux produced by the current in a circuit and interlinked with this circuit, a part may be interlinked with a second circuit also, and so by its change generate an e.m.f. in the second circuit, and part of the magnetic flux produced by Fig. 38. Mutual inductance between circuits. the current in a second circuit and interlinked with the second circuit may be interlinked also with the first circuit, and a change of current in the second circuit, that is, a change of magnet ...", "... c flux produced by Fig. 38. Mutual inductance between circuits. the current in a second circuit and interlinked with the second circuit may be interlinked also with the first circuit, and a change of current in the second circuit, that is, a change of magnetic flux produced by the current in the second circuit, then generates an e.m.f. in the first circuit. Diagrammatically the mutual inductance between two circuits can be sketched as shown by M in Fig. 38, by two coaxial coils, while the self-inductance is shown b ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2162-2971", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "snippets": [ "... ses in the manner as discussed in para- graph 13, that is, with a duration T = — - The permanent current i2 may be continuous, or alternating, or may be a changing current, as a transient of long duration, etc. The same reasoning applies to the voltage, magnetic flux, etc. Thus, let, in an alternating-current circuit traversed by current t'i, in Fig. 15 A, the conditions be changed, at the moment t = 0, so as to produce the current i2. The instantaneous value of the current ii at the moment t = 0 can be considered as ...", "... e resultant currents (shown in drawn line) must be zero at any moment, not only during the permanent condition, but also dur- ing the transition period existing before the permanent condi- tion is reached. It is interesting to apply this to the resultant magnetic field produced by three equal three-phase magnetizing coils placed under equal angles, that is, to the starting of the three-phase rotating magnetic field, or in general any polyphase rotating magnetic field. Fig. 18. — Construction of Starting Transient of ...", "... d existing before the permanent condi- tion is reached. It is interesting to apply this to the resultant magnetic field produced by three equal three-phase magnetizing coils placed under equal angles, that is, to the starting of the three-phase rotating magnetic field, or in general any polyphase rotating magnetic field. Fig. 18. — Construction of Starting Transient of Rotating Field. As is well known, three equal magnetizing coils, placed under equal angles and excited by three-phase currents, produce a result- an ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-20", "section_label": "Chapter 20: Single-Phase Induction Motors", "section_title": "Single-Phase Induction Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 21538-22301", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-20/", "snippets": [ "CHAPTER XX SINGLE-PHASE INDUCTION MOTORS 177. The magnetic circuit of the induction motor at or near synchronism consists of two magnetic fluxes superimposed upon each other in quadrature, in time, and in position. In the polyphase motor these fluxes are produced by e.m.fs. displaced in phase. In the monocyclic motor one ...", "... quadrature flux. Hence, approximately, the quadrature flux of a single-phase motor can be considered as proportional to its speed; that is, it is zero at standstill. Since the torque of the motor is proportional to the product of secondary current times magnetic flux in quadrature, it follows that the torque of the single-phase motor is equal to that of the same motor under the same condition of operation on a polyphase circuit, multiplied with the speed; hence equal to zero at standstill. Thus, while single-phase i ...", "... ion between the coils — that is, by using one as secondary to the other — or by impedances of different inductance factors connected with the different primary coils. 178. The starting devices of the single-phase induction motor by producing a quadrature magnetic flux can be subdivided into three classes: 1. Phase-Splitting Devices. Two or more primary circuits are used, displaced in position from each other, and either in series or in shunt with each other, or in any other way related, as by transformation. The impe ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-20", "section_label": "Chapter 20: Commutator Motors", "section_title": "Commutator Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 19458-20501", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "snippets": [ "... induced so as to give a rotary effort in the one direction, and in the other half the current is induced to COMMUTATOR MOTORS. 355 give a rotary effort in the opposite direction, as shown by the arrows in Fig. 157. In the induction motor a second magnetic field is used to act upon the currents induced by the first, or inducing magnetic field, and thereby cause a rotation. That means the motor consists of a primary electric circuit, inducing Fig. 157. in the armature the secondary currents, and a primary mag ...", "... he current is induced to COMMUTATOR MOTORS. 355 give a rotary effort in the opposite direction, as shown by the arrows in Fig. 157. In the induction motor a second magnetic field is used to act upon the currents induced by the first, or inducing magnetic field, and thereby cause a rotation. That means the motor consists of a primary electric circuit, inducing Fig. 157. in the armature the secondary currents, and a primary magnetizing circuit producing the magnetism to act upon the secondary currents. In t ...", "... ing circuit producing the magnetism to act upon the secondary currents. In the polyphase induction motor both functions of the primary circuit are usually combined in the same coils ; that is, each primary coil induces secondary currents, and pro- duces magnetic flux acting upon secondary currents induced by another primary coil. 356 AL TERNA TING-CURRENT PHENOMENA. 215. In the repulsion motor the difficulty due to the equal and opposite rotary efforts, caused by the induced armature currents when acted upon b ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-13", "section_label": "Chapter 13: Reactance Of Synchronous Machines", "section_title": "Reactance Of Synchronous Machines", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 23466-24022", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-13/", "snippets": [ "... synchronous machine — ^alternating-current generator, synchronous motor or synchronous condenser — consists of an armature containing one or more electric circuits traversed by alternating currents and synchronously revolving relative to a unidirectional magnetic field, excited by direct current. The armature circuit, like every electric circuit, has a resistance, r, in which power is being dissipated by the current, /, and an in- ductance, L, or reactance, a; = 2 irfL^ which represents the mag- netic flux produced by t ...", "... , and an in- ductance, L, or reactance, a; = 2 irfL^ which represents the mag- netic flux produced by the current in the armature circuit, and interlinked with this circuit. Thus, if ^^ = voltage induced in the armature circuit by its rotation through the magnetic field — or, as now more usually the case, the rotation of the magnetic field through the armature circuit — the terminal voltage of the armature circuit is ^ = ^o-(r+jx)/. In Fig. 110 is shown diagrammatically the path of the field flux, in two different po ...", "... he mag- netic flux produced by the current in the armature circuit, and interlinked with this circuit. Thus, if ^^ = voltage induced in the armature circuit by its rotation through the magnetic field — or, as now more usually the case, the rotation of the magnetic field through the armature circuit — the terminal voltage of the armature circuit is ^ = ^o-(r+jx)/. In Fig. 110 is shown diagrammatically the path of the field flux, in two different positions, A with an armature slot standing mid- way between two field pol ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-11", "section_label": "Chapter 12: Frequency Converter Or General Alternating Current Transformer", "section_title": "Frequency Converter Or General Alternating Current Transformer", "kind": "chapter", "sequence": 11, "number": 12, "location": "lines 14897-17124", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-11/", "snippets": [ "CHAPTER XII FREQUENCY CONVERTER OR GENERAL ALTERNATING- CURRENT TRANSFORMER 103. In general, an alternating-current transformer conafete of a magnetic circuit, interlinked with two electric circuits or sets of electric circuits, the primary circuit, in which power, sup- plied by the impressed voltage, is consumed, and the secondary circuit, in which a corresponding amount of electric power is produced; or in ot ...", "... in which the secondary is mounted niovably with regards to the primary, in such a manner that, while set in motion, it still remains in the primary field of force. This requires, i hat the induction motor field is not constant in one direction, but that a magnetic field exists in every direction, in other words that the magnetic field successively assumes all directions, as a so- called rotating field. The induction motor and the stationary transformer thus are merely two applications of the same structure, the former u ...", "... mary, in such a manner that, while set in motion, it still remains in the primary field of force. This requires, i hat the induction motor field is not constant in one direction, but that a magnetic field exists in every direction, in other words that the magnetic field successively assumes all directions, as a so- called rotating field. The induction motor and the stationary transformer thus are merely two applications of the same structure, the former using the mechanical thrust, the latter only the electrical power ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-19", "section_label": "Chapter 19: Commutatob Motobs", "section_title": "Commutatob Motobs", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 21339-22387", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "snippets": [ "... ve a rotary effort in the one direction, and in the other half the current is induced to 292 ALTERNATING-CURRENT PHENOMENA, [§ 193 give a rotary effort in the opposite direction, as shown by the arrows in Fig. 141. In the induction motor a second magnetic field is used to act upon the currents induced by the first, or inducing magnetic field, and thereby cause a rotation. That means the motor consists of a primary electric circuit, inducing Fig. 14h in the armature the secondary currents, and a primary mag ...", "... ed to 292 ALTERNATING-CURRENT PHENOMENA, [§ 193 give a rotary effort in the opposite direction, as shown by the arrows in Fig. 141. In the induction motor a second magnetic field is used to act upon the currents induced by the first, or inducing magnetic field, and thereby cause a rotation. That means the motor consists of a primary electric circuit, inducing Fig. 14h in the armature the secondary currents, and a primary magnetizing circuit producing the magnetism to act upon the secondary currents. In t ...", "... ng circuit producing the magnetism to act upon the secondary currents. In the polyphase induction motor both functions of the primary circuit are usually combined in the same coils ; that is, each primary coil inchices secondary currents, and pro- duces magnetic flux acting upon secondary currents induced by another primary coil. §1941 COMMUTATOR MOTORS. 194. In the repulsion motor the difficulty due to the equal and opposite rotary efforts, caused by the induced armature currents when acted upon by the induci ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-21", "section_label": "Chapter 21: Dibtobtiox Of Wavs-Shafe And Its Causes", "section_title": "Dibtobtiox Of Wavs-Shafe And Its Causes", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 23274-24559", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "snippets": [ "... effect will cause distortion of the current wave, while with a sine wave of current passing through the circuit, a distorting effect will cause higher harmonics of E.M.F. 213. In a conductor revolving with uniform velocity through a uniform and constant magnetic field, a sine wave of E.M.F. is induced. In a circuit with constant resistance and constant reactance, this sine wave of E.M.F. produces 1214] DISTORTION OF WAVE-SHAPE. 321 a sine wave of current. Thus distortion of the wave-shape or higher harmonics may be ...", "... of E.M.F. produces 1214] DISTORTION OF WAVE-SHAPE. 321 a sine wave of current. Thus distortion of the wave-shape or higher harmonics may be due to : lack of uniformity of the velocity of the revolving conductor ; lack of uniformity or pulsation of the magnetic field ; pulsation of the resis- tance ; or pulsation of the reactance. The first two cases, lack of uniformity of the rotation or of the magnetic field, cause higher harmonics of E.M.F. at open circuit. The last, pulsation of resistance and reac- tance, cause ...", "... to : lack of uniformity of the velocity of the revolving conductor ; lack of uniformity or pulsation of the magnetic field ; pulsation of the resis- tance ; or pulsation of the reactance. The first two cases, lack of uniformity of the rotation or of the magnetic field, cause higher harmonics of E.M.F. at open circuit. The last, pulsation of resistance and reac- tance, causes higher harmonics only with a current flowing in the circuit, that is, under load. Lack of uniformity of the rotation is of no practical in- tere ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-05", "section_label": "Lecture 5: Single-Energy Tra.Nsient Of Ironclad Circuit", "section_title": "Single-Energy Tra.Nsient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3387-3720", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-05/", "snippets": [ "LECTURE V. SINGLE-ENERGY TRA.NSIENT OF IRONCLAD CIRCUIT. 22. Usually in electric circuits; current, voltage, the magnetic field and the dielectric field are proportional to each other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field conta ...", "... the magnetic field and the dielectric field are proportional to each other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnetic materials, or if the dielectric field reaches densities beyond the dielectric strength of the carrier of the field, etc.; and the proportionality between current or voltage and their respective fields, the magnetic and the ...", "... he current, or the capacity is not constant, but varies with the voltage. The most important case is that of the ironclad magnetic cir- cuit, as it exists in one of the most important electrical apparatus, the alternating-current transformer. If the iron magnetic circuit contains an air gap of sufficient length, the magnetizing force con- sumed in the iron, below magnetic saturation, is small compared with that consumed in the air gap, and the magnetic flux, therefore, is proportional to the current up to the values where ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-05", "section_label": "Lecture 5: Single-Energy Transient Of Ironclad Circuit", "section_title": "Single-Energy Transient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2972-3286", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "snippets": [ "LECTURE V. SINGLE-ENERGY TRANSIENT OF IRONCLAD CIRCUIT. 22. Usually in electric circuits, current, voltage, the magnetic field and the dielectric field are proportional to each other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field conta ...", "... the magnetic field and the dielectric field are proportional to each other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnetic materials, or if the dielectric field reaches densities beyond the dielectric strength of the carrier of the field, etc. ; and the proportionality between current or voltage and their respective fields, the magnetic and the ...", "... he current, or the capacity is not constant, but varies with the voltage. The most important case is that of the ironclad magnetic cir- cuit, as it exists in one of the most important electrical apparatus, the alternating-current transformer. If the iron magnetic circuit contains an air gap of sufficient length, the magnetizing force con- sumed in the iron, below magnetic saturation, is small compared with that consumed in the air gap, and the magnetic flux, therefore, is proportional to the current up to the values where ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-14", "section_label": "Lecture 14: Alternating Current Railway Motor", "section_title": "Alternating Current Railway Motor", "kind": "lecture", "sequence": 14, "number": 14, "location": "lines 8649-9342", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-14/", "snippets": [ "... n direction to the current in the armature, and of the same number of ampere turns ; so that the armature ampere turns and the ampere turns of the compensating winding neutralize each other, and the armature i8o GENERAL LECTURES reaction, that is, the magnetic flux produced by the armature current, and the self-induotion caused by it, disappear. This compensating winding for neutralizing the armature self-induction was introduced by R. Eickemeyer in the early days of the alternating current commutator motor, and si ...", "... inding F, and a compensating winding C. Since the compensating winding cannot be identically at the same place as the armature winding (the one being located in slots in the pole faces, the other in slots in the armature face) there still exists a small magnetic flux produced by the armature winding : the \"leakage flux\", analogous to the leakage flux of the induction motor ; and the number of armature turns cannot be increased indefinitely, otherwise the armature self- induction, due to this leakage flux, would become ...", "... ature turns equal to 3 to 5 times the field turns ; at this proportion, the power factor is already very good at low speeds, and the motor is industrially satisfactory in this regard. For best results, that is, complete compensation and there- fore zero magnetic field of armature reaction, it is, however, necessary notlonly to have the same number of ampere turns in the compensating winding as on the armature, but also to have these ampere turns distributed in the same manner around the circumference. With the usual ar ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1120-1683", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-01/", "snippets": [ "... actance, X, refers to the wattless or reactive component of e.m.f., or the e.m.f. in quadrature with the current. 3. The principal sources of reactance are electromagnetism and capacity. Electromagnetism An electric current, i, in a circuit produces a magnetic flux surrounding the conductor in lines of magnetic force (or more correctly, lines of magnetic induction), of closed, circular, or other form, which alternate with the alternations of the current, INTRODUCTION 3 and thereby generate an e.m.f. in the condu ...", "... conductor in lines of magnetic force (or more correctly, lines of magnetic induction), of closed, circular, or other form, which alternate with the alternations of the current, INTRODUCTION 3 and thereby generate an e.m.f. in the conductor. Since the magnetic flux is in phase with the current, and the generated e.m.f. 90°, or a quarter period, behind the flux, this e.m.f. of self-induction lags 90°, or a quarter period, behind the current; that is, is in quadrature therewith, and therefore wattless. If now $ = the ...", "... is in phase with the current, and the generated e.m.f. 90°, or a quarter period, behind the flux, this e.m.f. of self-induction lags 90°, or a quarter period, behind the current; that is, is in quadrature therewith, and therefore wattless. If now $ = the magnetic flux produced by, and interlinked with, the current, i (where those lines of magnetic force which are interlinked ?i-fold, or pass around n turns of the conductor, are counted n times), the ratio, —, is denoted by L, and called the inductance of the circuit. ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-06", "section_label": "Chapter 6: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 11051-12221", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-06/", "snippets": [ "... preferable not to consider the relations between the different forms of energy at all, but to use the law of conservation of energy to relate the different forms of energy, which are involved. Thus, when mechanical motions are produced by the action of a magnetic field on an electric circuit, energy is consumed in the electric circuit, by an induced e.m.f. At the same time, the stored magnetic energy of the system may change. By the law of conservation of energy, we have: Electric energy consumed by the induced e.m.f, ...", "... is constant dming the motion of the armatm'e of the electromagnet, from its initial position 1, to its final position 2,1 = the length of this motion, or the stroke of the electromagnet, in centimeters, and n = number of turns of the magnet winding. The magnetic flux ^, and the inductance L=-^10-8 (2) to of the magnet, vary during the motion of its armature, from a ^^fiiiumum value, $, = Mil 108 (3) n ^ the initial position, to a maximum value, ^, = 12^ 108 (4) n ^ the end position of the armature. ...", "... ectromagnet 64. If a constant alternating potential, eo, is impressed upon an electromagnet, and the voltage consumed by the resistance, ir, can be neglected, the voltage consumed by the reactance, x, is constant and is the terminal voltage, eo, thus the magnetic flux, $, also is constant during the motion of the armature of the electromagnet. The current, i, however, varies, and decreases from a maximiun, ^l, in the initial position, to a minimum, 12, in the end position of the armature, while the inductance increases ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-23", "section_label": "Chapter 1: The Constants Of The Electric Circuit", "section_title": "The Constants Of The Electric Circuit", "kind": "chapter", "sequence": 23, "number": 1, "location": "lines 1317-1992", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "snippets": [ "... are conjugate pencils of circles. 2. Neither the power consumption in the conductor, nor the electromagnetic field, nor the electrostatic field, are pro- portional to the flow of energy through the circuit. The product, however, of the intensity of the magnetic field, , and the intensity of the electrostatic field, \"^ is proportional to the flow of energy or the power, P, and the power P is there- fore resolved into a product of two components, i and e, which are chosen proportional respectively to the intensity of ...", "... , and the intensity of the electrostatic field, \"^ is proportional to the flow of energy or the power, P, and the power P is there- fore resolved into a product of two components, i and e, which are chosen proportional respectively to the intensity of the magnetic field and of the electrostatic field V. That is, putting P = ie (1) we have = Li = the intensity of the electromagnetic field. (2) Mf = Ce = the intensity of the electrostatic field. (3) The component i, called the current, is defined as that fac ...", "... P = ie (1) we have = Li = the intensity of the electromagnetic field. (2) Mf = Ce = the intensity of the electrostatic field. (3) The component i, called the current, is defined as that factor of the electric power P which is proportional to the magnetic field, and the other component e, called the voltage, is defined as that factor of the electric power P which is proportional to the electrostatic field. Current i and voltage e, therefore, are mathematical fictions, factors of the power P, introduced to repre ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-107", "section_label": "Apparatus Section 1: Induction Machines: General", "section_title": "Induction Machines: General", "kind": "apparatus-section", "sequence": 107, "number": 1, "location": "lines 18949-19165", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-107/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-107/", "snippets": [ "... nt in a direct-current motor the direction of rotation remains the same. Thus theoretically any continuous-current motor should operate also with alternating currents. Obviously in this case not only the armature but also the magnetic field of the motor must be thoroughly laminated to exclude eddy currents, and care taken that the currents in the field and armature circuits reverse simultaneously. Obviously the simplest way of fulfilling the latter condition is ...", "... In the latter arrangement the armature winding of the motor is fed by one, the field winding by the other phase of a quarter-phase sys- tem, and thus the current in the armature brought approximately into phase with the magnetic flux of the field. Such an arrangement obviously loads the two phases of the system unsymmetrically, the one with the armature power current, the other with the lagging field current. To balance the system two such motors may ...", "... er so as to offer a closed sec- ondary to the primary circuits, irrespective of the relative motion. The primary consists of one or several circuits. In consequence of the relative motion of the primary and secondary, the magnetic circuit of the induction motor must be arranged so that the secondary while revolving does not leave the magnetic field of force. That means, the magnetic field of force must be of constant intensity in all directions, or, in ot ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-14", "section_label": "Chapter 16: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 14, "number": 16, "location": "lines 19374-20293", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-14/", "snippets": [ "... ine is a constant. While this is more or less approximately the case in many alternators, in others, especially in machines of large armature reaction, the reactance, x, is variable, and is different in the different positions of the armature coils in the magnetic circuit. This variation of the reactance causes phenomena which do not find their explanation by the theoretical calculations made under the assumption of constant reactance. It is known that synchronous motors or converters of large and variable reactance keep ...", "... ear if the generator field circuit is broken, or even reversed to a small negative value, in which tatter case the current is against the e.m.f., Ea, of the generator. Furthermore, a shuttle armature without any winding (Fig. 120) will in an alternating magnetic field revolve when once brought up to synchronism, and do considerable work as a motor. These phenomena are not due to remanent magnetism nor to the magnetizing effect of eddy currents, because they exist also in machines with laminated fields, and exist if th ...", "... s self-excitation by reactive armature currents. In a synchronous motor a lagging, in a generator a leading armature current magnetizes the field, and in such a case, even without any direct-current field excitation, there is a field excitation and thus a magnetic field flux, produced by the m.m.f. of the reactive component of the armature current*. In the polyphase machine, this is constant in intensity and direc- tion, in the single-phase machine constant in direction, hut pul- sating in intensity, and the intensity pu ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-20", "section_label": "Chapter 22: Unipolar Machines", "section_title": "Unipolar Machines", "kind": "chapter", "sequence": 20, "number": 22, "location": "lines 31716-32137", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-20/", "snippets": [ "... rce of the pole, N, and this voltage can be supplied to an external cir- cuit, D, by stationary brushes, Bi and B2) bearing on the ends of the revolving conductor, C. The voltage is: e = /$ 10-8, where / is the number of revolutions per second, $ the magnetic flux of the magnet, cut by the conductor, C. N Fig. 215. — Diagrammatic illustration of unipolar machine with two high- speed collectors. Such a machine is called a unipolar machine, as the conductor during its rotation traverses the same polarity, in di ...", "... shown in Fig. 216, the peripheral speed of motion of brush, J32, on its collector ring can be reduced. However, at least one brush, J5i, in Fig. 216, must bear on a collector ring (not shown in Figs. 215 and 216) at full conductor speed, because the total magnetic flux cut by the conductor, C, must pass through this collector ring on which Bi bears. Thus an essential char- acteristic of the unipolar machine is collection of the current from the periphery of the revolving conductor, at its maximum speed. It is the unsolv ...", "... a. 216. — Diagrammatic illustration of unipolar machine with one high- speed collector. minute, which has stood in the way of the commercial intro- duction of unipolar machines. Electromagnetic induction is due to the relative motion of con- ductor and magnetic field, and every electromagnetic device is thus reversible with regards to stationary and rotary elements. Howeyer, the hope of eliminating high-speed collector rings in the unipolar machine, by having the conductor standstill and the magnet revolve, is a falla ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-02", "section_label": "Chapter 2: Potential Series And Exponential Function", "section_title": "Potential Series And Exponential Function", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3492-6063", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-02/", "snippets": [ "... l one is found which satisfies the equation. In electrical engineering, currents and voltages are dealt with as functions of time. The current and c.m.f. giving the power lost in resistance are related to each other by Ohm's law. Current also produces a magnetic field, and this magnetic field by its changes generates an e.m.f. — the e.m.f. of self- inductance. In this case, e.m.f. is related to the change of current; that is, the differential coefficient of the current, and thus also to the differential coefficient of ...", "... sfies the equation. In electrical engineering, currents and voltages are dealt with as functions of time. The current and c.m.f. giving the power lost in resistance are related to each other by Ohm's law. Current also produces a magnetic field, and this magnetic field by its changes generates an e.m.f. — the e.m.f. of self- inductance. In this case, e.m.f. is related to the change of current; that is, the differential coefficient of the current, and thus also to the differential coefficient of e.m.f., since the e.m.f. ...", "... 1. 54. In a 4-pole 500-volt 50-kw. direct-current shunt motor, the resistance of the field circuit, inclusive of field rheostat, is 250 ohms. Each field pole contains 4000 turns, and produces at 500 volts impressed upon the field circuit, 8 megalines of magnetic flux per pole. What is the equation of the field current, and how much time after closing the field switch is required for the field cur- rent to reach 90 per cent of its final value? Let r be the resistance of the field circuit, L the inductance of the fie ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-03", "section_label": "Chapter 3: Law Of Electromagnetic Induction", "section_title": "Law Of Electromagnetic Induction", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 2012-2148", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-03/", "snippets": [ "CHAPTER III LAW OF ELECTROMAGNETIC INDUCTION 13. If an electric conductor moves relatively to a magnetic field, an e.m.f. is generated in the conductor which is propor- tional to the intensity of the magnetic field, to the length of the conductor, and to the speed of its motion perpendicular to the magnetic field and the direction of the conductor; or, in other wo ...", "CHAPTER III LAW OF ELECTROMAGNETIC INDUCTION 13. If an electric conductor moves relatively to a magnetic field, an e.m.f. is generated in the conductor which is propor- tional to the intensity of the magnetic field, to the length of the conductor, and to the speed of its motion perpendicular to the magnetic field and the direction of the conductor; or, in other words, proportional to the number of lines of magnetic force cut per second by the conductor. As a pract ...", "... 13. If an electric conductor moves relatively to a magnetic field, an e.m.f. is generated in the conductor which is propor- tional to the intensity of the magnetic field, to the length of the conductor, and to the speed of its motion perpendicular to the magnetic field and the direction of the conductor; or, in other words, proportional to the number of lines of magnetic force cut per second by the conductor. As a practical unit of e.m.f., the volt is defined by the e.m.f. generated in a conductor, which cuts 10^ = 100 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "section_label": "Chapter 14: Dielectric Losses", "section_title": "Dielectric Losses", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "... resistance,\" so the energy losses in the dielectric lead to a power component in the condensive reactance, which may be repre- sented by an \"effective resistance of dielectric losses\" or an \"effective conductance of dielectric losses.\" In the alternating magnetic field, power is consumed by mag- netic hysteresis. This is proportional to the frequency, and to the 1.6*'' power of the magnetic density, and is considerable, amounting in a closed magnetic circuit to 40 to 60 per cent, of the total volt-amperes. In the diel ...", "... effective conductance of dielectric losses.\" In the alternating magnetic field, power is consumed by mag- netic hysteresis. This is proportional to the frequency, and to the 1.6*'' power of the magnetic density, and is considerable, amounting in a closed magnetic circuit to 40 to 60 per cent, of the total volt-amperes. In the dielectric field, the energy losses usually are very much smaller, rarely amounting to more than a few per cent., though they may at high temperature in cables rise as high as 40 to 60 per cent. Th ...", "... except that at least a part of this dielectric loss is possibly consumed in chemical and mechanical disintegration of the insulating material, while the magnetic hysteresis loss is entirely converted to heat. Leakage 117. The eddy current losses in the magnetic field are the ih loss of the currents flowing in the magnetic material, and as such are proportional to the square of the frequency and of the mag- netic density: P = eyPB^ where 7 = conductivity of the magnetic material. This expression obviously holds on ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-21", "section_label": "Chapter 21: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 22302-23970", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-21/", "snippets": [ "CHAPTER XXI ALTERNATING-CURRENT GENERATOR 185. In the alternating-current generator, e.m.f. is generated in the armature conductors by their relative motion through a constant or approximately constant magnetic field. When yielding current, two distinctly different m.m.fs. are acting upon the alternator armature — the m.m.f. of the field due to the field-exciting spools, and the m.m.f. of the armature current. The former is constant, or approximately so, while the l ...", "... FiG. 129. directional; but pulsating in a single-phase alternator. In the polyphase alternator, when evenly loaded or balanced, the result- ant m.m.f. of the armature current is more or less constant. The e.m.f. generated in the armature is due to the magnetic flux passing through and interhnked with the armature con- ductors. This flux is produced by the resultant of both m.m.fs., that of the field, and that of the armature. On open-circuit, the m.m.f. of the armature is zero, and the e.m.f. of the armature is due ...", "... etrical. An exception to this statement may take place only in those types of alternators where the magnetic reluctance of the arma- ture is different in different directions; thereby, during the syn- chronous rotation of the armature, a pulsation of the magnetic flux passing through it is produced. This pulsation of the mag- netic flux generates e.m.f. in the field-spools, and thereby makes the field current pulsating also. Thus, we have, in this case, even on open-circuit, no rotation through a constant magnetic field ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-15", "section_label": "Chapter 15: The General Alternating-Current Transformer Or Frequency Converter", "section_title": "The General Alternating-Current Transformer Or Frequency Converter", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 12683-13648", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "snippets": [ "CHAPTER XV. THE GENERAL ALTERNATING-CURRENT TRANSFORMER OR FREQUENCY CONVERTER. 141. The simplest alternating-current apparatus is the alternating-current transformer. It consists of a magnetic- circuit, interlinked with two electric circuits or sets of electric circuits. The one, the primary circuit, is excited by an impressed E.M.F., while in the other, the secondary circuit, an E.M.F. is induced. Thus, in the primary circuit, power is consumed, in the ...", "... tion that the secondary circuit, while revolving with regard to the primary, does not leave the primary field of magnetic force, requires that this field is not undirectional, but that an active field exists in every direction. One way of producing such a magnetic field is by exciting different primary circuits angularly displaced in space with each other by currents of different phase. Another way is to excite the primary field in one direction only, and get the cross magnetization, or the angularly displaced magnetic ...", "... etic field is by exciting different primary circuits angularly displaced in space with each other by currents of different phase. Another way is to excite the primary field in one direction only, and get the cross magnetization, or the angularly displaced magnetic field, by the reaction of the secondary current. 220 ALTERNATING-CURRENT PHENOMENA. We see, consequently, that the stationary transformer and the induction motor are merely different applications of the same apparatus, comprising a magnetic circuit in- terl ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-17", "section_label": "Chapter 17: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16362-17596", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "snippets": [ "CHAPTER XVII. ALTERNATING-CURRENT GENERATOR. 182. In the alternating-current generator, E.M.F. is induced in the armature conductors by their relative motion through a constant or approximately constant magnetic field. When yielding current, two distinctly different M.M.Fs. are acting upon the alternator armature — the M.M.F. of the field due to the field-exciting 'spools, and the M.M.F. of the armature current. The former is constant, or approx- imately so, while th ...", "... may take place only in those types of alternators where the magnetic reluctance of the armature is different in different directions ; thereby, 298 AL TERNA TING-CURRENT PHENOMENA. during the synchronous rotation of the armature, a pulsa- tion of the magnetic flux passing through it is produced. This pulsation of the magnetic flux induces E.M.F. in the field spools, and thereby makes the field current pulsating also. Thus, we havet in this case, even on open circuit, no Fig. 126. rotation through a constant mag ...", "... c reluctance of the armature is different in different directions ; thereby, 298 AL TERNA TING-CURRENT PHENOMENA. during the synchronous rotation of the armature, a pulsa- tion of the magnetic flux passing through it is produced. This pulsation of the magnetic flux induces E.M.F. in the field spools, and thereby makes the field current pulsating also. Thus, we havet in this case, even on open circuit, no Fig. 126. rotation through a constant magnetic field, but rotation through a pulsating field, which makes the ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-02", "section_label": "Chapter 2: Multiple Squirrel-Cage Induction Motor", "section_title": "Multiple Squirrel-Cage Induction Motor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3543-5554", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-02/", "snippets": [ "... cage, and thus of higher reactance, a \"double squirrel-cage induction motor\" in derived, which to some extent combines the characteristics of the high- resistance and the low-resistance secondary. That is, at start- ing and low speed, the frequency of the magnetic flux in the arma- ture, and therefore the voltage induced in the secondary winding is high, and the high-resistance squirrel cage thus carries con- siderable current, gives good torque and torque efficiency, while the low-resistance squirrel cage is ineffectiv ...", "... nd the innermost squirrel cage, of low resistance ami high reactance, gives its torque at full speed, near synchronism. Mechanically, the rotor iron may be slotted down to the inner- most squirrel cage, so as to avoid the excessive reactance of a closed magnetic circuit, that is, have the magnetic leakage flux or self-inductive flux pass an air gap. 19. In the calculation of the standard induction motor, it is usual to start with the mutual magnetic flux, *, or rather with the voltage induced by this flux, the mutual in ...", "... uirrel cage, so as to avoid the excessive reactance of a closed magnetic circuit, that is, have the magnetic leakage flux or self-inductive flux pass an air gap. 19. In the calculation of the standard induction motor, it is usual to start with the mutual magnetic flux, *, or rather with the voltage induced by this flux, the mutual inductive voltage E — e, as it is most convenient, with the mutual inductive voltage, c, as starting point, to pass to the secondary current by the self-inductive impedance, to the primary cu ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "CHAPTER IV INDUCTION MOTOR WITH SECONDARY EXCITATION 38. While in the typical synchronous machine and eommu- tating machine the magnetic field is excited by a direct current, characteristic of the induction machine is, that the magnetic field is excited by an alternating current derived from the alter- nating supply voltage, just as in the alternating-current trans- former. As the alternating ma ...", "CHAPTER IV INDUCTION MOTOR WITH SECONDARY EXCITATION 38. While in the typical synchronous machine and eommu- tating machine the magnetic field is excited by a direct current, characteristic of the induction machine is, that the magnetic field is excited by an alternating current derived from the alter- nating supply voltage, just as in the alternating-current trans- former. As the alternating magnetizing current is a wattless reactive current, the result is, that the alternating-current input ...", "... input into the induction motor is always lagging, the more so, the larger a part of the total current is given by the magnetizing current. To secure good power-factor in an induction motor, the magnetizing current, that i«, the current which produces the magnetic field flux, must be kept as small as possible. This means as small an air gap between stator and rotor as mechanic- ally permissible, and as large a number of primary turns per pole, that is, as large a pole pitch, as economically permissible. In motors, in wh ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-48", "section_label": "Chapter 8: Velocity Of Propagation Of Electric Field", "section_title": "Velocity Of Propagation Of Electric Field", "kind": "chapter", "sequence": 48, "number": 8, "location": "lines 26095-27002", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "snippets": [ "... turn conductor, that is, a conductor without return conductor, equation (6) gives L = oo ; that is, a finite length of an infinitely long conductor without return conductor has an infinite inductance L and inversely, zero capacity C. In equation (6) the magnetic field is assumed as instantaneous, that is, the velocity of propagation of the magnetic field is neglected. With alternating currents traversing the conductor this is permissible when the distance to the return conductor is a negligible fraction of the wave len ...", "... ; that is, a finite length of an infinitely long conductor without return conductor has an infinite inductance L and inversely, zero capacity C. In equation (6) the magnetic field is assumed as instantaneous, that is, the velocity of propagation of the magnetic field is neglected. With alternating currents traversing the conductor this is permissible when the distance to the return conductor is a negligible fraction of the wave length; that is, if Z' is § negligible compared with -, where S = the speed of light and ...", "... quencies are required, and therefore the wave is of moderate length, that is, the velocity of propagation of the magnetic (and electrostatic) field must be considered when investigating the self-induction and the mutual induction of such a conductor. The magnetic field at a distance I from the conductor and at time t corresponds to the current in the conductor at the time t - t', where if is the time required for the electric field to travel the distance I, that is, t' = -, where $ = the speed of light; o or, the ma ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-03", "section_label": "Theory Section 3: Generation of E.m.f.", "section_title": "Generation of E.m.f.", "kind": "theory-section", "sequence": 3, "number": 3, "location": "lines 1033-1243", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-03/", "snippets": [ "i 3. GENERATION OF E.M.F. 15. A closed conductor, convolution or turn, revolving in a magnetic field, passes during each revolution through two positions of maximum inclosure of lines of magnetic force A in Fig. 5, and two positions of zero inclosure of lines of mag- netic force B in Fig. 5. 1 cm.3 refers to a cube w ...", "... . is, E = 4 fn$ absolute units, = 4fn3> ID\"8 volts. FIG. 5. — Generation of e.m.f. If / is given in hundreds of cycles, <£ in megalines, E = 4n$ volts. If a coil revolves with uniform velocity through a uniform magnetic field, the magnetism inclosed by the coil at any instant is, $ COS T where $ = the maximum magnetism inclosed by the coil arid T = angle between coil and its position of maximum inclosure of magnetism. The e.m.f. generated ...", "... ed in the coil, which varies with the rate of cutting or change of $ cos T, is thus, e = EQ sin T, where EQ is the maximum value of e.m.f., which takes place for T = 90°, or at the position of zero inclosure of magnetic flux since in this position the rate of cutting is greatest. 2 Since avg. (sin T) = -, the average generated e.m.f. is, GENERATION OF E.M.F. 13 Since, however, we found above that E = 4 fn& is the average generated ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-14", "section_label": "Chapter 14: The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "section_title": "The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14089-14918", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "snippets": [ "CHAPTER XIV. THE OSNI!RAIj AIiTEBNATINa-CUBBENT TBAKBFOBMSB. 131. The simplest alternating-current apparatus is the alternating-current transformer. It consists of a magnetic circuit, interlinked with two electric circuits or sets of electric circuits. The one, the primary circuit, is excited by an impressed E.M.F., while in the other, the secondary circuit, an E.M.F. is induced. Thus, in the primary circuit, power is consumed, in the ...", "... ition that the secondary circuit, while moving with regard to the primary, does not leave the primary field of magnetic force, requires that this field is not undirec- tional, but that an active field exists in every direction. One way of producing such a magnetic field is by exciting different primary circuits angularly displaced in space with each other by currents of different phase. Another way is to excite the primary field in one direction only, and get the cross magnetization, or the angularly displaced mag- neti ...", "... mag- netic field, by the reaction of the secondary current. 194 AL TERNA TING-CURRENT PHENOMENA. [§131 We see, consequently, that the stationary transformer and the induction motor are merely different applications of the same apparatus, comprising a magnetic circuit in- terlinked with two electric circuits. Such an apparatus can properly be called a ^^ general altertiating- current trans- former' The equations of the stationary transformer and those of the induction motor are merely specializations of the general ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-16", "section_label": "Chapter 16: Aiitebnatingh-Current Osnebator", "section_title": "Aiitebnatingh-Current Osnebator", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 17025-18828", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "snippets": [ "CHAPTER XVI. AIiTEBNATINGh-CURRENT OSNEBATOR. 159. In the alternating-current generator, E.M.F. is induced in the armature conductors by their relative motion through a constant or approximately constant magnetic field. When yielding current, two distinctly different M.M.Fs. are acting upon the alternator armature — the M.M.F. of the field due to the field-exciting spools, and the M.M.F. of the armature current. The former is constant, or approx- imately so, while the ...", "... place only in those types of alternators where the magnetic reluctance of the armature is different in different directions ; thereby, 1 160] AL TERN A TING-CURRENT GENERA TOR. 235 during the synchronous rotation of the armature, a pulsa- tion of the magnetic flux passing through it is produced. This pulsation of the magnetic flux induces E.M.F. in the field spools, and thereby makes the field current pulsating also. Thus, we have, in this case, even on open circuit, no Fig. 110. rotation through a constant mag ...", "... nce of the armature is different in different directions ; thereby, 1 160] AL TERN A TING-CURRENT GENERA TOR. 235 during the synchronous rotation of the armature, a pulsa- tion of the magnetic flux passing through it is produced. This pulsation of the magnetic flux induces E.M.F. in the field spools, and thereby makes the field current pulsating also. Thus, we have, in this case, even on open circuit, no Fig. 110. rotation through a constant magnetic field, but rotation through a pulsating field, which makes the ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-21", "section_label": "Chapter 23: Review", "section_title": "Review", "kind": "chapter", "sequence": 21, "number": 23, "location": "lines 32138-32819", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-21/", "snippets": [ "... er Inductively Compensated Single-phase Series Motor. — 193. Single-phase commutating machine with series field and inductive compensating winding. Eickemeyer Inductor Alternator. — 160. Inductor alternator with field coils parallel to shaft, so that the magnetic flux disposi- tion is that of a bipolar or multipolar machine, in which the multitooth inductor takes the place of the armature of the stand- ard machine. Voltage induction then takes place in armature coils in the pole faces, and the magnetic flux in the indu ...", "... so that the magnetic flux disposi- tion is that of a bipolar or multipolar machine, in which the multitooth inductor takes the place of the armature of the stand- ard machine. Voltage induction then takes place in armature coils in the pole faces, and the magnetic flux in the inductor re- verses, with a frequency much lower than that of the induced voltage. This type of inductor machine is specially adopted for moderately high frequencies, 300 to 2000 cycles, and used in in- ductor alternators and inductor converters. I ...", "... chronism it may be either. Poor power-factor and small output make it feasible only in very small BU6S, BUCt H motor meters. Inductor Machines. — XVII, 150. Synchronous machine, gen- erator or motor, in which field and armature coils stand still ami the magnetic field flux is constant, and the voltage is induced b) changing the flux path, that is, admitting and withdrawing the flux from the armature coils by means of a revolving inductor. The inducing Hux in the armature coils thus does not alternate, but pulsates with ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-02", "section_label": "Theory Section 2: Magnetism and E.m.f.", "section_title": "Magnetism and E.m.f.", "kind": "theory-section", "sequence": 2, "number": 2, "location": "lines 910-1032", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-02/", "snippets": [ "2. MAGNETISM AND E.M.F. 11. In an electric conductor moving relatively to a magnetic field, an e.m.f. is generated proportional to the rate of cutting of the lines of magnetic force by the conductor. Unit e.m.f. is the e.m.f. generated in a conductor cutting one line of magnetic force per second. 108 times u ...", "... temperature. The resistance r of a conductor of length I, area or section A, ... lp and resistivity p is r = -7\" 12. If the current in the electric circuit changes, starts, or stops, the corresponding change of the magnetic field of the current generates an e.m.f in the conductor carrying the current, which is called the e.m.f. of self-induction. If the e.m.f. in an electric circuit moving relatively to a magnetic field produces a current in the ...", "... corresponding change of the magnetic field of the current generates an e.m.f in the conductor carrying the current, which is called the e.m.f. of self-induction. If the e.m.f. in an electric circuit moving relatively to a magnetic field produces a current in the circuit, the magnetic field produced by this current is called its magnetic reaction. The fundamental law of self-induction and magnetic reaction is that these effects take place in such a directi ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-10", "section_label": "Theory Section 10: Hysteresis and Effective Resistance", "section_title": "Hysteresis and Effective Resistance", "kind": "theory-section", "sequence": 10, "number": 10, "location": "lines 3234-3585", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-10/", "snippets": [ "10. HYSTERESIS AND EFFECTIVE RESISTANCE 46. If an alternating current 01 = I, in Fig. 21, exists in a circuit of reactance x = 2 irfL and of negligible resistance, the HYSTERESIS AND EFFECTIVE RESISTANCE 49 magnetic flux produced by the current, 0$ = $, is in phase with the current, and the e.m.f. generated by this flux, or counter e.m.f. of self-inductance, OE'\" = E'\" = xl, lags 90 degrees be- hind the current. The e.m.f. consumed by ...", "... ssed upon a circuit of reactance x = 2 irfL and of negligible resistance, the current E\" 01 = I = - - lags 90 degrees behind the impressed e.m.f. x This current' is called the exciting or magnetizing current of the magnetic circuit, and is wattless. ' If the magnetic circuit contains iron or other magnetic mate- rial, energy is consumed in the magnetic circuit by a frictional resistance of the material against a change of magnetism, which is c ...", "... and of negligible resistance, the current E\" 01 = I = - - lags 90 degrees behind the impressed e.m.f. x This current' is called the exciting or magnetizing current of the magnetic circuit, and is wattless. ' If the magnetic circuit contains iron or other magnetic mate- rial, energy is consumed in the magnetic circuit by a frictional resistance of the material against a change of magnetism, which is called molecular magnetic friction. If the alte ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-106", "section_label": "Apparatus Section 9: Alternating-current Transformer: Reactors", "section_title": "Alternating-current Transformer: Reactors", "kind": "apparatus-section", "sequence": 106, "number": 9, "location": "lines 18813-18948", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-106/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-106/", "snippets": [ "IX. Reactors (Reactive Coils, Reactances) 129. The reactor consists of one electric circuit interlinked with a magnetic circuit, and its purpose is, not to transform power, but to produce wattless or reactive power, that is, lagging current, or what amounts to the same, leading voltage. While therefore theoretically we cannot speak of an ''efficienc ...", "... s high, that is, the efficiency low. In the transformer, the exciting ampere-turns are the (vector) difference between primary and secondary ampere-turns, are wasted, and therefore made as low as possible, by using a closed magnetic circuit. In the reactor, no secondary circuit exists, but the exciting ampere-turns are the purpose of the device, thus should be as large as possible. That is, to convert a trans- former into a reactor, the reluctance of the mag ...", "... uit. In the reactor, no secondary circuit exists, but the exciting ampere-turns are the purpose of the device, thus should be as large as possible. That is, to convert a trans- former into a reactor, the reluctance of the magnetic circuit must be increased so as to make the exciting ampere-turns equal to the total full-load ampere-turns of the structure as transformer. This is done by inserting an air gap into the magnetic circuit. Such a gap may be eithe ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-63", "section_label": "Apparatus Subsection 63: Direct-current Commutating Machines: C. Commutating Machines 197", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 197", "kind": "apparatus-subsection", "sequence": 63, "number": null, "location": "lines 11795-11863", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-63/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-63/", "snippets": [ "... e-turns armature reaction of the angle of shift of brushes TI requires an increase of field excitation by riFa. (Section VII.) 3. The distorting effect of armature reaction does not change the total m.m.f. producing the magnetic flux. If, however, mag- netic saturation is reached or approached in a part of the mag- netic circuit adjoining the air gap, the increase of magnetic density at the strengthened pole corner is less than the decrease at the w ...", "... reached or approached in a part of the mag- netic circuit adjoining the air gap, the increase of magnetic density at the strengthened pole corner is less than the decrease at the weakened pole corner, and thus the total magnetic flux with the same total m.m.f. is reduced, and to produce the same total magnetic flux an increased total m.m.f., that is, increase of field excitation, is required. This increase depends upon the saturation of the magnetic ...", "... he increase of magnetic density at the strengthened pole corner is less than the decrease at the weakened pole corner, and thus the total magnetic flux with the same total m.m.f. is reduced, and to produce the same total magnetic flux an increased total m.m.f., that is, increase of field excitation, is required. This increase depends upon the saturation of the magnetic circuit adjacent to the armature conductors. 4. The magnetic stray field of the mac ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-04", "section_label": "Chapter 4: Vector Representation", "section_title": "Vector Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2149-2759", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-04/", "snippets": [ "... mer, feeding through its secondary circuit an inductive load. For simplicity, we may neglect here the magnetic hysteresis, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the magnetic flux is zero and rising. The magnetic flux then passes its maxi- mum at the time ?? = 90°, and the phase of the magnetic flux thus is ?? = 90°, the flux thus represented by the vector 0* in Fig. 18, vertically downward. The e.m.f. generated by this mag- netic ...", "... cuit an inductive load. For simplicity, we may neglect here the magnetic hysteresis, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the magnetic flux is zero and rising. The magnetic flux then passes its maxi- mum at the time ?? = 90°, and the phase of the magnetic flux thus is ?? = 90°, the flux thus represented by the vector 0* in Fig. 18, vertically downward. The e.m.f. generated by this mag- netic flux in the secondary circuit, Ei, lag ...", "... s, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the magnetic flux is zero and rising. The magnetic flux then passes its maxi- mum at the time ?? = 90°, and the phase of the magnetic flux thus is ?? = 90°, the flux thus represented by the vector 0* in Fig. 18, vertically downward. The e.m.f. generated by this mag- netic flux in the secondary circuit, Ei, lags 90° behind the flux; thus its vector, OEi, passes the zero line, OA 90°, later th ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-46", "section_label": "Apparatus Section 3: Direct-current Commutating Machines: Generated E.m.fs.", "section_title": "Direct-current Commutating Machines: Generated E.m.fs.", "kind": "apparatus-section", "sequence": 46, "number": 3, "location": "lines 10778-10835", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-46/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-46/", "snippets": [ "... rect- current machine, as discussed in the preceding, is e = where e = generated e.m.f., / = frequency = number of pairs of poles X hundreds of rev. per sec., n = number of turns in series between brushes, and <£ = magnetic flux passing through the armature per pole, in megalines. In ring-wound machines, is one-half the flux per field pole, since the flux divides in the armature into two circuits, and each 178 ELEMENTS OF ELECTRICAL ENGIN ...", "... n a single-spiral multiple- wound armature with p poles. It is one-half as many in a double- spiral or double-reentrant, one-third as many in a triple-spiral winding, etc. By this formula, from frequency, series turns, and magnetic flux the e.m.f. is found, or inversely, from generated e.m.f., fre- quency, and series turns the magnetic flux per field pole is calculated: *--!-, 4/n From magnetic flux, and section and lengths of the different parts of the ...", "... double-reentrant, one-third as many in a triple-spiral winding, etc. By this formula, from frequency, series turns, and magnetic flux the e.m.f. is found, or inversely, from generated e.m.f., fre- quency, and series turns the magnetic flux per field pole is calculated: *--!-, 4/n From magnetic flux, and section and lengths of the different parts of the rnagnetic circuit, the densities and the ampere- turns required to produce these densities are derived, a ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-66", "section_label": "Apparatus Subsection 66: Direct-current Commutating Machines: C. Commutating Machines 201", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 201", "kind": "apparatus-subsection", "sequence": 66, "number": null, "location": "lines 11981-12083", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-66/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-66/", "snippets": [ "D. C. COMMUTATING MACHINES 201 is, in the armature during commutation an e.m.f. is generated by its rotation through a magnetic field. This magnetic field may be the magnetic field of armature reaction, or the reverse magnetic field of a commutating pole, or the fringe of the main field of the machine, into which the brushes are shifted. In this case ...", "D. C. COMMUTATING MACHINES 201 is, in the armature during commutation an e.m.f. is generated by its rotation through a magnetic field. This magnetic field may be the magnetic field of armature reaction, or the reverse magnetic field of a commutating pole, or the fringe of the main field of the machine, into which the brushes are shifted. In this case the commutation depend ...", "D. C. COMMUTATING MACHINES 201 is, in the armature during commutation an e.m.f. is generated by its rotation through a magnetic field. This magnetic field may be the magnetic field of armature reaction, or the reverse magnetic field of a commutating pole, or the fringe of the main field of the machine, into which the brushes are shifted. In this case the commutation depends upon the inductance and ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-03", "section_label": "Chapter 3: Iiaw Of Eucctbo-Maonimc Induction", "section_title": "Iiaw Of Eucctbo-Maonimc Induction", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 1973-2121", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-03/", "snippets": [ "CHAPTER III. IiAW OF EUCCTBO-MAONimC INDUCTION. 11. If an electric conductor moves relatively to a mag- netic field, an E.M.F. is induced in the conductor which is proportional to the intensity of the magnetic field, to the length of the conductor, and to the speed of its motion perpendicular to the magnetic field and the direction of the conductor ; or, in other words, proportional to the number of lines of magnetic force cut per second by the conductor. As a prac ...", "... 11. If an electric conductor moves relatively to a mag- netic field, an E.M.F. is induced in the conductor which is proportional to the intensity of the magnetic field, to the length of the conductor, and to the speed of its motion perpendicular to the magnetic field and the direction of the conductor ; or, in other words, proportional to the number of lines of magnetic force cut per second by the conductor. As a practical unit of E.M.F., the volt is defined as the E.M.F. induced in a conductor, which cuts 10« = 100, ...", "... second, of ' the flux inclosed by the turns, times 10~*. If the change of the flux inclosed by the turn, or by n turns, does not take place uniformly, the product of the number of turns, times change of flux per second, gives the average E.M.F. If the magnetic flux, *, alternates relatively to a number of turns, n — that is, when the turns either revolve through the flux, or the flux passes in and out of the turns, during each complete alternation or cycle, — the total flux is cut four times, twice passing into, and ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-03", "section_label": "Chapter 3: Law Of Electro-Magnetic Induction", "section_title": "Law Of Electro-Magnetic Induction", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 1606-1742", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-03/", "snippets": [ "CHAPTER III. LAW OF ELECTRO-MAGNETIC INDUCTION. 11. If an electric conductor moves relatively to a mag- netic field, an E.M.F. is induced in the conductor which is proportional to the intensity of the magnetic field, to the length of the conductor, and to the speed of its motion perpendicular to the magnetic field and the direction of the conductor ; or, in other words, proportional to the number of lines of magnetic force cut per second by the conductor. As a prac ...", "... 11. If an electric conductor moves relatively to a mag- netic field, an E.M.F. is induced in the conductor which is proportional to the intensity of the magnetic field, to the length of the conductor, and to the speed of its motion perpendicular to the magnetic field and the direction of the conductor ; or, in other words, proportional to the number of lines of magnetic force cut per second by the conductor. As a practical unit of E.M.F., the volt is defined as the E.M.F. induced in a conductor, which cuts 108 = 100, ...", "... r second, of the flux inclosed by the turns, times 10~8. If the change of the flux inclosed by the turn, or by n turns, does not take place uniformly, the product of the number of turns, times change of flux per second, gives the average E.M.F. If the magnetic flux, 4>, alternates relatively to a number of turns, n — that is, when the turns either revolve through the flux, or the flux passes in and out of the turns, the total flux is cut four times during each complete period or cycle, twice passing into, and twice ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-12", "section_label": "Chapter 14: Phase Conversion And Single-Phase Generation", "section_title": "Phase Conversion And Single-Phase Generation", "kind": "chapter", "sequence": 12, "number": 14, "location": "lines 17125-18412", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-12/", "snippets": [ "... , or inductance, or momentum or a combination thereof: Energy storage by capacity, that is, in the dielectric fu Id, required per kilovolt-ampere at 60 cycles about 200O <-.•■. ol space, at a cost of about $10. Inductance, that is. energy storage by the magnetic field, requires about 1000 c.e. per kilo- volt-ampere at 60 cycles, at a cost of $1, while energy storage by momentum, as kinetic mechanical energy, assuming iron moving at 30 meter-seconds, stores 1 kva. at 60 cycles by about 3 c.c., at a cost of 0.2c, thus is ...", "... the mass of the mechanical structure (motor, etc.) is revolving, and that the energy storage takes place by a pulsation of speed of per cent., then 1 kva. at 60 cycles would require 600 c.e. of terial, at 40c, Obviously, at the limits of dielectric or magnetic field strength, or at the limits of mechanical speeds, very much larger amounts of energy per bulk could be stored. Thus for instance, at the limits of steam-turbine rotor speeds, about 400 meter-seconds, in a very heavy material as tungsten, 1 e.c. of material ...", "... the voltage, eo, becomes a constant-current circuit, and this case is more fully discussed in Chapter XIV of \"Theory and Calculation of Electric Circuits \" as a constant-potential constant-current transforming device. Induction Phase Converter 130. The magnetic field of a single-phase induction motor at or near synchronism is a uniform rotating field, or nearly so, deviating from uniform intensity and uniform rotation only by the impedance drop of the primary winding. Thus, in any coil displaced in position from the s ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-16", "section_label": "Chapter 18: Surging Of Synchronous Motors", "section_title": "Surging Of Synchronous Motors", "kind": "chapter", "sequence": 16, "number": 18, "location": "lines 20975-21712", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-16/", "snippets": [ "... p, in solid field poles, etc., a torque is produced more or less proportional to the deviation of speed from synchronism. This power assumes the form, Pi = c2s, where c is a function of the conductivity of the eddy-current circuit and the intensity of the magnetic field of the machine, c2 is the power which would be required to drive the magnetic field of the motor through the circuits of the anti-surging device at full frequency, if the same relative proportions could be retained at full fre- quency as at the frequency ...", "... deviation of speed from synchronism. This power assumes the form, Pi = c2s, where c is a function of the conductivity of the eddy-current circuit and the intensity of the magnetic field of the machine, c2 is the power which would be required to drive the magnetic field of the motor through the circuits of the anti-surging device at full frequency, if the same relative proportions could be retained at full fre- quency as at the frequency of slip, s. That is, Pi is the power produced by the motor as induction machine at s ...", "... tive term represents a power: P2 = -h2s; (30) that is, a retarding torque during slow speed, or increasing £, and accelerating torque during high speed, or decreasing 0. The source of this torque may be found external to the motor, or internal, in its magnetic circuit. SURGING OF SYNCHRONOUS MOTORS 297 External sources of negative, Pi, may be, for instance, the magnetic field of a self-exciting, direct -current generator, driven r the synchronous motor. With decrease of Speed, this field 's, due to the decre ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-17", "section_label": "Chapter 19: Alternating- Current Motors In General", "section_title": "Alternating- Current Motors In General", "kind": "chapter", "sequence": 17, "number": 19, "location": "lines 21713-23905", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-17/", "snippets": [ "... uses a periodic variation of the mutual inductive reactance and so of the effective primary inductive reactance, (2) or the use of sharply defined and im- properly arranged teeth in both elements causes a periodic magnetic lock (opening and closing of the magnetic circuit, (3) and so a tendency to synchronize at the speed corresponding to this cycle. Synchronous machines have been discussed elsewhere. Here shall be considered only that type of motor in which the electric and magnetic relations between the slator and roto ...", "... . Commutator motors. There are, however, numerous intermediate forms, which belong in several classes, as the synchronous-induction motor, the c o oipe n sat ed-in due lion motor, etc. 172. An alternating current, /, in an electric circuit produces a magnetic flux, 41, interlinked with this circuit. Considering equivalent sine waves of / and *, 4> lags behind / by the angle of hysteretic lag, a. This magnetic flux, $, generates an e.m.f., 5 = 2 tt/;i, where / = frequency, n = number of turns of electric circuit. ...", "... pe n sat ed-in due lion motor, etc. 172. An alternating current, /, in an electric circuit produces a magnetic flux, 41, interlinked with this circuit. Considering equivalent sine waves of / and *, 4> lags behind / by the angle of hysteretic lag, a. This magnetic flux, $, generates an e.m.f., 5 = 2 tt/;i, where / = frequency, n = number of turns of electric circuit. This generated e.m.f., E, lags 90° behind the magnetic flux, *, hence consumes an e.m.f. 90° ahead of ♦, or 90—ci degrees ahead of /. This may be resolv ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-04", "section_label": "Theory Section 4: Power and Effective Values", "section_title": "Power and Effective Values", "kind": "theory-section", "sequence": 4, "number": 4, "location": "lines 1244-1572", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-04/", "snippets": [ "... = EQ sin 6. Since E0 = 2 irfn$, it follows that J' ; = 4.44 fn& ; is the effective alternating e.m.f. generated in a coil of turns n rotating at a frequency of / (in hundreds of cycles per second) through a magnetic field of megalines of force. This is the formula of the alternating-current generator. 21. The formula of the direct-current generator, E = holds even if the e.m.fs. generated in the individual turns are not sine waves, ...", "... The formula of the alternating-current generator, E = V2 *fn$, does not hold if the waves are not sine waves, since the ratios of average to maximum and of maximum to effective e.m.f. are changed. If the variation of magnetic flux is not sinusoidal, the effective generated alternating e.m.f. is, E = 7 \\/2 7 is called the form factor of the wave, and depends upon its shape, that is, the distribution of the magnetic flux in the magnetic field. ...", "... ed. If the variation of magnetic flux is not sinusoidal, the effective generated alternating e.m.f. is, E = 7 \\/2 7 is called the form factor of the wave, and depends upon its shape, that is, the distribution of the magnetic flux in the magnetic field. Frequently form factor is defined as the ratio of the effect- ive to the average value. This definition is undesirable since it gives for the sine wave, which is always considered the standard wave, ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-13", "section_label": "Theory Section 13: Alternating-current Transformer", "section_title": "Alternating-current Transformer", "kind": "theory-section", "sequence": 13, "number": 13, "location": "lines 4465-5263", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-13/", "snippets": [ "... . Let TI = resistance, x\\ = 2TrfSz = self-inductive or leakage reactance of secondary circuit, r0 = resistance, XQ = 2irfSi = self -inductive or leakage reactance of primary circuit, where S2 and Si refer to that magnetic flux which is interlinked with the one but not with the other circuit. Let a ratio of — — • — - turns (ratio of transformation), primary An alternating e.m.f. E0 impressed upon the primary electric circuit causes a curre ...", "... with the one but not with the other circuit. Let a ratio of — — • — - turns (ratio of transformation), primary An alternating e.m.f. E0 impressed upon the primary electric circuit causes a current, which produces a magnetic flux $ inter- linked with primary and secondary circuits. This flux gener- ates e.m.fs. EI and E{ in secondary and in primary circuit, which Tjl are to each other as the ratio of turns, thus Ei = — - Let E = secondary ...", "... al thereto by the ratio of turns and in phase there- FIG. 34. — Vector diagram of e.m.fs. and currents in a transformer. with is the e.m.f. generated in the primary OEi = Ef where To generate e.m.f. EI and Ei} the magnetic flux 0$ = is required, 90 time degrees ahead of OE\\ and OEi. To produce flux $ the m.m.f. of F ampere-turns is required, as determined from the dimensions of the magnetic circuit, and thus the primary current /oo, repres ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-21", "section_label": "Apparatus Introduction 21: Introduction", "section_title": "Introduction", "kind": "apparatus-introduction", "sequence": 21, "number": null, "location": "lines 8292-8517", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-21/", "snippets": [ "... . Standard- izing Committee, is used in the following discussion. It refers only to the apparatus transforming between electric and electric and between electric and mechanical power. 1st. Commutating machines, consisting of a magnetic field and a closed-coil armature, connected with a multi-segmental commutator. 121 122 ELEMENTS OF ELECTRICAL ENGINEERING 2d. Synchronous machines, consisting of a undirectional mag- netic field and an armature revolving relative ...", "... Induction machines, consisting of an alternating mag- netic circuit or circuits interlinked with two electric circuits or sets of circuits moving with regard to each other. 5th. Stationary induction apparatus, consisting of a magnetic circuit interlinked with one or more electric circuits. 6th. Electrostatic and electrolytic apparatus as condensers and polarization cells. Apparatus changing from one to a different form of electric energy have been defined as: A. ...", "... ervice, or with shunt characteristic for constant speed and adjustable speed work, especially where high starting torque efficiency is required. They usually are of single-phase type. (2) While in commutating machines the magnetic field is, INTRODUCTION 123 almost always stationary and the armature rotating, synchronous machines were built with stationary field and revolving armature, or with stationary armature and revolving field, or as inductor machines ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-22", "section_label": "Apparatus Section 1: Synchronous Machines: General", "section_title": "Synchronous Machines: General", "kind": "apparatus-section", "sequence": 22, "number": 1, "location": "lines 8518-8657", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-22/", "snippets": [ "... inal voltage and the generated e.m.f. are in synchronism with, that is, of the same frequency as, the speed of rotation. These machines consist of an armature, in which e.m.f. is generated by the rotation relatively to a magnetic field, and a continuous magnetic field, excited either by direct current, or by the reaction of displaced phase armature currents, or by per- manent magnetism. The formula for the e.m.f. generated in synchronous machines, commonly ...", "... m.f. are in synchronism with, that is, of the same frequency as, the speed of rotation. These machines consist of an armature, in which e.m.f. is generated by the rotation relatively to a magnetic field, and a continuous magnetic field, excited either by direct current, or by the reaction of displaced phase armature currents, or by per- manent magnetism. The formula for the e.m.f. generated in synchronous machines, commonly called alternators, is E = S ...", "... ents, or by per- manent magnetism. The formula for the e.m.f. generated in synchronous machines, commonly called alternators, is E = S2irn3> = 4. where n is the number of armature turns in series interlinked with the magnetic flux <1> (in megalines per pole), / the frequency of rotation (in hundreds of cycles per second), E the e.m.f. gen- erated in the armature turns. This formula assumes a sine wave of e.m.f. If the e.m.f. wave differs from ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-18", "section_label": "Chapter 18: Polyphase Induction Motors", "section_title": "Polyphase Induction Motors", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17717-20445", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-18/", "snippets": [ "CHAPTER XVIII POLYPHASE INDUCTION MOTORS 155. The induction motor consists of a magnetic circuit inter- linked with two electric circuits or sets of circuits, the primary and the secondary. It therefore is electromagnetically the same structure as the transformer. The difference is, that in the transformer secondary and primary are stationary, and th ...", "... e two limiting cases. In the induction motor, only the mechanical force be- tween primary and secondary is used, but not the transfer of electrical energy, and thus the secondary circuits are closed upon themselves. Hence the induction motor consists of a magnetic circuit interlinked with two electric circuits or sets of circuits, the primary and the secondary circuit, which are movable with regard to each other. In general a number of primary and a number of secondary circuits are used, angularly displaced around the peri ...", "... ry quantities, the values reduced to the primary system shall be exclusively used, so that, to derive the true secondary values, these quan- tities have to be reduced backward again by the factor a^b ni^pi 157. Let \"J> = total maximum flux of the magnetic field per motor pole. We then have E = \\/2 TT/io/ ^ 10~^ = effective e.m.f. generated by the magnetic field per primary circuit. Counting the time from the moment where the rising mag- netic flux of mutual induction, (flux interlinked with both electric ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-26", "section_label": "Chapter 26: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 32540-33010", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-26/", "snippets": [ "... e current are increased. In consequence hereof alterna- tors and synchronous motors of iron-clad unitooth construction — that is, machines giving waves with pronounced higher harmonics — may give with the same number of turns on the armature, and the same magnetic flux per field-pole at the same frequency, a higher output than machines built to produce sine waves. 255. This explains an apparent paradox: If in the three-phase star-connected generator with the mag- netic field constructed as shown diagrammatically in F ...", "... le at the same frequency, a higher output than machines built to produce sine waves. 255. This explains an apparent paradox: If in the three-phase star-connected generator with the mag- netic field constructed as shown diagrammatically in Fig. 188 the magnetic flux per pole = 4>, the number of turns in series per circuit = n, the frequency = /, the e.m.f. between any two collector rings is E = \\/2Trf2n^ 10-^ . since 2 n armature turns simultaneously interlink with the magnetic flux, . The e.m.f. per armature ...", "... agrammatically in Fig. 188 the magnetic flux per pole = 4>, the number of turns in series per circuit = n, the frequency = /, the e.m.f. between any two collector rings is E = \\/2Trf2n^ 10-^ . since 2 n armature turns simultaneously interlink with the magnetic flux, . The e.m.f. per armature circuit is e = \\/2 7r/n«J>10-8; hence the e.m.f. between collector rings, as resultant of two e.m.fs., e, displaced by 60° from each other, is E = e\\/3 = V2 7r/V3n$10-^ 376 ALTERNATING-CURRENT PHENOMENA while the sa ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1224-1727", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "snippets": [ "... r, refers to the wattless component of E.M.F., or the E.M.F. in quadrature with the current. 3. The principal sources of reactance are electro-mag- netism and capacity. ELECTRO-MAGNETISM, An electric current, /, flowing through a circuit, produces a magnetic flux surrounding the conductor in lines of magnetic force (or more correctly, lines of magnetic induc- tion), of closed, circular, or other form, which alternate with the alternations of the current, and thereby induce an E.M.F. in the conductor. Since the mag ...", "... lux surrounding the conductor in lines of magnetic force (or more correctly, lines of magnetic induc- tion), of closed, circular, or other form, which alternate with the alternations of the current, and thereby induce an E.M.F. in the conductor. Since the magnetic flux is in phase with the current, and the induced E.M.F. 90°, or a quarter period, behind the flux, this E.M.F. of self-indHc- tancc lags 90°, or a quarter period, behind the current ; that is, is in quadrature therewith, and therefore wattless. If now <> = ...", "... in phase with the current, and the induced E.M.F. 90°, or a quarter period, behind the flux, this E.M.F. of self-indHc- tancc lags 90°, or a quarter period, behind the current ; that is, is in quadrature therewith, and therefore wattless. If now <> = the magnetic flux produced by, and inter, linked with, the current / (where those lines of magnetic force, which are interlinked //-fold, or pass around n turns of the conductor, are counted ;/ times), the ratio, o//, is denoted by Z, and called self -inductance^ or the co ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-22", "section_label": "Chapter 20: Ri", "section_title": "Ri", "kind": "chapter", "sequence": 22, "number": 20, "location": "lines 24560-25119", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "snippets": [ "... ber of turns on the armature, and the same mag- netic flux per field pole at the same frequency, a higher output than machines built to produce sine waves. 227. This explains an apparent paradox : If in the three-phase star-connected generator with the magnetic field constructed as shown diagrammatically in Fig. 162, the magnetic flux per pole = J/, the number of turns in series per circuit = ;/, the frequency = N^ the E.M.F. between any two collector rings is: since 2;/ armature turns simultaneously interlink with t ...", "... ole at the same frequency, a higher output than machines built to produce sine waves. 227. This explains an apparent paradox : If in the three-phase star-connected generator with the magnetic field constructed as shown diagrammatically in Fig. 162, the magnetic flux per pole = J/, the number of turns in series per circuit = ;/, the frequency = N^ the E.M.F. between any two collector rings is: since 2;/ armature turns simultaneously interlink with the magnetic flux O. The E.M.F. per armature circuit is : e == V2^ ...", "... structed as shown diagrammatically in Fig. 162, the magnetic flux per pole = J/, the number of turns in series per circuit = ;/, the frequency = N^ the E.M.F. between any two collector rings is: since 2;/ armature turns simultaneously interlink with the magnetic flux O. The E.M.F. per armature circuit is : e == V2^iV//*10-»; hence the E.M.F. between collector rings, as resultant of two E.M.Fs. c displaced by 60° from each other, is : 342 AL TERNA TING-CURRENT PHENOMENA. [§ 227 while the same E.M.F. was fou ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 963-1366", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "snippets": [ "... , refers to the wattless component of E.M.F., or the E.M.F. in quadrature with the current. 3. The principal sources of reactance are electro-mag- netism and capacity. ELECTRO— MAGNETISM. An electric current, i, flowing through a circuit, produces a magnetic flux surrounding the conductor in lines of magnetic force (or more correctly, lines of magnetic induc- tion), of closed, circular, or other form, which alternate with the alternations of the current, and thereby induce an E.M.F. in the conductor. Since the mag ...", "... lux surrounding the conductor in lines of magnetic force (or more correctly, lines of magnetic induc- tion), of closed, circular, or other form, which alternate with the alternations of the current, and thereby induce an E.M.F. in the conductor. Since the magnetic flux is in phase with the current, and the induced E.M.F. 90°, or a quarter period, behind the flux, this E.M.F. of self -induc- tance lags 90°, or a quarter period, behind the current ; that is, is in quadrature therewith, and therefore wattless. If now 4> ...", "... n phase with the current, and the induced E.M.F. 90°, or a quarter period, behind the flux, this E.M.F. of self -induc- tance lags 90°, or a quarter period, behind the current ; that is, is in quadrature therewith, and therefore wattless. If now 4> = the magnetic flux produced by, and inter- linked with, the current i (where those lines of magnetic force, which are interlinked w-fold, or pass around n turns of the conductor, are counted n times), the ratio, $ / z, is denoted by L, and called self -inductance, or the co ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-23", "section_label": "Chapter 23: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 21983-22448", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "snippets": [ "... ber of turns on the armature, and the same mag- netic flux per field pole at the same frequency, a higher output than machines built to produce sine waves. 248. This explains an apparent paradox : If in the three-phase star-connected generator with the magnetic field constructed as shown diagrammatically in Fig. 162, the magnetic flux per pole = $, the number of turns in series per circuit = n, the frequency = N, the E.M.F. between any two collector rings is: E= V2~7T^2;z10-8. since 2« armature turns simultaneou ...", "... ole at the same frequency, a higher output than machines built to produce sine waves. 248. This explains an apparent paradox : If in the three-phase star-connected generator with the magnetic field constructed as shown diagrammatically in Fig. 162, the magnetic flux per pole = $, the number of turns in series per circuit = n, the frequency = N, the E.M.F. between any two collector rings is: E= V2~7T^2;z10-8. since 2« armature turns simultaneously interlink with the magnetic flux 3>. The E.M.F. per armature ci ...", "... agrammatically in Fig. 162, the magnetic flux per pole = $, the number of turns in series per circuit = n, the frequency = N, the E.M.F. between any two collector rings is: E= V2~7T^2;z10-8. since 2« armature turns simultaneously interlink with the magnetic flux 3>. The E.M.F. per armature circuit is : hence the E.M.F. between collector rings, as resultant of two E.M.Fs. e displaced by 60° from each other, is : 406 ALTERNATING-CURRENT PHENOMENA. while the same E.M.F. was found by direct calculation from n ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-09", "section_label": "Chapter 10: Hysteresis Motor", "section_title": "Hysteresis Motor", "kind": "chapter", "sequence": 9, "number": 10, "location": "lines 14551-14761", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-09/", "snippets": [ "CHAPTER X HYSTERESIS MOTOR 98. In it revolving magnetic field, a circular iron disk, or iron cylinder of uniform magnetic reluctance in the direction of the revolving field, is set in rotation, even if subdivided so as to preclude the production of eddy currents. Thin rotation is due to the effect of hysteresis of t ...", "... even if subdivided so as to preclude the production of eddy currents. Thin rotation is due to the effect of hysteresis of the revolving disk or cylinder, and such a motor may thus be called a hysteresis motor. Let / be the iron disk exposed to a rotating magnetic field or resultant m.m.f. The axis of resultant magnetization in the disk, /, does not coincide with the axis of the rotating field, but lags behind the latter, thus producing a couple. That is, the component of magnetism in a direction of the rotating disk, /, ...", "... parent torque efficiency: Q = volt-ampere input, HYSTERESIS MOTOR 169 and the power of the motor is: P = (1 - s) D = (1 - s) m$$ sin a, where s = slip as fraction of synchronism. The apparent efficiency is: p n = (1 — *) sin a. Since in a magnetic circuit containing an air gap the angle, a, is small, a few degrees only, it follows that the apparent efficiency of the hysteresis motor is low, the motor consequently unsuitable for producing large amounts of mechanical power. From the equation of torque it fo ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-36", "section_label": "Chapter 14: Short-Circuit Currents Of Alternators", "section_title": "Short-Circuit Currents Of Alternators", "kind": "chapter", "sequence": 36, "number": 14, "location": "lines 14549-15353", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "snippets": [ "... self-inductance; that is, the current in the armature represents a m.m.f. which with lagging current, as at short circuit, is demagnetizing or opposing the impressed m.m.f. of field excitation, and by combining therewith to a resultant m.m.f. reduces the magnetic flux from that corre- sponding to the field excitation to that corresponding to the resultant of field excitation and armature reaction, and thus reduces the generated e.m.f. from the nominal generated e.m.f., eOJ to the virtual generated e.m.f., er The armatu ...", "... field excitation to that corresponding to the resultant of field excitation and armature reaction, and thus reduces the generated e.m.f. from the nominal generated e.m.f., eOJ to the virtual generated e.m.f., er The armature current also produces a local magnetic flux in the armature iron and pole- faces which does not interlink with the field coils, but is a true self-inductive flux, and therefore is represented by a reactance xr Combined with the effective resistance, rv of the armature winding, this gives the self-i ...", "... eaction, xv differs, however, essentially from the true self-inductive reactance, xv in that xl is instantaneous in its action, while the effective reactance of armature reaction, xv requires an appreciable time to develop: x2 represents the change of the magnetic field flux produced by the armature m.m.f. The field flux, however, can- not change instantaneously, as it interlinks with the field exciting coil, and any change of the field flux generates an e.m.f. in the field coils, changing the field current so as to reta ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... ties 249 rectification 249 rectifiers 222 resistivities 9 starting 249 Arcing ground on lines and cables, as periodic transient phenomenon . . 23 Armature reactance, reaction and short-circuit current of alternator 199 Attenuation of alternating magnetic flux in iron 361 constants 434 of traveling wave, and loading 462 Booster, response to change of load 158 Brush arc machine 221, 230, 242, 248 Building up of direct-current generator 32 of overcompounded direct-current machine 49 Cable, high-potentia ...", "... of electric field 5 shunting direct-current circuit 133 specific, numerical values 11 suppressing pulsations in direct-current circuit 134 Cast iron, effective penetration of alternating current 378 Cathode of arcs 249 Charge of condenser 51 of magnetic field 27 Circuit, complex, see Complex circuit. control by periodic transient phenomena 220, 223 electric, speed of propagation in 422 Closed circuit transmission line 306 Col al 392, 394 Commutation and rectification 222 as transient phenomenon 40 ...", "... voltage in opening direct-current circuit 26 Distance attenuation constant 434 in velocity measure . 435 Distortionless circuit 441, 447 Distributed series capacity 348 Distribution of alternating-current density in conductor 369 of alternating magnetic flux in iron 355 Divided circuit, general equations 122 continuous-current circuit without capacity 126 Dynamostatic machine 220 Effective current of condenser discharge 70 voltage and power of oscillating-current generator. . . 81 layer of alternating ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-03", "section_label": "Lecture 3: Gravitation And The Gravitational Fleld", "section_title": "Gravitation And The Gravitational Fleld", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2389-3594", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-03/", "snippets": [ "... d its place is taken by the conception of the field of force, or, more correctly, the energy field. The energy field is a storage of energy in space, character- ized by the property of exerting a force on any body susceptible to this energy — that is, a magnetic field on a magnetizable body, a gravitational field on a gravitational mass, etc. Light, or, in general, radiation, is an electromagnetic wave — ^that is, an alternation or periodic variation of the electromagnetic field^ — and the difference between the alt ...", "... ny point of space is determined by two constants, the intensity and the direction, and the force exerted by the field on a susceptible body is proportional to the field intensity and is in the direction of the energy field. Thus the force exerted by the magnetic field on a magnetic material is: F = HP (1) 46 GRAVITATION AND THE GRAVITATIONAL FIELD 47 where H is the magnetic field intensity and P the magnetic mass, the same quantity which in the days of action at a distance was called the magnetic pole strength, ...", "... susceptible body is proportional to the field intensity and is in the direction of the energy field. Thus the force exerted by the magnetic field on a magnetic material is: F = HP (1) 46 GRAVITATION AND THE GRAVITATIONAL FIELD 47 where H is the magnetic field intensity and P the magnetic mass, the same quantity which in the days of action at a distance was called the magnetic pole strength, and which is related to the magnetic flux $ by: $ = AtP. The force exerted by an electric field on an electrified body ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-101", "section_label": "Apparatus Section 4: Alternating-current Transformer: Regulation", "section_title": "Alternating-current Transformer: Regulation", "kind": "apparatus-section", "sequence": 101, "number": 4, "location": "lines 17538-18397", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-101/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-101/", "snippets": [ "... can- not occupy the same space, and in addition some insulation — more or less depending on the voltage — must be between them, there is thus a space between primary and secondary through which the primary current can send magnetic flux which does not interlink with the secondary winding, but is a self-induc- tive or leakage flux and in the same manner the secondary current sends self-inductive or leakage flux through the space between primary and secondary ...", "... lf-inductive or leakage flux through the space between primary and secondary winding. These fluxes give rise to the self -inductive or leakage reactances x\\ and Xz of the transformer. Or in other words, two paths exist for magnetic flux in the transformer: the path surrounding primary and secondary coils, through which flows the mutual magnetic flux of the transformer, which is the useful flux, that is, the flux which transfers the power from primary to s ...", "... self -inductive or leakage reactances x\\ and Xz of the transformer. Or in other words, two paths exist for magnetic flux in the transformer: the path surrounding primary and secondary coils, through which flows the mutual magnetic flux of the transformer, which is the useful flux, that is, the flux which transfers the power from primary to secondary circuit; and the space between pri- mary and secondary winding through which the self-inductive or leakage ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-18", "section_label": "Theory Section 18: Equivalent Sine Waves", "section_title": "Equivalent Sine Waves", "kind": "theory-section", "sequence": 18, "number": 18, "location": "lines 7381-7736", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-18/", "snippets": [ "... c co\" co\"co\"co'Nco>i-r ^^^ooooooo 1— «O ..» 00 00^2 ^ ^ ^ se ^ oo oo . < r-l CO ?CI> i-H QJ CO EQUIVALENT SINE WAVES 109 Fig. 41 and Table I, the number of primary turns is 500, the length of the magnetic circuit 50 cm., and its section shall be chosen so as to give a maximum density B = 15,000. At this density the hysteretic cycle is as shown in Fig. 42 and Table II. FIG. 41. — Wave-shape of e.m.f. in example 88. What is ...", "... ENTS OF ELECTRICAL ENGINEERING Since the effective value of impressed e.m.f. is = 1000, the 1 000 instantaneous values are eQ = e^-^ as given in column (4). Since the e.m.f. e0 is proportional to the rate of change of magnetic flux, that is, to the differential coefficient of B} B is proportional to the integral of the e.m.f., that is, to Se0 plus an integration constant. 2e0 is given in column (5), and the integration constant follows from the con ...", "... ign, to B at 0°. The integration constant is, therefore, 1 SO -it n i ^ and by subtracting 7324 from the values in column (5) the values of B' of column (6) are found as the relative instantaneous values of magnetic flux density. Since the maximum magnetic flux density is 15,000 the in- 15 000 stantaneous values are B = B' ' . , plotted in column (7). From the hysteresis cycle in Fig. 42 are taken the values of magnetizing forc ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-38", "section_label": "Apparatus Section 17: Synchronous Machines: Short-circuit Currents of Alternators", "section_title": "Synchronous Machines: Short-circuit Currents of Alternators", "kind": "apparatus-section", "sequence": 38, "number": 17, "location": "lines 10190-10429", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-38/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-38/", "snippets": [ "... nt is limited only by the arma- ture self-inductance, and not by the armature reaction, and some appreciable time — occasionally several seconds — elapses before the armature reaction becomes effective. At short circuit, the magnetic field flux is greatly reduced by the demagnetizing action of the armature current, and the gen- SYNCHRONOUS MACHINES 161 erated e.m.f. thereby reduced from the nominal value EQ to the virtual value Ez; the latter is consumed ...", "... to the virtual value Ez; the latter is consumed by the armature self- inductive impedance z, or self-inductive reactance, which is practically the same in most cases. The armature self-inductance is instantaneous, since the magnetic field rises simultaneously with the armature current which produces it; armature reaction, however, requires an appre- ciable time to reduce the magnetic flux from the open-circuit value to the much lower short-circuit value, since ...", "... in most cases. The armature self-inductance is instantaneous, since the magnetic field rises simultaneously with the armature current which produces it; armature reaction, however, requires an appre- ciable time to reduce the magnetic flux from the open-circuit value to the much lower short-circuit value, since the magnetic field flux is surrounded by the field exciting coils, which act as a short-circuited secondary opposing a rapid change of field flux; tha ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-35", "section_label": "Chapter 35: Balanced Symmetrical Polyphase Systems", "section_title": "Balanced Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 35, "number": 35, "location": "lines 37453-37957", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-35/", "snippets": [ "... f the polyphase system, in the resolution of the polyphase system into its constituent single-phase systems the effective value of the constant has to be used, which corresponds to the resultant effect. This, for instance, is the case in calcu- lating the magnetic field of the induction machine — which is energized by the combination of all phases — or the armature reaction of synchronous machines, etc. For instance, in the induction machine, from the generated e.m.f., e — in Chapter XVIII — the magnetic flux of the mac ...", "... ating the magnetic field of the induction machine — which is energized by the combination of all phases — or the armature reaction of synchronous machines, etc. For instance, in the induction machine, from the generated e.m.f., e — in Chapter XVIII — the magnetic flux of the machine is calculated, and from the magnetic flux and the dimensions of the magnetic circuit: length and section of air-gap, and length and section of the iron part, follows the ampere-turns excitation, that is, the ampere turns, Fo, required to pr ...", "... is energized by the combination of all phases — or the armature reaction of synchronous machines, etc. For instance, in the induction machine, from the generated e.m.f., e — in Chapter XVIII — the magnetic flux of the machine is calculated, and from the magnetic flux and the dimensions of the magnetic circuit: length and section of air-gap, and length and section of the iron part, follows the ampere-turns excitation, that is, the ampere turns, Fo, required to produce the magnetic flux. The resultant m.m.f. of m equal ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-06", "section_label": "Chapter 7: Higher Harmonics In Induction Motors", "section_title": "Higher Harmonics In Induction Motors", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 12398-13955", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-06/", "snippets": [ "... * Theoretical Elements of Electrical Enginccr- ing\" and in \"Theory and Calculation of Alternating-current Phenomena,\" is based on the assumption of the sine wave. That U, it is assumed that the voltage impressed upon the motor per phase, and therefore the magnetic flux and the current, KM sine waves, and it is further assumed, that the distribution of the winding on the circumference of the armature or primary, is sinusoidal in space. While in most eases this is sufficicntly the ease, it is not always so, and especially ...", "... further assumed, that the distribution of the winding on the circumference of the armature or primary, is sinusoidal in space. While in most eases this is sufficicntly the ease, it is not always so, and especially the space or air-gap distribution of the magnetic flux may sufficiently differ from sine shape, to exert an appreciable effect on the torque at lower speeds, and require consideration where motor action and braking action with considerable power is required throughout the entire range of speed. Let then: r ...", "... ltage of the second motor phase, which lags 90° or behind the first motor phase, is: = e,eos^«- gj + c3 + 8) eos (? 0 3*- cos(.5«- •(♦-$■ A3*- 1 . cost 3 - «■( + *}) + etcoalS - + «odb(7#-«t + 5) + *«*(&* -■•-£) + ■ • ■ W The magnetic flux produced by these (wo voltages thus con- sists of a series of component fluxes, corresponding respective]] HIGHER HARMONICS 145 to the successive components. The secondary currents induced by these component fluxes, and the torque produced by the seco ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-09", "section_label": "Chapter 9: Wave Screens. Even Harmonics", "section_title": "Wave Screens. Even Harmonics", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 16964-17631", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-09/", "snippets": [ "... s to an appreciable extent. Such resonant wave screen, however, has the serious disadvan- tage to require very high constancy of /, since the resonance condi- tion between C» and Ln depends on the square of /, 79. Even harmonics are produced in a closed magnetic circuit by the superposition of a continuous current upon the alternating wave. With an alternating sine wave impressed upon an iron magnetic circuit, saturation, or in general the lack of proportional- 158 ELECTRIC CIRCUITS ity between magnetic flux and ...", "... resonance condi- tion between C» and Ln depends on the square of /, 79. Even harmonics are produced in a closed magnetic circuit by the superposition of a continuous current upon the alternating wave. With an alternating sine wave impressed upon an iron magnetic circuit, saturation, or in general the lack of proportional- 158 ELECTRIC CIRCUITS ity between magnetic flux and m.m.f., produces a, wave-shape dis- tortion, that is, higher harmonics, of voltage with a sine wave of current, of current with a sine wave of ...", "... d magnetic circuit by the superposition of a continuous current upon the alternating wave. With an alternating sine wave impressed upon an iron magnetic circuit, saturation, or in general the lack of proportional- 158 ELECTRIC CIRCUITS ity between magnetic flux and m.m.f., produces a, wave-shape dis- tortion, that is, higher harmonics, of voltage with a sine wave of current, of current with a sine wave of impressed voltage. The constant term of a wave, however, is the first even harmonic, and thus, if the impres ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... e have _ r _ r 14 L hence, by substitution, / = — je -J J- dec a, ^, = — jer yjj- dec a, a = the final equations of the oscillating discharge, in symbolic ex- pression. 23 INDEX Admittance, with oscillating cur- rents, 348 Air gap in magnetic circuit reducing wave distortion, 145 Alloys, resistance, 2 Alternating component of power of general system, 317 current electromagnet, 95 magnetic characteristic, 51 Alternations by capacity inductance shunt to arc, 187 Aluminum cell as condenser, 10 Am ...", "... Balance of quarterphase system on singlephase load, 322 of singlephase load, 319 of threephase system on single- phase load, 325 of unbalanced power of system, 319 Bends in magnetic reluctivity curve, 49 Bismuth, diamagnetism, 77 Bridged gap in magnetic circuit, wave distortion, 148 C Cable armor as circuit, 330 equation of induced current, 336 Capacity, 1 and inductance shunting circuit, 181 inductance shunt to arc pro- ducing alternations, 187 with oscillating current, 347 and reactance as wave s ...", "... circuit, 178 Carbon, resistance, 21 Cathode, 6 Cell, 7 355 356 INDEX Characteristic, magnetic, 50 Chemical action in electrolytic con- duction, 6 Chromium, magnetic properties, 83 Circuit with distributed leakage, 330 magnetic, 43 Closed magnetic circuit, wave dis- tortion, 139 C/obalt iron alloy, magnetic, 78 magnetic properties, 80 Coefficient of hysteresis, 61 Coherer action of pyroelectric con- ductor, 19 Compensating voltage balancing un- balanced power, 320 Condenser, electrostatic, 9 power e ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-49", "section_label": "Chapter 9: High-Frequency Conductors", "section_title": "High-Frequency Conductors", "kind": "chapter", "sequence": 49, "number": 9, "location": "lines 27003-27760", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "snippets": [ "... ear the path of a lightning stroke, as \"side discharge.\" The inductance is reduced by the unequal current distribution in the conductor, which, by deflecting most of the current into the outer layer of the conductor, reduces or practically eliminates the magnetic field inside of the conductor. The lag of the mag- netic field in space, behind the current in the conductor, due to the finite velocity of radiation, also reduces the inductance to less than that from the conductor surface to a distance of one- half wave. An e ...", "... the finite velocity of radiation, also reduces the inductance to less than that from the conductor surface to a distance of one- half wave. An exact determination of the inductance is, how- ever, not possible; the inductance is represented by the electro- magnetic field of the conductor, and this depends upon the presence and location of other conductors, etc., in space, on the length of the conductor, and the distance from the return con- ductor. Since very high frequency currents, as lightning dis- charges, frequently ...", "... return con- ductor. Since very high frequency currents, as lightning dis- charges, frequently have no return conductor, but the capacity at the end of the discharge path returns the current as \" dis- placement current,\" the extent and distribution of the magnetic field is indeterminate. If, however, the conductor under con- sideration is a small part of the total discharge — as the ground connection of a lightning arrester, a small part of the discharge path from cloud to ground — and the frequency very high, so that th ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... ctric circuit, as a change of load; or, disturbances entering the circuit from the outside or originating in it, etc. Periodic phenomena are the alternating currents and voltages, pulsating currents as those produced by rectifiers, the distribution of the magnetic flux in the air-gap of a machine, or the distribution of voltage around the commutator of the direct-current machine, the motion of the piston in the steam-engine cylinder, the variation of the. mean daily temperature with the seasons of the year, etc. The c ...", "... It therefore is of importance in engineering to translate thejicite or the table \"^ of numerical values of a periodic function into a mathematical expression thereof. • ' , (B) If one of the engineering quantities, as the e.m.f. of an alternator or the magnetic flux in the air-gap of an electric machine, is given as a general periodic function in the form of a trigonometric series, to determine therefrom other engineer- ing quantities, as the current, the generated e.m.f., etc. A. Evaluation of the Constants of the ...", "... i2 / / o / X ^ } i \\ 1 0 1 2 1 t 1 5 1 i 2 »- i 1 i 28 3Q Fig. 51. Magnetization Curve. Example i. Determine that magnetic density (B, at which tlie permeability /it of a sample of iron is a maximum. The relation between magnetic field intensity 5C, magnetic density (35 and permeability jk cannot be expressed in a mathematical equation, and is therefore usually given in the form of an 1400 1200 ^ , -■ b. ■V -\"ml ^ N \\ -800- -600- ^ X ■ s \\, / / \\ \\ ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-05", "section_label": "Theory Section 5: Self-inductance and Mutual Inductance", "section_title": "Self-inductance and Mutual Inductance", "kind": "theory-section", "sequence": 5, "number": 5, "location": "lines 1573-1784", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-05/", "snippets": [ "... l to the mutual induc- tance of the first upon the second circuit, as will be seen, and thus is called the mutual inductance between the two circuits. The number of interlinkages of an electric circuit with the lines of magnetic flux produced by unit current in this circuit and not interlinked with a second circuit is called the self- inductance of the circuit. If i = current in a circuit of n turns, = flux produced thereby and interlinked with ...", "... the inductance of the circuit. If $ is proportional to the current i and the number of turns n, ni n2 . , $ = — , and L = — the inductance. 01 (K (ft is called the reluctance and ni the m.m.f. of the magnetic circuit. In magnetic circuits the reluctance (R has a position similar to that of resistance r in electric circuits. The reluctance (R, and therefore the inductance, is not con- stant in circuits containing magnetic materials, such ...", "... position similar to that of resistance r in electric circuits. The reluctance (R, and therefore the inductance, is not con- stant in circuits containing magnetic materials, such as iron, etc. If (Ri is the reluctance of a magnetic circuit interlinked with two electric circuits of n\\ and n% turns respectively, the flux produced by unit current in the first circuit and interlinked with the second circuit is -- and the mutual inductance of the first (HI upo ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-104", "section_label": "Apparatus Section 7: Alternating-current Transformer: Types of Transformers", "section_title": "Alternating-current Transformer: Types of Transformers", "kind": "apparatus-section", "sequence": 104, "number": 7, "location": "lines 18521-18665", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-104/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-104/", "snippets": [ "VH. Types of Transformers 123. As the transformer consists of a magnetic circuit inter- linked with two electric circuits, two constructive arrangements are possible : The electric circuits may be inside, and surrounded by the magnetic circuit as shell, shell-type transformer; or the magnetic circuit may be ...", "... H. Types of Transformers 123. As the transformer consists of a magnetic circuit inter- linked with two electric circuits, two constructive arrangements are possible : The electric circuits may be inside, and surrounded by the magnetic circuit as shell, shell-type transformer; or the magnetic circuit may be arranged inside, as core, and sur- rounded by the electric circuits, core-type transformer. In their simplest form, Fig. 163 shows diagrammatically the core-type ...", "... of a magnetic circuit inter- linked with two electric circuits, two constructive arrangements are possible : The electric circuits may be inside, and surrounded by the magnetic circuit as shell, shell-type transformer; or the magnetic circuit may be arranged inside, as core, and sur- rounded by the electric circuits, core-type transformer. In their simplest form, Fig. 163 shows diagrammatically the core-type transformer, with the iron Fe as inside circular core, ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-108", "section_label": "Apparatus Section 2: Induction Machines: Polyphase Induction Motor", "section_title": "Induction Machines: Polyphase Induction Motor", "kind": "apparatus-section", "sequence": 108, "number": 2, "location": "lines 19166-20427", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-108/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-108/", "snippets": [ "II. Polyphase Induction Motor 1. INTRODUCTION 135. The typical induction motor is the polyphase motor. By gradual development from the direct-current shunt motor we arrive at the polyphase induction motor. The magnetic field of any induction motor, whether supplied by polyphase, monocyclic, or single-phase e.m.f., is at normal condition of operation, that is, near synchronism, a polyphase field. Thus to a certain extent all induction motors can ...", "... aginary quantities we have the primary current, /o = e V&i2 + 622, etc. INDUCTION MACHINES 313 The torque of the polyphase induction motor (or any other motor or generator) is proportional to the product of the mutual magnetic flux and the component of ampere-turns of the sec- ondary, which is in phase with the magnetic flux in time, but in quadrature therewith in direction or space. Since the generated e.m.f. is proportional to the mutual magnetic f ...", "... 13 The torque of the polyphase induction motor (or any other motor or generator) is proportional to the product of the mutual magnetic flux and the component of ampere-turns of the sec- ondary, which is in phase with the magnetic flux in time, but in quadrature therewith in direction or space. Since the generated e.m.f. is proportional to the mutual magnetic flux and the num- ber of turns, but in quadrature thereto in time, the torque of the induction ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-79", "section_label": "Apparatus Subsection 79: Direct-current Commutating Machines: C. Commutating Machines 219", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 219", "kind": "apparatus-subsection", "sequence": 79, "number": null, "location": "lines 13019-13119", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-79/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-79/", "snippets": [ "... laminated, since the mag- netic flux is alternating. The alternation of the field flux induces an e.m.f. of self induction in the field winding. In the shunt motor, this causes the field exciting current and with it the magnetic field flux to lag and thereby to be out of phase with the armature current which, to represent work, must essentially be an energy current, and thereby reduces output and efficiency and hence requires some method of compensation ...", "... position exists on the commutator of the alternating- current motor where the armature coil does not contain an induced e.m.f., but in the position midway between the brushes the e.m.f. induced by the rotation through the magnetic field is a maximum; in the position of commutation the e.m.f. induced by the alternation of the field flux is a maximum. To overcome the destructive sparking caused by the short circuit of the latter e.m.f. by the commutator b ...", "... Low impressed frequency, so as to give low values to the induced e.m.f. This is the cause of the desire for abnormally low frequencies, as 15 and even 8 cycles, in alternating-current railway electrification. 5. Low magnetic flux per pole. This is the reason why alternating-current commutator motors of large power usually have such a large number of poles. These very severe limitations of the design of alternating-cur- rent commutating motors a ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... f the coordinate axes. INDEX Absolute values of complex quanti- ties, 37 Actual generated e.m.f., alternator, 272 Admittance, 55 of dielectric, 154 due to eddy currents, 137 to hysteresis, 129 Admittivity of dielectric circuit, 160 Air-gap in magnetic circuit, 119, 132 Ambiguity of vectors, 39 Amplitude, 6, 20 Apparent capacity of distorted wave, 386 efficiency of induction motor, 234 impedance of transformer, 201 torque efficiency of induction motor, 234 Arc causing harmonics, 353 as pulsating resis ...", "... Diametrical connection of trans- formers, six -phase, 429 Dielectric circuit, 159 density, 152 field, 1.50 hysteresis, 112, 1.50 strength. 161 Direct-current system, erhciency, 441 Displacement current. 152 Disruptive gradient. 165 Distortion by magnetic field, resist- ance and reactance pulsa- tion. a42 of magnetizing current. 117 of wave, see Harmonics by hysteresis, 116 Distributed capacity. 168 Double delta connections of trans- formers to sis-phase. 428 frequency power and torque with distorted wave, ...", "... 2 Diametrical connection of trans- formers, six-phase, 429 Dielectric circuit, 159 density, 152 field, 150 hysteresis, 112, 150 strength, 161 Direct-current system, efficiency, 441 Displacement current, 152 Disruptive gradient, 165 Distortion by magnetic field, resist- ance and reactance pulsa- tion, 342 of magnetizing current, 117 of wave, see Harmonics by hysteresis, 116 Distributed capacity, 168 Double delta connections of trans- formers to six-phase, 428 frequency power and torque with distorted wave, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-04", "section_label": "Chapter 4: Graphic Befrisxintation", "section_title": "Graphic Befrisxintation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2122-2743", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "snippets": [ "... er, feeding through its secondary circuit an inductive load. For simplicity, we may neglect here the magnetic hysteresis, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the magnetic flux is zero. The phase of the flux, that is, the amplitude of its maximum value, is 90° in this case, and, consequently, the phase of the induced E.M.F., is 180% §21] GRAPHIC REPRESENTATION. 29 since the induced E.M.F. lags 90° behind the inducing ...", "... , we get the flux, 4», required to induce this E.M.F., from the equation — ^i = V2 7r«iA^*10-«. where — El = secondary induced E.M.F., in effective volts, jV — frequency, in cycles per second. f/i = number of secondary turns. 4> = maximum value of magnetic flux, in webers. The derivation of this equation has been given in a preceding chapter. This magnetic flux, 4>, is represented by a vector, O^, at 30 AL TERNA TING-CURRENT PHENOMENA, [§ 22 the phase 90^ and to induce it an M.M.F., $F, is required, which ...", "... El = secondary induced E.M.F., in effective volts, jV — frequency, in cycles per second. f/i = number of secondary turns. 4> = maximum value of magnetic flux, in webers. The derivation of this equation has been given in a preceding chapter. This magnetic flux, 4>, is represented by a vector, O^, at 30 AL TERNA TING-CURRENT PHENOMENA, [§ 22 the phase 90^ and to induce it an M.M.F., $F, is required, which is determined by the magnetic characteristic of the iron, and the section and length of the magnetic circ ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-04", "section_label": "Chapter 4: Graphic Representation", "section_title": "Graphic Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 1743-2321", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "snippets": [ "... er, feeding through its secondary circuit an inductive load. For simplicity, we may neglect here the magnetic hysteresis, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the magnetic flux is zero. The phase of the flux, that is, the amplitude of its maximum value, is 90° in this case, and, consequently, the phase of the induced E.M.F., is 180°, GRAPHIC REPRESEiVTA TIOiV. 29 since the induced E.M.F. lags 90° behind the inducing flux ...", "... dary induced E.M.F., Ely we get the flux» 3>, required to induce this E.M.F., from the equation — where — £i = secondary induced E.M.F. , in effective volts, JV = frequency, in cycles per second, ;/1 = number of secondary turns, 3> = maximum value of magnetic flux, in webers. The derivation of this equation has been given in a preceding chapter. This magnetic flux, 4>, is represented by a vector, O = maximum value of magnetic flux, in webers. The derivation of this equation has been given in a preceding chapter. This magnetic flux, 4>, is represented by a vector, O ^1.5, #2, #2.5, and B3 are drawn equidistant ...", "... in the relative distances 0.5, 1, 1.5, 2, 2.5, and 3 (where la = 1 is the length of air gap). They give the effective values: BQ BQ.S BI BI.Z BZ Bz.s B3 718 373 184 119 91 69 57 That is, the pulsation of magnetic flux rapidly disappears toward the interior of the magnet pole, and still more rapidly the energy loss by eddy currents, which is proportional to the square of the magnetic density. 54. In calculating the effect of eddy curren ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-65", "section_label": "Apparatus Section 13: Direct-current Commutating Machines: Commutation", "section_title": "Direct-current Commutating Machines: Commutation", "kind": "apparatus-section", "sequence": 65, "number": 13, "location": "lines 11905-11980", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-65/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-65/", "snippets": [ "... ited by the brush, and the current iQ in the coil begins to die out, or rather to change at a rate depending upon the internal resistance and the inductance of the coil A and the e.m.f. gener- ated in the coil by the magnetic flux of armature reaction and by the field magnetic flux. The higher the internal resistance the faster is the change of current, and the higher the inductance the slower the current changes. Thus two cases have to be di ...", "... begins to die out, or rather to change at a rate depending upon the internal resistance and the inductance of the coil A and the e.m.f. gener- ated in the coil by the magnetic flux of armature reaction and by the field magnetic flux. The higher the internal resistance the faster is the change of current, and the higher the inductance the slower the current changes. Thus two cases have to be dis- tinguished. 1. No magnetic flux enters the armatu ...", "... and by the field magnetic flux. The higher the internal resistance the faster is the change of current, and the higher the inductance the slower the current changes. Thus two cases have to be dis- tinguished. 1. No magnetic flux enters the armature at the position of the brushes, that is, no e.m.f. is generated in the armature coil under commutation, except that of its own self-inductance. In this case the commutation is entirely determined by ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-15", "section_label": "Chapter 15: Induction Motob", "section_title": "Induction Motob", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 14919-17024", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "snippets": [ "... econdary quantities ex- clusively, the values reduced to the primary system shall be used, so that, to derive the true secondary values, these quantities have* to be reduced backwards again by the factor np «iA 142. Let * = total maximum flux of the magnetic field per motor pole. It is then E = V2ir«iV*10\"® = effective E.M.F. induced by the mag- netic field per primary circuit. Counting the time from the moment where the rising magnetic flux of mutual induction * (flux interlinked with both electric circuits, ...", "... in by the factor np «iA 142. Let * = total maximum flux of the magnetic field per motor pole. It is then E = V2ir«iV*10\"® = effective E.M.F. induced by the mag- netic field per primary circuit. Counting the time from the moment where the rising magnetic flux of mutual induction * (flux interlinked with both electric circuits, primary and secondary) passes through zero, in complex quantities, the magnetic flux is denoted by and the primary induced E.M.F., j5 = — ^; where e = V2 TTfiN^ 10~* may be conside ...", "... ced by the mag- netic field per primary circuit. Counting the time from the moment where the rising magnetic flux of mutual induction * (flux interlinked with both electric circuits, primary and secondary) passes through zero, in complex quantities, the magnetic flux is denoted by and the primary induced E.M.F., j5 = — ^; where e = V2 TTfiN^ 10~* may be considered as the \" Active E.M.F. of the motor.\" Since the secondary frequency is s Ny the secondary induced E.M.F. (reduced to primary system) is -^1 = — se ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-07", "section_label": "Chapter 7: Shaping Of Waves : General", "section_title": "Shaping Of Waves : General", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 12222-12961", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-07/", "snippets": [ "... ternator, is superior in transformers and similar devices, as it transform s tho energy with less hysteresis loss. The peaked voltage wave. Fig. 4:8, gives a flat-topped wave of magnetism. Fig. 47, and therciby transforms the voltage with a lesser maximum magnetic flux, than ^ sine wave of the same effective value, that is, the same powc^r. the hysteresis loss depends on the maximum value of t\\u) mag- 5tic flux, the reduction of the maximum value of tho magncitic; fl^Jx, due to a peaked voltage wave, results in a lower ...", "... machine, commutating machine, etc., the wave of voltage induced in a single armature conductor or \"face conductor\" equals the wave of field flux distribution around the periphery of the magnet field, modified, however, by the reluctance pulsations of the magnetic circuit, where such exist. As the latter produce higher harmonics, they are in general objectionable and to be avoided as far as possible. By properly selecting the length of the pole arc and the length of the air-gap between field and armature, a sinusoidal fie ...", "... distributed winding and the use of frac- tional pitch. Individual high harmonics, or pairs of high harmon- ics, are occasionally met, such as the seventeenth and ninteenth, or the thirty-fifth and thirty-seventh, etc. They are due to the pulsation of the magnetic field flux caused by the pulsation of the SHAPING OF WAVES 121 field reluctance by the passage of the armature slots, and occa- sionally, under load, by magnetic saturation of the armature self- inductive flux, that is, flux produced by the current in an arm ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-05", "section_label": "Chapter 6: Empirical Curves", "section_title": "Empirical Curves", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 16483-21988", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-05/", "snippets": [ "... ues can be taken from the plotted curve, no general conclusions can be derived from it, no general investigations based on it regarding the conditions of efficiency, output, etc. An illustration hereof is afforded by the comparison of the electric and the magnetic circuit. In the electric circuit, the relation between e.m.f. and e current is given by Ohm's law, i = -, and calculations are uni- versally and easily made. In the magnetic circuit, however, the term corresponding to the resistance, the reluctance, is not a co ...", "... c. An illustration hereof is afforded by the comparison of the electric and the magnetic circuit. In the electric circuit, the relation between e.m.f. and e current is given by Ohm's law, i = -, and calculations are uni- versally and easily made. In the magnetic circuit, however, the term corresponding to the resistance, the reluctance, is not a constant, and the relation between m.m.f. and magnetic flux cannot be expressed by a general law, but only by an empirical curve, the magnetic characteristic, and as the result, ...", "... een e.m.f. and e current is given by Ohm's law, i = -, and calculations are uni- versally and easily made. In the magnetic circuit, however, the term corresponding to the resistance, the reluctance, is not a constant, and the relation between m.m.f. and magnetic flux cannot be expressed by a general law, but only by an empirical curve, the magnetic characteristic, and as the result, calcula- tions of magnetic circuits cannot be made as conveniently and as general in nature as calculations of electric circuits. If by ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... nctions were APPENDIX A. 275 derived the Abelian functions. In physics and in engineering, integration of special functions in this manner frequently leads to new special functions. For instance, in the study of the propagation through space, of the magnetic field of a conductor, in wireless telegraphy, lightning protection, etc., we get new functions. If ^=/(0 is the current in the conductor, as function of the time t, at a distance x from the conductor the magnetic field lags by the X time ti = -, where S is t ...", "... y of the propagation through space, of the magnetic field of a conductor, in wireless telegraphy, lightning protection, etc., we get new functions. If ^=/(0 is the current in the conductor, as function of the time t, at a distance x from the conductor the magnetic field lags by the X time ti = -, where S is the speed of propagation (velocity of light). Since the field intensity decreases inversely propor- tional to the distance x, it thus is proportional to y= — - — ; (41) and the total magnetic flux then is / 2 ...", "... nductor the magnetic field lags by the X time ti = -, where S is the speed of propagation (velocity of light). Since the field intensity decreases inversely propor- tional to the distance x, it thus is proportional to y= — - — ; (41) and the total magnetic flux then is / 2= j ydx A'-l) -j^T^'i' <*2) If the current is an alternating current, that is, f (t) a trigonometric function of time, equation (42) leads to the functions, /sin ; X \"J dx: cos X ^ -ax. (43) If the current is a dh-ect c ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-06", "section_label": "Lecture 6: Higher Harmonics Of The Generator Wave", "section_title": "Higher Harmonics Of The Generator Wave", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3133-3507", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-06/", "snippets": [ "... e. Since there are a number of conductors in series on the armature, the voltage wave is more evened out than that of a single conductor ; but still it is not a sine wave, that is, contains harmonics of which the third is the lowest. 2nd. The change of magnetic flux by the passage of open armature slots over the field pole produces harmonics of e. m. f . ; that is, when a large open armature slot stands in front of the field pole, the magnetic reluctance is high ; the magnetism is lower than when no slot is in front ...", "... r of phases, the higher harmonics : 2m — i and 2m + i are produced. 4th. The terminal voltage under load is the resultant of the induced e. m. f, and the e. m. f. consumed by the reactance of the armature circuit ; that is, the reactance produced by the magnetic flux produced by the armature current in the arma- ture iron. This armature reactance is not constant, but peri- odically varies, more or less, with double frequency; that is, when the armature coil is in front of the field pole its magnetic circuit is differe ...", "... oduced by the magnetic flux produced by the armature current in the arma- ture iron. This armature reactance is not constant, but peri- odically varies, more or less, with double frequency; that is, when the armature coil is in front of the field pole its magnetic circuit is different than when it is between the field poles, and the reactance therefore is different. This pulsation of armature reactance produces the third harmonic, since it is of double frequency. The most common and prominent harmonic so is the third ha ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-08", "section_label": "Lecture 8: Arc Lamps And Arc Lighting", "section_title": "Arc Lamps And Arc Lighting", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 7141-8510", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-08/", "snippets": [ "... onstant-current transformer to direct current without requiring moving machinery. The Brush machine in its principle essentially is a quarter- phase constant-current alternator with rectifying commutator. An alternator of low armature reaction and strong magnetic field regulates for constant potential: the change of armature reaction, resulting from a change of load, has little effect on the field and thereby on the terminal voltage, if the armature reaction is low. An alternator of very high armature reaction and weak ...", "... and thereby on the terminal voltage, if the armature reaction is low. An alternator of very high armature reaction and weak field, however, regulates for constant current: if the m.m.f., that is, the ampere-turns required in the field coil to produce the magnetic flux, are small compared with the field ampere-turns required to take care of the armature reaction, and the resultant or magnetism-producing field ampere-turns thus the small difference between total field excitation and armature reaction, a moderate increase ...", "... small difference between total field excitation and armature reaction, a moderate increase of armature current and thereby of armature reaction makes it equal to the field excitation, and leaves no ampere-turns for producing the mag- netism; that is, the magnetic flux and thereby the machine voltage disappear. Thus, in such a machine, the current out- put at constant field excitation rises very little, from full volt- age down to short circuit, or, in other words, the machine regulates for approximately constant curren ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-07", "section_label": "Theory Section 7: Inductance in Alternating-current Circuits", "section_title": "Inductance in Alternating-current Circuits", "kind": "theory-section", "sequence": 7, "number": 7, "location": "lines 2250-2717", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-07/", "snippets": [ "... nding angle at which the current reaches its zero value in the ascendant. If such a sine wave of alternating current i = IQ sin 2 irft or i = IQ sin 6 passes through a circuit of resistance r and induc- tance L, the magnetic flux produced by the current and thus its interlinkages with the current, iL = IoL sin 0, vary in a wave 32 ELEMENTS OF ELECTRICAL ENGINEERING line similar also to that of the current, as shown in Fig. 11 as $. The ...", "... ission line, the m.m.f. is I; thus the magnetizing force in a zone dlx at distance lx from center of wire (Fig. 12) is / = 0 7 Z TTlx and the field intensity in this zone is H = 4 irf = 2 y— Thus Lx the magnetic flux in this zone is d* . H ldli m hence, the total magnetic flux between the wire and the return wire is L XI* d* = $ — | CfcSF = ^.f6| -y— = 2 1 1 IQge -j — > LX I'd 2 2 neglecting the ...", "... dlx at distance lx from center of wire (Fig. 12) is / = 0 7 Z TTlx and the field intensity in this zone is H = 4 irf = 2 y— Thus Lx the magnetic flux in this zone is d* . H ldli m hence, the total magnetic flux between the wire and the return wire is L XI* d* = $ — | CfcSF = ^.f6| -y— = 2 1 1 IQge -j — > LX I'd 2 2 neglecting the flux inside the transmission wire. 36 ELEMENTS OF ELECTRICAL E ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-112", "section_label": "Apparatus Section 6: Induction Machines: Phase Converter", "section_title": "Induction Machines: Phase Converter", "kind": "apparatus-section", "sequence": 112, "number": 6, "location": "lines 21647-21812", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-112/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-112/", "snippets": [ "... 1 L o ~~z tor circuit of phase converter. The current in the secondary of the phase converter is then /! = / + /'+ I\", where ^ I = load current = ~ „ I' = eY = exciting current of quadrature magnetic flux, €S I' = - ; — : — = current required to revolve the machi ri+jsxi and the primary current is ?•'-&> !', where /' = eY = exciting current of main magnetic flux. INDUCTION MACHINES 353 From these currents the ...", "... „ I' = eY = exciting current of quadrature magnetic flux, €S I' = - ; — : — = current required to revolve the machi ri+jsxi and the primary current is ?•'-&> !', where /' = eY = exciting current of main magnetic flux. INDUCTION MACHINES 353 From these currents the e.m.fs. are derived in a similar manner as in the induction motor or generator. Due to the internal losses in the phase converter, the e.m.fs. of the two circuits, the m ...", "... nge of load. At the same time, since the condenser current is derived by double 354 ELEMENTS OF ELECTRICAL ENGINEERING transformation in the multitooth structure of the induction machine, which has a practically uniform magnetic field, irre- spective of the shape of the primary impressed e.m.f. wave, the application of the condenser becomes feasible irrespective of the wave shape of the generator. Usually the tertiary circuit in this case is arranged on ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-30", "section_label": "Apparatus Section 9: Synchronous Machines: Magnetic Characteristic or Saturation Curve", "section_title": "Synchronous Machines: Magnetic Characteristic or Saturation Curve", "kind": "apparatus-section", "sequence": 30, "number": 9, "location": "lines 9554-9650", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-30/", "snippets": [ "... ally the change from the unsaturated to the over-saturated por- tion of the curve is more gradual; thus the knee is less pronounced in the magnetic characteristic of the synchronous machines, since the different parts of the magnetic circuit approach saturation successively. The dependence of the terminal voltage upon the field excita- tion, at constant full-load current through the amature into a 148 ELEMENTS OF ELECTRICAL ENGINEERING non-inductive circuit, i ...", "... a greater increase of field excitation is required in the presence of saturation than in the absence thereof. In addition thereto, due to the counter m.m.f. of the armature current, the magnetic stray field, that is, that magnetic flux which leaks from field pole to field pole through the air, increases under load, especially with inductive load where the armature m.m.f. directly opposes the field, and thus a still further increase of density is required ...", "... rom field pole to field pole through the air, increases under load, especially with inductive load where the armature m.m.f. directly opposes the field, and thus a still further increase of density is required in the field magnetic circuit under load. In consequence thereof, at high saturation the load saturation curve differs more from the no-load saturation curve than corresponds to the synchronous impedance of the machine. SYNCHRONOUS MACHINES 149 The r ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-33", "section_label": "Apparatus Section 12: Synchronous Machines: Starting of Synchronous Motors", "section_title": "Synchronous Machines: Starting of Synchronous Motors", "kind": "apparatus-section", "sequence": 33, "number": 12, "location": "lines 9749-9820", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-33/", "snippets": [ "... is due to the magnetic attraction of the armature currents upon the remanent magnetism left in the field poles by the currents of the preceding phase, and to the eddy currents produced therein. Let Fig. 72 represent the magnetic circuit of a polyphase synchronous motor. The m.m.f. of the polyphase armature currents acting upon the successive projections or teeth of the armature, 1, 2, 3, etc., reaches a maximum in them successively; that is, the armature ...", "... increases that caused by remanent magnetism or hysteresis, due to the higher permeability of the field poles. Thus the torque per volt-ampere input is approximately the same in either case, but with laminated i FIG. 72. — Magnetic circuit of a polyphase synchronous motor. poles the impressed voltage required in starting is higher and the current lower than with solid field poles. In either case, at full impressed e.m.f. the starting current of a synchronous ...", "... chronous motor is large, since in the absence of a counter e.m.f. the total impressed e.m.f. has to be consumed by the impedance of the armature cir- cuit. Since the starting torque of the synchronous motor is due to the magnetic flux produced by the alternating armature cur- rents, or the armature reaction, synchronous motors of high armature reaction are superior in starting torque. Very frequently in synchronous motors a squirrel-cage wind- ing is used i ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-48", "section_label": "Apparatus Subsection 48: Direct-current Commutating Machines: C. Commutating Machines", "section_title": "Direct-current Commutating Machines: C. Commutating Machines", "kind": "apparatus-subsection", "sequence": 48, "number": null, "location": "lines 10845-10940", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-48/", "snippets": [ "... le on the armature surface, the distance from the next field pole is ld = Vk2 + lx2, and the density thus, approximately, B C FIG. 92. — Distribution of mganetic flux under a single pole. Herefrom the distribution of magnetic flux is calculated and plotted in Fig. 92, for a single pole BC, along the armature sur- face A, for the length of air gap la = 1, and such a m.m.f. as to L FIG. 93. — Distribution of magnetic force and flux at no loa ...", "... ELECTRICAL ENGINEERING between C and E} at which the m.m.f. of the field equals zero, is called the \"neutral.\" The distribution of m.m.f. of field excitation is thus given by the line F in Fig. 91. The distribu- tion of magnetic flux as shown in Fig. 91 by BQ is derived by the formula 4irF B 10 I where This distribution of magnetic flux applies only to the no-load condition. Under load, that is, if the armature carries current, the distribut ...", "... distribution of m.m.f. of field excitation is thus given by the line F in Fig. 91. The distribu- tion of magnetic flux as shown in Fig. 91 by BQ is derived by the formula 4irF B 10 I where This distribution of magnetic flux applies only to the no-load condition. Under load, that is, if the armature carries current, the distribution of flux is changed by the m.m.f. of the armature current, or armature reaction. J FIG. 94. — Distribution of ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-84", "section_label": "Apparatus Section 5: Synchronous Converters: Armature Reaction", "section_title": "Synchronous Converters: Armature Reaction", "kind": "apparatus-section", "sequence": 84, "number": 5, "location": "lines 15161-15475", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-84/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-84/", "snippets": [ "... e direct- current reaction. Hence, the armature reaction oscillates with twice the fre- quency of the alternating current, and with full intensity, and since it is in quadrature with the field excitation, tends to shift the magnetic flux rapidly across the field poles, and thereby tends to cause sparking and power losses. This oscillating reaction is, however, reduced by the damping effect of the mag- netic field structure. It is somewhat less in the two-ci ...", "... e from coil to coil, while the alternating current is the same in a whole section of the armature between adjacent leads. Thus while the resultant reactions neutralize, a local effect remains which in its relation to the magnetic field oscillates with a period equal to the time of motion of the armature through the angle between adjacent alternating leads; that is, double frequency in a single-phase converter (in which it is equal in magnitude to the di ...", "... e reaction discussed above), sextuple frequency in a three-phase converter, and quadruple frequency in a four- phase converter. The amplitude of this oscillation in a polyphase converter is small, arid its influence upon the magnetic field is usually neg- ligible, due to the damping effect of the field spools, which act like a short-circuited winding for an oscillation of magnetism. A polyphase converter on unbalanced circuit can be con- sidered as a combinat ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-86", "section_label": "Apparatus Section 7: Synchronous Converters: Variable Ratio Converters (\"split Pole\" Converters)", "section_title": "Synchronous Converters: Variable Ratio Converters (\"split Pole\" Converters)", "kind": "apparatus-section", "sequence": 86, "number": 7, "location": "lines 15586-15734", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-86/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-86/", "snippets": [ "VII. Variable Ratio Converters (\"Split Pole\" Converters) 98. With a sine wave of alternating voltage, and the com- mutator brushes set at the magnetic neutral, that is, at right angles to the resultant magnetic flux, the direct voltage of a SYNCHRONOUS CONVERTERS 253 converter is constant at constant impressed alternating voltage. It equals the maximum value of the alternating voltage between two diametrically opposite points of t ...", "... or Y voltage of the polyphase system. A change of the direct voltage, at constant impressed alter- nating voltage, can be produced — Either by changing the position angle between the commu- tator brushes and the resultant magnetic flux, so that the direct voltage between the brushes is not the maximum diametrical alternating voltage but only a part thereof, Or by changing the maximum diametrical alternating voltage, at constant effective impressed voltage, ...", "... wo, a smaller one, the regulating pole, and a larger one, the main pole. By varying the excitation of the regulating pole from maximum in one direction, to maximum in the opposite direction, the direction of the resultant magnetic field flux, and the effective width of the field pole, and with the latter the wave shape, are varied. To keep the wave shape variation local in the converter, so as not to reflect it into the primary supply circuit, the pro ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-96", "section_label": "Apparatus Section 2: Alternating-current Transformer: Excitation", "section_title": "Alternating-current Transformer: Excitation", "kind": "apparatus-section", "sequence": 96, "number": 2, "location": "lines 16912-17026", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-96/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-96/", "snippets": [ "... 30 FIG. 153. — Excitation and core loss of transformer. and does not become zero at no load or open circuit, but a small and lagging current ^o remains at no load, which is called the exciting current. It produces the magnetic flux and supplies the losses in the iron, so-called \"core loss.\" Its reactive com- ponent, imj is called the magnetizing current, and is usually greatly distorted in wave shape, while the energy component, 280 ELEMENTS OF EL ...", "... urves are given in Fig. 153, with the impressed volts as abscissae, and the total exciting current, and core loss as ordinates. The exciting current is usually not proportional to the voltage, due to the use of a closed magnetic circuit, and for the same reason, the power-factor of the exciting current is fairly high, from 40 to 60 per cent., except at high voltages, where magnetic saturation causes an abnormal increase of the magnetizing current. The po ...", "... The power-factor is shown on Fig. 153. IE. Losses and Efficiency 113. The losses in the transformer are (a) The core loss, comprising the loss by hysteresis and eddy currents in the iron. This depends on the maximum magnetic flux, and thus on the induced voltage: and as the induced voltage is practically equal to the impressed voltage 61, at constant impressed voltage, the core loss is practi- cally constant, and is often assumed as constant, that ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-16", "section_label": "Chapter 16: Power, And Double-Frequency Quantities In", "section_title": "Power, And Double-Frequency Quantities In", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 16077-16520", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-16/", "snippets": [ "... ANTITIES 185 140. Like power, torque in alternating apparatus is a double- frequency vector product also, of magnetism and m.m.f. or current, and thus can be treated in the same way. In an induction motor, for instance, the torque is the product of the magnetic flux in one direction into the component of secondary current in phase with the magnetic flux in time, but in quadrature position therewith in space, times the number of turns of this current, or since the generated e.m.f. is in quad- rature and proportional t ...", "... ctor product also, of magnetism and m.m.f. or current, and thus can be treated in the same way. In an induction motor, for instance, the torque is the product of the magnetic flux in one direction into the component of secondary current in phase with the magnetic flux in time, but in quadrature position therewith in space, times the number of turns of this current, or since the generated e.m.f. is in quad- rature and proportional to the magnetic flux and the number of turns, the torque of the induction motor is the pro ...", "... e direction into the component of secondary current in phase with the magnetic flux in time, but in quadrature position therewith in space, times the number of turns of this current, or since the generated e.m.f. is in quad- rature and proportional to the magnetic flux and the number of turns, the torque of the induction motor is the product of the generated e.m.f. into the component of secondary current in quadrature therewith in time and space, or the product of the secondary current into the component of generated e. ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-24", "section_label": "Chapter 24: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 25682-29374", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-24/", "snippets": [ "... (equivalent) resistance, r, and (equivalent) reactance, x = 2 irfL, containing the impressed e.m.f., eo and the counter e.m.f., d, of the syn- chronous motor ^; that is, the e.m.f. generated in the motor arma- ture by its rotation through the (resultant) magnetic field. Let i = current in the circuit (effective values). The mechanical power delivered by the synchronous motor (including friction and core loss) is the electric power consumed by the counter e.m.f., ei; hence ■p = iei cos {i, 6]); (1) thus, cos (t, ...", "... Co = e.m.f. at motor terminals, z = internal impedance of the motor; if So = terminal voltage of the generator, z = total impedance of line and motor; if eo = e.m.f. of generator, that is, e.m.f. generated in generator armature by its rotation through the magnetic field, z includes the generator impedance also. 316 ALTERNATING-CURRENT PHENOMENA form a triangle, that is, ei and e are components of eo, it is (Figs. 159 and 160), eo' e-^ + 6^ + 2 ee\\ cos (ei, e), hence, cos (ei, e) = eo 2-ei2 2 — p, ...", "... ur- rent output affords a means of automatically varying the excitation with the load. 230. The investigation of a variation of the armature reaction and the self-induction, that is, of the synchronous reactance, with the position of the armature in the magnetic field, and so the intensity and phase of the current in its effect on the charac- teristic curves of the synchronous motor, can be carried out in the same manner as done for the alternating-current generator in Chapter XX. In the graphical and the symbolic in ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-12", "section_label": "Chapter 12: Power, And Double Frequency Quantities In General", "section_title": "Power, And Double Frequency Quantities In General", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 9381-9740", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "snippets": [ "... compensated. 106. Like power, torque in alternating apparatus is a double frequency vector product also, of magnetism and M.M.F. or current, and thus can be treated in the same way. In an induction motor, for instance, the torque is the product of the magnetic flux in one direction into the com- ponent of secondary induced current in phase with the magnetic flux in time, but in quadrature position therewith in space, times the number of turns of this current, or since the induced E.M.F. is in quadrature and proporti ...", "... also, of magnetism and M.M.F. or current, and thus can be treated in the same way. In an induction motor, for instance, the torque is the product of the magnetic flux in one direction into the com- ponent of secondary induced current in phase with the magnetic flux in time, but in quadrature position therewith in space, times the number of turns of this current, or since the induced E.M.F. is in quadrature and proportional to the magnetic flux and the number of turns, the torque of the induction motor is the product ...", "... tion into the com- ponent of secondary induced current in phase with the magnetic flux in time, but in quadrature position therewith in space, times the number of turns of this current, or since the induced E.M.F. is in quadrature and proportional to the magnetic flux and the number of turns, the torque of the induction motor is the product of the induced E.M.F. into the component of secondary current in quadrature therewith in time and space, or the product of the induced current into the component of induced E.M.F. i ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-11", "section_label": "Chapter 11: Instability Of Circuits: Induction And Syn Chronous Motors", "section_title": "Instability Of Circuits: Induction And Syn Chronous Motors", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 21382-22633", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-11/", "snippets": [ "... stand- still, etc. Oscillatory instability in induction-motor circuits, as the result of the relation of load to speed and electric supply, is rare. It has been observed, especially in single-phase motors, in cases of considerable oversaturation of the magnetic circuit. Oscillatory instability, however, is typical of the synchronous machine, and the hunting of synchronous machines has probably been the first serious problem of cimiulative oscillations in electric circuits, and for a long time has limited the industrial ...", "... s, inductivity of the damper winding is very harmful, and it is essential to design the damper winding as non- inductive as possible to give efficient damping. With the change of position, p, the current, and thus the ar- mature reaction, and with it the magnetic flux of the machine, changes. A flux change can not be brought about instantly, as it represents energy stored, and as a result the magnetic flux of the machine does not exactly correspond with the position, p, but lags behind it, and with it the synchronizing ...", "... efficient damping. With the change of position, p, the current, and thus the ar- mature reaction, and with it the magnetic flux of the machine, changes. A flux change can not be brought about instantly, as it represents energy stored, and as a result the magnetic flux of the machine does not exactly correspond with the position, p, but lags behind it, and with it the synchronizing force, F, as shown in Fig. 104, lags more or less, depending on the design of the machine. The synchronizing power of the machine, Fv, in ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-14", "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "section_title": "Constant-Potential Constant-Current Trans Formation", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "... aratus, as trans- formers from constant potential to constant ciurent, or regula- tors, this variation of series inductive reactance with the load is usually accomplished automatically by the mechanical motion caused by the mechanical force exerted by the magnetic field of the current, upon the conductor in which the ciurent exists. For instance, in the constant-current transformer, as shown diagrammatically in Fig. 114, the secondary coils, S, are arranged so that they can move away from the primary coils, P, or in- v ...", "... nt transformer, as shown diagrammatically in Fig. 114, the secondary coils, S, are arranged so that they can move away from the primary coils, P, or in- versely. Primary and secondary currents are proportional to each other, as in any transformer, and the magnetic field between primary and secondary coils, or the magnetic stray field, in which the secondary coils float, is proportional to either current. The magnetic repulsion between primary coils and secondary coils is proportional to the current (or rather its ampere- ...", "... y coils. Any increase of secondary ciurrent, as, for instance, caused by short-circuiting a part of the secondary load, then increases the repulsion between primary and secondary coils, and the secondary coils move away from the primary; hence more of the magnetic flux produced by the primary coils passes between primary and secondary, as stray field, or self-inductive flux, less passes through the secondary coils, and therefore the second- ary generated voltage decreases with the separation of the coils, and also there ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-10", "section_label": "Chapter 6: Alternating Magnetic Flux Distribution. 355", "section_title": "Alternating Magnetic Flux Distribution. 355", "kind": "chapter", "sequence": 10, "number": 6, "location": "lines 904-937", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-10/", "snippets": [ "CHAPTER VI. ALTERNATING MAGNETIC FLUX DISTRIBUTION. 355 48. Magnetic screening by secondary currents in alternating fields. 355 49. The differential equations of alternating magnetic flux in a lamina. 356 50. Their integral equations. 357 51. Terminal conditions, and the final equatio ...", "CHAPTER VI. ALTERNATING MAGNETIC FLUX DISTRIBUTION. 355 48. Magnetic screening by secondary currents in alternating fields. 355 49. The differential equations of alternating magnetic flux in a lamina. 356 50. Their integral equations. 357 51. Terminal conditions, and the final equations. 358 52. Equations for very thick laminae. 360 53. Wave length, attenuation, depth of penetration. 361 54. Numerical example, with frequencies of 6 ...", "... the final equations. 358 52. Equations for very thick laminae. 360 53. Wave length, attenuation, depth of penetration. 361 54. Numerical example, with frequencies of 60, 1000 and 10,000 cycles per second. 362 55. Depth of penetration of alternating magnetic flux in different metals. 363 56. Wave length, attenuation, and velocity of penetration. 365 57. Apparent permeability, as function of frequency, and damping. 366 58. Numerical example and discussion. 367" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-35", "section_label": "Chapter 13: Transient Term Of The Rotating Field", "section_title": "Transient Term Of The Rotating Field", "kind": "chapter", "sequence": 35, "number": 13, "location": "lines 13936-14548", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-35/", "snippets": [ "CHAPTER XIII. TRANSIENT TERM OF THE ROTATING FIELD. 106. The resultant of np equal m.m.fs. equally displaced from each other in space angle and in time-phase is constant in intensity, and revolves at constant synchronous velocity. When acting upon a magnetic circuit of constant reluctance in all directions, such a polyphase system of m.m.fs. produces a revolving magnetic flux, or a rotating field. (\" Theory and Calculation of Alternating Current Phenomena,\" 4th edition, Chapter XXXIII, paragraph 368.) That is, if np ...", "... from each other in space angle and in time-phase is constant in intensity, and revolves at constant synchronous velocity. When acting upon a magnetic circuit of constant reluctance in all directions, such a polyphase system of m.m.fs. produces a revolving magnetic flux, or a rotating field. (\" Theory and Calculation of Alternating Current Phenomena,\" 4th edition, Chapter XXXIII, paragraph 368.) That is, if np equal mag- netizing coils are arranged under equal space angles of - np electrical degrees, and connected to ...", "... re $ Zi is the maximum value (hence — — the effective value) of the \\ V2 I m.m.f. of each coil. In starting, that is, when connecting such a system of mag- netizing coils to a polyphase system of e.m.fs., a transient term appears, as the resultant magnetic flux first has to rise to its constant value. This transient term of the rotating field is the resultant of the transient terms of the currents and therefore the m.m.fs. of the individual coils. 107. If, then, $ = nl = maximum value of m.m.f. of each coil, w ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-56", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit", "section_title": "Power And Energy Of The Complex Circuit", "kind": "chapter", "sequence": 56, "number": 7, "location": "lines 33528-34202", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "snippets": [ "... rom the rest of the circuit, is proportional to the length of the section, A', to its trans- fer constant, s, and to the sum of the power of main wave and reflected wave. 51. The energy stored by the inductance L of a circuit element dXj that is, in the magnetic field of the circuit, is 'LV dwl =-^~A where U = inductance per unit length of circuit expressed by the distance coordinate A. Since L = the inductance per unit length of circuit, of distance coordinate Z, and X = i cos (/'i ^,), (1) thus, — cos (f\\ dy ...", "... i\\y = E.M.F. at motor terminals, z = internal impedances of the motor; if eo= terminal voltage of the generator, s = total impedance of line and motor; if ^f^ = E.M.F. of generator, that is, E.M.F. induced in generator armature by its rotation through the magnetic field, z includes the generator impedance also. f6 ALTERNATJNG-CURRENT PHENOMENA. [S 184 The displacement of phase between current i and E.M.F. = si consumed by the impedance s is : cos (*>) = sin (»>) = Since the three E.M.Fs. acting in the closed cir ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-20", "section_label": "Chapter 20: Beactiox Machines", "section_title": "Beactiox Machines", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 22388-23273", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "snippets": [ "... ine is a constant. While this is more or less approximately thd case in many alternators, in others, especially in machines of large arma- ture reaction, the reactance x is variable, and is different in the different positions of the armature coils in the magnetic circuit. This variation of the reactance causes phenomena which do not find their explanation by the theoretical cal- culations made under the assumption of constant reactance. It is known that synchronous motors of large and variable reactance keep in synchroni ...", "... or do not disappear if the gene- rator field is broken, or even reversed to a small negative value, in which latter case the current flows against the E.M.F. E^ of the generator. Furthermore, a shuttle armature without any winding will in an alternating magnetic field revolve when once brought up to synchronism, and do considerable work as a motor. These phenomena are not due to remanant magnetism nor to the magnetizing effect of Foucault currents, because 206, 206] REACTION MACHINES, 809 they exist also in machi ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-19", "section_label": "Chapter 19: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 18053-19457", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "snippets": [ "... cuit of (equivalent) resistance r and (equivalent) reactance x = 2 TT NL, containing the impressed E.M.F. e0* and the counter E.M.F. et of the syn- chronous motor; that is, the E.M.F. induced in the motor arma- ture by its rotation through the (resultant) magnetic field. Let i = current in the circuit (effective values). The mechanical power delivered by the synchronous motor (including friction and core loss) is the electric power consumed by the C. E.M.F. e1; hence — p = *>! cos ft,^), (1) thus, — * If f0 = E. ...", "... * If f0 = E.M.F. at motor terminals, z = internal impedance of the motor; if eo= terminal voltage of the generator, z = total impedance of line and motor; if t0= E.M.F. of generator, that is, E.M.F. induced in generator armature by its rotation through the magnetic field, z includes the generator impedance also. SYNCHRONOUS MOTOR. 339 The displacement of phase between current i and E.M.F. = z i consumed by the impedance z is : cos (ie) = - sin (/ — - — 4 1000 ^ .- •\"J **** ^ S. X * d2-2«50n ^, _ ...", "... UO Degrees > Fig. 59. Quarter-phase rectification. small compared with the total field m.m.f. and the armature reaction, and so greatly varies with a small variation of armature current. As result, a very great distortion of the field occurs, and the magnetic flux is concentrated at the pole corner. This gives an e.m.f. wave which has a very sharp and high peak, with very long flat zero, and so cannot be approximated by an equiva- lent sine wave, but the actual e.m.f. curves have to be used in a more exact investig ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "LECTURE VIII. TRAVELING WAVES. 33. In a stationary oscillation of a circuit having uniformly distributed capacity and inductance, that is, the transient of a circuit storing energy in the dielectric and magnetic field, current and voltage are given by the expression i = ioe-\"^ cos ((/> T CO — 7), ^ . . e = eoe~\"' sin ((^ =F co — 7), where T co — 7), ) where 0 is the time angle, co the distance angle, u the exponential decrement, or the \"power-dissipation constant,\" and i0 and eQ the max ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-01", "section_label": "Chapter 1: The General Number", "section_title": "The General Number", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 915-3491", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-01/", "snippets": [ "... olutions of differential equations frequently appear in this form, and then are reduced to the polar or the rectangular form. 37. For instance, the differential equation of the distribu- tion of alternating current in a flat conductor, or of alternating magnetic flux in a flat sheet of iron, has the form : and is integrated by y = A£~^'^, where. V=\\/-2jc^=±{l-j)c; hence, 2/=^£+(i-^*)\"^+A2£-^^~^*K This expression, reduced to the polar form, is y = Aie'^''^(cos ex -j sin ex) +A2£~''''(cos ex+j sin ex). THE GE ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-05", "section_label": "Lecture 5: Long Distance Transmission", "section_title": "Long Distance Transmission", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2562-3132", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-05/", "snippets": [ "... d or symmetrical, that is, have the same potential differences from all the conductors to the ground. Any electric circuit, and so also the transmission line, contains inductance and capacity, and therefore stores energy as electromagnetic energy in the magnetic field due to the cur- rent, and as electrostatic energy, or electrostatic charge, due to the voltage. LONG DISTANCE TRANSMISSION 69 If: e = voltage, C = capacity. i = current, L = inductance. the electrostatic energy is : e*C 2 and the electromagnet ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... y high armature reaction and relatively weak field excitation; that is, the armature ampere turns are nearly equal and opposite to the field ampere turns, and thus both very large compared with the difference, the resultant ampere turns, which produce the magnetic field. A moderate increase of current and consequent increase of armature ampere turns therefore greatly reduces the resultant ampere turns and ARC LIGHTING 221 so the field magnetism and the voltage, (that is, the machine tends to regulate for constant cur ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-105", "section_label": "Apparatus Section 8: Alternating-current Transformer: Autotransformer", "section_title": "Alternating-current Transformer: Autotransformer", "kind": "apparatus-section", "sequence": 105, "number": 8, "location": "lines 18666-18812", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-105/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-105/", "snippets": [ "... ons, that is, by e\\ X ii + £2 X iz FIG. 172. — Diagram of trans- former. FIG. 173. — Diagram of auto- transformer. (the turns being proportional to the voltage, the turn section to the current, the same magnetic flux assumed). But since 61 = aez and i\\ = — , e\\i\\ = e2i2, and the size of the transformer Fig. 172 thus is proportional to 2 e-#2, that is, to 2 P, or twice the output. In the autotransformer Fig. 173, the nz ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-113", "section_label": "Apparatus Section 7: Induction Machines: Frequency Converter or General Alternating-current Transformer", "section_title": "Induction Machines: Frequency Converter or General Alternating-current Transformer", "kind": "apparatus-section", "sequence": 113, "number": 7, "location": "lines 21813-21922", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-113/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-113/", "snippets": [ "... e synchronous alternator further discussed in the \"Theory and Calculation of Electrical Apparatus.\" As far as its transformer action is concerned, the frequency 356 ELEMENTS OF ELECTRICAL ENGINEERING converter is an open magnetic circuit transformer, that is, a trans- former of relatively high magnetizing current. It combines therewith, however, the action of an induction motor or generator. Excluding the case of over-synchronous rotation, it is approxi- mately ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-114", "section_label": "Apparatus Section 8: Induction Machines: Concatenation of Induction Motors", "section_title": "Induction Machines: Concatenation of Induction Motors", "kind": "apparatus-section", "sequence": 114, "number": 8, "location": "lines 21923-22191", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-114/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-114/", "snippets": [ "... f e.m.f. in the internal impedance of the first motor, equal those of the first motor. With increasing speed, the frequency and the e.m.f. impressed upon the second motor decrease proportionally to each other, and thus the magnetic flux and the magnetic density in the second motor, and its ex- citing current, remain constant and equal to those of the first motor, neglecting internal losses; that is, when connected in con- catenation the magnetic density, cu ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-17", "section_label": "Theory Section 17: Impedance and Admittance", "section_title": "Impedance and Admittance", "kind": "theory-section", "sequence": 17, "number": 17, "location": "lines 6814-7380", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-17/", "snippets": [ "... current i in the circuit. Such counter e.m.fs. may be due to inductance, as self-induc- tance, or mutual inductance, to capacity, chemical polarization, etc. The counter e.m.f. of self-induction, or e.m.f. generated by the magnetic field produced by the alternating current i, is repre- sented by a quantity of the same dimensions as resistance, and measured in ohms: reactance x. The e.m.f. consumed by reactance x is in quadrature with the current, that cons ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-25", "section_label": "Apparatus Section 4: Synchronous Machines: Self-inductance", "section_title": "Synchronous Machines: Self-inductance", "kind": "apparatus-section", "sequence": 25, "number": 4, "location": "lines 8907-9034", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-25/", "snippets": [ "... f armature reaction, FlQ 50._Diagram of e m fs> and depends upon the phase relation in loaded generator, in the same manner. If EI = real generated voltage, 0i = lag of current behind generated voltage EI, the magnetic flux produced by the arma- ture current I is in phase with the current, and thus the counter e.m.f. of self-inductance is in quadrature behind the current, and therefore the e.m.f. consumed by self-inductance is in quadrature ah ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-31", "section_label": "Apparatus Section 10: Synchronous Machines: Efficiency and Losses", "section_title": "Synchronous Machines: Efficiency and Losses", "kind": "apparatus-section", "sequence": 31, "number": 10, "location": "lines 9651-9718", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-31/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-31/", "snippets": [ "... ng the losses, and the latter is therefore com- monly used. The losses consist of the following: the resistance loss in the armature; the resistance loss in the field circuit; the hysteresis and eddy current losses in the magnetic circuit; the friction and windage losses, and eventually load losses, that is, losses due to eddy currents and hysteresis produced by the load current in the armature. The resistance loss in the armature is proportional to the sq ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-40", "section_label": "Apparatus Subsection 40: Direct-current Commutating Machines: C. Commutating Machines", "section_title": "Direct-current Commutating Machines: C. Commutating Machines", "kind": "apparatus-subsection", "sequence": 40, "number": null, "location": "lines 10475-10519", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-40/", "snippets": [ "... armature is best adapted; the smooth-core type is hardly ever used nowadays. Either of these types can be drum wound or ring wound. The drum winding has the advantage of lesser self-inductance and lesser distortion of the magnetic field, and is generally less difficult to construct and thus mostly preferred. By the arma- ture winding, commutating machines are divided into multiple- wound and series-wound machines. The difference between multiple and series arm ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-50", "section_label": "Apparatus Section 5: Direct-current Commutating Machines: Effect of Saturation on Magnetic Distribution", "section_title": "Direct-current Commutating Machines: Effect of Saturation on Magnetic Distribution", "kind": "apparatus-section", "sequence": 50, "number": 5, "location": "lines 11025-11046", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-50/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-50/", "snippets": [ "... the demagnetized pole corner the magnetic density decreases, at the strengthened pole corner increases, proportionally to the m.m.f. The distribution of m.m.f. obviously is not affected by satu- ration, but the distribution of magnetic flux is greatly changed thereby. To investigate the effect of saturation, in Figs. 96 to 99 the assumption has been made that the air gap is reduced to one-half its previous value, la = 0.5, thus consuming only one- half as ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-55", "section_label": "Apparatus Subsection 55: Direct-current Commutating Machines: C. Commutating Machines 189", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 189", "kind": "apparatus-subsection", "sequence": 55, "number": null, "location": "lines 11301-11386", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-55/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-55/", "snippets": [ "... ction of the shift of brushes has to be reversed with the re- versal of rotation. In railway motors this cannot be done with- out objectionable complication, therefore the brushes have to be set midway, and the use of the magnetic flux at the edge of the next pole, as commutating flux, is not feasible. In this case a commutating pole is used, to give, without mechanical shifting of the brushes, the same effect which a brush shift would give. Therefore ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-60", "section_label": "Apparatus Section 9: Direct-current Commutating Machines: Saturation Curves", "section_title": "Direct-current Commutating Machines: Saturation Curves", "kind": "apparatus-section", "sequence": 60, "number": 9, "location": "lines 11695-11710", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-60/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-60/", "snippets": [ "... e at open circuit and normal speed, as function of the ampere-turns per pole field excitation. Such curves are of the shape shown in Fig. 105 as A. Owing to the remanent magnetism or hysteresis of the iron part of the magnetic circuit, the saturation curve taken with decreasing field excitation usually does not coincide with that taken with increasing field excitation, but is higher, and by gradually first increasing the field excitation from zero to maxim ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-77", "section_label": "Apparatus Subsection 77: Direct-current Commutating Machines: C. Commutating Machines", "section_title": "Direct-current Commutating Machines: C. Commutating Machines", "kind": "apparatus-subsection", "sequence": 77, "number": null, "location": "lines 12929-13007", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-77/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-77/", "snippets": [ "... of arma- ture reaction. 10 60 FIG. 121 100 120 _110 160 ISO -Series motor speed curve. The torque of the series motor is shown also in Fig. 121, derived as proportional to A X i, that is, current X magnetic flux. Compound Motors 76. Compound motors can be built with cumulative com- pounding and with differential compounding. Cumulative compounding is used to a considerable extent, as in elevator motors, etc., to secure economy of c ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-02", "section_label": "Chapter 2: Instantaneous Values And Integral Values", "section_title": "Instantaneous Values And Integral Values", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 1684-2011", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-02/", "snippets": [ "... eous values, as determined by wave-meter or oscillograph. Measurement of the alternating wave after rectification by a unidirectional conductor, as an arc, gives the inean value with direct-current instruments, that is, instruments employing a permanent magnetic field, and the effective value with alternating- current instruments. Voltage determination by spark-gap, that is, by the striking distance, gives a value approaching the maximum, especially with spheres as electrodes of a diameter larger than the spark- gap. ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-27", "section_label": "Chapter 27: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 33011-34776", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-27/", "snippets": [ "... wer-factor exists without corresponding phase displacement, the circuit-factor being less than one-half. Such circuits, for instance, are those including alternating arcs, reaction machines, synchronous induction motors, react- ances with over-saturated magnetic circuit, high potential lines in which the maximum difference of potential exceeds the corona voltage, polarization cells and in general electrolytic conductors above the dissociation voltage of the electrolyte, etc. Such cir- cuits cannot correctly, and in many ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-29", "section_label": "Chapter 29: Symmetrical Polyphase Systems", "section_title": "Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 29, "number": 29, "location": "lines 34929-35255", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-29/", "snippets": [ "... the angle /3 is tan d ^ — cot jS; hence d = ~ ^ o' That is, the m.m.f. produced by a symmetrical ?i-phase system revolves with constant intensity, V2 and constant speed, in synchronism with the frequency of the system; and, if the reluctance of the magnetic circuit is constant, the magnetism revolves with constant intensity and constant speed also, at the point acted upon symmetrically by the n m.m.fs. of the n-phase system. This is a characteristic feature of the symmetrical polyphase system. 272. In the three- ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-32", "section_label": "Chapter 32: Transformation Of Polyphase Systems", "section_title": "Transformation Of Polyphase Systems", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 36062-36514", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-32/", "snippets": [ "... sformers. 291. As an instance may be considered the transformation of the symmetrical balanced three-phase system, E sin /3, E sin (^ - 120), E sin (^ - 240), into an unsymmetrical balanced quarter-phase system, E' sin /3, E' sin (/3 - 90). Let the magnetic flux of the two transformers be chosen in quad- rature $ cos iS and $ cos (/S — 90). Then the e.m.fs. generated per turn in the transformers are e sin /3 and e sin (/3 — 90) ; 424 ALTERNATING-CURRENT PHENOMENA hence, in the primary circuit the first pha ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-24", "section_label": "Chapter 24: Symmetbicaii Polyphase Ststems", "section_title": "Symmetbicaii Polyphase Ststems", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 25271-25604", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-24/", "snippets": [ "... the angle /3 is : tan a> = cot P ; That is, the M.M.F. produced by a symmetrical «-phase system revolves with constant intensity : F = ,— » V2 and constant speed, in synchronism with the frequency of the system ; and, if the reluctance of the magnetic circuit §238] SYMMETRICAL POLYPHASE SYSTEMS. 355 is constant, the magnetism revolves with constant intensity and constant speed also, at the point acted upon symmetri- cally by the ;/ M.M.Fs. of the //-phase system. This is a characteristic feature of the sy ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-27", "section_label": "Chapter 27: Tbansfobmation Of Polyphase Systems", "section_title": "Tbansfobmation Of Polyphase Systems", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 26428-26583", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-27/", "snippets": [ "... NA, [§ 257 257. As an instance may be considered the transforma- tion of the symmetrical balanced three-phase system E sin )3, E sin (^ — 120), E sin (fi — 240), in an unsymmetrical balanced quarter-phase system : E' sin )3, E' sin {fi - 90). Let the magnetic flux of the two transformers be <^ cos fi and <^ cos ()3 — 90). Then the E.M.Fs. induced per turn in the transformers ^^^ ^sin)3 and ^sin()3-90); hence, in the primary circuit the first phase, E sin /8, will give, in the first transformer, Efe primary turns ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "section_label": "Chapter 30: Quartbr-Fhase System", "section_title": "Quartbr-Fhase System", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... jr = 2 IT N L = inductive reactance, Xc = l/2vN'C = capacity reactance of the total primary circuit, including the primary coil of the transformer. If ^/ = El dec o denotes the electromotive force induced in the secondary of the transformer by the mutual magnetic flux ; that is, by the oscillating magnetism interlinked with the primary and secondary coil, we have /j = £i Vi dec a = secondary current. Hence, // = / /i dec a = pE' Fj dec a = primary load current, or component of primary current corresponding to second ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "... er factor exists without corresponding phase displace- ment, the circuit factor being less than one-half. Such circuits, for instance, are those including alternat- ing arcs, reaction machines, synchronous induction motors, reactances with over-saturated magnetic circuit, high poten- tial lines in which the maximum difference of potential ex- ceeds the voltage at which brush discharges begin, polariza- tion cells, and in general electrolytic conductors above the dissociation voltage of the electrolyte, etc. Such circuits ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-26", "section_label": "Chapter 26: Symmetrical Polyphase Systems", "section_title": "Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 23781-24053", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-26/", "snippets": [ "... — ^ That is, the M.M.F. produced by a symmetrical «-phase system revolves with constant intensity : SYMMETRICAL POLYPHASE SYSTEMS. 439 F= — • V25 and constant speed, in synchronism with the frequency of the system ; and, if the reluctance of the magnetic circuit is constant, the magnetism revolves with constant intensity and constant speed also, at the point acted upon symmetri- cally by the n M.M.Fs. of the w-phase system. This is a characteristic feature of the symmetrical poly- phase system. 266. In the th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-29", "section_label": "Chapter 29: Transformation Of Polyphase Systems", "section_title": "Transformation Of Polyphase Systems", "kind": "chapter", "sequence": 29, "number": 29, "location": "lines 24805-25135", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-29/", "snippets": [ "... sformers. 285. As an instance may be considered the transforma- tion of the symmetrical balanced three-phase system E sin ft, E sin (ft — 120), E sin (ft — 240), in an unsymmetrical balanced quarter-phase system : E' sin ft, E' sin (ft — 90). Let the magnetic flux of the two transformers be (/> cos £ and cos (ft — 90). Then the E.M.Fs. induced per turn in the transformers e sin ft and e sin (ft — 90) ; hence, in the primary circuit the first phase, E sin ft, will give, in the first transformer, E/e primary ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-32", "section_label": "Chapter 32: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 25904-27405", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "snippets": [ "... 2 TT NL = inductive reactance, xc = 1 / 2 TT N C = capacity reactance of the total primary circuit, including the primary coil of the transformer. If EI = EI dec a denotes the electromotive force induced in the secondary of the transformer by the mutual magnetic flux ; that is, by the oscillating magnetism interlinked with the primary and secondary coil, we have Iv = E^ Yl dec a = secondary current. Hence, // = / 7X dec a = pEJ Yl dec a = primary load current, or component of primary current corresponding to second ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-05", "section_label": "Chapter 5: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 9062-11050", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-05/", "snippets": [ "... 25 per cent, powdered manganese metal, and 75 per cent, powdered antimony metal, heated together to a moderate temperature — in a test-tube — gives a strongly mag- netic black powder, which can be used like iron filings, to show the lines of forces of the magnetic field, but has not further beeo investigated. A considerable number of such magnetic manganese alloys have been investigated by Heusler and others, and their constants are given in the following table. It is supposed that these magnetic manganese alloys are ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-12", "section_label": "Chapter 8: Velocity Of Propagation Op Electric Field. 387", "section_title": "Velocity Of Propagation Op Electric Field. 387", "kind": "chapter", "sequence": 12, "number": 8, "location": "lines 972-1013", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-12/", "snippets": [ "... 387 68. Equations of decrease of electric field with the dis- tance. 388 69. Effect of return conductor on distance decrement of field. 389 70. Inductance of length I of infinitely long conductor with- out return conductor. 390 71. Equations of magnetic flux, effective resistance of radia- tion, inductance and impedance. 391 72. Evaluation of functions sil al and col al. 394 73. Self-inductive impedance, and numerical example. 395 74. Discussion of effective resistance and radiated power, as function of ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-20", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit. 513", "section_title": "Power And Energy Of The Complex Circuit. 513", "kind": "chapter", "sequence": 20, "number": 7, "location": "lines 1228-1261", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-20/", "snippets": [ "CHAPTER VII. POWER AND ENERGY OF THE COMPLEX CIRCUIT. 513 50. Instantaneous power. Effective or mean power. Power transferred. 513 51. Instantaneous and effective value of energy stored in the magnetic field ; its motion along the circuit, and varia- tion with distance and with time. 513 52. The energy stored in the electrostatic field and its compo- nents. Transfer of energy between electrostatic and electromagnetic field. 517 53. Energy stored in a circ ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... coil for generating oscillating currents. A 100-kv-amp. react- ive coil has approximately the same size as a 50-kw. trans- former and can indeed be made from such a transformer, of ratio 1 : 1, by connecting the two coils in series and inserting into the magnetic circuit an air gap of such length as to give the rated magnetic density at the rated current. A very large oscillating-current generator, therefore, would consist of 100-kv-amp. condenser and 100-kv-amp. reactor. 46. Assuming the condenser to be designed for 10 ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-37", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 37, "number": 1, "location": "lines 15354-15625", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "snippets": [ "CHAPTER I. INTRODUCTION. 1. Whenever in an electric circuit a sudden change of the circuit conditions is produced, a transient term appears in the circuit, that is, at the moment when the change begins, the circuit quantities, as current, voltage, magnetic flux, etc., cor- respond to the circuit conditions existing before the change, but do not, in general, correspond to the circuit conditions brought about by the change, and therefore must pass from the values corresponding to the previous condition to the valu ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-41", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 41, "number": 1, "location": "lines 19260-19338", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "snippets": [ "... tential lightning arresters (multi-gap arrester), etc. (b) The distribution of alternating current in solid conductors and the increase of effective resistance and decrease of effective inductance resulting therefrom. (c) The distribution of alternating magnetic flux in solid iron, or the screening effect of eddy currents produced in the iron, and the apparent decrease of permeability and increase of power consumption resulting therefrom. (d) The distribution of the electric field of a conductor through space, resul ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... r second, and the quarter-wave frequency of a line of 10 = 700 miles would be S / = — =67 cycles per sec. ; 4 LQ hence, fairly close to the standard frequency of 60 cycles. The loss of power in the line, and thus the increase of induc- tance by the magnetic field inside of the conductor (which would not exist in a conductor of perfect conductivity or zero resistance loss), the increase of capacity by insulators, poles, etc., lowers the frequency below that corresponding to the velocity of light and brings it neare ..." ] } ] }, { "id": "alternating-current", "label": "Alternating Current", "aliases": [ "a.c.", "alternating current", "alternating currents", "alternating-current" ], "total_occurrences": 1661, "matching_section_count": 266, "matching_source_count": 15, "source_totals": [ { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 325, "section_count": 37 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 287, "section_count": 32 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 190, "section_count": 20 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 181, "section_count": 52 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 167, "section_count": 29 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 152, "section_count": 31 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 134, "section_count": 15 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 92, "section_count": 17 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 42, "section_count": 6 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 29, "section_count": 6 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 21, "section_count": 7 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 18, "section_count": 5 }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 16, "section_count": 3 }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "occurrence_count": 6, "section_count": 5 }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-18", "section_label": "Chapter 20: Single-Phase Commutator Motors", "section_title": "Single-Phase Commutator Motors", "kind": "chapter", "sequence": 18, "number": 20, "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 33, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "CHAPTER XX SINGLE-PHASE COMMUTATOR MOTORS I. General 189. Alternating-current commutating machines have so far become ef industrial importance mainly as motors of the series or varying-speed type, for single-phase railroading, and as con- stant-speed motors or adjustable-speed motors, where efficient acceleration under heavy torque ...", "... field magnetism of the alter- nating-current motor must be in phase with the armature cur- rent, or nearly so. This is inherently the case with the series type of motor, in which the same current traverses field coils and armature windings. Since in the alternating-current transformer the primary and secondary currents and the primary voltage and the secondary voltage are proportional to each other, the different circuits of the alternating-current commutator motor may be connected with each other directly (in shunt or in s ...", "... the same current traverses field coils and armature windings. Since in the alternating-current transformer the primary and secondary currents and the primary voltage and the secondary voltage are proportional to each other, the different circuits of the alternating-current commutator motor may be connected with each other directly (in shunt or in series, according to the type of the motor) or inductively, with the interposition of a 331 332 ELECTRICAL APPARATUS transformer, and for this purpose either a separate tr ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "section_label": "Chapter 16: Induction Motor", "section_title": "Induction Motor", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 31, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "CHAPTER XVI. INDUCTION MOTOR. 151. A specialization of the general alternating-current transformer is the induction motor. It differs from the stationary alternating-current transformer, which is also a specialization of the general transformer, in so far as in the stationary transformer only the transfer of electrical energy from primary ...", "CHAPTER XVI. INDUCTION MOTOR. 151. A specialization of the general alternating-current transformer is the induction motor. It differs from the stationary alternating-current transformer, which is also a specialization of the general transformer, in so far as in the stationary transformer only the transfer of electrical energy from primary to secondary is used, but not the mechanical force acting between the two, and therefore ...", "... ction motor, only the mechanical force between primary and secondary is used, but not the transfer of electrical energy, and thus the secondary circuits closed upon themselves. Transformer and induction motor thus are the two limiting cases of the general alternating- current transformer. Hence the induction motor consists of a magnetic circuit interlinked with two electric circuits or sets of circuits, the primary and the secondary circuit, which are movable with regard to each other. In general a num- ber of primary and a nu ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-11", "section_label": "Chapter 12: Frequency Converter Or General Alternating Current Transformer", "section_title": "Frequency Converter Or General Alternating Current Transformer", "kind": "chapter", "sequence": 11, "number": 12, "location": "lines 14897-17124", "status": "candidate", "occurrence_count": 31, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-11/", "snippets": [ "CHAPTER XII FREQUENCY CONVERTER OR GENERAL ALTERNATING- CURRENT TRANSFORMER 103. In general, an alternating-current transformer conafete of a magnetic circuit, interlinked with two electric circuits or sets of electric circuits, the primary circuit, in which power, sup- plied by the impressed voltage, is consumed, an ...", "CHAPTER XII FREQUENCY CONVERTER OR GENERAL ALTERNATING- CURRENT TRANSFORMER 103. In general, an alternating-current transformer conafete of a magnetic circuit, interlinked with two electric circuits or sets of electric circuits, the primary circuit, in which power, sup- plied by the impressed voltage, is consumed, and the secondary circuit, in which a corresponding amo ...", "... elled and move. This repulsion is used in the constant-current transformer for regulating the current for constancy independent of the load. In the induction motor, this mechanical force is made use of for doing the work: the induction motor represents an alternating-current transformer, in which the secondary is mounted niovably with regards to the primary, in such a manner that, while set in motion, it still remains in the primary field of force. This requires, i hat the induction motor field is not constant in one directio ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-17", "section_label": "Chapter 19: Alternating- Current Motors In General", "section_title": "Alternating- Current Motors In General", "kind": "chapter", "sequence": 17, "number": 19, "location": "lines 21713-23905", "status": "candidate", "occurrence_count": 30, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-17/", "snippets": [ "CHAPTER XIX ALTERNATING- CURRENT MOTORS IN GENERAL 171. The starting point of the theory of the polyphase and single-phase induction motor usually is the general alternating- current transformer. Coining, however, to the commutator motors, this method becomes less suitable, and the foll ...", "CHAPTER XIX ALTERNATING- CURRENT MOTORS IN GENERAL 171. The starting point of the theory of the polyphase and single-phase induction motor usually is the general alternating- current transformer. Coining, however, to the commutator motors, this method becomes less suitable, and the following more general method preferable. In its general form the alternating-current motor consists of one or more stationary electric circuits magnetica ...", "... polyphase and single-phase induction motor usually is the general alternating- current transformer. Coining, however, to the commutator motors, this method becomes less suitable, and the following more general method preferable. In its general form the alternating-current motor consists of one or more stationary electric circuits magnetically related to one or more rotating electric circuits. These circuits can be excited by alternating currents, or some by alternating, others by direct current, or closed upon themselves, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-12", "section_label": "Chapter 12: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 10718-13483", "status": "candidate", "occurrence_count": 29, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-12/", "snippets": [ "... s determined : 1. By direct comparison with a known resistance (Wheat- stone bridge method, etc.). This method gives what may be called the true ohmic resist- ance of the circuit. 2. By the ratio: Volts consumed in circuit Amperes in circuit In an alternating-current circuit, this method gives, not the resistance of the circuit, but the impedance, z = \\/f^ + x^. 3. By the ratio: Power consumed, (Current) 2 where, however, the \"power\" does not include the work done by the circuit, and the counter e.m.fs. represent ...", "... ance, z = \\/f^ + x^. 3. By the ratio: Power consumed, (Current) 2 where, however, the \"power\" does not include the work done by the circuit, and the counter e.m.fs. representing it, as, for instance, in the case of the counter e.m.f. of a motor. In alternating-current circuits, this value of resistance is the power coefficient of the e.m.f.. Power component of e.m.f. Total current It is called the elective resistance of the circuit, since it represents the effect, or power, expended by the circuit. The power coeffi- ...", "... he elective resistance of the circuit, since it represents the effect, or power, expended by the circuit. The power coeffi- cient of current, Power component of current ^ \" Total e.m.f. ' is called the effective conductance of the circuit. Ill 112 ALTERNATING-CURRENT PHENOMENA In the same way, the value, Wattless component of e.m.f. X = Total current is the effective reactance, and Wattless component of current Total e.m.f. is the effective suscepta7ice of the circuit. While the true ohmic resistance re ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 28, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... .007 957 1 81 - .007 858 0 x> 80 j»fe 79 X sil|s=(-l) + 1 2~2 INDEX PAGE Acceleration constant of traveling wave 466 Air blast, action in oscillating-current generator 75 pressure required in oscillating-current generator 75 Alternating-current circuit and transient term of fundamental frequency 473 distribution in conductor 369 transformer operating oscillating-current generator 87 transmission, equations of traveling wave 477 wave as traveling wave without attenuation 472 Alternator cont ...", "... oscillating-current generator 87 transmission, equations of traveling wave 477 wave as traveling wave without attenuation 472 Alternator control by periodic transient term of field excitation 223 Aluminum cell rectifier 222 effective penetration of alternating current 378 Amplitude of traveling wave 465 of wave 438 Arc, and spark 249 continuity at cathode 249 lamp, control by inductive shunt to operating mechanism 131 machine 230 as rectifier 221 current control 220 properties 249 rectification 249 re ...", "... it 112 range in electric circuit 13 representing electrostatic component of electric field 5 shunting direct-current circuit 133 specific, numerical values 11 suppressing pulsations in direct-current circuit 134 Cast iron, effective penetration of alternating current 378 Cathode of arcs 249 Charge of condenser 51 of magnetic field 27 Circuit, complex, see Complex circuit. control by periodic transient phenomena 220, 223 electric, speed of propagation in 422 Closed circuit transmission line 306 Col al 392, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-15", "section_label": "Chapter 15: The General Alternating-Current Transformer Or Frequency Converter", "section_title": "The General Alternating-Current Transformer Or Frequency Converter", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 12683-13648", "status": "candidate", "occurrence_count": 27, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "snippets": [ "CHAPTER XV. THE GENERAL ALTERNATING-CURRENT TRANSFORMER OR FREQUENCY CONVERTER. 141. The simplest alternating-current apparatus is the alternating-current transformer. It consists of a magnetic- circuit, interlinked with two electric circuits or sets of electric circuits. The one, the primary cir ...", "CHAPTER XV. THE GENERAL ALTERNATING-CURRENT TRANSFORMER OR FREQUENCY CONVERTER. 141. The simplest alternating-current apparatus is the alternating-current transformer. It consists of a magnetic- circuit, interlinked with two electric circuits or sets of electric circuits. The one, the primary circuit, is excited by an impressed E.M.F., while in the other, the secondary ...", "CHAPTER XV. THE GENERAL ALTERNATING-CURRENT TRANSFORMER OR FREQUENCY CONVERTER. 141. The simplest alternating-current apparatus is the alternating-current transformer. It consists of a magnetic- circuit, interlinked with two electric circuits or sets of electric circuits. The one, the primary circuit, is excited by an impressed E.M.F., while in the other, the secondary circuit, an E.M.F. is induced. Thus, i ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-19", "section_label": "Chapter 21: Regulating Pole Converters", "section_title": "Regulating Pole Converters", "kind": "chapter", "sequence": 19, "number": 21, "location": "lines 30088-31715", "status": "candidate", "occurrence_count": 27, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-19/", "snippets": [ "... ion 232. With the brushes in quadrature position to the resultant magnetic flux, and at normal voltage ratio, the direct -current generator armature reaction of the converter equals the syn- chronous-motor armature reaction of the power component of the alternating current, and at unity power-faetor the converter thus has no resultant armature reaction, while with a lagging or leading current it has the magnetizing or demagnetizing re- action of the wattless component of the current. If by a sliift of the resultant flux fr ...", "... h the brushes, by angle, t, the direct voltage is reduced by factor cos r, the direct current and therewith the direct-current armature reaction are increased, by factor, -. as by the law of conservation of energy the direct-current output must equal the alternating-current input (neglecting losses). The dueet- current armature reaction, ff, therefore ceases to be equal to the armature reaction of the alternating energy current, 5F», but is greater by factor, '■ The alternating-current armature reaction, Su, at no | place ...", "... direct-current output must equal the alternating-current input (neglecting losses). The dueet- current armature reaction, ff, therefore ceases to be equal to the armature reaction of the alternating energy current, 5F», but is greater by factor, '■ The alternating-current armature reaction, Su, at no | placement, is in quadrature position with the magnetic flux. REGULATING POLE CONVERTERS 427 The direct-current armature reaction, £, however, appears in the position of the brushes, or shifted against quadrature position ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-01", "section_label": "Lecture 1: General Review", "section_title": "General Review", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 154-565", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-01/", "snippets": [ "... used only at low voltage, no to 600 volts, while economical transmission requires the use of as high voltage as possible. For many purposes, as electrolytic work, direct current is necessary; for others, as railroading, preferable; while for transmission, alternating current is preferable, due to the great difficulty of generating and converting high voltage direct current. In the design of any of the steps through which electric power passes, the requirements of all the other steps so must be taken into consideration. Of the ...", "... d under the subdivisions: I. General distribution for lighting and power. Long distance transmission. Generation. Control and protection. Electric railway. Electrochemistry. Lighting. Character of Electric Power. Electric power is used as — a. Alternating current and direct current. b. Constant potential and constant current. c. High voltage and low voltage. a. Alternating current is used for transmission, and for general distribution with the exception of the centers of large cities; direct current is usually ...", "... ol and protection. Electric railway. Electrochemistry. Lighting. Character of Electric Power. Electric power is used as — a. Alternating current and direct current. b. Constant potential and constant current. c. High voltage and low voltage. a. Alternating current is used for transmission, and for general distribution with the exception of the centers of large cities; direct current is usually applied for railroading. For power distribution, both forms of current are used; in electrochemistry, direct current must b ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-03", "section_label": "Lecture 3: Light And Power Distribution", "section_title": "Light And Power Distribution", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 983-1526", "status": "candidate", "occurrence_count": 25, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-03/", "snippets": [ "... rent, and with the large mains and feeders, which are gener- ally used, even the starting of large elevator motors has no appreciable effect, and the supply of power to electric elevators represents a very important use of direct current distribution. In alternating current distribution systems, the effect on the voltage regulation, when starting a motor, is far more severe; since alternating current motors in starting usually take a larger current than direct current motors starting with the same torque on the same voltage; ...", "... able effect, and the supply of power to electric elevators represents a very important use of direct current distribution. In alternating current distribution systems, the effect on the voltage regulation, when starting a motor, is far more severe; since alternating current motors in starting usually take a larger current than direct current motors starting with the same torque on the same voltage; and the current of the alternating current motor is lagging, the voltage drop caused by it in the reactance is therefore far gre ...", "... e effect on the voltage regulation, when starting a motor, is far more severe; since alternating current motors in starting usually take a larger current than direct current motors starting with the same torque on the same voltage; and the current of the alternating current motor is lagging, the voltage drop caused by it in the reactance is therefore far greater than would be caused by the same current taken by a non-inductive load, as lamps. Furthermore, alternating current supply mains usually are of far smaller capacity, ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-14", "section_label": "Lecture 14: Alternating Current Railway Motor", "section_title": "Alternating Current Railway Motor", "kind": "lecture", "sequence": 14, "number": 14, "location": "lines 8649-9342", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-14/", "snippets": [ "FOURTEENTH LECTURE ALTERNATING CURRENT RAILWAY MOTOR. mN a direct current motor, whether a shunt or a series motor, the motor still revolves in the same direction, if the impressed e. m. f. be reversed, as field and arma- ture both reverse. Since a reversal of voltage does not change the ope ...", "... he motor still revolves in the same direction, if the impressed e. m. f. be reversed, as field and arma- ture both reverse. Since a reversal of voltage does not change the operation of the motor, such a direct current motor there- fore can operate also on alternating current. With an alter- nating voltage supply, the field magnetism of the motor also alternates ; the motor field must therefore be laminated, to avoid excessive energy losses and heating by eddy currents (cur- rents produced in the field iron by the alternation ...", "... e armature, reverse simultaneously. In the series motor, in which the same current traverses field and armature, the field magnetism and the armature current are necessarily in phase with each other, or nearly so. Only the series or varying speed type of alternating current commutator motor has so far become of industrial importance. In the alternating current motor in addition to the voltage consumed by the resistance of the motor circuit and that con- sumed by the armature rotation, voltage is also consumed by self-induc ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-17", "section_label": "Chapter 17: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16521-17716", "status": "candidate", "occurrence_count": 23, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-17/", "snippets": [ "CHAPTER XVII THE ALTERNATING-CURRENT TRANSFORMER 141. The simplest alternating-current apparatus is the trans- former. It consists of a magnetic circuit interlinked with two electric circuits, a primary and a secondary. The primary circuit is excited by an impressed e.m.f., while in the sec ...", "CHAPTER XVII THE ALTERNATING-CURRENT TRANSFORMER 141. The simplest alternating-current apparatus is the trans- former. It consists of a magnetic circuit interlinked with two electric circuits, a primary and a secondary. The primary circuit is excited by an impressed e.m.f., while in the secondary circuit an e.m.f. is generated. Thus, in the ...", "... called the self-inductive or leakage reactance of the trans- former; while the flux surrounding both coils may be con- sidered as mutual inductive reactance. This cross-flux of self-induction does not generate e.m.f. in the secondary circuit, 187 188 ALTERNATING-CURRENT PHENOMENA and is thus, in general, objectionable, by causing a drop of voltage and a decrease of output. It is this cross-flux, how- ever, or flux of self-inductive reactance, which is utilized in special transformers, to secure automatic regulation, for ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-47", "section_label": "Chapter 7: Distribution Of Alternating-Current Density In Conductor", "section_title": "Distribution Of Alternating-Current Density In Conductor", "kind": "chapter", "sequence": 47, "number": 7, "location": "lines 24981-26094", "status": "candidate", "occurrence_count": 23, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "snippets": [ "CHAPTER VII. DISTRIBUTION OF ALTERNATING-CURRENT DENSITY IN CONDUCTOR. 59. If the frequency of an alternating or oscillating current is high, or the section of the conductor which carries the current is very large, or its electric conductivity or its magnetic per- meability high, the current density i ...", "... ductor, caused by the magnetic flux inside of the conductor. The phase of the current inside of the conductor also differs from that on the surface and lags behind it. In consequence of this unequal current distribution in a large conductor traversed by ^alternating currents, the effective resist- ance of the conductor may be far higher than the ohmic resist- ance, and the conductor also contains internal inductance. In the extreme case, where the current density in the interior of the conductor is very much lower than on th ...", "... e surface, or even negligible, due to this \"screening effect/' as it has been called, the current can be 'assumed to exist only in a thin surface layer of the conductor, of thickness lp ; that is, in this case the effective resistance of the conductor for alternating currents equals the ohmic resistance of a conductor section equal to the periphery of the conductor times the \" thickness of penetration.\" Where this unequal current distribution throughout the con- ductor section is considerable, the conductor section is not ful ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "section_label": "Chapter 10: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "... ermined : — 1.) By direct comparison with a known resistance (Wheat- stone bridge method, etc.). This method gives what may be called the true ohmic resistance of the circuit. 2.) By the ratio : Volts consumed in circuit Amperes in circuit In an alternating-current circuit, this method gives, not the resistance of the circuit, but the impedance, 3.) By the ratio : r__ Power consumed . (Current)2 where, however, the \"power\" does not include the work done by the circuit, and the counter E.M.Fs. representing it ...", "... impedance, 3.) By the ratio : r__ Power consumed . (Current)2 where, however, the \"power\" does not include the work done by the circuit, and the counter E.M.Fs. representing it, as, for instance, in the case of the counter E.M.F. of a motor. In alternating-current circuits, this value of resistance is the energy coefficient of the E.M.F., _ Energy component of E.M.F. Total current It is called the effective resistance of the circuit, since it represents the effect, or power, expended by the circuit. The energy ...", "... eptance of the circuit. While the true ohmic resistance represents the expendi- ture of energy as heat inside of the electric conductor by a current of uniform density, the effective resistance repre- sents the total expenditure of energy. Since, in an alternating-current circuit in general, energy is expended not only in the conductor, but also outside of it, through hysteresis, secondary currents, etc., the effective resistance frequently differs from the true ohmic resistance in such way as to represent a larger expendi ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-24", "section_label": "Chapter 24: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 25682-29374", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-24/", "snippets": [ "... impedance, then the e.m.f. consumed by the resistance is £'11 = ri, and is in phase with the current; hence represented by vector OEn] and the e.m.f. consumed by the reactance is E2 = xi, and 90° ahead of the current; hence the e.m.f. consumed 301 302 ALTERNATING-CURRENT PHENOMENA by the impedance hE = ViEuY\" + (£'2)^ or = i -s/r\"^ -\\- x- = iz, X and ahead of the current by the angle 8, where tan 8 = ~. We have now acting in circuit the e.m.fs., E, Ei, E^; or Ei and E are components of E^, that is, E^i is the diagona ...", "... n in drawn line, the generator diagram in dotted line. As seen, for small values of Ei the potential drops in the alter- nator and in the line. For the value of Ei = Eq the potential rises in the generator, drops in the line, and rises again in the 304 ALTERNATING-CURRENT PHENOMENA Fig. 146. Fig. 147. SYNCHRONOUS MOTOR 305 Fig. 148. Fig. 149. 20 306 ALTERNATING-CURRENT PHENOMENA motor. For larger values of E\\, the potential rises in the alter- nator as well as in the line, so that the highest potenti ...", "... nator and in the line. For the value of Ei = Eq the potential rises in the generator, drops in the line, and rises again in the 304 ALTERNATING-CURRENT PHENOMENA Fig. 146. Fig. 147. SYNCHRONOUS MOTOR 305 Fig. 148. Fig. 149. 20 306 ALTERNATING-CURRENT PHENOMENA motor. For larger values of E\\, the potential rises in the alter- nator as well as in the line, so that the highest potential is the generated e.m.f. of the motor, the lowest potential the generated e.m.f. of the generator. It is of interest ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1120-1683", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-01/", "snippets": [ "CHAPTER I INTRODUCTION 1. In the practical applications of electrical energy, we meet with two different classes of phenomena, due respectively to the continuous current and to the alternating current. The continuous-current phenomena have been brought within the realm of exact analytical calculation by a few fundamental laws : c 1. Ohm's law: i = -, where r, the resistance, is a constant r of the circuit. 2. Joule's law: P = ^^r, where P is ...", "... .m.fs. in a closed circuit = 0, if the e.m.f. consumed by the resistance, ir, is also considered as a counter e.m.f., and all the e.m.fs. are taken in their proper direction. (b) The sum of all the currents directed toward a distributing point = 0. In alternating-current circuits, that is, in circuits in which the currents rapidly and periodically change their direction, these laws cease to hold. Energy is expended, not only in the con- ductor through its ohmic resistance, but also outside of it ; energy is stored up and ...", "... is stored up and returned, so that large currents may exist simultaneously with high e.m.fs., without representing any considerable amount of expended energy, but merely a surging fo and fro of energy; the ohmic resistance ceases to be the deter- 1 2 ALTERNATING-CURRENT PHENOMENA mining factor of current value; currents may divide into com- ponents, each of which is larger than the undivided current, etc. 2. In phice of the above-mentioned fundamental laws of continuous currents, we find in alternating-current circuits ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-83", "section_label": "Apparatus Section 4: Synchronous Converters: Armature Current and Heating", "section_title": "Synchronous Converters: Armature Current and Heating", "kind": "apparatus-section", "sequence": 83, "number": 4, "location": "lines 13889-15160", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-83/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-83/", "snippets": [ "IV. Armature Current and Heating 88. The current in the armature conductors of a converter is the difference between the alternating-current input and the direct-current output. SYNCHRONOUS CONVERTERS 233 In Fig. 127, ai, a2 are two adjacent leads connected with the collector rings DI, D2 in an n-phase converter. The alternating e.m.f. between a\\ and a2, a ...", "... SYNCHRONOUS CONVERTERS 233 In Fig. 127, ai, a2 are two adjacent leads connected with the collector rings DI, D2 in an n-phase converter. The alternating e.m.f. between a\\ and a2, and thus the power component of the alternating current in the armature section between a\\ and a2, will reach a maximum when this section is midway between the brushes BI and Bz, as shown in Fig. 127. The direct current in every armature coil reverses at the mo- ment when ...", "... hen this section is midway between the brushes BI and Bz, as shown in Fig. 127. The direct current in every armature coil reverses at the mo- ment when the coil passes under brush BI or B2, and is thus a rec- tangular alternating current as shown in Fig. 128 as 7. At the moment when the power com- ponent of the alternating current is a maximum, an armature coil d midway between two adjacent alternating leads ai and a2 is midway between the brushes BI a ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-10", "section_label": "Chapter 10: F", "section_title": "F", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 8269-10499", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "snippets": [ "... ermined : — 1.) By direct comparison with a known resistance (Wheat- stone bridge method, etc.). This method gives what may be called the true ohmic resistance of the circuit. 2.) By the ratio : Volts consumed in circu it Amperes in circuit In an alternating-current circuit, this method gives, not the resistance of the circuit, but the impedance, z = V/^ + x\\ 3.) By the ratio : __ Power consumed __ (E.M.F.)' . (Current)* Power consumed ' where, however, the \"power*' and the \"E.M.F.\" do not include the work don ...", "... consumed __ (E.M.F.)' . (Current)* Power consumed ' where, however, the \"power*' and the \"E.M.F.\" do not include the work done by the circuit, and the counter E.M.Fs. representing it, as, for instance, in the case of the counter E.M.F. of a motor. In alternating-current circuits, this value of resistance is the energy coefficient of the E.M.F., — Energy compon ent of E.M.F. Total current It is called the effective resistance of the circuit, since it represents the effect, or power, expended by the circuit. The ener ...", "... eptance of the circuit. While the true ohmic resistance represents the expendi- ture of energy as heat inside of the electric conductor by a current of uniform density, the effective resistance repre- sents the total expenditure of energy. Since, in an alternating-current circuit in general, energy is expended not only in the conductor, but also outside of it, through hysteresis, secondary currents, etc., the effective resistance frequently differs from the true ohmic resistance in such way as to represent a larger expendi ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-40", "section_label": "Chapter 4: Arc Rectification", "section_title": "Arc Rectification", "kind": "chapter", "sequence": 40, "number": 4, "location": "lines 17755-19259", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "snippets": [ "... low temperature of the boiling point of mercury, enclosure in glass is feasible with the mercury arc. II. MERCURY ARC RECTIFIER. 17. Depending upon the character of the alternating supply, whether a source of constant alternating potential or constant alternating current, the direct-current circuit receives from the rectifier either constant potential or constant current. Depend- ing on the character of the system, thus constant-potential rectifiers and constant-current rectifiers can be distinguished. They differ somewha ...", "... ired amount. In the constant-potential rectifier, instead of the transformer ACS and the reactive coils A a and Ba, generally a compensator or auto-transformer is used, as shown in Fig. 61, in which the 252 TRANSIENT PHENOMENA two halves of the coil, AC and BC, are made of considerable self-inductance against each other, as by their location on different magnet cores, and the reactive coil at c frequently omitted. The modification of the equations resulting herefrom is obvious. Such auto-transformer also ...", "... hown in Fig. 61. The rectified or direct voltage of the constant-current rectifier is somewhat less than one-half of the alternating voltage supplied by the transformer secondary AB, the rectified or direct current somewhat more than double the effective alternating current supplied by the transformer. In the constant-potential rectifier, in which the currents are larger, and so a far smaller angle of overlap 0 is permissible, the direct-current voltage therefore is very nearly the mean value of half the alternating voltag ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "... point to point ; and it is no longer possible to treat the circuit in the usual manner by the vector diagram. This phenomenon is especially noticeable in long-distance lines, in underground cables, and to a certain degree in the high-potential coils of alternating-current transformers for very high voltage. It has the effect that not only the E.M.Fs., but also the currents, at the beginning, end, and different points of the conductor, are different in intensity and in phase. Where the capacity effect of the line is small ...", "... of the surrounding medium = 1 in air ; / = length of conductor = 5 x 106 cm. ; d = distance of conductors from each other = 50 cm. ; 8 = diameter of conductor = 1 cm. Since C = .3 microfarads, the capacity reactance is x — 106 / 2 TT NC ohms, 160 ALTERNATING-CURRENT PHENOMENA. where N '= frequency; hence, at N = 60 cycles, x = 8,900 ohms ; and the charging current of the line, at E = 20,000 volts, becomes, ^ = E / x = 2.25 amperes. The resistance of 100 km of line of 1 cm diameter is 22 ohms ; therefore, at 10 ...", "... x) I (r-jx)(g+jt)-\\} 2 Jf 110. ^.) Z«W capacity represented by three condensers^ in the middle and at the ends of the line. Denoting, in Fig. 85, the E.M.F. and current in receiving circuit by £, 7, the E.M.F. at middle of line by £' ', 162 ALTERNATING-CURRENT PHENOMENA. the current on receiving side of line by /', the current on generator side of line by 7\", the E.M.F., viz., current at generator by £0, f0, Iff _L I 85. Distributed Capacity. otherwise retaining the same denotations as in A.), We ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-14", "section_label": "Chapter 14: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 11605-12682", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "snippets": [ "CHAPTER XIV. THE ALTERNATING-CURRENT TRANSFORMER. 126. The simplest alternating-current apparatus is the transformer. It consists of a magnetic circuit interlinked with two electric circuits, a primary and a secondary. The primary circuit is excited by an impressed E.M.F., while in the sec ...", "CHAPTER XIV. THE ALTERNATING-CURRENT TRANSFORMER. 126. The simplest alternating-current apparatus is the transformer. It consists of a magnetic circuit interlinked with two electric circuits, a primary and a secondary. The primary circuit is excited by an impressed E.M.F., while in the secondary circuit an E.M.F. is induced. Thus, in the pr ...", "... al to the current flowing in the electric circuit, or rather, the ampere- turns or M.M.F. increase with the increasing load on the transformer, and constitute what is called the self-induc- tance of the transformer ; while the flux surrounding both 194 ALTERNATING-CURRENT PHENOMENA. coils may be considered as mutual inductance. This cross- flux of self-induction does not induce E.M.F. in the second- ary circuit, and is thus, in general, objectionable, by causing a drop of voltage and a decrease of output. It is this cros ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-08", "section_label": "Lecture 8: Arc Lamps And Arc Lighting", "section_title": "Arc Lamps And Arc Lighting", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 7141-8510", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-08/", "snippets": [ "... total voltage consumed by the arc and the steadying device increases with increase of current, and pulsations of current thus limit themselves. All arc lamps for use on constant voltage supply thus contain a sufficiently high steadying resistance, or, in alternating-current circuits, a steadying reactance. Arc lamps for use on constant-current circuits, that is, cir- cuits in which the current is kept constant by the source of power supply, as the constant-current transformer or the arc machine, require no steadying resist ...", "... hich is closed in case of the failure of one lamp to operate, must have such a resistance, or reactance with alter- nating currents, that the remaining lamp still receives its proper voltage, even if the other lamp fails and its shunt circuit closes. With alternating-current lamps, this does not require a reactance of such size that the potential difference across the reactance equals that across the lamp, which it replaces, but the reactance must be larger; that is, give a higher potential difference at its terminals, than t ...", "... e shunt circuit RMN, and omitting the shunt magnet P, as, with a change of arc length, the main current and thereby the pull of the series magnet S varies, and the control thus can be done by the series magnet. Such a lamp then is called a series lamp. An alternating-current series lamp is shown diagrammatically in Fig. 52. In starting, the series magnet S pulls up the electrode B by the clutch G, in the same manner as in Fig. 50. With increasing arc length and thus increasing voltage consumed by the arc, the current in ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-14", "section_label": "Chapter 14: The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "section_title": "The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14089-14918", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "snippets": [ "CHAPTER XIV. THE OSNI!RAIj AIiTEBNATINa-CUBBENT TBAKBFOBMSB. 131. The simplest alternating-current apparatus is the alternating-current transformer. It consists of a magnetic circuit, interlinked with two electric circuits or sets of electric circuits. The one, the primary circuit, is excited by an impressed E.M.F., while in the other, the secondary c ...", "CHAPTER XIV. THE OSNI!RAIj AIiTEBNATINa-CUBBENT TBAKBFOBMSB. 131. The simplest alternating-current apparatus is the alternating-current transformer. It consists of a magnetic circuit, interlinked with two electric circuits or sets of electric circuits. The one, the primary circuit, is excited by an impressed E.M.F., while in the other, the secondary circuit, an E.M.F. is induced. Thus, in ...", "... in- terlinked with two electric circuits. Such an apparatus can properly be called a ^^ general altertiating- current trans- former' The equations of the stationary transformer and those of the induction motor are merely specializations of the general alternating-current transformer equations. Quantitatively the main differences between induction motor and stationary transformer are those produced by the air-gap between primary and secondary, which is re- quired to give the secondary mechanical movability. This air-gap ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-02", "section_label": "Lecture 2: General Distribution", "section_title": "General Distribution", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 566-982", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-02/", "snippets": [ "... uch tie feeders also permit most stations to operate without storage battery reserve, that is, to concentrate the storage batteries in a few stations, from which in case of a breakdown of the system, the other stations are supplied over the tie feeders. ALTERNATING CURRENT DISTRIBUTION The system of feeders and mains allows the most perfect voltage regulation in the distributing mains. It is however applicable only to direct current distribution in a territory of GENERAL DISTRIBUTION 27 very concentrated load, as in th ...", "... h feeder represents a large amount of power; with alternating cur- rent systems, the inductive drop forbids the concentration of such large currents in a single conductor. That is, conductors of one million circular mils cannot be used economically in an alternating current system. The resistance of a conductor is inversely proportional to the size or section of the conductor, hence decreases rapidly with increasing current: a conductor of one million circular mils is one-tenth the resistance of a conductor of 100,000 circ ...", "... 0 the reactance is 1.76 times the resistance, and the latter conductor is likely to give a voltage drop far in excess of the ohmic resistance drop. The ratio of reactance to resistance therefore rapidly increases with increasing size of conductor, and for alternating currents, large conductors cannot therefore be used economically where close voltage regulation is required. With alternating currents it therefore is preferable to use several smaller conductors in multiple : two conductors of 28 GENERAL LECTURES No. I in m ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-25", "section_label": "Chapter 25: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 29375-32539", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-25/", "snippets": [ "... distortion of the wave-shape or higher har- monics may be due to lack of uniformity of the velocity of the revolving conductor; lack of uniformity or pulsation of the magnetic field; pulsation of the resistance or pulsation of the reactance. 341 342 ALTERNATING-CURRENT PHENOMENA The first two cases, lack of uniformity of the rotation or of the magnetic field, cause higher harmonics of e.m.f. at open circuit. The last, pulsation of resistance and reactance, causes higher har- monics only when there is current in the cir ...", "... sing higher harmonics under load. 3d. Pulsation of the resistance, causing higher harmonics under load also. Taking up the different causes of higher harmonics, we have : Lack of Uniformity and Pulsation of the Magnetic Field. 234. Since most of the alternating-current generators con- tain definite and sharply defined field-poles covering in different types different proportions of the pitch, in general the mag- netic flux interlinked with the armature coil will not vary as a sine wave, of the form $ cos /3, but as ...", "... trical also. In unitooth alternators the total generated e.m.f. has the same shape as that generated in a single turn. With the conductors more or less distributed over the surface of the armature, the total generated e.m.f. is the resultant of 344 ALTERNATING-CURRENT PHENOMENA several e.m.fs. of different phases, and is thus more uniformly varying; that is, more sinusoidal, approaching sine shape to within 3 per cent, or less, as for instance the curves Fig. 172 and Fig. 173 show, which represent the no-load and ful ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-21", "section_label": "Chapter 23: Review", "section_title": "Review", "kind": "chapter", "sequence": 21, "number": 23, "location": "lines 32138-32819", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-21/", "snippets": [ "... re: Brush Arc Machine. — 141-144. A quarter-phase constant- current alternator with rectifying commutators. Thomson-Houston Arc Machine. — 141-144. A three-phase F-connected constant-current alternator with rectifying commu- tator. The development of alternating-current series arc lighting by constant-current transformers greatly reduced the importance of the arc machine, and when in the magnetite lamp arc lighting returned to direct current, the development of the mercury-arc rectifier superseded the arc machine. Asyn ...", "... rs greatly reduced the importance of the arc machine, and when in the magnetite lamp arc lighting returned to direct current, the development of the mercury-arc rectifier superseded the arc machine. Asynchronous Motor. — Name used for all those types of alternating-current (single-phase or polyphase) motors or motor couples, which approach a definite synchronous speed at no-load, and slip below this speed with increasing load. 459 400 ELECTRICAL APPARATUS Brush Arc Machine. — (Sec1 \"Are Machines.'1} Compound Alter ...", "... converts the induction machine into a synchronous machine (Danielson motor). A good induction motor gives a poor syn- chronous motor, but a bad induction motor, of very low power- factor, gives a good synchronous motor, of good power-factor, etc. 5. An alternating-current commutating machine, as low-fre- quency exciter, 52. The couple then is asynchronous. This permits a wide range of power-factor and speed control as motor. As generator it is one form of the Stanley induction generator discussed under (2). 6. A Condense ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... of voltage, and vice versa; and so limits itself. While therefore arcs can be operated on a constant cur- rent system, to run arc lamps on constant potential, some cur- rent limiting device is necessary in series with the arc, as a resistance; or, in an alternating current circuit, a reactance. The voltage consumed by the resistance is proportional to the current, and a resistance of 8 ohms inserted in series to the arc would thus consume the voltage shown in straight line II in Fig. 47. The voltage consumed by the arc plus ...", "... a constant current circuit, with series connection of from 50 to 100 lamps on one circuit. With the exception of a few of the larger cities, all the street lighting by arc lamps in this country is done by constant current systems, either direct current or alternating current. For direct current constant current supply, separate arc light machines have been built, and are still largely used. In these machines, inherent regulation for constant current is produced by using a very high armature reaction and relatively weak fiel ...", "... commuta- tor shifts the connection over from the phase of falling e. m. f. to that of rising e. m. f., and thereby is able to control as high as 3,000 volts per commutator ring. With the development of the mercury arc rectifier, which converts constant alternating current into constanit direct current, arc machines are going out of use. The arc machine necessarily must be a small unit, since 100 to 150 lamps in series give already as high a voltage as is safe to use in arc circuits, but do not yet represent much power; and ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "... to an arc, and a reactance inserted into the low-tension pri- mary of the step-up transformer, to limit the discharge current, as shown diagrammatically in Fig. 31. If the Geissler tube has a considerable diameter, 3 to 5 cm., the Geissler discharge with alternating current is striated; that 102 RADIATION, LIGHT, AND ILLUMINATION. is, disk-shaped bright spots with diffused outlines alternate with less luminous spaces, about as shown in Fig. 32. The distance between the luminous disks increases with decrease of the gas ...", "... arc stream shows its spectrum, so that luminescent material can be fed into the carbon arc from either terminal. (3) At the temperature of the carbon arc all gases and vapors have become good conductors, and a carbon arc thus can operate equally well on alternating current as on direct current; that is, the voltage required to maintain the carbon arc is. sufficient, after the reversal of current, to restart it through the hot carbon vapor. A typical arc is shown in Fig. 35 as the magnetite arc, with a lower negative termi ...", "... , . '.. i \\. , : ; ,- ,. . - 112 RADIATION, LIGHT, AND ILLUMINATION. positive, and start an arc between A and C by touching C to A. I draw this arc to about 4 cm. length, and without touching C with B, as soon as the conducting vapor stream of the arc AC (the inner core A of Fig. 35) touches B, as shown in Fig. 36, the arc leaves C and goes to B, that is, by the arc AC I have started arc AB. If I had separate resistances in series with the terminals B and (7, the arc AC would also continue to exist after it ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-09", "section_label": "Chapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "section_title": "Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 4674-6992", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-09/", "snippets": [ "CHAPTER IX CIRCUITS CONTAINING RESISTANCE, INDUCTIVE REACTANCE, AND CONDENSIVE REACTANCE 53. Having, in the foregoing, re-established Ohm's law and Kirchhoff 's laws as being also the fundamental laws of alternating- current circuits, when expressed in their complex form, E = ZI, or, 7 = YE, and \"EE = 0 in a closed circuit, S/ = 0 at a distributing point, where E, I, Z, Y, are the expressions of e.m.f., current, impe- dance, and admittance in complex quantities — these ...", "... ing not only the intensity, but also the phase, of the alternating wave — we can now — by application of these laws, and in the same manner as with continuous-current circuits, keeping in mind, however, that E, I, Z, Y, are complex quanti- ties— calculate alternating-current circuits and networks of circuits containing resistance, inductive reactance, and conden- sive reactance in any combination, without meeting with greater difficulties than when dealing with continuous-current circuits. It is obviously not possible to disc ...", "... e.m.f. at receiver terminals decrease steadily with increasing ro. (6) If r is neghgible compared with x, as in a wattless receiver circuit, / = — . — , E = Eo — /-- — ; Vro' + x^ Vro^ + x^' or, for small values of ro, I = ^, E = Eo; X 62 ALTERNATING-CURRENT PHENOMENA that is, the current and e.m.f. at receiver terminals remain approximately constant for small values of ro, and then de- crease with increasing rapidity. In the general equations, x appears in the expressions for / and E only as x^, so that ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-18", "section_label": "Chapter 18: Polyphase Induction Motors", "section_title": "Polyphase Induction Motors", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17717-20445", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-18/", "snippets": [ "... the circuits utilized to trans- mit electric power to the secondary, while in the induction motor the secondary is movable with regards to the primary, and the mechanical forces between the primary, and secondary utilized to produce motion. In the general alternating-current trans- former or frequency converter we shall find an apparatus trans- mitting electric as well as mechanical energy, and comprising both, induction motor and transformer, as the two limiting cases. In the induction motor, only the mechanical force be- t ...", "... entirely unessential, it is preferable to reduce all secondary quantities to the primary system, by the ratio of transformation, a; thus if E'l = secondary e.m.f, per circuit. El = aE'i = secondary e.m.f. per circuit reduced to primary system ; 210 ALTERNATING-CURRENT PHENOMENA if I' I = secondary current per circuit, Ii = -J- = secondary current per circuit reduced to primary system ; if r'l = secondary resistance per circuit, Vi = a-hr'i = secondary resistance per circuit reduced to pri- mary system; if x'l = s ...", "... = To -}- jxo = impedance per primary circuit; ri = resistance per secondary circuit reduced to primary system; Xi = reactance per secondary circuit reduced to primary system, at full frequency/; 1 Complete discussion hereof, see Chapter XXXIII. 212 ALTERNATING-CURRENT PHENOMENA hence, sxi = reactance per secondary circuit at slip s, and Zi = ri + jsxi — secondary internal impedance. 158. We now have, Primary generated e.m.f., E = — e. Secondary generated e.m.f.. El = — se. Hence, Secondary current, ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-01", "section_label": "Chapter 1: The General Number", "section_title": "The General Number", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 915-3491", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-01/", "snippets": [ "... starting point, just as in Fig. 2. That is, 5-3 = 2 (Fig. 2), 5-7 = 2 (Fig. 3). In the case where we can subtract 7 from 5, we get the same distance from the starting point as when we subtract 3 from 5, 4 ENGINEERING MATHEMATICS. but the distance AC in Fig. 3, while the same, 2 steps, as in Fig. 2, is different in character, the one is toward the left, the other toward the right. That means, we have two kinds of distance units, those to the right and those to the left, and have to find some way to di ...", "... tance 2 in Fig. 3 is toward the left of the starting point A, that is, in that direction, in which we step when subtracting, and it thus appears natural to distinguish it from the distance 2 in Fig. 2, by calling the former— 2, while we call the distance AC in Fig. 2: +2, since it is in the direction from A, in which we step in adding. This leads to a subdivision of the system of absolute numbers, 1, 2, 3, . . . into two classes, positive numbers, + 1, +2, +3, ...: and negative numbers, -1,-2, -3, .. ...", "... 4, the negative number would be toward the left (or inversely, choosing the positive toward the left, would give the negative toward the right). If then we take a number, as +2, which represents a dis- tance AB, and multiply by (—1)^ we get the distance AC= —2 14 ENGINEERING MATHEMATICS. in opposite direction from A, Inversely, if we take AC= -2, and multiply by (-1), we get AB=+2; that is, multiplica- tion by (-1) reverses the direction, turns it through 180 deg. If we multiply +2 by V^l~ we get +2 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-13", "section_label": "Chapter 13: Ths Alternating^Cnrrent Traxsfobmer", "section_title": "Ths Alternating^Cnrrent Traxsfobmer", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 12673-14088", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "snippets": [ "CHAPTER XIII. THS ALTERNATING^CnRRENT TRAXSFOBMER. 116. The simplest alternating-current apparatus is the transformer. It consists of a magnetic circuit interlinked with two electric circuits, a primary and a secondary. The primary circuit is excited by an impressed E.M.F., while in the secondary circuit an E.M.F. is induced. Thus, in the pr ...", "... magnetic flux is E 1()» W'2.irNn To produce the magnetism, *, of the transformer, a M.M.F. of JF ampere-turns is required, which is determined by the shape and the magnetic characteristic of the iron, in the manner discussed in Chapter X. §119] ALTERNATING-CURRENT TRANSFORMER. 169 For instance, in the closed magnetic circuit transformer^ the maximum magnetic induction is (» = *, where 5 = the cross-section of magnetic circuit. 119. To induce a magnetic density, (B, a M.M.F. of 3C^ ampere-turns maximum is requi ...", "... o, and the difference of phase between the primary impressed E.M.F. and the primary current is /8o = Eo 0^0. ^ In the secondary circuit : Counter E.M.F. of resistance is /i^i in opposition with/i, and represented by the vector OEi / ; / 172 ALTERNATING-CURRENT PHENOMENA, [§121 Counter E.M.F. of reactance is I\\Xxy 90° behind /i, and represented by the vector OEu ; Induced E.M.Fs., E{ represented by the vector 0E(. Hence, the secondary terminal voltage, by combination of OEy^, OEi^ and 0E{ by means of the pa ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 963-1366", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "snippets": [ "CHAPTER I. INTRODUCTION. 1. IN the practical applications of electrical energy, we meet with two different classes of phenomena, due respec- tively to the continuous current and to the alternating current. The continuous-current phenomena have been brought within the realm of exact analytical calculation by a few fundamental laws : — 1.) Ohm's law : i = e j r, where r, the resistance, is a constant of the circuit. 2.) Joule's law: P= izr, where P is t ...", "... s. in a closed circuit = 0, if the E.M.F. consumed by the resistance, ir, is also con- sidered as a counter E.M.F., and all the E.M.Fs. are taken in their proper direction. b.) The sum of all the currents flowing towards a dis- tributing point = 0. In alternating-current circuits, that is, in circuits con- veying curr'ents which rapidly and periodically change their 2 ALTERNATING-CURRENT PHENOMENA. direction, these laws cease to hold. Energy is expended, not only in the conductor through its ohmic resistance, but also ...", "... ll the E.M.Fs. are taken in their proper direction. b.) The sum of all the currents flowing towards a dis- tributing point = 0. In alternating-current circuits, that is, in circuits con- veying curr'ents which rapidly and periodically change their 2 ALTERNATING-CURRENT PHENOMENA. direction, these laws cease to hold. Energy is expended, not only in the conductor through its ohmic resistance, but also outside of it ; energy is stored up and returned, so that large currents may flow, impressed by high E.M.Fs., without re ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-84", "section_label": "Apparatus Section 5: Synchronous Converters: Armature Reaction", "section_title": "Synchronous Converters: Armature Reaction", "kind": "apparatus-section", "sequence": 84, "number": 5, "location": "lines 15161-15475", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-84/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-84/", "snippets": [ "... or without lead or lag, as is usually done in converters, the direct- current armature reaction consists in a polarization in quadra- ture behind the field magnetism. The armature reaction due to the power component of the alternating current in a synchro- nous motor consists of a polarization in quadrature ahead of the field magnetism, which is opposite to the armature reaction as direct-current generator. Let m = total number of turns on the bipolar armature ...", "... ave that is, the resultant m.m.f. in any direction T has the phase 6 = r, and the intensity, rcFiA/2 ~^~ thus revolves in space with uniform velocity and constant in- tensity, in synchronism with the frequency of the alternating current. 248 ELEMENTS OF ELECTRICAL ENGINEERING Since in the converter, Fl = ^M, TTU we have the resultant m.m.f. of the power component of the alternating current in the n-phase converter. This m.m.f. revolves synchronous ...", "... tant in- tensity, in synchronism with the frequency of the alternating current. 248 ELEMENTS OF ELECTRICAL ENGINEERING Since in the converter, Fl = ^M, TTU we have the resultant m.m.f. of the power component of the alternating current in the n-phase converter. This m.m.f. revolves synchronously in the armature of the converter; and since the armature rotates at synchronism, the resultant m.m.f. stands still in space, or, with regard to the field poles, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-21", "section_label": "Chapter 21: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 22302-23970", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-21/", "snippets": [ "CHAPTER XXI ALTERNATING-CURRENT GENERATOR 185. In the alternating-current generator, e.m.f. is generated in the armature conductors by their relative motion through a constant or approximately constant magnetic field. When yielding current, two distinctly different m.m.fs. are acting ...", "CHAPTER XXI ALTERNATING-CURRENT GENERATOR 185. In the alternating-current generator, e.m.f. is generated in the armature conductors by their relative motion through a constant or approximately constant magnetic field. When yielding current, two distinctly different m.m.fs. are acting upon the alternator armature — the m.m.f. o ...", "... he armature is due to the m.m.f. of the field-coils only. In this case the e.m.f. is, in general, a maximum at the moment when the armature coil faces the position midway between adjacent field-coils, as shown in Fig. 129, and thus incloses 259 260 ALTERNATING-CURRENT PHENOMENA no magnetism. The e.m.f. wave in this case is, in general, symmetrical. An exception to this statement may take place only in those types of alternators where the magnetic reluctance of the arma- ture is different in different directions; th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1224-1727", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "snippets": [ "CHAPTER I. INTRODUCTION. 1. In the practical applications of electrical energy, we meet with two different classes of phenomena, due respec- tively to the continuous current and to the alternating current. The continuous-current phenomena have been brought within the realm of exact analytical calculation by a few fundamental laws : — 1.) Ohm's law : i = e j r, where r, the resistance, is a constant of the circuit. 2.) Joule's law : P= i^r, where P is ...", "... s. in a closed circuit = 0, if the E.M.F. consumed by the resistance, ir^ is also con- sidered as a counter E.M.F., and all the E.M.Fs. are taken in their proper direction. b,) The sum of all the currents flowing towards a dis- tributing point = 0. In alternating-current circuits, that is, in circuits con- veying currents which rapidly and periodically change their 2 AL TKRXA TING-CURRKXT PHEXOMEXA. [ § 2 direction, these laws cease to hold. Energy is expended, not only in the conductor through its ohmic resistance, bu ...", "... hmic resistance ceases to be the determining factor of current strength ; currents may divide into components, each of which is larger than the undivided current, etc. 2. In place of the above-mentioned fundamental laws of continuous currents, we find in alternating-current circuits the following : Ohm's law assumes the form, i = c j Sy where r, the apparent resistance, or impcdaiue^ is no longer a constant of the circuit, but depends upon the frequency of the cur- rents ; and in circuits containing iron, etc., also upon t ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "... equency, N, and to the electric conductivity, y, of the iron ; hence, can be expressed by The power consumed by eddy currents is proportional to their square, and inversely proportional to the electric con- ductivity, and can be expressed by W= 130 ALTERNATING-CURRENT PHENOMENA. or, since, ($>N is proportional to the induced E.M.F., E, in the equation it follows that, TJie loss of power by eddy currents is propor- tional to the square of the E.M.F., and proportional to tlie electric conductivity of the iron ; or, ...", "... cases are : (a). Laminated iron. (b). Iron wire. 1 ' 1 89. (a). Laminated Iron. Let, in Fig. 79, i d = thickness of the iron plates ; (B = maximum magnetic induction ; JV = frequency ; y = electric conductivity of the iron. Fi 1.79. 132 ALTERNATING-CURRENT PHENOMENA. Then, if x is the distance of a zone, d x, from the center of the sheet, the conductance of a zone of thickness, */x, and of one cm length and width is y^x ; and the magnetic flux cut by this zone is (Bx. Hence, the E.M.F. induced in this zon ...", "... 000411 joules; / = .0411 watts; P = 41.1 watts. 90. (6): Iron Wire. Let, in Fig. 80, d = diameter of a piece of iron wire ; then if x is the radius of a circular zone of thickness, d x, and one cm in length, the conductance of this pig. so. 134 ALTERNATING-CURRENT PHENOMENA. zone is, y^/x/2 TT x, and the magnetic flux inclosed by the zone is (B x2 *. Hence, the E.M.F. induced in this zone is : 8£ = V2 7r2^(B x2, in C.G.S. units, and the current produced thereby is, , in C.G.S. units. The power consumed in ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-19", "section_label": "Chapter 19: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 18053-19457", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "snippets": [ "... lem, generator of induced E.M.F. EQ, and motor of induced' E.M.F. El; or, more general, two alternators of induced E.M.Fs., E0, Elf connected together into a circuit of total impedance, Z. Since in this case several E.M.Fs. are acting in circuit 322 ALTERNATING-CURRENT PHENOMENA. with the same current, it is convenient to use the current, /, as zero line OI of the polar diagram. Fig. 188. If I=i= current, and Z = impedance, r = effective resistance, x = effective reactance, and s = Vr2 -f x2 = absolute value of imped ...", "... ain conditions, however, £Q is in the same, E^ in opposite direction, with the current ; that is, both ma- chines are generators. 199. It is seen that in these diagrams the E.M.Fs. are- considered from the point of view of the motor ; that is,. 324 ALTERNATING-CURRENT PHENOMENA. work done as synchronous motor is considered as positive, work done as generator is negative. In the chapter on syn- chronizing generators we took the opposite view, from the generator side. In a single unit-power transmission, that is, one ...", "... and rises again in the motor. For larger values of Ely thfe potential rises in the alternator as well as in the line, so that the highest potential is the induced E.M.F. of the motor, the lowest potential the induced E.M.F. of the gen- erator. 326 ALTERNATING-CURRENT PHENOMENA, It is of interest now to investigate how the values of these quantities change with a change of the constants. Fig. 747. 201. A. — Constant impressed E.M.F. Ev, constant current strength I = i, variable motor excitation Ev (Fig. 142.) I ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "... ctance which is inversely pro- portional to the frequency (capacity, etc.). The impedance for the nth harmonic is, r —Jnn xm This term can be considered as the general symbolic expression of the impedance of a circuit of general wave shape. 412 ALTERNATING-CURRENT PHENOMENA. Ohm's law, in symbolic expression, assumes for the general alternating wave the form, /-Jo, E = IZ or, Z = £or, Z = r -n The symbols of multiplication and division of the terms E, /, ^f, thus represent not algebraic operation, but ...", "... e value of the E.M.F. s, the absolute value of the current, is, 255. The double frequency power (torque, etc.) equa- tion of the general alternating wave has the same symbolic expression as with the sine wave : = Pl +JPJ 1 where, 41-4 ALTERNATING-CURRENT PHENOMENA. The jn enters under the summation sign of the \" watt- less power \" 1$, so that the wattless powers of the different harmonics cannot be algebraically added. i Thus, The total \" true power\" of a general alternating current circuit is the al ...", "... 1 where, 41-4 ALTERNATING-CURRENT PHENOMENA. The jn enters under the summation sign of the \" watt- less power \" 1$, so that the wattless powers of the different harmonics cannot be algebraically added. i Thus, The total \" true power\" of a general alternating current circuit is the algebraic sum of the powers of the individual harmonics. The total \"wattless power\" of a general alternating current circuit is not the algebraic, but the absolute sum of the wattless powers of the individual harmonics. Thus, regarding ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-02", "section_label": "Lecture 2: Conclusions From The Relativity Theory", "section_title": "Conclusions From The Relativity Theory", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 736-2388", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... f light when superimposed, may give a beam of double intensity, or may extinguish each other and give darkness, or may give anything between these two 14 RELATIVITY AND SPACE extremes. This can be explained only by assuming light to be a wave, like an alternating current. Depending on their phase relation, the combination of two waves (as two beams of light or two alternating currents) may be anything between their sum and their difference. Thus the two alternating currents consumed by two incandescent lamps add, being i ...", "... may give anything between these two 14 RELATIVITY AND SPACE extremes. This can be explained only by assuming light to be a wave, like an alternating current. Depending on their phase relation, the combination of two waves (as two beams of light or two alternating currents) may be anything between their sum and their difference. Thus the two alternating currents consumed by two incandescent lamps add, being in phase; the two alternating currents consumed respectively by an inductance and by a capacity subtract, giving a re ...", "... ned only by assuming light to be a wave, like an alternating current. Depending on their phase relation, the combination of two waves (as two beams of light or two alternating currents) may be anything between their sum and their difference. Thus the two alternating currents consumed by two incandescent lamps add, being in phase; the two alternating currents consumed respectively by an inductance and by a capacity subtract, giving a resultant equal to their difference; that is, if they are equal, they extinguish each other. T ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-27", "section_label": "Chapter 27: Balanced And Unbalanced Polyphase Systems", "section_title": "Balanced And Unbalanced Polyphase Systems", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 24054-24488", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-27/", "snippets": [ "... , the power is : p = ei = 2 £Ssin ft sin (ft — S) = £S(cos a — cos (2 £ — a)), and the average value of power : Substituting this, the instantaneous value of power is found as : Hence the power, or the flow of energy, in an ordinary single-phase alternating-current circuit is fluctuating, and varies with twice the frequency of E.M.F. and current, unlike the power of a continuous-current circuit, which is constant : /-** If the angle of lag £ = 0 it is : p = P (1 — cos 2 0) ; hence the flow of power varies be ...", "... +.'.'.;.. is constant, and it is called an unbalanced system if the flow of energy varies periodically, as in the single-phase sys- tem ; and the ratio of the minimum value to the maximum value of power is called the balance factor of the system. 442 ALTERNATING-CURRENT PHENOMENA. Hence in a single-phase system on non-inductive circuit, that is, at no-phase displacement, the balance factor is zero ; and it is negative in a single-phase system with lagging or leading current, and becomes = — 1, if the phase displace- me ...", "... re system and the three-phase system. It shares with the latter the polyphase feature, and with the Edison three- * Also called \"polyphase monocyclic system,\" since the E.M.F. triangle is similar to that usual in the single-phase monocyclic system. 444 ALTERNATING-CURRENT PHENOMENA. wire system the feature that the potential difference be- tween the outside wires is higher than between middle wire and outside wire. By such a pair of transformers the two primary E.M.Fs. of 120° displacement of phase are transformed into ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-11", "section_label": "Chapter 11: Phase Control", "section_title": "Phase Control", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 9767-10717", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-11/", "snippets": [ "... ine, by varying the phase relation of the current in the circuit, has been called \"phase control,\" and is used to a great extent, especially in the transmission of three-phase power for conversion to direct current by synchronous converters for 7 97 98 ALTERNATING-CURRENT PHENOMENA railroading, and in the voltage control at the receiving end of very long high voltage transmission lines. It requires a receiving circuit in which, independent of the load, a lagging or leading component of current can be produced at will. S ...", "... receiving synchronous machine, that is, voltage corresponding to its field excitation, and eo = nominal induced e.m.f. of generator, Z also includes the synchronous impedance of both machines, and of step-up and step-down transformers, where used, 100 ALTERNATING-CURRENT PHENOMENA It is Eo = e + ZI, or, ^0 = (e + ri + xi') - j{n' - xi), (l) and in absolute value we have Co'- - (e + ri + xi'Y + {ri' - xi)\\ (2) This is the fundamental equation of phase control, giving the relation of the two voltages, e and eo, w ...", "... reactance x at maximum current, im, is from equation (10), • ' ' (12) ^m 2x that is, in this case of the maximum load which can be delivered at e, with unity power-factor at eo, the total current, /, leads the receiver voltage, e, by 45°. 102 ALTERNATING-CURRENT PHENOMENA Substituting the value, i' , of equation (10), which compensates for the Hne reactance, x, and so gives unity power-factor at eo, into equation (2), gives as required supply voltage eo. 62^2 {x — r) {e — 2 ix)-\\/e^ — 4:i^x^ .,o\\ ^\" = 2x^ + ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-13", "section_label": "Chapter 13: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 13484-14333", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-13/", "snippets": [ "... nergy per cubic centimeter, in ergs per cycle, is w = e\\fB~; hence, the total loss of power by eddy currents is P = e\\\\T~B\"~ 10-7 watts, and the equivalent conductance due to eddy currents is _ P _ 10 6X? _ 0.507 tXZ^ ^ ~ E^~ 2 ir'-An^ ~ An^ 138 ALTERNATING-CURRENT PHENOMENA •^du where I = length of magnetic circuit, A = section of magnetic circuit, n = number of turns of electric circuit. The coefficient of eddy currents, e, depends merely upon the shape of the constituent parts of the magnetic circuit; ...", "... rgs = 0.000411 joules; p = 0.0411 watts; P = 41.4 watts. ' In some of the modern silicon steels used for transformer iron, X reaches values as low as 2 X 10*, and even lower; and the eddy current losses are reduced in the same proportion (1915). 140 ALTERNATING-CURRENT PHENOMENA 108. (6) Iron Wire. Let, in Fig. 92, d = diameter of a piece of iron wire; then if u is the radius of a circular zone of thickness, du, and one cen- timeter in length, the conductance of this zone is ^ — , and the magnetic flux inclosed by th ...", "... ergs = 0.000154 joules, p = 0.0154 watts, P = 1.54 watts, hence very much less than in sheet iron of equal thickness. 109. Comparison of sheet iron and iron wire. If di = thickness of lamination of sheet iron, and di = diameter of iron wire. 142 ALTERNATING-CURRENT PHENOMENA the eddy current coefficient of sheet iron being 61 = ^ di^ 10-«, and the eddy current coefficient of iron wire the loss of power is equal in both — other things being equal — if 61 = 62; that is, if dz\"\" = %di\\ or da = 1.63-(/i. It follo ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-30", "section_label": "Chapter 30: Balanced And Unbalanced Polyphase Systems", "section_title": "Balanced And Unbalanced Polyphase Systems", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 35256-35691", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-30/", "snippets": [ "... s (2 /3 - e)), and the average value of power, P = EI cos e. Substituting this, the instantaneous value of power is found as cos (2/3 - e)^ _ P A _ cos(2)£J- d)\\ \\ cos 0 / ' Hence the power, or the flow of energy, in an ordinary single- phase, alternating-current circuit is fluctuating, and varies with twice the frequency of e.m.f. and current, unlike the power of a continuous-current circuit, which is constant, p = ei. If the angle of lag, ^ = 9, it is, p - P(l - cos 2/3); hence the flow of energy varies be ...", "... e current lags or leads the e.m.f. by angle d, the power varies between P(l ^)andP(l +-^), \\ cos 6/ \\ cos 6/ that is, becomes negative for a certain part of each half-wave. That is, for a time during each half-wave, energy flows back into 405 406 ALTERNATING-CURRENT PHENOMENA the generator, while during the other part of the half-wave the generator sends out energy, and the difference between both is the effective power of the circuit. lid = 90°, it is p = — EI sin 2 (3; that is, the effective power P = 0, and t ...", "... system is an unsymmetrical balanced system. 3. The symmetrical n-phase system, with equal load and equal phase-displacement in all n branches, is a balanced system. For, let e.- = E\\/2 sin I (3 ^j = e.m.f . ; ii = /\\/2 sin 1^ — 9 j = current; 408 ALTERNATING-CURRENT PHENOMENA the instantaneous value of power is p = Si Biii 1 = 2 EI h sin (p - ^~) sin (i3 - 0 ^) ' \" \" / 4 7rA 1 = £7 I Si cos e - Si cos (2^-9 -j ; or p = nEI cos ^ = P, or constant. 277. An unbalanced polyphase system is the so-called inverted ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-13", "section_label": "Chapter 15: Synchronous Rectifier", "section_title": "Synchronous Rectifier", "kind": "chapter", "sequence": 13, "number": 15, "location": "lines 18413-19373", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-13/", "snippets": [ "... irectional but pul- sating, as shown by e0 in Fig. 74. If receiver circuit and supply circuit both are non-inductive, the current in the receiver circuit is a pulsating unidirectional current, shown as i0 in dotted lines in Fig. 74, and derived from the alternating current, i, Fig. 72, in the supply circuit. If, however, the receiver circuit is inductive, as a machine field, then the current, i«, in Fig. 75, pulsates less than the voltage, ee, which produces it, and the current thus does not go down in wo, but is continuou ...", "... it, and the current thus does not go down in wo, but is continuous, and its pulsation the less, the higher the in- ductance. The current, i, in the alternating supply circuit, how- 234 SYNCHRONOUS RECTIFIER 235 Fia. 72. — Alternating sine wave. AC or DC Fig. 73. — Rectifying commutator. Fig. 74. — Rectified wave on non inductive load. Fig. 75. — Rectified wave on-inductive load. Fig. 76. — Alternating supply wave to rectifier on inductive load. 236 ELECTRICAL A I'I'A if A TU8 ever, fr ...", "... in Fig. 76. Thus the cur- rent in the alternating part and that, in the rectified part of the- circuit can not he the same, but a difference must exist, as shown as i' in Fig. 77. This current, (■', passes between the two parts Fid. 78. — Rectifier with AC ami D.C. aliunl resist of the circuit, as arc at. the rectifier brushes, and causes I lie recti- fying commutator to spark, if there is any appreciable inductance in the circuit. The intensity of the sparking current depends on the inductance of the rec ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-14", "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "section_title": "Constant-Potential Constant-Current Trans Formation", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "CHAPTER XIV CONSTANT-POTENTIAL CONSTANT-CURRENT TRANS- FORMATION 127. The generation of alternating-current electric power prac- tically always takes place at constant voltage. For some pur- poses, however, as for operating series arc circuits, and to a lim- ited extent also for electric furnaces, a constant, or approximately constant alternating current is req ...", "... ion of alternating-current electric power prac- tically always takes place at constant voltage. For some pur- poses, however, as for operating series arc circuits, and to a lim- ited extent also for electric furnaces, a constant, or approximately constant alternating current is required. While constant alter- nating-current arcs have largely come out of use and their place taken by constant direct-current luminous arc circuits, or incan- descent lamps, the constant direct current is usually derived by rectification of constan ...", "... s required. While constant alter- nating-current arcs have largely come out of use and their place taken by constant direct-current luminous arc circuits, or incan- descent lamps, the constant direct current is usually derived by rectification of constant alternating-current supply circuits. Such constant alternating currents are usually produced from constant- voltage supply circuits by means of constant or variable inductive reactances, and may be produced by the combination of inductive and condensive reactances; and the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-87", "section_label": "Apparatus Section 9: Synchronous Converters: Inverted Converters", "section_title": "Synchronous Converters: Inverted Converters", "kind": "apparatus-section", "sequence": 87, "number": 9, "location": "lines 15735-15810", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-87/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-87/", "snippets": [ "IX. Inverted Converters 100. . Converters may be used to change either from alter- nating to direct current or as inverted converters from direct to alternating current. While the former use is by far the more 256 ELEMENTS OF ELECTRICAL ENGINEERING frequent, sometimes inverted converters are desirable. Thus in low-tension direct-current systems outlying districts have been supplied by co ...", "... shift the load from the direct to the alternating generators, or inversely, and thus be operated either way according to the distribution of load on the system. Or inverted operation may be used in emergencies to produce alternating current. When converting from alternating to direct current, the speed of the converter is rigidly fixed by the frequency, and cannot be varied by its field excitation, the variation of the latter merely changing the phase relatio ...", "... nverting from alternating to direct current, the speed of the converter is rigidly fixed by the frequency, and cannot be varied by its field excitation, the variation of the latter merely changing the phase relation of the alternating current. When converting, however, from direct to alternating current as the only source of alternating current, that is, not running in multiple with engine- or turbine-driven alternating-current generators, the speed of the converter ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-89", "section_label": "Apparatus Section 11: Synchronous Converters: Double-current Generators", "section_title": "Synchronous Converters: Double-current Generators", "kind": "apparatus-section", "sequence": 89, "number": 11, "location": "lines 15893-15982", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-89/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-89/", "snippets": [ "XI. Double-current Generators 102. Similar in appearance to the converter, which changes from alternating to direct current, and to the inverted converter, which changes from direct to alternating current, is the double- current generator; that is, a machine driven by mechanical power and producing direct current as well as alternating current from the same armature, which is connected to commutator and col- lector rings in ...", "... ing to direct current, and to the inverted converter, which changes from direct to alternating current, is the double- current generator; that is, a machine driven by mechanical power and producing direct current as well as alternating current from the same armature, which is connected to commutator and col- lector rings in the same way as in the converter. Obviously the use of the double-current generator is limited to those sizes and speeds at which a good d ...", "... relatively high speed; while high-frequency low-speed double-current generators are undesirable. The essential difference between double-current generator and converter is, however, that in the former the direct current and the alternating current are not in opposition as in the latter, but in the same direction, and the resultant armature polarization thus the sum of the armature polarization of the direct current and of the alternating current. Since at the same ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-10", "section_label": "Chapter 10: Resistance And Reactance Of Transmission", "section_title": "Resistance And Reactance Of Transmission", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6993-9766", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-10/", "snippets": [ "CHAPTER X RESISTANCE AND REACTANCE OF TRANSMISSION LINES 65. In alternating-current circuits, voltage is consumed in the feeders of distributing networks, and in the lines of long- distance transmissions, not only by the resistance, but also by the reactance, of the line. The voltage consumed by the resistance is in phase, while the volt ...", "... f the receiver circuit is Y = g, since 6 = 0. We have then current, lo ^ Eg; impressed voltage: Eo ^ E + Zoh = E{1 -|- Zog). Hence — voltage at receiver circuit, ^ ^ Eo ^ Eo I -{-Zog I -\\- gro -{- jgxo' current, .° 1 + Zog 1 + f/ro + jgxo 80 ALTERNATING-CURRENT PHENOMENA Hence, in absolute values — voltage at receiver circuit, h = ^ V(l + gror + g^xo^' current, J _ Eog \" V(l + groP + g^xo' The ratio of e.m.fs. at receiver circuit and at generator, or supply circuit, is E 1 Eo V(l + gro)' + g^xo\" an ...", "... elivered over an inductive Hne is less than the output de- livered over a non-inductive line of the same resistance — that is, which can be delivered by continuous currents with the same generator potential. In Fig. 69 are shown, for the constants, 82 ALTERNATING-CURRENT PHENOMENA Eo = 1000 volts, Zo = 2.5 + 6j; that is, ro = 2.5 ohms, Xo = 6 ohms, Zo = 6.5 ohms, with the current 7o as abscissas, the values. e.m.f . at receiver circuit, E, (Curve I) ; output of transmission, P, (Curve II) ; efficiency of transmission ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-22", "section_label": "Chapter 22: Armature Reactions Of Alternators", "section_title": "Armature Reactions Of Alternators", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 23971-25134", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-22/", "snippets": [ "CHAPTER XXII ARMATURE REACTIONS OF ALTERNATORS 192. The change of the terminal voltage of an alternating current generator, resulting from a change of load at constant field excitation, is due to the combined effect of armature reaction and armature self-induction. The counter m.m.f. of the armature current, or armature reaction, combines with the impressed m.m.f. o ...", "... high armature reaction, as a low-frequency, high-speed alternator of large capacity; relatively little in a machine of low armature reaction and high self-induction, as a high-frequency unitooth alternator, 193. Graphically, the internal reactions of the alternating- current generator can be represented as follows: Let the impressed m.m.f., or field excitation, Fo, be repre- sented by the vector OFo, in Fig. 139, chosen for convenience as vertical axis. Let the armature current, I, be represented by vector 01. This current, ...", "... l axis. Let the armature current, I, be represented by vector 01. This current, /, gives armature reaction Fi = nl, where ?i = number of effective turns of the armature, and is repre- sented by the vector, OFi, with the two quadrature components, 274 ALTERNATING-CURRENT PHENOMENA OF' i, in line with the field m.m.f., Oh\\ — and usually opposite thereto — and OF\", in quadrature with OF^. OFo combined with OFi gives the resultant m.m.f., OF, with the quadrature components, OF' = OFo — 0F\\, and OF\". The m.m.f., OF, prod ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... he frequency, A^, and to the electric conductivity, y, of the iron ; hence, can be expressed by The power consumed by eddy currents is proportional to their square, and inversely proportional to the electric con- ductivity, and can be expressed by 130 ALTERNATING-CURRENT PHENOMENA. [§ 87 or, since, (S>N is proportional to the induced E.M.F., E, in the equation it follows that, The loss of power by eddy currents is propor- tional to the square of the E.M.F., and proportional to the electric conductivity of the iron ; or ...", "... mum possible demagnetizing ampere-turns acting upon the center of the lamina, are a/9 /= -^-^^ Ni&jn 10-» = .55o^(By7» 10 -• = .boly iV(B /^ 10 ~* ampere-turns per cm. Example : ^ = .1 cm, N= 100, (B = 6,000, or / = 2.775 ampere-turns per cm. 138 ALTERNATING-CURRENT PHENOMENA. [§§93,94 93. In iron wire of diameter /, the current in a tubular zone of dx thickness and x radius is V2 ///= TT N(S>jx dxlO~^ amperes; hence, the total current is V2 = — ;- TT N(SijI^ 10 \" * amperes. Hence, the maximum possible demag ...", "... reference to a particular case, where the shape of the -conductor and the distribution of the magnetic field are known. Only in the case where the magnetic field is produced by the current flowing in the conductor can a general solu- tion be given. The alternating current in the conductor produces a magnetic field, not only outside of the conductor, but inside of it also ; and the lines of magnetic force which dose themselves inside of the conductor induce E.M.Fs. in their interior only. Thus the counter E.M.F. of self- i ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-08", "section_label": "Chapter 8: Circuits Containing Resistance, Inductance, And Capacity", "section_title": "Circuits Containing Resistance, Inductance, And Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3577-5333", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "snippets": [ "CHAPTER VIII. CIRCUITS CONTAINING RESISTANCE, INDUCTANCE, AND CAPACITY. 42. Having, in the foregoing, reestablished Ohm's law and Kirchhoff's laws as being also the fundamental laws of alternating-current circuits, when expressed in their com- plex form, E = ZS, or, / = YE, and *%E = 0 in a closed circuit, S/ = 0 at a distributing point, where E, I, Z, Y, are the expressions of E.M.F., current, impedance, and admittance in complex quantities, — these ...", "... ng not only the intensity, but also the phase, of the alternating wave, — we can now — by application of these laws, and in the same manner as with continuous- current circuits, keeping in mind, however, that E, I, Z, Y, are complex quantities — calculate alternating-current cir- cuits and networks of circuits containing resistance, induc- tance, and capacity in any combination, without meeting with greater difficulties than when dealing with continuous- current circuits. It is obviously not possible to discuss with any com ...", "... , tan (phase) = ^aginary component ^ real component a.} If x is negligible with respect to r, as in a non-induc- tive receiving circuit, 1= -=3_ r+ r. and the current and E.M.F. at receiver terminals decrease steadily with increasing r0 . 60 ALTERNATING-CURRENT PHENOMENA. b.} If r is negligible compared with x, as in a wattless receiver circuit, 7= E° , £ = £. X - or, for small values of r0 , /=— °, ^ = ^0; that is, the current and E.M.F. at receiver terminals remain approximately constant for small val ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-22", "section_label": "Chapter 22: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 21190-21982", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "snippets": [ "CHAPTER XXII. DISTORTION OF WAVE-SHAPE AND ITS CAUSES. 233. In the preceding chapters we have considered the alternating currents and alternating E.M.Fs. as sine waves or as replaced by their equivalent sine waves. While this is sufficiently exact in most cases, under certain circumstances the deviation of the wave from sine shape becomes of importance, and with certain distortions ...", "... armonics of E.M.F. 234. In a conductor revolving with uniform velocity through a uniform and constant magnetic field, a sine wave of E.M.F. is induced. In a circuit with constant resistance and constant reactance, this sine wave of E.M.F. produces 384 ALTERNATING-CURRENT PHENOMENA. a sine wave of current. Thus distortion of the wave-shape or higher harmonics may be due to : lack of uniformity of the velocity of the revolving conductor ; lack of uniformity or pulsation of the magnetic field ; pulsation of the resis- tanc ...", "... g higher harmonics under load. 3d. Pulsation of the resistance, causing higher harmonics under load also. Taking up the different causes of higher harmonics we have : — Lack of Uniformity and Pulsation of tJie Magnetic Field. 235. Since most of the alternating-current generators contain definite and sharply defined field poles covering in different types different proportions of the pitch, in general the magnetic flux interlinked with the armature coil will not vary as simply sine wave, of the form : $ cos /?, but ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-06", "section_label": "Chapter 6: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 11051-12221", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-06/", "snippets": [ "... ar. The electromagnet, and all electrodynamic machinery, are based on the use of these mechanical forces between electric conductors and magnetic fields. So also is that type of trans- former which transforms constant alternating voltage into con- stant alternating current. In most other cases, however, these mechanical forces are not used, and therefore are often neglected in the design of the apparatus, under the assumption that the construction used to withstand the ordinary mechanical strains to which the apparatus may ...", "... . „ t^o „ dwo force as r = -^^ or F = -^r- I dl Since the induced e.m.f., which consumes (or produces) the electric energy, and also the stored magnetic energy, depend on MAGNETISM 93 the current and the mductance of the electric circuit, and in alternating-current circuits the impressed voltage also depends on the inductance of the circuit, the inductance can frequently be expressed by supply voltage and current; and by substituting this in equation (1), the mechanical work of the magnetic forces can thus be expres ...", "... energy, will be illustrated by some examples, and the general equations then given. 2. The Constant-current Electromagnet 62. Such magnets are most direct-current electromagnets, and also the series operating magnets of constant-current arc lamps on alternating-current circuits. Let io = current, which is constant dming the motion of the armatm'e of the electromagnet, from its initial position 1, to its final position 2,1 = the length of this motion, or the stroke of the electromagnet, in centimeters, and n = number of ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-10", "section_label": "Chapter 10: Instability Of Circuits : The Arc", "section_title": "Instability Of Circuits : The Arc", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 17632-21381", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-10/", "snippets": [ "... no current passes the condenser circuit, and the current and voltage in A thus are constant, i = 7, e = eo. Suppose now a pulsation of the current, i, should be produced in circuit. A, as shown as i in Fig. 89. Then, with constant-sup- ply current, 7, an alternating current, z'l = 7 - z, would traverse the condenser circuit, C, since the continuous com- ponent of current can not traverse the condenser, C. INSTABILITY OF CIRCUITS 187 Due to the pulsation of current, i in A, the voltage, 6, of cir- cuit, A, would pulsat ...", "... rection as the current pulsation, if A is a resistance, in opposite direction, if A is an arc; in either case, however, they are in phase with the current pulsation, and the alternating vol- tage on the condenser, Ci = Co — e, thus is in phase with the alternating current, ii, that is, capacity, C, and inductance, L, neutralize. Thus, the only pulsation of current and voltage, which could occur in a circuit, A, shimted by capacity and inductance, is that of the resonance frequency of capacity and inductance. Suppose the ...", "... i, in this circuit then would be in the same direction as i, that is, would be as shown in dotted line by e' in Fig. 89. In the condenser circuit, C, the alternat- ing component of voltage thus would be e\\ — e! — 6o, thus would be in opposition to the alternating current, ij, as shown in Fig. 89 in dotted line. That is, it would require a supply of power to maintain such pulsation. Thus, with a dead resistance as circuit. A, or in general with A as a circuit of rising volt-ampere characteristic, the maintenance of a res ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-15", "section_label": "Chapter 15: Constant-Voltage Series Operation", "section_title": "Constant-Voltage Series Operation", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 27996-29301", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-15/", "snippets": [ "... with another lamp in series, would accomplish this: if a lamp burns out, its shunting film cutout punctures and puts the second lamp in circuit. However, in general such arrange- ment is too complicated for use. As practically all such circuits would be alternating-current circuits, and thus alternating currents only need to be considered, the question arises, whether a reactance shunting each lamp would not give the desired effect. Suppose each lamp, of resist- ance, r, is shunted by a reactance, x, which is sufficiently l ...", "... mplish this: if a lamp burns out, its shunting film cutout punctures and puts the second lamp in circuit. However, in general such arrange- ment is too complicated for use. As practically all such circuits would be alternating-current circuits, and thus alternating currents only need to be considered, the question arises, whether a reactance shunting each lamp would not give the desired effect. Suppose each lamp, of resist- ance, r, is shunted by a reactance, x, which is sufficiently large not to withdraw too much current fr ...", "... ing, total voltage, eo = n(l — p)^i + np ^2 (19) it is (20) = n/ substituting (17), Co = nl g g — jhi \"^ 62 J 1 - p , . 11 — jc (21) or. hence, absolute, nl 1 — p(l — oc) + jap g I - JC nt 60 = - V[l-p(l -ac)Y + a^p^ (22) smce. y = gy/l + c^ thus, the current in the series circuit. I = e^y n VU - p(l- ac)Y + d^^ (24) CONSTANT-VOLTAGE SERIES OPERATION 303 158. For, p = 0, or full-load, it is thus. io = ^ (25) n i = ^^ (26) ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-21", "section_label": "Apparatus Introduction 21: Introduction", "section_title": "Introduction", "kind": "apparatus-introduction", "sequence": 21, "number": null, "location": "lines 8292-8517", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-21/", "snippets": [ "INTRODUCTION 1. By the direction of the energy transmitted, electric machines have been divided into generators and motors. By the character of the electric power they have been distinguished as direct- current and as alternating-current apparatus. With the advance of electrical engineering, however, these subdivisions have become unsatisfactory and insufficient. The division into generators and motors is not based on any characteristic feature of the apparatu ...", "... tus have been introduced which are neither motors nor generators, as the synchronous machine producing wattless lag- ging or leading current, etc., and the different types of converters. The subdivision into direct-current and alternating-current apparatus is unsatisfactory, since it includes in the same class apparatus of entirely different character, as the induction motor and the alternating-current generator, or the constant-potential commutating machine and the rect ...", "... fferent types of converters. The subdivision into direct-current and alternating-current apparatus is unsatisfactory, since it includes in the same class apparatus of entirely different character, as the induction motor and the alternating-current generator, or the constant-potential commutating machine and the rectifying arc light machine. Thus the following classification, based on the characteristic features of the apparatus, as adopted by the A. I. E. E. Standard- ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-20", "section_label": "Chapter 20: Single-Phase Induction Motors", "section_title": "Single-Phase Induction Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 21538-22301", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-20/", "snippets": [ "... , and becomes zero at standstill. That is, they are not self-starting, but some starting device has to be used. Such a starting device may either be mechanical or electrical. All the electrical starting devices essentially consist in impress- 245 24G ALTERNATING-CURRENT PHENOMENA ing upon the motor at standstill a magnetic quadrature flux. This may be produced either by some outside e.m.f., as in the monocyclic starting device, or by displacing the circuits of two or more primary coils from each other, either by mutual ...", "... , as an inductive reactance and a resistance, or an inductive and a condensive reactance connected in series across the mains. The investigation of these starting-devices offers a very instructive application of the symbolic method of investiga- tion of alternating-current phenomena, and a study thereof is thus recommended to the reader.^ ' See paper on the Single-phase Induction Motor, A. I. E. E. Transactions, 1898. SINGLE-PHASE INDUCTION MOTORS 247 179. Occasionally, no special motors are built for single-phase ope ...", "... magnetic flux, and represented by ^ constant admittance, 7oS the primary exciting admittance of the motor, and the secondary exciting current, that is, that component of primary current corresponding to the secondary current which gives the excita- 248 ALTERNATING-CURRENT PHENOMENA tion for the quadrature magnetic flux. This latter magnetic flux is equal to the main magnetic flux, $o, at synchronism, and falls off with decreasing speed to zero at standstill, if no starting device is used, or to $i = $of at standstill if b ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-27", "section_label": "Chapter 27: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 33011-34776", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-27/", "snippets": [ "... , A = 22n-i(a„i+i„a„ii),^ 1 1 The index 2n — 1 in the S sign denotes that only the odd values of n are considered. If the wave contained even harmonics, the even vahies of n would also be considered, and the index in the 2 sign would be n. 379 380 ALTERNATING-CURRENT PHENOMENA where jn = V - 1, and the index of the j„ merely denotes that the j's of differ- ent indices, n, while algebraically identical, physically represent different frequencies, and thus cannot be combined. The general wave of e.m.f. is thus repre ...", "... is E = ^/22n-i(e/ + e„u2)^ the absolute value of the current, 1 is / = ^/S2.-1(^/ + ZV^'). 261. The double frequency power (torque, etc.) equation of the general alternating wave has the same symbolic expression as with the sine wave, 382 ALTERNATING-CURRENT PHENOMENA P = [EI] = Pi + jP^ = [Ely -{- j[Ei]j 1 1 where Pi = [Ely = i:2n-i(e„ii„i + e^iHV^), 1 1 J The jn enters under the summation sign of the reactive or \"wattless power,\" P', so that the wattless powers of the different harmonics canno ...", "... may be called the \"circuit-factor.\" ■la It consists of a real term, p, the power-factor, and a series of imaginary terms, in^n, the inductance factors of the individual harmonics. The absolute value of the circuit-factor. as a rule, is < 1. 384 ALTERNATING-CURRENT PHENOMENA - 262. Some applications of this symbolism will explain its mechanism and its usefulness more fully. First Example. — Let the e.m.f., 5 1 be impressed upon a circuit of the impedance, Z = r^jr. [nxr. - ^) = 10+ i„(lOn- ^) that is, conta ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-25", "section_label": "Chapter 25: Baiianced And Unbaxiancbd Polyphase Systema", "section_title": "Baiianced And Unbaxiancbd Polyphase Systema", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 25605-26027", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-25/", "snippets": [ "... Elsm )8 sin 03 - u») = -£'/(cos w — sin (2 /3 — w)), and the average value of power : 7^= EI cos w. Substituting this, the instantaneous value of power is found as : \\^ cos w J Hence the power, or the flow of energy, in an ordinary single-phase alternating-current circuit is fluctuating, and varies with twice the frequency of E.M.F. and current, unlike the power of a continuous-current circuit, which is constant : p -= €t. If the angle of lag w = it is : / = /^ (1 - sin 2 )3) ; hence the flow of power var ...", "... cted in opposite direction with respect to their primaries. Such a system takes an interrriediate position between the Edison three- wire system and the three-phase system. It shares with the latter the polyphase feature, and with the Edison three- 860 ALTERNATING-CURRENT PHENOMENA. [§ wire system the feature that the potential difference be- tween the outside wires is higher than between middle wire and outside wire. By such a pair of transformers the two primary E.M.Fs. of 120° displacement of phase are transformed in ...", "... Load of 90* Lag. Fig. 169. Quart€r-ph€is9 System on Non^inductioe Loot. Fig. 170. Quarter-phase System on inductive Load of 60' Lag, AL TEKNA nXC-CUI^RENT PHENOMENA. [ % 244 « 245, 246] BALANCED POL YPIIASE SYSTEMS. 245. The flow of power in an alternating-current system is a most important and characteristic feature of the system, and by its nature the systems may be classified into : Monocyclic systems, or systems with a balance factor zero or negative. Polycyclic systems, with a positive balance factor. Bal ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "... R IV INDUCTION MOTOR WITH SECONDARY EXCITATION 38. While in the typical synchronous machine and eommu- tating machine the magnetic field is excited by a direct current, characteristic of the induction machine is, that the magnetic field is excited by an alternating current derived from the alter- nating supply voltage, just as in the alternating-current trans- former. As the alternating magnetizing current is a wattless reactive current, the result is, that the alternating-current input into the induction motor is always la ...", "... ous machine and eommu- tating machine the magnetic field is excited by a direct current, characteristic of the induction machine is, that the magnetic field is excited by an alternating current derived from the alter- nating supply voltage, just as in the alternating-current trans- former. As the alternating magnetizing current is a wattless reactive current, the result is, that the alternating-current input into the induction motor is always lagging, the more so, the larger a part of the total current is given by the magneti ...", "... s, that the magnetic field is excited by an alternating current derived from the alter- nating supply voltage, just as in the alternating-current trans- former. As the alternating magnetizing current is a wattless reactive current, the result is, that the alternating-current input into the induction motor is always lagging, the more so, the larger a part of the total current is given by the magnetizing current. To secure good power-factor in an induction motor, the magnetizing current, that i«, the current which produces the ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-12", "section_label": "Chapter 12: Reactance Of Induction Apparatus", "section_title": "Reactance Of Induction Apparatus", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 22634-23465", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-12/", "snippets": [ "CHAPTER XII REACTANCE OF INDUCTION APPARATUS 109. An electric current passing through a conductor is ac- companied by a magnetic field surrounding this conductor, and this magnetic field is as integral a part of the phenomenon, as is the energy dissipation by the resistance of the conductor. It is represented by the inductance, L, of the conductor, or the n ...", "... in the conductor. Every circuit thus has a resistance, and an inductance, however small the latter may be in the so-called \"non-inductive\" circuit. With continuous current in stationary conditions, the inductance, L, has no effect on the energy flow; with alternating current of frequency, /, the inductance, L, consumes a voltage 2 x/Li, and is, therefore, represented by the reactance, x = 2x/L, which is measured in ohms, and differs from the ohmic resistance, r, merely by being wattless or reactive, that is, representing not ...", "... e 2 x/Li, and is, therefore, represented by the reactance, x = 2x/L, which is measured in ohms, and differs from the ohmic resistance, r, merely by being wattless or reactive, that is, representing not dissipation of energy, but surging of energy. Every alternating-current circuit thus has a resistance and a reactance, the latter representing the effect of the magnetic field of the current in the conductor. When dealing with alternating-current apparatus, especially those having several circuits, it must be realized, howev ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-39", "section_label": "Chapter 3: Mechanical Rectification", "section_title": "Mechanical Rectification", "kind": "chapter", "sequence": 39, "number": 3, "location": "lines 15963-17754", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-39/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-39/", "snippets": [ "CHAPTER III. MECHANICAL RECTIFICATION. 9. If an alternating-current circuit is connected, by means of a synchronously operated circuit breaker or rectifier, with a second circuit in such a manner, that the connection between the two circuits is reversed at or near the moment when the alternating voltage passes zero, then ...", "... the two circuits is reversed at or near the moment when the alternating voltage passes zero, then in the second circuit current and voltage are more or less unidirectional, although they may not be constant, but pulsating. If i = instantaneous value of alternating current, and i0 = instantaneous value of rectified current, then we have, before reversal, i0 = i, and after reversal, i0 = — i\\ that is, during the reversal of the circuit one of the currents must reverse. Since, however, due to the self-inductance of the circui ...", "... are: 1. If r = r0 = 0, that is, during rectification both circuits are short circuited. Such short-circuit rectification is feasible only in limited-current circuits, as on arc lighting machines, or in * If the circuit is reversed at the moment when the alternating current passes zero, due to self-inductance of the rectified circuit its current differs from zero, and an arc still appears at the rectifier. 229 230 TRANSIENT PHENOMENA cases where the voltage of the rectified circuit is only a small part of the total vol ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... e latter functions, and tan a or cot a resubstituted in the final result, if the latter contains sin a . . - , or its reciprocal. cos a In electrical engineering tan a or cot a frequently appears as the starting-point of calculation of the phase of alternating currents. For instance, if a is the phase angle of a vector 98 ENGINEERING MATHEMATICS. quantity, tan a is given as the ratio of the vertical component over the horizontal component, or of the reactive component over the power component. In this case, if m ...", "... en from it through a constant resistance. Transient phenomena occur during a change in the condition of an electric circuit, as a change of load; or, disturbances entering the circuit from the outside or originating in it, etc. Periodic phenomena are the alternating currents and voltages, pulsating currents as those produced by rectifiers, the distribution of the magnetic flux in the air-gap of a machine, or the distribution of voltage around the commutator of the direct-current machine, the motion of the piston in the steam- ...", "... the series of trigonometric functions (3) is univalent,, it follows that the periodic function (6), y=fo{d)f must be uni- valent, to be represented by a trigonometric series. 77. The ; most ; important periodic functions in electrical engineering are the alternating currents and e.m.fs. Usually they are, in first approximation, represented by a single trigo- nometric function, as : i = io cos {O—ix))] or, e = eo sin (d—d); that is, they are assumed as sine waves. 108 ENGINEERING MATHEMATICS. f ■ . Theoretically, o ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-07", "section_label": "Theory Section 7: Inductance in Alternating-current Circuits", "section_title": "Inductance in Alternating-current Circuits", "kind": "theory-section", "sequence": 7, "number": 7, "location": "lines 2250-2717", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-07/", "snippets": [ "7. INDUCTANCE IN ALTERNATING-CURRENT CIRCUITS 34. An alternating current i = IQ sin 2irft or i — I0 sin 0 can be represented graphically in rectangular coordinates by a curved line as shown in Fig. 10, with the instantaneous values FIG. 10. — Alternating ...", "7. INDUCTANCE IN ALTERNATING-CURRENT CIRCUITS 34. An alternating current i = IQ sin 2irft or i — I0 sin 0 can be represented graphically in rectangular coordinates by a curved line as shown in Fig. 10, with the instantaneous values FIG. 10. — Alternating sine wave. i as ordinates and the ...", "... ted by i = /0 sin 2 IT/ (t - t'), or i = /osin (6 — 8'), where tf and 6' are respectively the time and the corresponding angle at which the current reaches its zero value in the ascendant. If such a sine wave of alternating current i = IQ sin 2 irft or i = IQ sin 6 passes through a circuit of resistance r and induc- tance L, the magnetic flux produced by the current and thus its interlinkages with the current, iL = IoL sin 0, vary in a wave ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-79", "section_label": "Apparatus Subsection 79: Direct-current Commutating Machines: C. Commutating Machines 219", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 219", "kind": "apparatus-subsection", "sequence": 79, "number": null, "location": "lines 13019-13119", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-79/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-79/", "snippets": [ "D. C. COMMUTATING MACHINES 219 In the alternating-current commutator motor, the field struc- ture as well as the armature must be laminated, since the mag- netic flux is alternating. The alternation of the field flux induces an e.m.f. of self induction in the field winding. In t ...", "... induced in the armature coil by its rotation through the field flux, and in the continuous current machine the coil is without voltage except whatever voltage may be intentionally produced by the com- mutating flux. In the alternating-current motor, however, the field flux induces voltage also in the armature coil by its alternation, and this voltage is a maximum in the position of commutation, and when short-circuited by the commutator brush tends to produce a ...", "... rnation, and this voltage is a maximum in the position of commutation, and when short-circuited by the commutator brush tends to produce an excessive current and cause spark- ing. No position exists on the commutator of the alternating- current motor where the armature coil does not contain an induced e.m.f., but in the position midway between the brushes the e.m.f. induced by the rotation through the magnetic field is a maximum; in the position of commutation t ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-04", "section_label": "Chapter 4: Vector Representation", "section_title": "Vector Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2149-2759", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-04/", "snippets": [ "... ngle, ^ = 10 A = 2ir — (where to to = time of one complete cycle or period), is counted from the moment of time where the revolving vector 01 in Fig. 8 stands in position Oil, then this sine wave would be represented by i = I cos (?? - i?i), 19 20 ALTERNATING-CURRENT PHENOMENA where ??i — IiOA may be called the phase of the wave, and I = QJi the amplitude or intensity. At the time, «> = ??i, that is, the angle, ??i, after the moment of time represented by position OIi, i = I, and 01 passes through the horizontal OA ...", "... r instance, two sine waves, OEi, and OE2 (Fig- H), are superposed — as, for instance, two e.m.fs. acting in the same cir- cuit— their resultant wave is represented by OE, the diagonal of a parallelogram with OEi and OE2 as sides. As the projection of 22 ALTERNATING-CURRENT PHENOMENA the diagonal of a parallelogram equals the sum of the projections of the sides, during the rotation of the parallelogram OE1EE2, the projection of OE on the horizontal OA, that is, the instan- taneous value of the wave represented by vector OE, ...", "... nter e.m.fs. of resistance and of reactance are included. (6) The resultant of all the currents toward a distributing point, as found by the parallelogram of sine waves, is zero. The power equation expressed graphically is as follows: The power of an alternating-current circuit is represented in vector representation by the product of the current, I, into the projection of the e.m.f., E, upon the current, or by the e.m.f., E, into the projection of the current, I, £3 Eo upon the e.m.f., or by IE cos d, where A ^,-- ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "CHAPTER XV DISTRIBUTED CAPACITY, INDUCTANCE, RESISTANCE, AND LEAKAGE 127. In the foregoing, the phenomena causing loss of energy in an alternating-current circuit have been discussed; and it has been shown that the mutual relation between current and e.m.f. can be expressed by two of the four constants: power component of e.m.f., in phase with current, and = current X effective resistance, or r; reactive ...", "... point to point; and it is no longer possible to treat the circuit in the usual manner by the vector diagram. This phenomenon is especially noticeable in long-distance lines, in underground cables, and to a certain degree in the high-poten- tial coils of alternating-current transformers for very high vol- tage and also in high frequency circuits. It has the effect that not only the e.m.fs., but also the currents, at the beginning, end, and different points of the conductor, are different in intensity and in phase. Where th ...", "... , and the differential equations based thereon integrated. Or the phenomena occurring in the circuit can be investigated graphically by the method given in Chapter VI, §39, by dividing the circuit into a sufficiently large number of sections or fine 170 ALTERNATING-CURRENT PHENOMENA elements, and then passing from line element to line element, to construct the topographic circuit characteristics. 129. It is thus desirable to first investigate the limits of appli- cability of the approximate representation of the line by o ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-15", "section_label": "Chapter 15: Induction Motob", "section_title": "Induction Motob", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 14919-17024", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "snippets": [ "CHAPTER XV. INDUCTION MOTOB. 140. A specialization of the general alternating-current transformer is the induction motor. It differs from the sta- tionary alternating-current transformer in so far as the two sets of electric circuits — the primary or excited, and the secondary or induced, circuits — are movable with regard to each other ; ...", "CHAPTER XV. INDUCTION MOTOB. 140. A specialization of the general alternating-current transformer is the induction motor. It differs from the sta- tionary alternating-current transformer in so far as the two sets of electric circuits — the primary or excited, and the secondary or induced, circuits — are movable with regard to each other ; and that in general a number of primary and a number of secondary circuits are used, angu ...", "... and s = percentage slip ; sN = frequency of armature or secondary E.M.F., and (1 — s) J\\r= frequency of rotation of armature. In its reaction upon the primary circuit, however, the armature current is of the same frequency as the primary f 208 ALTERNATING-CURRENT PHENOMENA. [§141 current, since it is carried around mechanically, with such a frequency as always to have the same phase relation, in the same position, with regard to the primary current. 141. Let the primary system consist of/ equal circuits, displa ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-20", "section_label": "Chapter 20: Commutator Motors", "section_title": "Commutator Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 19458-20501", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "snippets": [ "... cles per second, N: = frequency of rotation or speed in cycles per second, and k = N^/ N speed we have frequency thus, gl = — 2-TrnJV® {sin X cos /? + k cos X sin B\\ 10~8, or, since $ = — — — — , et = e V2 {sin X cos /3 + k cos X sin fi\\. 360 ALTERNATING-CURRENT PHENOMENA. 218. Introducing now complex quantities, and counting the time from the zero value of rising magnetism, the mag- netism is represented by /4>, the primary induced E.M.F., E = — e, the secondary induced E.M.F., £1 = — e {sin X +j\"k cos X|; he ...", "... tor, with increasing speed, the angle of secondary closed circuit, X, has to be reduced to get maximum torque. 219. At A = 45° we have, (rx V2 + r + £*)2 + (^ V2 + x - krf and the power, p= ^k (x, + r,K)_ (r, V2 + r + kx)*+(xi ^2 + x - krf' 362 ALTERNATING-CURRENT PHENOMENA. this is a maximum, at constant X = 45°, for — — = 0, which dk gives, k = 1 At X = 0 we have, T-- fa + kxf + (*t - krf that is, T = 0 at k = 0, or, the motor is not self-starting, when X = 0. P = dP which is a maximum at con ...", "... sed, the direction of rotation remains the same, since field magnetism and armature current have reversed their sign, and their prod- Fig. 162. Series Motor. net, the torque, thus maintained the same sign. There- fore such a motor, when supplied by an alternating current, will operate also, provided that the reversals in field and in armature take place simultaneously. In the series motor this is necessarily the case, the same current passing through field and through armature. With an alternating current in the field, ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-29", "section_label": "Chapter 7: Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "section_title": "Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "kind": "chapter", "sequence": 29, "number": 7, "location": "lines 6798-7825", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "snippets": [ "CHAPTER VII. RESISTANCE, INDUCTANCE, AND CAPACITY IN SERIES IN ALTERNATING-CURRENT CIRCUIT. 65. Let, at time t = 0 or 0 = 0, the e.m.f., e = E cos (0 - 00), (1) be impressed upon a circuit containing in series the resistance, r, the inductance, L, and the capacity, C. The inductive reactance is x = 2 TT/L 1 and the condensive reac ...", "... e 4 x xc = 22,500 and r2 = 40,000; therefore r2 > 4 x xc, RESISTANCE, INDUCTANCE, AND CAPACITY 95 that is, the start is logarithmic, and z0 = 200, s = 132, and 7 = 0. 20 60 80 100 120 140 160 180 200 Degrees Fig. 20. Starting of an alternating-current circuit, having capacity, inductance and resistance in series. Logarithmic start. In Fig. 20 the circuit is closed at the moment 00 = 0, that is, at the maximum value of the impressed e.m.f., giving from the equations (18) and (19), since i0 = 0, e0 = 0, ...", "... the impressed e.m.f., giving from the equations (18) and (19), since i0 = 0, e0 = 0, and i = 5 {cos 6 - 1.26 s-2-22' + 0.26 £-°'452' } el = 375 {sin0 + 0.57 (e-»-»«_fi-o.462*)}p 0 20 40 100 120 140 160 180 200 Degrees Fig. 21. Starting of an alternating-current circuit having capacity, inductance and resistance in series. Logarithmic start. In Fig. 21 the circuit is closed at the moment 00 = 90°, that is, at the zero value of the impressed e.m.f., giving the equa- tions i = 5 {sinfl + 0.57 Or2'22' - fi-o-«\")} ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-81", "section_label": "Apparatus Section 1: Synchronous Converters: General", "section_title": "Synchronous Converters: General", "kind": "apparatus-section", "sequence": 81, "number": 1, "location": "lines 13189-13795", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-81/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-81/", "snippets": [ "I. General 82. For long-distance transmission, and to a certain extent also for distribution, alternating currents, either polyphase or single-phase, are extensively used. For many applications, however, as especially for electrolytic work, direct currents are required, and are usually preferred also for electrical railroading and for low-te ...", "... re is almost always preferred. Mechanically the converter has the advantage that no transfer of mechanical energy takes place, since the torque consumed by the generation of the direct current and the torque produced by the alternating current are applied at the same armature con- ductors, while in a direct-current generator driven by a syn- chronous motor the power has to be transmitted mechanically through the shaft. EC. Ratio of e.m.fs. and of Currents 83. I ...", "... produces between two collector rings connected with two opposite points of the commutator an alternating e.m.f. of —-= X the direct-current v2 voltage, at a frequency equal to the fre- quency of rotation. Since every alternating- current generator is reversible, such a direct- current machine with two collector rings, when supplied with an alternating e.m.f. of 1 X the direct-current voltage at the fre- quency of rotation, will run as synchronous motor, o ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-85", "section_label": "Apparatus Section 6: Synchronous Converters: Reactive Currents and Compounding", "section_title": "Synchronous Converters: Reactive Currents and Compounding", "kind": "apparatus-section", "sequence": 85, "number": 6, "location": "lines 15476-15585", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-85/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-85/", "snippets": [ "VI. Reactive Currents and Compounding 96. Since the polarization due to the power component of the alternating current as synchronous motor is in quadrature ahead of the field magnetization, the polarization or magnetizing effect of the lagging component of alternating current is in phase, that of the leading component of alternating current ...", "... ing 96. Since the polarization due to the power component of the alternating current as synchronous motor is in quadrature ahead of the field magnetization, the polarization or magnetizing effect of the lagging component of alternating current is in phase, that of the leading component of alternating current in oppositon to the field magnetization; that is, in the converter no magnetic distortion exists, and no armature reaction at all if the current is in phas ...", "... alternating current as synchronous motor is in quadrature ahead of the field magnetization, the polarization or magnetizing effect of the lagging component of alternating current is in phase, that of the leading component of alternating current in oppositon to the field magnetization; that is, in the converter no magnetic distortion exists, and no armature reaction at all if the current is in phase with the impressed e.m.f., while the- armature reaction is demagn ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "section_label": "Chapter 14: Dielectric Losses", "section_title": "Dielectric Losses", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "... conduction loss through the resistance of the dielectric. In a homogeneous dielectric of electric conductivity 7 (usually very low) and specific capacity or permittivity k, if: I = thickness of the dielectric, A = area or cross-section, e = impressed alternating-current voltage, effective value, the dielectric capacity of the material is: JcA ^ ~~ I and the capacity susceptance: 152 ALTERNATING-CURRENT PHENOMENA hence the current passing through the dielectric as capacity- current or \"displacement current,\" is: ...", "... ific capacity or permittivity k, if: I = thickness of the dielectric, A = area or cross-section, e = impressed alternating-current voltage, effective value, the dielectric capacity of the material is: JcA ^ ~~ I and the capacity susceptance: 152 ALTERNATING-CURRENT PHENOMENA hence the current passing through the dielectric as capacity- current or \"displacement current,\" is: ^ ^^ 2 7r//cA iQ = eo — 2 TTjCe = — -. — e The conductance of the dielectric is: yA hence, the current, conducted through the dielectri ...", "... akage current is large compared with the capacity current, that is, 2iTJCe negligible compared with ge. In this case, Xi and x-i are negligible compared with ri and r-^, and: e (15) V r\\ + ri Q e2 ri + r2 P e2 ri + Ti V = 1 156 ALTERNATING-CURRENT PHENOMENA and as in this case ri and r^ are the effective ohmic resistance of the dielectric, all the quantities are independent of the frequency; that is, the case is one of simple conduction. 120 (c) If in the first layer the leakage is negligible com ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-16", "section_label": "Chapter 16: Power, And Double-Frequency Quantities In", "section_title": "Power, And Double-Frequency Quantities In", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 16077-16520", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-16/", "snippets": [ "CHAPTER XVI POWER, AND DOUBLE-FREQUENCY QUANTITIES IN GENERAL 135. Graphically, alternating currents and voltages are repre- sented by vectors, of which the length represents the intensity, the direction the phase of the alternating wave. The vectors generally issue from the center of coordinates. In the topographical method, however, which is more con- ...", "... lated by multiplication and division of complex quantities in the same way as current, voltage, resistance, and conductance are related by Ohm's law in direct-current circuits. In direct-current circuits, power is the product of current into voltage. In alternating-current circuits, if the product, is not the power; that is, multiplication and division, which are correct in the inter-relation of current, voltage, impedance, do not give a correct result in the inter-relation of voltage, current, power. The reason is, that ...", "... edance, do not give a correct result in the inter-relation of voltage, current, power. The reason is, that E and / are vectors of the same fre- quency, and Z a constant numerical factor or \"operator,\" which thus does not change the frequency. 179 180 ALTERNATING-CURRENT PHENOMENA The power, P, however, is of double frequency compared with E and /, that is, makes a complete wave for every half wave of E or 7, and thus cannot be represented by a vector in the same diagram with E and I. Po = EI is a quantity of the same ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-33", "section_label": "Chapter 33: Efficiency Of Systems", "section_title": "Efficiency Of Systems", "kind": "chapter", "sequence": 33, "number": 33, "location": "lines 36515-37127", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-33/", "snippets": [ "... nd, On the basis of the maximum potential difference between any conductor of the system and the ground ; or 3rd. On the basis of the minimum potential difference in the system, or the potential difference per circuit or phase of the system. 431 432 ALTERNATING-CURRENT PHENOMENA In low-potential circuits, as secondary networks, where the potential is not limited by the insulation strain, but by the potential of the apparatus connected into the system, as incan- descent lamps, the proper basis of comparison is equality ...", "... uality of the minimum difference of potential between any pair of wires connected to the receiving apparatus. 295. 1st. Comparison on the basis of equality of the minimum difference of potential, in low-potential lighting circuits: In the single-phase, alternating-current circuit, if e = e.m.f., i = current, r = resistance per line, the total power is = ei, the loss of power, 2 ih\\ Using, however, a three-wire system: the potential between outside wires and neutral being given equal to e, the potential between the outsid ...", "... eded. Obviously, a single-phase, five-wire system will be a system of distribution at the potential, 4 e, and there- fore require only one-sixteenth of the copper of the single-phase system in the outside wires; and if each of the three neutral 28 434 ALTERNATING-CURRENT PHENOMENA wires is of one-half the cross-section of the outside wires, seven- sixty-fourths or 10.93 per cent, of the copper. Coming now to the three-phase system with the potential, e, between the lines as delta potential, if i = the current per line ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-08", "section_label": "Chapter 8: Capacity", "section_title": "Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3872-6370", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "snippets": [ "CHAPTER VIII. — 2,t-, it raises, if ;r < — 2 jr, it lowers, the voltage. We see, then, that a reactance inserted in series in an alternating-current circuit will lower the voltage at the «45] RESISTANCE, INDUCTANCE, CAPACITY, 63 receiver terminals only when of the same sign as the reac- tance of the receiver circuit ; when of opposite sign, it will lower the voltage if larger, raise the volt ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-18", "section_label": "Chapter 16: Il", "section_title": "Il", "kind": "chapter", "sequence": 18, "number": 16, "location": "lines 19346-21338", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-18/", "snippets": [ "... llelogram E^Eq, in the same way, we have : OE^ = E^= induced E.M.F. of the motor, OE^ = E^ = E.M.F. at motor terminals or at end of line, OE^ = E^ = E.M.F. at generator terminals, or at beginning of line. OEq = Eq = induced E.M.F. of generator. 262 ALTERNATING-CURRENT PHENOMENA. 179^ The phase relation of the current with the E.M.Fs. E^y Eqj depends upon the current strength and the E.M.Fs. E^ and Eq, 179. Figs. 123 to 125 show several such diagrams for different values of E^t but the same value of / and Eq, ...", "... d E.M.F. E^ here acting in the same way as the condenser capacity in Chapter IX. Fig. 131. 183. D. E^ =^ constant ; P ^ constant. If the power of a synchronous motor remains constant, wc have (Fig. 131) / x OE^ = constant, or, since OE^ = 272 ALTERNATING-CURRENT PHENOMENA. 18a /r, I = OE^jr, and: OE^ x OE^ = OE\"^ x E'E^' = constant. Hence we get the diagram for any value of the current /, at constant power Pi , by making OE^ = /^, E^Eq^ = P^ j C erecting in E^ a perpendicular, which gives two points of in ...", "... , 9,000, E = 1 ,000 46 < ^ < 2,200, E = 6.000 340 < ^, < 1,920, jP = 9,000 540 < ^1 < 1,750, E = 12,000 920 < ^i < 1,320, 12,000 watts, and give : 1 < / < 49 Fig. 132. 7 < / < 43 Fig. 133. 11.8 < / < 38.2 Fig. 134. 20 < / < 30 Fig. 153. ALTERNATING-CURRENT PHENOMENA. [j 183 ■Fig. '3S. As seen, the permissible value of counter E.M.F, £\", and of current /, becomes narrower with increasing output. § 184] SYNCJ/KONOL7S MOTOR. 275 In the diagrams, different points of E^ are marked with 1, 2, 3 . . ., whe ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-09", "section_label": "Chapter 9: Resistance And Reactance Of Transmission Lines", "section_title": "Resistance And Reactance Of Transmission Lines", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 5334-6956", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "snippets": [ "CHAPTER IX. RESISTANCE AND REACTANCE OF TRANSMISSION LINES. 57. In alternating-current circuits, E.M.F. is consumed in the feeders of distributing networks, and in the lines of long-distance transmissions, not only by the resistance, but also by the reactance, of the line. The E.M.F. consumed by the resistance is in phase, while the E.M.F. ...", "... the purpose of reg- ulation. Its susceptance, b, however, can be changed by shunting the circuit with a reactance, and will be increased by a shunted inductance, and decreased by a shunted con- densance. Hence, for the purpose of investigation, the 84 ALTERNATING-CURRENT PHENOMENA. receiver circuit can be assumed to consist of two branches, a conductance, g, — the non-inductive part of the circuit, — shunted by a susceptance, b, which can be varied without expenditure of energy. The two components of current can thus be ...", "... or circuit, 62. b.} Dependence of the output upon the conductance of the receiver circuit. At a given susceptance, ^, of the receiver circuit, its output, P — Eo = AOX, the instantaneous values of the three waves, OB, OC, OD, are their projections upon OX, and the sum of the projections of OB ...", "... re included. b.} The resultant of all the currents flowing towards a GRAPHIC REPRESENTATION. 23 distributing point, as found by the parallelogram of sine waves, is zero. The energy equation expressed graphically is as follows : The power of an alternating-current circuit is repre- sented in polar coordinates by the product of the current , /, into the projection of the E.M.F., E, upon the current, or by the E.M.F., E, into the projection of the current, /, upon the E.M.F., or by IE cos 17. Suppose, as an instan ...", "... 15, OI, is the current, — OEr = E.M.F. consumed by resistance, OEr' = counter E.M.F. of resistance, OEX = E.M.F. consumed by inductance, OEX' = counter E.M.F. of inductance, OEZ = E.M.F. consumed by impedance, OEt ' = counter E.M.F. of impedance. 26 ALTERNATING-CURRENT PHENOMENA. Obviously, these counter E.M.Fs. are different from, for instance, the counter E.M.F. of a synchronous motor, in so far as they have no independent existence, but exist only through, and as long as, the current flows. In this respect they are ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-30", "section_label": "Chapter 30: Efficiency Of Systems", "section_title": "Efficiency Of Systems", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 25136-25597", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-30/", "snippets": [ "... he basis of equality of the minimum difference of potential between any pair of wires connected to the receiving apparatus. 289. 1st. Comparison on the basis of equality of the minimum difference of potential, in low potential lighting circuits : 4TO ALTERNATING-CURRENT PHENOMENA. In the single-phase alternating-current circuit, if e — E.M.F., i = current, r— resistance per line, the total power is = ei, the loss of power 2z'V. Using, however, a three-wire system, the potential be- tween outside wires and neutral bein ...", "... tential between any pair of wires connected to the receiving apparatus. 289. 1st. Comparison on the basis of equality of the minimum difference of potential, in low potential lighting circuits : 4TO ALTERNATING-CURRENT PHENOMENA. In the single-phase alternating-current circuit, if e — E.M.F., i = current, r— resistance per line, the total power is = ei, the loss of power 2z'V. Using, however, a three-wire system, the potential be- tween outside wires and neutral being given = e, the potential between the outside wires ...", "... ngle-phase system. Coming now to the quarter-phase system with common return and potential e per branch, denoting the current in the outside wires by z'2, the current in the central wire is *a V2 ; and if the same current density is chosen for all 472 ALTERNATING-CURRENT PHENOMENA. three wires, as the condition of maximum efficiency, and the resistance of each outside wire denoted by rz, the re- sistance of the central wire = r2/V2, and the loss of power per outside wire is z'22 r2 , in the central wire 2 z'22 r2 / V2 = ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-32", "section_label": "Chapter 32: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 25904-27405", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "snippets": [ "... tside of the coordinate axes. APPENDIX II. OSCILLATING CURRENTS. INTRODUCTION. 308. An electric current varying periodically between constant maximum and minimum values, — that is, in equal time intervals repeating the same values, — is called an alternating current if the arithmetic mean value equals zero ; and is called a pulsating current if the arithmetic mean value differs from zero. Assuming the wave as a sine curve, or replacing it by the equivalent sine wave, the alternating current is charac- terized by th ...", "... e values, — is called an alternating current if the arithmetic mean value equals zero ; and is called a pulsating current if the arithmetic mean value differs from zero. Assuming the wave as a sine curve, or replacing it by the equivalent sine wave, the alternating current is charac- terized by the period or the time of one complete cyclic change, and the amplitude or the maximum value of the current. Period and amplitude are constant in the alter- nating current. A very important class are the currents of constant perio ...", "... instance of the pendu- lum,— in which the amplitude of the vibration decreases in constant proportion. Since the amplitude of the oscillating current varies, constantly decreasing, the oscillating current differs from 497 498 APPENDIX II. the alternating current in so far that it starts at a definite time, and gradually dies out, reaching zero value theoreti- cally at infinite time, practically in a very short time, short even in comparison with the time of one alternating half- wave. Characteristic constants of ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-04", "section_label": "Chapter 5: Single-Phase Induction Motor", "section_title": "Single-Phase Induction Motor", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 8555-10582", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-04/", "snippets": [ "CHAPTER V SINGLE-PHASE INDUCTION MOTOR 60. As more fully discussed in the chapters on the single-phase induction motor, in \" Theoretical Elements of Electrical Engineer- ing\" and \" Theory and Calculation of Alternating-current Phenomena,\" the single-phase induction motor has inherently, no torque at standstill, that is, when used without special device to produce such torque by converting the motor into an unsym- metrical ployphase motor, etc. The magnetic flux at standstill i ...", "... ue ratio and torque efficiency of the single- phase induction motor with starting device, by comparison with the same motor as polyphase motor, by means of the calculation of the voltages, e'y eh e2, etc., and this calculation is simply that of a compound alternating-current circuit, containing the induc- tion motor as an effective impedance. That is, since the only determining factor in the starting torque is the voltage impressed upon the motor, the internal reactions of the motor do not come into consideration, but the mot ...", "... ther words, the consideration of the internal 102 ELECTRICAL APPARATUS reaction of the motor is eliminated by the comparison with the polyphase motor. In calculating the effective impedance of the motor at stand- still, we consider the same as an alternating-current transformer, and use the equivalent circuit of the transformer, as discussed in Chapter XVII of \"Theory and Calculation of Alternating- current Phenomena.\" That is, the induction motor is con- sidered as two impedances, Za and Z(, connected in series to t ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-14", "section_label": "Chapter 16: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 14, "number": 16, "location": "lines 19374-20293", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-14/", "snippets": [ "... tizing effect of eddy currents, because they exist also in machines with laminated fields, and exist if the alternator is brought up to synchronism by external means and the rema- nent magnetism of the field poles destroyed beforehand by application of an alternating current. These phenomena can uol be explained under the assump- tion of a constant synchronous reactance: because in ilu- oast al no-field excitation, the e.m.f. or counter e.m.f. of the machine REACTION MACHINES 2fil let mi mi H MVO, ;md the only ...", "... n ilu- oast al no-field excitation, the e.m.f. or counter e.m.f. of the machine REACTION MACHINES 2fil let mi mi H MVO, ;md the only cm. I', existing in tlic- al tern (it in1 is the e.m.f. of self-induction; that is, the e.m.f. induced by the alternating current upon itself. If, however, the synchronous reactance is constant, (he counter e.m.f. of self-induction is in quadrature with the current and wattless; that is, can neither produce nor consume energy. In the synchronous motor running without field excitati ...", "... f. of self-induction is in quadrature with the current and wattless; that is, can neither produce nor consume energy. In the synchronous motor running without field excitation, always a large lag of the current behind the impressed e.m.f. exists; and an alternating-current generator will yield an e.m.f. without field excitation only when closed by an external circuit of large negative reactance; that is, a circuit in which the current the e.m.f., as a condenser, or an overexcited synchronous iotor, etc. 14S. The usual ex ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-07", "section_label": "Chapter 7: Shaping Of Waves : General", "section_title": "Shaping Of Waves : General", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 12222-12961", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-07/", "snippets": [ "CHAPTER VII SHAPING OF WAVES : GENERAL 69. In alternating-current engineering, the sine wave, as shown in Fig. 46, is usually aimed at as the standard. This is not duo to any inherent merit of the sine wave. For all those pm-poses, where the energy developed by the cur- rent in a resistance is the object, as for incand ...", "... ss by hysteresis in these two secondary loops, which is considerable due to the high mean magnetic density, at which the secondary loop is traversed, so that in spite of the reduced maximum dux density, the hysteresis loss may be increased. Therefore, in alternating-current engineering, the aim gener- 114 ELECTRIC CIRCUITS ally is to produce and use a wave which is a sine wave or nearly so. 60. In an alternating-current generator, synchronous or in- duction machine, commutating machine, etc., the wave of voltage induce ...", "... at in spite of the reduced maximum dux density, the hysteresis loss may be increased. Therefore, in alternating-current engineering, the aim gener- 114 ELECTRIC CIRCUITS ally is to produce and use a wave which is a sine wave or nearly so. 60. In an alternating-current generator, synchronous or in- duction machine, commutating machine, etc., the wave of voltage induced in a single armature conductor or \"face conductor\" equals the wave of field flux distribution around the periphery of the magnet field, modified, however ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-24", "section_label": "Chapter 2: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 24, "number": 2, "location": "lines 1993-2658", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "snippets": [ "... is made that after establishing the circuit a sufficient time has elapsed for the currents and potential differences to reach their final or permanent values, that is, become constant, with continuous current, or constant periodic functions of time, with alternating current. In the first moment, however, after establishing the circuit, the currents and potential differences in the circuit have not yet reached their permanent values, that is, the electrical conditions of the circuit are not yet the normal or permanent ones, b ...", "... ric current problem there- fore includes besides the permanent term, constant or periodic, l /i >c- Gradual or Logarithm o start of current: Oscillatory or 1 S arjthui e start rigonometrio s I**™** [rtartV Fig. 4. Starting of an alternating-current circuit having inductance. a transient term, which disappears after a time depending upon the circuit conditions, from an extremely small fraction of a second to a number of seconds. These transient terms appear in closing the circuit, opening the circ ...", "... existence of two energy-storing constants, as capacity and inductance, which permit a surge of energy from the one to the other, and there- with an overreaching. 17. Transient terms may occur periodically and in rapid suc- cession, as when rectifying an alternating current by synchro- nously reversing the connections of the alternating impressed e.m.f. with the receiver circuit (as can be done mechanically or without moving apparatus by undirectional conductors, as arcs). At every half wave the circuit reversal starts a tra ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "... uit comprising sections of different constants, must be a traveling wave, that is, must be accompanied by power transfer between the sections of the circuit.* A traveling wave, equation (4), would correspond to the case of effective power in a permanent alternating-current circuit, while the stationary wave of the uniform circuit corresponds to the case of reactive power. Since one of the most important applications of the traveling wave is the investigation of the compound circuit, it is desirable * In oscillogram Fig. ...", "... S 'Sc 8 o I o -3 S TRAVELING WAVES. 99 c3 °- 9 2S| o a; a- ffl la O (M S o o « I >^ o \"^ o , to the standard form given in \"Transient Phenomena,\" Section III. 36. Obviously, traveling waves and standing waves may occur simultaneous ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-17", "section_label": "Theory Section 17: Impedance and Admittance", "section_title": "Impedance and Admittance", "kind": "theory-section", "sequence": 17, "number": 17, "location": "lines 6814-7380", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-17/", "snippets": [ "... ADMITTANCE 82. In direct-current circuits the most important law is Ohm's law, e -i or e r ir, or r = -.> where e is the e.m.f. impressed upon resistance r to produce current i therein. Since in alternating-current circuits a current i through a resistance r may produce additional e.m.fs. therein, when apply- a ing Ohm's law, i — - to alternating-current circuits, e is the IMPEDANCE AND ADMITTANCE ' 99 total e.m.f. resulting f ...", "... he e.m.f. impressed upon resistance r to produce current i therein. Since in alternating-current circuits a current i through a resistance r may produce additional e.m.fs. therein, when apply- a ing Ohm's law, i — - to alternating-current circuits, e is the IMPEDANCE AND ADMITTANCE ' 99 total e.m.f. resulting from the impressed e.m.f. and all e.m.fs. produced by the current i in the circuit. Such counter e.m.fs. may be due to inductance, as self-induc- ...", "... ch counter e.m.fs. may be due to inductance, as self-induc- tance, or mutual inductance, to capacity, chemical polarization, etc. The counter e.m.f. of self-induction, or e.m.f. generated by the magnetic field produced by the alternating current i, is repre- sented by a quantity of the same dimensions as resistance, and measured in ohms: reactance x. The e.m.f. consumed by reactance x is in quadrature with the current, that consumed by resistance r in phase with ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-05", "section_label": "Chapter 5: Symbolic Method", "section_title": "Symbolic Method", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2760-3266", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-05/", "snippets": [ "CHAPTER V SYMBOLIC METHOD 25. The graphical method of representing alternating-current phenomena affords the best means for deriving a clear insight into the mutual relation of the different alternating sine waves entering into the problem. For numerical calculation, however, the graphical method is generally not well suited, owing to the ...", "... For the Algebra of Complex Quantities see Appendix I. For a more complete discussion thereof see \" Engineering Mathematics.\" 30. In the vector diagram, the sine wave is represented in intensity as well as phase by one complex quantity, a + jb, 3 34 ALTERNATING-CURRENT PHENOMENA where a is the horizontal and h the vertical component of the wave; the intensity is given by i = Va2 + 62, the phase by tan 6 = — a and a = i cos 6, b = i sin 6] hence the wave, a + jh, can also be expressed by ?'(cos d -\\- j sin ...", "... ce, the sine waves, a + jb and a' + jb', combined give the sine wave, I = {a + a') +j(6 + 6'). It will thus be seen that the combination of sine waves is reduced to the elementary algebra of complex quantities. 31. If / = I + ji' is a sine wave of alternating current, and r is the resistance, the voltage consumed by the resistance is in phase with the current, and equal to the product of the current and resistance. Or rl = ri -\\- jri'. If L is the inductance, and x = 2x/L the inductive react- ance, the e.m.f. prod ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 3267-3618", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-06/", "snippets": [ "... therefore represented by a vector, OIi (Fig. 26), or by 7] = — i — ji'. Or, if the difference of potential from terminal B to terminal A is denoted by the E = e -\\- je', the difference of potential from A to B is El = — e — je'. Hence, in dealing with alternating-current sine waves it is necessary to consider them in their proper direction with regard to the circuit. Especially in more complicated circuits, as inter- linked polyphase systems, careful attention has to be paid to this point. 37. Let, for instance, in Fig. ...", "... ially in more complicated circuits, as inter- linked polyphase systems, careful attention has to be paid to this point. 37. Let, for instance, in Fig. 27, an interlinked three-phase system be represented diagrammatically as consisting of three 39 40 ALTERNATING-CURRENT PHENOMENA voltages, of equal intensity, differing in phase by one-third of a period. Let the voltages in the direction from, the common con- nection, 0, of the three branch circuits to the terminals, Ai, A 2, Az, be represented by Ei, E^, E3. Then the di ...", "... ead of current OTu The same applies to the other two phases, and it thus follows that to produce the voltage triangle, E1E2E3, at the terminals of the consumer's circuit, the voltage triangle, Ei^^Ez^^Ea^^, is required at the generator terminals. 42 ALTERNATING-CURRENT PHENOMENA Repeating the same operation for the internal impedance of the generator, we get E^^E^^^ = /ro, and parallel to OTi, W^^'^ = Ixo, and 90° ahead of OIi, and thus as triangle of (nominal) gen- erated e.m.fs. of the generator, Ei^E2°Ez^. In Fig ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-23", "section_label": "Chapter 23: Synchronizing Alternators", "section_title": "Synchronizing Alternators", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 25135-25681", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-23/", "snippets": [ "CHAPTER XXIII SYNCHRONIZING ALTERNATORS 203. All alternators, when brought to synchronism with each other, operate in parallel more or less satisfactorily. This is due to the reversibility of the alternating-current machine; that is, its ability to operate as synchronous motor. In consequence thereof, if the driving power of one of several parallel-operating generators is withdrawn, this generator will keep revolving in synchronism as a synchronous motor; and the pow ...", "... re so sensitive in this respect that it is difficult to operate them in parallel. The same applies in getting out of step. 207. When running in synchronism, nearly all types of ma- chines will operate satisfactorily; a medium amount of armature 294 ALTERNATING-CURRENT PHENOMENA reaction is preferable, however, such as is given by modern alter- nators— not too high to reduce the synchronizing power too much, nor too low to make the machine unsafe in case of accident, such as falling out of step, etc. If the armature ...", "... - je\\ = (e + iiVi + i'lXi) -f j(iiXi — i'\\r^; E2 = e -{- I2Z2, or 62 + je'2 = (e + ^'2^2 + ^'2a;2) + j(i2X2 — ^''2^2) ; / = /i 4- h, or eg — jeb = (h + 22) - j{i'i + i'2). This gives the equations: ei = e + iiri + i'lXi; 62 = e -\\- 22r2 + ^'2X2; 296 ALTERNATING-CURRENT PHENOMENA e'l = iiXi — i'lVi', e'l = iiXi — i'^Ti; eg = ii + i2\\ eh = i'l + i'2; 62- + €2^ = 02^ or eight equations with nine variables, ei, e'l, e^, e'2, ii, i'\\, ii, i'2, e. Combining these equations by twos, eiri + e'lXi = eri + iiZi^; e2r2 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-04", "section_label": "Chapter 4: Graphic Befrisxintation", "section_title": "Graphic Befrisxintation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2122-2743", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "snippets": [ "... e included. b.) The resultant of all the currents flowing towards a §17] GRAPHIC REPRESENTATION. 23 distributing point, as found by the parallelogram of sine waves, is zero. The energy equation expressed graphically is as follows : The power of an alternating-current circuit is repre- sented in polar coordinates by the product of the current ; /, into the projection of the E.M.F., Ey upon the current, or by the E.M.F., E, into the projection of the current, /, upon the E.M.F., or IE cos (/j^). 17. Suppose, as an ins ...", "... ent, repre- sented by OE^ in the diagram. The self-inductance of the line induces an E.M.F. which is proportional to the current / and reactance -r, and lags a quarter of a period, or 90°, behind the current. To overcome this counter E.M.F. /' 24 ALTERNATING-CURRENT PHENOMENA. [§18 of self-induction, an E.M.F. of the value Ix is required, in phase 90® ahead of the current, hence represented by- vector OEj^. Thus resistance consumes E.M.F. in phase,, and reactance an E.M.F. 90° ahead of the current. The E.M.F. o ...", "... the current, — OEr = OE/ = OE^ = OE^' = OE, = OE/ = E.M.F. consumed by resistance, counter E.M.F. of resistance, E.M.F. consumed by inductance, counter E.M.F. of inductance, E.M.F. consumed by impedance, counter E.M.F. of impedance. 26 ALTERNATING-CURRENT PHENOMENA. [§§19,20 Obviously, these counter E.M.Fs. are different from, for instance, the counter E.M.F. of a synchronous motor, in so far as they have no independent existence, but exist only through, and as long as, the current flows. In this respect ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "section_title": "Dibtbisnted Capacity, Inductance, Besistance, And", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "... longer possible to treat the circuit in the usual manner by the vector diagram. This phenomenon is especially noticeable in long-distance lines, in underground cables, especially concentric cables, and to a certain degree in the high-potential coils of alternating- current transformers. It has the effect that not only the E.M.Fs., but also the currents, at the beginning, end, and different points of the conductor, are different in intensity and in phase. Where the capacity effect of the line is small, it may with sufficie ...", "... 1 + (r -yx) ^^+ y* -i^-ih (r -jx)* 105. ^.) Z««^ capacity represented by three condensers, in the middle and at the ends of the line. Denoting, in Fig. 85, the E.M.F. and current in receiving circuit by E, I, the E.M.F. at middle of line by E', 154 ALTERNATING-CURRENT PHENOMENA, [§ 105 the current on receiving side of line by /', the current on generator side of line^by /\", the RM.P'., viz., current at generator by -fo* />» D iTE ZUI ITi JJT 3t II! Pig. 85. Distributed Capacity. Otherwise retaining the sa ...", "... ting conditions only. These equations, (4) and (5), are of the form : '^=wig-Jb,)(r-jx). (6) and are integrated by w •= at *\"*, where c is the basis of natural logarithms ; for, differen- tiating this, we get, d^w dx- = v^at^ = i^w\\ 160 ALTERNATING-CURRENT PHENOMENA. [§110 hence, v^ = {g -j'^c) ir - Jx) -, or, V = ± ^ {g-'jf^c){^-jx) ; hence, the general integral is : w = / t ' ^ \\ VD / ^ ^ /\\ E.= 26^0. i,'i oj ) s. \\ y ^ ^ \\ / ■^ s / \\\\ 1 ^ / / \\ ^ ^1// ,^ ^/ Ui^ im\"t' \" fin 'y\\ \" \" ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-19", "section_label": "Chapter 19: Commutatob Motobs", "section_title": "Commutatob Motobs", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 21339-22387", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "snippets": [ "... the primary circuit will not exert a rotary effect upon the armature while at rest, since in half of the armature coils the cur- rent is induced so as to give a rotary effort in the one direction, and in the other half the current is induced to 292 ALTERNATING-CURRENT PHENOMENA, [§ 193 give a rotary effort in the opposite direction, as shown by the arrows in Fig. 141. In the induction motor a second magnetic field is used to act upon the currents induced by the first, or inducing magnetic field, and thereby cause a ...", "... ce is shown, in Fig. 145, the power output as ordinates, with the speed k = A\\/ .V as abscissae, of a repulsion motor of the constants, ^0 = 100. r = .1 r, = .05 giving the power, „_ 10.000 {.02 + 1-41 j^-. 05^} (.171 + 2*)-+(3.14-.l*)'- 300 ALTERNATING-CURRENT PHENOMENA. [§ 19» SERIES MOTOR. SHUNT MOTOR. 199. If, in a continuous-current motor, series motor as well as shunt motor, the current is reversed, the direction of rotation remains the same, since field magnetism and armature current have reversed the ...", "... ed, the direction of rotation remains the same, since field magnetism and armature current have reversed their sign, and their prod- fig. 1A6. Series Motor. uct, the torque, thus maintained the same sign. There- fore such a motor, when supplied by an alternating current, will operate also, provided that the reversals in field and in armature take place simultaneously. In the series motor this is necessarily the case, the same current passing through field and through armature. With an alternating current in the field, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-20", "section_label": "Chapter 20: Beactiox Machines", "section_title": "Beactiox Machines", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 22388-23273", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "snippets": [ "CHAPTER XX. BEACTIOX MACHINES. 204. In the chapters on Alternating-Current Genera- tors and on Induction Motors, the assumption has been made that the reactance x of the machine is a constant. While this is more or less approximately thd case in many alternators, in others, especially in machines of large arma- ture reaction, t ...", "... se 206, 206] REACTION MACHINES, 809 they exist also in machines with laminated fields, and exist if the alternator is brought up to synchronism by external means and the remanant magnetism of the field poles de- stroyed beforehand by application of an alternating current. 205. These phenomena cannot be explained under the assumption of a constant synchronous reactance ; because in this case, at no-field excitation, the E.M.F. or counter E.M.F. of the machine is zero, and the only E.M.F. exist- ing in the alternator is t ...", "... n of a constant synchronous reactance ; because in this case, at no-field excitation, the E.M.F. or counter E.M.F. of the machine is zero, and the only E.M.F. exist- ing in the alternator is the E.M.F. of self-induction; that is, the E.M.F. induced by the alternating current upon itself. If, however, the synchronous reactance is constant, the counter E.M.F. of self-induction is in quadrature with the current and wattless; that is, can neither produce nor consume energy. In the synchronous motor running without field excita- ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-21", "section_label": "Chapter 21: Dibtobtiox Of Wavs-Shafe And Its Causes", "section_title": "Dibtobtiox Of Wavs-Shafe And Its Causes", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 23274-24559", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "snippets": [ "CHAPTER XXI. DIBTOBTIOX OF WAVS-SHAFE AND ITS CAUSES. 212. In the preceding chapters we have considered the alternating currents and alternating E.M.Fs. as sine waves or as replaced by their equivalent sine waves. While this is sufficiently exact in most cases, under certain circumstances the deviation of the wave from sine shape becomes of importance, and no longer, and it may n ...", "... ng higher harmonics under load. 3d. Pulsation of the resistance, causing higher harmonics under load also. Taking up the different causes of higher harmonics we have : — Lack of Uniformity and Pulsation of the Magnetic Field, 214. Since most of the alternating-current generators contain definite and sharply defined field poles covering in different types different proportions of the pitch, in general the magnetic flux interlinked with the armature coil will not vary as simply sine wave, of the form : * cos )3, but ...", "... reactance due to synchronous rotation, as dis- cussed in chapter on Reaction Machines. In Figs. 148 and 149, at a sine wave of impressed E.M.F., the distorted current waves have been constructed. Inversely, if a sine wave of current, / = /cos P, 328 ALTERNATING-CURRENT PHENOMENA. [§217 passes through a circuit of synchronously varying reac- tance; as for instance, the armature of a unitooth alterna- tor or synchronous motor — or, more general, an alternator whose armature reluctance is different in different positions ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 2774-3131", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-06/", "snippets": [ "... (Fig. 26), or by 7l = — i —ji'> Or, if the difference of potential from terminal B to terminal A is denoted by the E = e + je' , the difference of potential from A to B is El = — e — je' . 44 ALTERNA TING-CURRENT PHENOMENA. Hence, in dealing with alternating-current sine waves, it is necessary to consider them in their proper direction with regard to the circuit. Especially in more complicated circuits, as interlinked polyphase systems, careful attention has to be paid to this point. -*' Fig. 28. 34. Let, for ...", "... e same induced generator E.M.F. triangle E°E£E°, the E.M.Fs. at the receiver's circuit, Ev Ez, E9 fall off more with lagging, less with leading current, than with non- inductive load. 36. As further instance may be considered the case of a single phase alternating current circuit supplied over a cable containing resistance and distributed capacity. 48 ALTERNATING-CURRENT PHENOMENA. Let in Fig. 33 the potential midway between the two terminals be assumed as zero point 0. The two terminal voltages at the receiver circuit ...", "... off more with lagging, less with leading current, than with non- inductive load. 36. As further instance may be considered the case of a single phase alternating current circuit supplied over a cable containing resistance and distributed capacity. 48 ALTERNATING-CURRENT PHENOMENA. Let in Fig. 33 the potential midway between the two terminals be assumed as zero point 0. The two terminal voltages at the receiver circuit are then represented by the points E and El equidistant from 0 and opposite each other, and the two cu ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-12", "section_label": "Chapter 12: Power, And Double Frequency Quantities In General", "section_title": "Power, And Double Frequency Quantities In General", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 9381-9740", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "snippets": [ "CHAPTER XII. POWER, AND DOUBLE FREQUENCY QUANTITIES IN GENERAL. 102. Graphically alternating currents and E.M.F's are represented by vectors, of which the length represents the intensity, the direction the phase of the alternating wave. The vectors generally issue from the center of co-ordinates. In the topographical method, however, which is more conv ...", "... nce are related by multiplication and division of complex quantities similar as current, E.M.F., resistance, and conductance are related by Ohms law in direct current circuits. In direct current circuits, power is the product of cur- rent into E.M.F. In alternating current circuits, if The product, P0 = EI= (Ml - *\"/\") +j (W POWER, AND DOUBLE FREQUENCY QUANTITIES. 151 is not the power; that is, multiplication and division, which are correct in the inter-relation of current, E.M.F., impe- dance, do not give a correct ...", "... r factor. PJ — = q = sin w = inductance factor of the circuit, and the general expression of power is, = Q (cos co -\\-j sin o>) 104. The introduction of the double frequency vector product P = \\E I~\\ brings us outside of the limits of alge- 154 ALTERNATING-CURRENT PHENOMENA. bra, however, and the commutative principle of algebra, a X b = b X a, does not apply any more, but we have, [El] unlike [IE] since we have [EIJ = [IEJ [EI]J=-[IE]J that is, the imaginary component reverses its sign by the interchan ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-26", "section_label": "Chapter 4: Inductance And Resistance In Alternating Current Circuits", "section_title": "Inductance And Resistance In Alternating Current Circuits", "kind": "chapter", "sequence": 26, "number": 4, "location": "lines 3515-4071", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-26/", "snippets": [ "CHAPTER IV. INDUCTANCE AND RESISTANCE IN ALTERNATING- CURRENT CIRCUITS. • 26. In alternating-current circuits, the inductance L, or, as it is usually employed, the reactance x = 2 nfL, where / = fre- quency, enters the expression of the transient as well as the permanent term. At the moment 0 = 0, let the e.m.f. ...", "CHAPTER IV. INDUCTANCE AND RESISTANCE IN ALTERNATING- CURRENT CIRCUITS. • 26. In alternating-current circuits, the inductance L, or, as it is usually employed, the reactance x = 2 nfL, where / = fre- quency, enters the expression of the transient as well as the permanent term. At the moment 0 = 0, let the e.m.f. e = E cos (0 — 00) be impressed upon a c ...", "... tegral equation becomes E --« i = - cos (0 - 00 - 0X) + As x , (7) where A is still indefinite, and is determined by the initial con- ditions of the circuit, as follows : for 0 = 0, i = 0; hence, substituting in (7), E 0 = -cos (00 + 0J + A, ALTERNATING-CURRENT CIRCUITS 43 or, A -_|cos & + *!), <(8) z and, substituted in (7), i = -z | cos (I? - 00- 0J- i~x° cos (00 + OJ j (9) is the general expression of the current in the circuit. If at the starting moment 0 = 0 the current is not zero but = iw we ha ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 557-1002", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-01/", "snippets": [ "... otor. 6. The study and calculation of the permanent phenomena in electric circuits arc usually far simpler than are the study and calculation of transient phenomena. However, only the phe- nomena of a continuous-current circuit are really permanent. The alternating-current phenomena are transient, as the e.m.f. continuously and periodically changes, and with it the current, the stored energy, etc. The theory of alternating-current phe- nomena, as periodic transients, thus has been more difficult than that of continuous-curr ...", "... omena. However, only the phe- nomena of a continuous-current circuit are really permanent. The alternating-current phenomena are transient, as the e.m.f. continuously and periodically changes, and with it the current, the stored energy, etc. The theory of alternating-current phe- nomena, as periodic transients, thus has been more difficult than that of continuous-current phenomena, until methods were devised to treat the periodic transients of the alternating-current circuit as permanent phenomena, by the conception of the \" ...", "... with it the current, the stored energy, etc. The theory of alternating-current phe- nomena, as periodic transients, thus has been more difficult than that of continuous-current phenomena, until methods were devised to treat the periodic transients of the alternating-current circuit as permanent phenomena, by the conception of the \" effective values,\" and more completely by the introduction of the general number or complex quantity, which represents the periodic func- tion of time by a constant numerical value. In this featur ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 460-882", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "snippets": [ "... otor. 6. The study and calculation of the permanent phenomena in electric circuits are usually far simpler than are the study and calculation of transient phenomena. However, only the phe- nomena of a continuous-current circuit are really permanent. The alternating-current phenomena are transient, as the e.m.f. continuously and periodically changes, and with it the current, the stored energy, etc. The theory of alternating-current phe- nomena, as periodic transients, thus has been more difficult than that of continuous-curr ...", "... omena. However, only the phe- nomena of a continuous-current circuit are really permanent. The alternating-current phenomena are transient, as the e.m.f. continuously and periodically changes, and with it the current, the stored energy, etc. The theory of alternating-current phe- nomena, as periodic transients, thus has been more difficult than that of continuous-current phenomena, until methods were devised to treat the periodic transients of the alternating-current circuit as permanent phenomena, by the conception of the \" ...", "... with it the current, the stored energy, etc. The theory of alternating-current phe- nomena, as periodic transients, thus has been more difficult than that of continuous-current phenomena, until methods were devised to treat the periodic transients of the alternating-current circuit as permanent phenomena, by the conception of the \" effective values,\" and more completely by the introduction of the general number or complex quantity, which represents the periodic func- tion of time by a constant numerical value. In this featur ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-08", "section_label": "Lecture 8: Generation", "section_title": "Generation", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 3781-4217", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-08/", "snippets": [ "... er, this is not feasible, but a higher voltage or even a different form of power (alternating instead of direct) is necessary in the generating station than that re- quired by the user, to enable transmission and distribution; and then usually three-phase alternating current is generated. I. For isolated plants, and in general distribution of such small extent as to be within range of 220 volt distribution, 220 volt direct current generators are used, operating a three- wire system, either two no volt machines, supplying the ...", "... or by compensator and collector rings on the 220 volt generator. That is, two diametrically opposite (electrically) points of the armature winding are connected to collector rings, (so giving an alternaiting current voltage on those col- lector rings), an alternating current compensator (transformer with a single winding) is connected between the collector rings, and the neutral brought out from the center of the compen- sator, as shown diagrammatically in Fig. 24. This arrange- ment is now most commonly used. Fig. 24 Fo ...", "... s have practically disappeared, and have been replaced by converter substations, receiving power from a 6600, 11,000 or 13,200 volts, and usually 25 cycles. 2. For street railway, 600 volt direct current generators main generating station, as three-phase alternating current of are still used to a considerable extent, where the railway system is of moderate extent. In large railway systems, and roads covering greater distances, as interurban trolley lines, io8 GENERAL LECTURES direct generation of 600 volts direct current ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-10", "section_label": "Lecture 10: Regulation And Control", "section_title": "Regulation And Control", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 4595-4930", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-10/", "snippets": [ "... h local circuit, either the trolley circuit is cut between the feeders, or the boosting kept below the critical value. If the distances are too great for boosters, inverted con- verters in the generating station are used to change from direct current to alternating current; the alternating current is sent by step-up and step-down transformers to the substation and changed to direct current by rotary converters. If a considerable amount of power is required at a dis- tance, it is more convenient at the generating station to ...", "... the trolley circuit is cut between the feeders, or the boosting kept below the critical value. If the distances are too great for boosters, inverted con- verters in the generating station are used to change from direct current to alternating current; the alternating current is sent by step-up and step-down transformers to the substation and changed to direct current by rotary converters. If a considerable amount of power is required at a dis- tance, it is more convenient at the generating station to use, instead of inverte ...", "... f power is required at a dis- tance, it is more convenient at the generating station to use, instead of inverted converters, double current generators, that is, generators having commutator and collector rings. If most of the power is used at a distance, alternating current generators are used with rotary converters and fre- quently one converter substation is located in the generating station. Inverted converters and double current generators are now used less, since usually the systems are now so large as to REGULATION ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-13", "section_label": "Lecture 13: Electric Railway: Motor Characteristics", "section_title": "Electric Railway: Motor Characteristics", "kind": "lecture", "sequence": 13, "number": 13, "location": "lines 7124-8648", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-13/", "snippets": [ "... requires as small a power fluctuation as possible. The pull required of the railway motor during accelera- tion, on heavy grades, etc., is, however, many times greater than in free running. In a constant speed motor, as a direct current shunt motor or an alternating current induction motor, the power consumption is approximately proportional to the torque of the motor and thus to the draw bar pull that is given by it. With such motors, the fluctuation of power consump- tion would thus be as great as the fluctuation of pull r ...", "... the motor. At this current io, the speed is highest; with increase of current it drops first very rapidly, and then more slowly; and the higher the saturation of the motor field is, the slower becomes the drop of speed at high currents. The single-phase alternating current motors are either directly or inductively series motors, and so give the same general characteristics as the direct current series motor. In the alternating current motors, however, in addition to the ir drop an ix drop exists ; that is, in addition to th ...", "... motor field is, the slower becomes the drop of speed at high currents. The single-phase alternating current motors are either directly or inductively series motors, and so give the same general characteristics as the direct current series motor. In the alternating current motors, however, in addition to the ir drop an ix drop exists ; that is, in addition to the voltage con- sumed by the resistance, still further voltage is consumed by self-induction; and the voltage e available for the armature rotation thus drops still f ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-15", "section_label": "Lecture 15: Electrochemistry", "section_title": "Electrochemistry", "kind": "lecture", "sequence": 15, "number": 15, "location": "lines 9343-9686", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-15/", "snippets": [ "... d, and with the sodium hydrate from the other side (these form NaCl and ClOsNa, that is, sodium chloride and sodium chlorate. In this way considerable industries have developed, pro- ducing electrolytically caustic soda, bleaching soda, and chlorates. Alternating current is used very little for electrolytic work, as with organic compounds to produce oxidation and reduction at the same time; that is, act on the compound in rapid succession by oxygen and hydrogen, the one during the one, the other during the next half wave ...", "... produce oxidation and reduction at the same time; that is, act on the compound in rapid succession by oxygen and hydrogen, the one during the one, the other during the next half wave of current. Very active metals like manganese and silicon dissolve by alternating current; that is, one-half wave dissolves, but the other does not deposit again. Very inert metals like platinum are deposited by alternat- ing current; that is, the negative half wave deposits by alter- nating current, but the positive half wave does not dissol ...", "... to 100 volts; the graphite furnace takes from 10 to 20 volts. To get very high temperatures a very large amount of energy has to be concentrated in one furnace; and with the moderate voltage used, this requires very large currents, thousands of amperes. Alternating currents are almost exclu- sively used, since it is easier to produce very large alternating currents by transformers, and since it is easier to control alter- nating than direct currents. Electric heat necessarily is very much more expensive than heat produced ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-04", "section_label": "Theory Section 4: Power and Effective Values", "section_title": "Power and Effective Values", "kind": "theory-section", "sequence": 4, "number": 4, "location": "lines 1244-1572", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-04/", "snippets": [ "... 72r. Either EI = E, then, the total power in the circuit is con- sumed by the resistance, or EI < E} then only a part of the power is consumed by the resistance, the remainder by some counter e.m.f., E — EI. If an alternating current i = I0 sin 6 passes through a resist- ance r, the power consumed by the resistance is, i*r = 702r sin2 0 = ^r C1 ~ cos 2 0), & thus varies with twice the frequency of the current, between zero and 70V. The avera ...", "... ~ cos 2 0), & thus varies with twice the frequency of the current, between zero and 70V. The average power consumed by resistance r is, avg. since avg. (cos) = 0. 16 ELEMENTS OF ELECTRICAL ENGINEERING Thus the alternating current i = IQ since 0 consumes in a resist- ance r the same effect as a continuous current of intensity The value / = —7= is called the effective value of the alter- V2 nating current i = IQ sin 0; since it gives the ...", "... n& ; is the effective alternating e.m.f. generated in a coil of turns n rotating at a frequency of / (in hundreds of cycles per second) through a magnetic field of megalines of force. This is the formula of the alternating-current generator. 21. The formula of the direct-current generator, E = holds even if the e.m.fs. generated in the individual turns are not sine waves, since it is the average generated e.m.f. The formula of the alternating-cur ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-113", "section_label": "Apparatus Section 7: Induction Machines: Frequency Converter or General Alternating-current Transformer", "section_title": "Induction Machines: Frequency Converter or General Alternating-current Transformer", "kind": "apparatus-section", "sequence": 113, "number": 7, "location": "lines 21813-21922", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-113/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-113/", "snippets": [ "VH. Frequency Converter or General Alternating-current Transformer 159. The e.m.fs. generated in the secondary of the induction machine are of the frequency of slip, that is, synchronism minus speed, thus of lower frequency than the impressed e.m.f. in the range from standstil ...", "... olts 25 cycles to quarter phase 2500 volts 62.5 cycles. Thus, a frequency converter can be called a \"general alter- nating-current transformer.\" For its theoretical discussion and calculation, see \" Theory and Calculation of Alternating-current Phenomena.\" The action and the equations of the general alternating-current INDUCTION MACHINES 355 transformer are essentially those of the stationary alternating- current transformer, except that the ratio of secondary to p ...", "... converter can be called a \"general alter- nating-current transformer.\" For its theoretical discussion and calculation, see \" Theory and Calculation of Alternating-current Phenomena.\" The action and the equations of the general alternating-current INDUCTION MACHINES 355 transformer are essentially those of the stationary alternating- current transformer, except that the ratio of secondary to primary generated e.m.f . is not the ratio of turns but the ratio of. the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-02", "section_label": "Chapter 2: Instantaneous Values And Integral Values", "section_title": "Instantaneous Values And Integral Values", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 1684-2011", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-02/", "snippets": [ "... and therefore pulsating potential differ- ences across parts of a circuit can, however, be produced from an alternating induced e.m.f. by the use of asymmetrical circuits, as arcs, some electrochemical cells, as the aluminum-carbon cell, etc. Most of the alternating-current rectifiers are based on the use of such asymmetrical circuits. In the following we shall almost exclusively consider the alter- nating wave, that is, the wave whose true arithmetic mean value = 0. Frequently, by mean value of an alternating wave, the a ...", "... only integral value of an alternating wave which is of practical importance, as directly connected with the me- chanical system of units, is that value which represents the same power or effect as the periodical wave. This is called the effective 14 ALTERNATING-CURRENT PHENOMENA value. Its square is equal to the mean square of the periodic function, that is: The effective value of an alternating wave, or the value repre- senting the same effect an the periodically varying wave, is the square root of the mean square. ...", "... ll the prod- ucts which give 0 as mean square, the effective value I = VM(Ai2 ^ A2' -\\- A^^ -{-... -\\- B,' + B2' + 53^.. T The mean value does not give a simple expression, and is of no general interest. INSTANTANEOUS AND INTEGRAL VALUES 15 12. All alternating-current instruments, as ammeter, volt- meter, etc., measure and indicate the effective value. The maxi- mum value and the mean value can be derived from the curve of instantaneous values, as determined by wave-meter or oscillograph. Measurement of the alternati ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-03", "section_label": "Chapter 3: Law Of Electromagnetic Induction", "section_title": "Law Of Electromagnetic Induction", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 2012-2148", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-03/", "snippets": [ "... / = number of complete cycles per second, or the frequency of the flux, $, the average e.m.f. generated in n turns is Eavg. = 4 71$/ 10-« volts. This is the fundamental equation of electrical engineering, and applies to continuous-current, as well as to alternating- current, apparatus. 16 LAW OF ELECTROMAGNETIC INDUCTION 17 14. In continuous-current machines and in many alternators, the turns revolve through a constant magnetic field; in other alternators and in induction motors, the magnetic field revolves; in transfo ...", "... gh a constant magnetic field; in other alternators and in induction motors, the magnetic field revolves; in transformers, the field alternates with respect to the sta- tionary turns; in other apparatus, alternation and rotation occur simultaneously, as in alternating-current commutator motors. Thus, in the continuous-current machine, if n = number of turns in series from brush to brush, $ = flux inclosed per turn, and / = frequency, the e.m.f. generated in the machine is E = 4/i$/10~^ volts, independent of the number of pole ...", "... 'S VOltS. Since the maximum e.m.f. is given by we have ^max. = 2 7rW$/ 10-8 volts. And since the effective e.m.f. is given by Emax. E. eff. — V2 we have Eeff. = V2 wn^f 10-^ = 4.44 nf^ 10-« volts, which is the fundamental formula of alternating-current induc- tion by sine waves. 15. If, in a circuit of n turns, the magnetic flux, , inclosed by the circuit is produced by the current in the circuit, the ratio, flux X number of turns X 10\"^ current ' is called the inductance, L, of the circuit, in ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-07", "section_label": "Chapter 7: Polar Coordinates And Polar Diagrams", "section_title": "Polar Coordinates And Polar Diagrams", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 3619-4087", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-07/", "snippets": [ "... the alternating wave may be repre- sented in intensity and phase by the length and direction of- a vector, OC, Fig. 38, and its analytical expression would then be c = OC cos (0 - 0o). This leads to a second vector representation of alternating 48 ALTERNATING-CURRENT PHENOMENA waves, differing from the crank diagram discussed in Chapter IV. It may be called the time diagram or polar diagram, and is used to a considerable extent in the literature, thus must be familiar to the engineer, though in the following we shal ...", "... e.m.fs. of resistance and of reactance are included. (6) The resultant of all the currents toward a distributing point, as found by the parallelo- gram of sine waves, is zero. The power equation expressed graphically is as follows: The power of an alternating- current circuit is represented in polar coordinates by the product of the current, I, into the projec- tion of the e.m.f., E, upon the current, or by the e.m.f., E, into the projection of the current, /, upon the e.m.f., or by IE cos d, where 9 = angle of time- ...", "... Figs. 41, 42, 43, 44, 45. These figures are the reverse, or mirror image of each other. That is, the crank diagrams, turned around the horizontal (or any other axis) , so as they would be seen in a mirror, are the time diagrams, and inversely. 4 50 ALTERNATING-CURRENT PHENOMENA The polar diagram, Fig. 46, of a current: i = I cos' (?9 - 0) represented by vector 01, E^-^ Fig. 43. Fig. 45. lagging behind the voltage: e = £' cos (?? — a) represented by vector OE, by angle e^ = ^ - a then means: Fig. 4 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-08", "section_label": "Chapter 8: Admittance, Conductance, Susceptance", "section_title": "Admittance, Conductance, Susceptance", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 4088-4673", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-08/", "snippets": [ "... ies-connected resistances is equal to the sum of the individual resistances; the joint conduct- ance of a number of parallel-connected conductances is equal to the sum of the individual conductances. 64 ADMITTANCE, CONDUCTANCE, SUSCEPTANCE 55 49. In alternating-current circuits, instead of the term resist- ance we have the term impedance, Z = r -\\- jx, with its two components, the resistance, r, and the reactance, x, in the formula of Ohm's law, E = IZ. The resistance, r, gives the component of e.m.f. in phase with the ...", "... represents the coefficient of current in quadrature with the e.m.f., or wattless or reactive component, hE, of the current. g is called the conductance, and h the susceptance, of the cir- cuit. Hence the conductance, g, is the power component, and 56 ALTERNATING-CURRENT PHENOMENA the susceptance, h, the wattless component, of the admittance, Y = g ~ jb, while the numerical value of admittance is y = Vg' + h^; the resistance, r, is the power component, and the reactance, X, the wattless component, of the impedance, Z ...", "... susceptance, h, are shown as functions of the varying resistance, r. As shown, the absolute value of admittance, susceptance, and conductance are plotted in full Unes, and in dotted line the absolute value of impedance, / 1 z = \\/r2 + x2 = -• y 58 ALTERNATING-CURRENT PHENOMENA Obviously, if the resistance, r, is constant, and the reactance,* X, is varied, the values of conductance and susceptance are merely exchanged, the conductance decreasing steadily from ^ = - to 0, and the susceptance passing from 0 at x = 0 t ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-19", "section_label": "Chapter 19: Induction Generators", "section_title": "Induction Generators", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 20446-21537", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-19/", "snippets": [ "... on generator, however, can operate only if the phase relation of current and e.m.f., that is, the power-factor required by the external circuit, exactly coincides with the internal power-factor of the induction generator. This requires that 237 238 ALTERNATING-CURRENT PHENOMENA the power-factor either of the external circuit or of the induction generator varies with the voltage, so as to permit the generator and the external circuit to adjust themselves to equality of power-factor. Beyond magnetic saturation the po ...", "... ency generated by machine. We then have the secondary generated e.m.f., se: thus, the secondary current. li = Z — r^^ = e{ai - ja2), where, , S'Xi ai = —^—, — ^ — ^ and 02 = the primary exciting current, ioo = EY^ = e {go - j6o), 240 ALTERNATING-CURRENT PHENOMENA thus, the total primary current, /o = /] + /oo ^ e{bi - J62), where, &]=«! + go and 62= 02 + i>o; the primary impedance voltage, E' = /o(ro+j[l - s]xo); the primary generated e.m.f. is, e(l - s). Thus, primary terminal voltage, ^0 ...", "... . P^ _ hiCx + &2C2 the power-factor, cos t* = &1C1 + 62C2 or. /V ^ 62C1 — &1C2 Po^ ~ &1C1 -f- 62C2 In Fig. 126 is plotted the load characteristic of a constant- speed induction generator, at constant terminal voltage eo = HO, 16 242 ALTERNATING-CURRENT PHENOMENA and the constants: Yq - 0.01 - 0.1 i; Zq = 0.1 + 0.3 j, and Zi = 0.1 + 0.3i. 176. As an example may be considered a power transmission from an induction generator of constants Yq, Zq, Zi, over a line of impedance, Z = r + jx, into a synchrono ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-26", "section_label": "Chapter 26: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 32540-33010", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-26/", "snippets": [ "... The quintuple harmonic causes a flat-topped or even double- peaked wave with flat zero. With increasing phase displacement the wave becomes of the type called saw-tooth wave also. The flat zero rises and becomes a third peak, while of the two former 372 ALTERNATING-CURRENT PHENOMENA peaks, one rises, the otlier decreases, and the wave gradually changes to a triple-peaked wave with one main peak, and a sharp zero. As seen, with the triple harmonic, flat top or double peak coincides with sharp zero, while the quintuple har ...", "... he resistance of the circuit from generator terminals to condenser is Ir = OmE, or, ■pi r = 0.06 J-- The reactance e.m.f. between generator terminals and con- denser is, for the fundamental frequency, Ix = 0.15E, or, jP X = 0.15 J-; 374 ALTERNATING-CURRENT PHENOMENA thus the reactance corresponding to the frequency {2 k — 1)/ of the higher harmonic is x{2k- 1) = 0.15 (2 fc- 1) J- The capacity current at fundamental frequency is, i = 0.2 /; hence, at the frequency {2 k — 1)/, i = 0.2 (2 k - 1) e' ^ ...", "... ltaneously interlink with the magnetic flux, . The e.m.f. per armature circuit is e = \\/2 7r/n«J>10-8; hence the e.m.f. between collector rings, as resultant of two e.m.fs., e, displaced by 60° from each other, is E = e\\/3 = V2 7r/V3n$10-^ 376 ALTERNATING-CURRENT PHENOMENA while the same e.m.f. was found from the number of turns, the magnetic flux, and the frequency by direct calculation to be equal to 2 e; that is, the two values found for the same e.m.f. have the proportion ■\\/3:2 = 1 ; 1.154. This discrepanc ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-29", "section_label": "Chapter 29: Symmetrical Polyphase Systems", "section_title": "Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 29, "number": 29, "location": "lines 34929-35255", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-29/", "snippets": [ "... TT . ..... — , IS represented by multiplication with 27r , . . 27r COS h 7 sin — = e, n 71 the e.m.fs. of the symmetrical polyphase system are E; 27r . . . 2 ( 27r , . . 27r\\ (cos \\- J sin — = Eel \\ n n I ' E •■ \\ 11 ' \" 399 400 ALTERNATING-CURRENT PHENOMENA E ( cos — + j sin — ) = Ee'-, ^ I 2 (t? - 1) TT , . . 2 (n - 1) 7r\\ ^ n-\\ E { cos --^ ~ + J sm -^ —-) - E^-^. The next e.m.f . is again, ^(cos 2 X + i sin 2 x) = J^e\" = E. Hence, it is 2 TT , . . 2 TT „ /— e = cos — + 7 sin — = V 1 • ...", "... . The four e.m.fs. of the four-phase system are, e^E = E, jE, -E, -jE. They are in pairs opposite to each other, E and — E; jE and — jE. H^nce can be produced by two coils in quadrature with each other, analogous as the two-phase system, or ordinary alternating current system, can be produced by one coil. Thus the symmetrical quarter-phase system is a four-phase system. Higher systems than the quarter-phase or four-phase system have not been very extensively used, and are thus of less practical interest. A symmetrica ...", "... e.m.f. 7 = effective value of current. Hence, F = n'l = effective m.m.f. of one of the magnetizing coils. Then the instantaneous value of the m.m.f. of the coil acting in the direction, , is n f. = FV2sin (^-^■) = n'l \\/2 sin (& ^) * 26 402 ALTERNATING-CURRENT PHENOMENA The two rectangular space components of this m.m.f. are /T r- Zirl . [^ ZTn\\ = n L \\/2 COS sin 1/3 I n \\ n / and ft, f ■ 2 7ri h = }i Sin — - ,^^.27rt. /^ 2ti\\ = n i v2 sm sin \\B ) • n \\ n I Hence the m.m.f. of this coil can b ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-32", "section_label": "Chapter 32: Transformation Of Polyphase Systems", "section_title": "Transformation Of Polyphase Systems", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 36062-36514", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-32/", "snippets": [ "... uarter-phase system, E' sin /3, E' sin (/3 - 90). Let the magnetic flux of the two transformers be chosen in quad- rature $ cos iS and $ cos (/S — 90). Then the e.m.fs. generated per turn in the transformers are e sin /3 and e sin (/3 — 90) ; 424 ALTERNATING-CURRENT PHENOMENA hence, in the primary circuit the first phase, E sin /3, will give, in E the first transformer, — primary turns ; m the second transformer, 0 primary turns. The second phase, E sin (j3 — 120), will give, in the first trans- former, -^ — p ...", "... stant voltage at unequal distribution of load, that is, becomes inoperative. In high-potential systems in this case excessive voltages may be induced by resonance with the line capacity. For instance, if only one phase of the secondary triangle is 426 ALTERNATING-CURRENT PHENOMENA loaded, the other two unloaded, the primary current of the loaded phase must return over the other two transformers, which, at open secondaries, act as very high reactances, thus limiting the current and consuming practically all the voltage, a ...", "... , but is dangerous in high potential circuits, being liable to produce destructive voltages by its electrostatic un- balancing. 5. The main and teaser, or T connection of transformers be- tween three-phase systems, is shown in Fig. 212. One of the 428 ALTERNATING-CURRENT PHENOMENA two transformers is wound for V3 2 times the voltage of the other (the altitude of the equilateral triangle), and connected with one of its ends to the center of the other transformer. From the point one-third inside of the teaser trans ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-35", "section_label": "Chapter 35: Balanced Symmetrical Polyphase Systems", "section_title": "Balanced Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 35, "number": 35, "location": "lines 37453-37957", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-35/", "snippets": [ "... les, 80,000 volts and 90 per cent, power-factor at 100 miles from the generating station, with approximately 10 per cent, loss of power in the transmission line, and with the line conductors arranged in a triangle 6 ft. distant from each other. 29 450 ALTERNATING-CURRENT PHENOMENA 10,000 kw. total power delivered gives 3,333 kw. per line or single-phase branch (F power). 3,333 kw. at 90 per cent, power-factor gives 3,700 kv.-amp. 80,000 volts between the lines gives 80,000 -^ \\^ = 46,100 volts from line to neutral, or ...", "... re 43.6 per cent, induc- tance factor, the current is represented by 7 = 80 (0.9 - 0.436 j) =72-35 j. ^ Or. ii fi = permeability, k = dielectric constant of the medium sur- rounding the conductor, it is hence, V [^ I = \\W or. C = (4) 452 ALTERNATING-CURRENT PHENOMENA This gives: Voltage at receiver circuit, e = 46,100 volts; current in receiver circuit, Z = 72 — 35 j amp. ; impedance voltage of half the line, ZI = 3410 + 2260 j volts. Hence, the condenser voltage, Ei = e -\\- ZI = 49,510 + 2260 j volts ...", "... e system, 1 = 5 ' 6 n and for a quarter-phase system, with two coils in quadrature, n V2 In the investigation of the armature reaction of synchronous machines. Chapter XXII, the armature reaction of an 7«-phase machine is, by §271, Worn/ . 454 ALTERNATING-CURRENT PHENOMENA where m = number of phases, no = number of turns per phase, effective, that is, allow- ing for the spread of turns over an arc of the periph- ery in machines of distributed winding, I = current per phase, and when, in Chapter XX, the arm ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... rtheless the system becomes unbalanced, and the two e.m.fs. at the end of the hne are neither equal in magnitude, nor in quadrature with each other. B. One Branch Loaded, One Unloaded Zi = Z2 = Z, Z -^• (a) Fi = 0, F2 = F, {b) Fi = Y, Y, = 0. 464 ALTERNATING-CURRENT PHENOMENA Substituting these values in (4), gives: (a) (b) 1 + YZ E\\ = E 1 + V2 - i V2 i + rz^ + ^\"2 V2 = ^ 1 = ^ I 1 1 + V2 + V2 YZ 2.414 + 1.414 E'2 = jE 1 1 + YZ = jE 1 + \\/2 V~2 1 E\\ = E 1 + ...", "... all values of subtrahend and minuend. From the definition of addition as multiple numeration, and subtraction as its inverse operation, it follows: c - (- 6) = c + 6, thus: (- 1) X (- 1) = 1; that is, the negative unit is defined by (— 1)^ = 1. 468 ALTERNATING-CURRENT PHENOMENA 315. The reverse operation of multiplication introduces the operation of division. If a y. h = c, it is c ^ = a. In the system of integral numbers this operation can only be carried out if 6 is a factor of c. To make it possible to ...", "... gers or fractions, positive or negative, rational or irrational. Any attempt to extend the system of numbers beyond the complex quantity, leads to numbers, in which the factors of a product are not interchangeable, in which one factor of a product 470 ALTERNATING-CURRENT PHENOMENA may be zero without the product being zero, etc., and which thus cannot be treated by the usual methods of algebra, that is, are extra-algebraic numbers. Such for instance are the double fre- quency vector products of Chapter XV. Algebraic Op ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-05", "section_label": "Chapter 5: Symbouc Mbthod", "section_title": "Symbouc Mbthod", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2744-3229", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "snippets": [ "CHAPTER V. SYMBOUC MBTHOD. 23. The graphical method of representing alternating- current phenomena by polar coordinates of time affords the best means for deriving a clear insight into the mutual rela- tion of the different alternating sine waves entering into the problem. For numerical calculation, however, the graphical method is frequently ...", "... is shown in Fig. 21. Obvi* ously, no exact numerical values can be taken from a par- allelogram as flat as OF^FF^,, and from the combination of vectors of the relative magnitudes 1 : 6 :100. Hence the importance of the graphical method consists 84 ALTERNATING-CURRENT PHENOMENA. [§§24,25 not SO much in its usefulness for practical calculation, as to aid in the simple understanding of the phenomena involved. 24. Sometimes we can calculate the numerical values trigonometrically by means of the diagram. Usually, how- ...", "... For instance, the sine waves, — a +jb and combined give the sine wave — I^{a + a')+j{b + b'). It will thus be seen that the combination of sine waves is reduced to the elementary algebra of complex quantities. 29. If /= / +ji' is a sine wave of alternating current, and r is the resistance, the E.M.F. consumed by the re- sistance is in phase with the current, and equal to the prod- uct of the current and resistance. Or — r/= ri '\\' jri\\ If L is the inductance, and j: = 2 tt NL the reactance, the E.M.F. produced ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-28", "section_label": "Chapter 28: Copper Efficiency Of Systems", "section_title": "Copper Efficiency Of Systems", "kind": "chapter", "sequence": 28, "number": 28, "location": "lines 26584-27052", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-28/", "snippets": [ "... tween any pair of wires connected to the receiving apparatus. 260. 1st. Comparison on the basis of equality of the minimum difference of potential^ in low potential lighting circuits : 382 AL TEKXA TING-CURRENT PHENOMENA. [ § 260 In the single-phase alternating-current circuit, if ^ = E.M.F., /= current, r= resistance per line, the total power is = ciy the loss of power 2/^^. Using, however, a three-wire system, the potential be- tween outside wires and neutral being given = ^, the potential between the outside wires ...", "... in distribution for lighting — that is, with the same minimum potential, and with the same number of wires — the single-phase system is superior to any polyphase system. The continuous-current system is equivalent in this comparison to the single-phase alternating-current system of the same effective potential, since the comparison is made on the basis of effective potential, and the power depends upon the effective potential also. 386 AL TERNA TING-CURRENT PHENOMENA. [§261 261. Comparison on the Basis of Equality of t ...", "... tem, and thus makes the action of the continuous-current potential on the insulation more severe than that of an equal alternating potential. Besides, at the voltages which came under consideration, the continuous current is excluded to begin with. 388 ALTERNATING-CURRENT PHENOMENA, [§262 Thus we get : If a given power is to be transmitted at a given loss, and a given maximum difference of potential in the system, that is, with the same strain on the insulation, the amount of copper required is : 2 Wires : Single-phas ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-05", "section_label": "Chapter 5: Symbolic Method", "section_title": "Symbolic Method", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2322-2773", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-05/", "snippets": [ "... g index. For a more exact definition of this complex imaginary quantity, reference may be made to the text books of mathematics. 28. In the polar diagram of time, the sine wave is represented in intensity as well as phase by one complex quantity — 38 ALTERNATING-CURRENT PHENOMENA. where a is the horizontal and b the vertical component of the wave ; the intensity is given by — the phase by — tan -\\-j sin <3), ...", "... expressions. For instance, the sine waves, — a +jb and combined give the sine wave — 7- (a + It will thus be seen that the combination of sine waves is reduced to the elementary algebra of complex quantities. 29. If /= i +/z' is a sine wave of alternating current, and r is the resistance, the E.M.F. consumed by the re- sistance is in phase with the current, and equal to the prod- uct of the current and resistance. Or — rl ' — ri -\\- jri' . If L is the inductance, and x = 2 TT NL the reactance, the E.M.F. produc ...", "... nominator by (r+jx) to eliminate the imaginary from the denominator, we have — T _ or, if E = e -\\-je' is the impressed E.M.F., and 7 = i ' -\\- ji' the current flowing in the circuit, its impedance is — 0 +./>') O'-./*'') «'+^*'' . ' ~ ei' ' 40 ALTERNATING-CURRENT PHENOMENA. 30. If C is the capacity of a condenser in series in a circuit of current I = i + //', the E.M.F. impressed upon the terminals of the condenser is E = - - , 90° behind the current ; and may be represented by — - - , or jx^ /, where x^ = - i ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-18", "section_label": "Chapter 18: Synchronizing Alternators", "section_title": "Synchronizing Alternators", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17597-18052", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-18/", "snippets": [ "CHAPTER XVIII. SYNCHRONIZING ALTERNATORS. 189. All alternators, when brought to synchronism with each other, will operate in parallel more or less satisfactorily. This is due to the reversibility of the alternating-current machine ; that is, its ability to operate as synchronous motor. In consequence thereof, if the driving power of one of sev- eral parallel-operating generators is withdrawn, this gene- rator will keep revolving in synchronism as a synchronous motor ; and ...", "... of by phase adjustment of the machines. Thus rigid mechanical connection is not desirable for parallel operation of alternators. 191. The second important condition of parallel opera- tion is uniformity of speed ; that is, constancy of frequency. 312 ALTERNATING-CURRENT PHENOMENA. If, for instance, two alternators are driven by independent single-cylinder engines, and the cranks of the engines hap- pen to be crossed, the one engine will pull, while the other is near the dead-point, and conversely. Consequently, alter- ...", "... nternal impedance, and K2 =gz ~\\~ jb10-8. since 2« armature turns simultaneously interlink with the magnetic flux 3>. The E.M.F. per armature circuit is : hence the E.M.F. between collector rings, as resultant of two E.M.Fs. e displaced by 60° from each other, is : 406 ALTERNATING-CURRENT PHENOMENA. while the same E.M.F. was found by direct calculation from number of turns, magnetic flux, and frequency to be equal to 2e; that is the two values found for the same E.M.F. have the proportion V3 : 2 = 1 : 1.154. Fig. 178. Three-phase Star- ...", "... magnetism do not increase the maximum value of magnetism, or even lower it by a coincidence of their negative maxima with the positive maximum of the fundamental, — in this case all the power represented by these higher harmonics of E.M.F. will be 408 ALTERNATING-CURRENT PHENOMENA. transformed without an increase of the hysteretic loss, or even with a decreased hysteretic loss. Obviously, if the maximum of the higher harmonic wave of magnetism coincides with the maximum of the funda- mental, and thereby makes the wave ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-26", "section_label": "Chapter 26: Symmetrical Polyphase Systems", "section_title": "Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 23781-24053", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-26/", "snippets": [ "... n/T 2 7T . . 2 7T where, e = vl = cos -- \\-j sin — • . n n 1.) « = 1 e = 1 c«'^ = .£, the ordinary single-phase system. 2.) « = 2 e = - 1 J £ = £ and - £. Since — ^ is the return of E, n = 2 gives again the single-phase system. 3 -1-/V3 436 ALTERNATING-CURRENT PHENOMENA. The three E.M.Fs. of the three-phase system are : -i-yV3 Consequently the three-phase system is the lowest sym- metrical polyphase system. 4.) n = 4, c = cos — +/ sin — =/, £2 = — 1, e3 = - /. 4 4 The four E.M.Fs. of the four-phase sy ...", "... The four E.M.Fs. of the four-phase system are: *£ = £, J£, -E, -JE. They are in pairs opposite to each other : E and — E • j E and —JE. Hence can be produced by two coils in quadrature with each other, analogous as the two-phase system, or ordinary alternating-current system, can be produced by one coil. Thus the symmetrical quarter-phase system is a four- phase system. Higher systems, than the quarter-phase or four-phase system, have not been very extensively used, and are thus of less practical interest. A symmetr ...", "... pace components of this M.M.F. are ; and Hence the M.M.F. of this coil can be expressed by the symbolic formula : fi n \\ n Thus the total or resultant M.M.F. of the n coils dis- placed under the n equal angles is : or, expanded : n 438 ALTERNATING-CURRENT PHENOMENA. It is, however : cos'2 — + / sin — cos — = £ ( 1 + cos — +/ sin —] n n n V w w / \\ / sin 2=1 cos ?Z£+ysin«2=£= ^Yl - cos i^'-ysin4^' « » • « z y « « _ ^ /I _ ,2A X 2(1-^ and, since: 5t<2< = 0, it is, /= nn'f^ (-sin ft _ y co ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-28", "section_label": "Chapter 28: Interlinked Polyphase Systems", "section_title": "Interlinked Polyphase Systems", "kind": "chapter", "sequence": 28, "number": 28, "location": "lines 24489-24804", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-28/", "snippets": [ "... is called the delta connection, from the similarity of its diagrammatic representation with the Greek letter Delta, as shown in Fig. 182. In consequence hereof we distinguish between star- connected and ring-connected generators, motors, etc., or 454 ALTERNATING-CURRENT PHENOMENA. Fig. 198. in three-phase systems Y- connected and delta-connected apparatus. 279. Obviously, the polyphase system as a whole does not differ, whether star connection or ring connection is used in the generators or other apparatus ; and t ...", "... circuits, the E.M.F. per circuit = E, and the common connection or neutral point is denoted by zero, the potentials of the n terminals are : or in general : t* JS, at the z'th terminal, where : * = 0, 1, 2 ....»- 1, e = cos — +j sin — = -\\/l. 456 ALTERNATING-CURRENT PHENOMENA. Hence the E.M.F. in the circuit from the zth to the £* terminal is : Eki = ** E — ^E = (c* — e') E. The E.M.F. between adjacent terminals i and i + 1 is : (e.+i -J)E = e* (e - 1) E. In a generator with ring-connected circuits, the E.M.F. ...", "... om the terminal i of the gen- erator, or the star current. Zt = the impedance of the line connected to a terminal i of the generator, including generator impedance. EL = the E.M.F. at the end of line connected to a ter- minal i of the generator. 458 ALTERNATING-CURRENT PHENOMENA. Eik = the difference of potential between the ends of the lines i and k. Iik = the current passing from line i to line k. Zik = the impedance of the circuit between lines i and k. Iio, Iioo . . . . = the current passing from line i to neu- ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-12", "section_label": "Chapter 14: Phase Conversion And Single-Phase Generation", "section_title": "Phase Conversion And Single-Phase Generation", "kind": "chapter", "sequence": 12, "number": 14, "location": "lines 17125-18412", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-12/", "snippets": [ "... ditions. 126. Phase conversion is of industrial importance in changing from single-phase to polyphase, and in changing from polyphase to single-phase. Conversion from single-phase to polyphase has been of con- siderable importance in former times, when alternating-current generating systems were single-phase, and alternating-current motors required polyphase for their operation. With the prac- tically universal introduction of three-phase electric power leration, polyphase supply is practically always available for ition ...", "... changing from single-phase to polyphase, and in changing from polyphase to single-phase. Conversion from single-phase to polyphase has been of con- siderable importance in former times, when alternating-current generating systems were single-phase, and alternating-current motors required polyphase for their operation. With the prac- tically universal introduction of three-phase electric power leration, polyphase supply is practically always available for itionary electric motors, at least motors of larger size, and n ve ...", "... , con- nected aiTuss the single-phase mains, .4 ami li. The common connection, C, between the two impedances, Z, and Z>. then is dis- placed in phase from the single-phase supply voltage. A and B, and gives with the same a system of out-of-phase voltages, AC, Cli and .4 if, or a — more or less unsymmetrical — three-phase Iriaiude. Or, between this common connection, C, and the middle, D, of an autotransformer connected between the single- phase mains, AB, a quadrature voltage, CD, is produced. This ■monocyc ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-15", "section_label": "Chapter 17: Inductor Machines", "section_title": "Inductor Machines", "kind": "chapter", "sequence": 15, "number": 17, "location": "lines 20294-20974", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-15/", "snippets": [ "... receiving power by direct-current supply, as direct-current motor, and producing high-frequency alternating power in the inductor pole-face winding. 161. If the inductor alternator, Fig. 139, instead of with direct current, is excited with low-frequency alternating current, that *t :o. 140. — Voltage wiive of inductor niter nth -jitiB.il- [ill.- , an alternating current, passed through the field coil, F, of a requency low compared with that generated by the machine as inductor alternator, then the high-frequency c ...", "... ower in the inductor pole-face winding. 161. If the inductor alternator, Fig. 139, instead of with direct current, is excited with low-frequency alternating current, that *t :o. 140. — Voltage wiive of inductor niter nth -jitiB.il- [ill.- , an alternating current, passed through the field coil, F, of a requency low compared with that generated by the machine as inductor alternator, then the high-frequency current generated .• the machine as inductor alternator is not of constant ampli- tude, but of a periodically ...", "... uld then give a voltage and current, pulsating 282 ELECTRICAL APPARATUS with the frequency of the exciting current, but of a power, as many times greater, as the machine output is greater than the exciting power. Thus such an inductor alternator with alternating-current excitation can be used as amplifier. This obviously applies equally much to the other types, as shown in Figs. 13(i. 137 and 138. Suppose now the exciting current is a telephone or micro- phone current, the rectified generated current then pulsates with ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-22", "section_label": "Chapter 24: Conclusion", "section_title": "Conclusion", "kind": "chapter", "sequence": 22, "number": 24, "location": "lines 32820-33531", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-22/", "snippets": [ "... utating pole became of material advantage in reducing size and cost of apparatus, and its general introduction followed. Similarly we have seen the three-phase transformer find gen- eral introduction, after it had been unused for many years; so also the alternating-current commutator motor, etc. Thus for a progressive engineer, it is dangerous not to be fjuuil- iar with the characteristics ^iiit! possibilities of the known but 472 CONCLUSION 473 unused types of apparatus, since at any time circumstances may arise wh ...", "... movable with regards to each other, and of which one may be called the primary cir- cuit, the other the secondary circuit. The magnetic field of the induction machine inherently must be an alternating field (usually a polyphase rotating field) excited by alternating currents. Synchronous machines are machines in which the frequency of rotation has a fixed and rigid relation to the frequency of the supply voltage. Usually the frequency of rotation is the same as the frequency of the. supply voltage: in the standard synchron ...", "... a definite percentage thereof; so also it is in the induction machine concatenated to a synchronous machine, etc. Commutating machines are machines having a distributed armature winding connected to a segmental commutator. They may be direct-current or alternating-current machines. Unipolar machines are machines in which the induction is produced by the constant rotation of the conductor through a constant and continuous magnetic field. 476 ELECTRICAL APPARATUS The list of machine types and their definitions, given in ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-04", "section_label": "Chapter 4: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 6942-9061", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-04/", "snippets": [ "... are in the Ballistic galvanometer method the magnetic creepage at lower B, and at higher B the sharp-pointed shape of the hysteresis loop, which makes the area between rising and decreasing characteristic difficult to determine. In the wattmeter method by alternating current, varying constant errors are the losses in the instruments, the eddy-current losses which change with the changing flux dis- tribution by magnetic screening in the iron, with the temperature, etc., by wave-shape distortion, the unequality of the inner and ...", "... f the inner and outer length of the magnetic circuit, etc. 46. Symmetrical magnetic cycles, that is, cycles performed be- tween equal but opposite magnetic flux densities, +B and — B, are industrially the most important, as they occur in practically all alternating-current apparatus. Unsymmetrical cycles, that is, cycles between two different values of magnetic flux density, Bi and B2, which may be of different, or may be of the same sign, are of lesser industrial importance, and therefore have been little investigated unti ...", "... se, but pulsates between a high and a low value in the same direction, and the hysteresis loss thus is that of an unsymmetrical non-reversing cycle. Unsymmetrical cycles occur in transformers and reactors by the superposition of a direct current upon the alternating current, as discussed in the chapter \"Shaping of Waves,'' or by the equiva- lent thereof, such as the suppression of one-half wave of the alter- nating current. Thus, in the transformers and reactors of many types of rectifiers, as the mercury-arc rectifier, the ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-23", "section_label": "Chapter 1: The Constants Of The Electric Circuit", "section_title": "The Constants Of The Electric Circuit", "kind": "chapter", "sequence": 23, "number": 1, "location": "lines 1317-1992", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "snippets": [ "... eases by the amount consumed in the conductor, and a power gradi- ent exists in the circuit along or parallel with the conductor. (Thus, while the voltage may decrease from generator to receiver circuit, as is usually the case, or may increase, as in an alternating-current circuit with leading current, and while the current may remain constant throughout the circuit, or decrease, as in a transmission line of considerable capacity with a leading or non-inductive receiver circuit, the flow of energy always decreases from gene ...", "... the conductor and delivered at the receiving end; again, the flow of electric energy cannot be stopped instantly, but first the energy stored in the electric field has to be expended. As result hereof, where the flow of electric energy pulsates, as in an alternating- current circuit, continuously electric energy is stored in the field during a rise of the power, and returned to the circuit again during a decrease of the power. The electric field of the conductor exerts magnetic and elec- trostatic actions. The magnetic act ...", "... he different parts of the electrostatic circuit are different, and the capacity therefore has to be calculated piecemeal, or by integration. The dielectric constant K of different materials varies over a relative narrow range only. It is approximately: AC = 1 in the vacuum, in air and in other gases, K = 2 to 3 in oils, paraffins, fiber, etc., K = 3 to 4 in rubber and gutta-percha, K = 3 to 5 in glass, mica, etc., reaching values as high as 7 to 8 in organic compounds of heavy metals, as lead stearate, an ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-41", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 41, "number": 1, "location": "lines 19260-19338", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "snippets": [ "... the electric quantities at another point in space, as, for instance, current and potential difference at the generator end of a transmission line with those at the receiving end of the line, or current density at the surface of a solid conductor carrying alternating current, as the rail return of a single-phase railway, with the current density at the center or in general inside of the conductor, or the distribution of alternating magnetism inside of a solid iron, as a lamina of an alternating-current transformer, etc. In su ...", "... olid conductor carrying alternating current, as the rail return of a single-phase railway, with the current density at the center or in general inside of the conductor, or the distribution of alternating magnetism inside of a solid iron, as a lamina of an alternating-current transformer, etc. In such transient phenom- ena in space, the electric quantities, which appear as functions of space or distance, are not the instantaneous values, as in the preceding chapters, but are alternating currents, e.m.fs., etc., characterized b ...", "... a solid iron, as a lamina of an alternating-current transformer, etc. In such transient phenom- ena in space, the electric quantities, which appear as functions of space or distance, are not the instantaneous values, as in the preceding chapters, but are alternating currents, e.m.fs., etc., characterized by intensity and phase, that is, they are periodic functions of time, and the analytical method of dealing with such phenomena therefore introduces two independent variables, time t and distance I, that is, the electric quant ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... the line and back, the effects of successive impulses add themselves, and large currents and high e.m.fs. may be produced by small impulses, that is, low impressed alternating e.m.fs., or inversely, when once started, even with zero impressed e.m.f., such alternating currents traverse the lines for some time, gradually decreasing in intensity by the energy consumption in the conductor, and so fading out. The condition of this phenomenon of electrical resonance thus is that alternating impulses occur at time intervals equal t ...", "... the two ends of the line, the former of four times the capacity of either of the two latter (the first approximation giving linear, the second a para- bolic distribution). For further investigation of these approximations see \"Theory and Calculation of Alternating-Current Phenomena/' 4th edition, pages 225 to 233. If, however, the wave of impressed e.m.f. contains appreciable higher harmonics, some of the latter, may approach resonance frequency and thus cause trouble. For instance, with a line of 150 miles length, the r ...", "... and in phase with the e.m.f. of the line. This current represents consumption of power, and is therefore analogous to the e.m.f. consumed by resistance, while the condenser current and the e.m.f. of inductance are wattless or reactive. Furthermore, the alternating current passing over the line pro- duces in all neighboring conductors secondary currents, which react upon the primary current and thereby introduce e.m.fs. of mutual inductance into the primary circuit. Mutual induc- tance is neither in phase nor in quadrature ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-48", "section_label": "Chapter 8: Velocity Of Propagation Of Electric Field", "section_title": "Velocity Of Propagation Of Electric Field", "kind": "chapter", "sequence": 48, "number": 8, "location": "lines 26095-27002", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "snippets": [ "... infinitely long conductor without return conductor has an infinite inductance L and inversely, zero capacity C. In equation (6) the magnetic field is assumed as instantaneous, that is, the velocity of propagation of the magnetic field is neglected. With alternating currents traversing the conductor this is permissible when the distance to the return conductor is a negligible fraction of the wave length; that is, if Z' is § negligible compared with -, where S = the speed of light and VELOCITY OF PROPAGATION OF ELECTRIC F ...", "... is permissible when the distance to the return conductor is a negligible fraction of the wave length; that is, if Z' is § negligible compared with -, where S = the speed of light and VELOCITY OF PROPAGATION OF ELECTRIC FIELD 391 / = the frequency of alternating current. It obviously is not permissible in a conductor having no return conductor. If a conductor conveying an alternating current has no return conductor, its circuit is closed by electrostatic capacity, either the distributed capacity of the conductor or capa ...", "... negligible compared with -, where S = the speed of light and VELOCITY OF PROPAGATION OF ELECTRIC FIELD 391 / = the frequency of alternating current. It obviously is not permissible in a conductor having no return conductor. If a conductor conveying an alternating current has no return conductor, its circuit is closed by electrostatic capacity, either the distributed capacity of the conductor or capacity connected to the ends of the conductor. To produce in such a case con- siderable currents, either the conductor must be ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-50", "section_label": "Chapter 1: General Equations", "section_title": "General Equations", "kind": "chapter", "sequence": 50, "number": 1, "location": "lines 27761-28694", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "snippets": [ "... , as discussed in Section III, by the four constants, namely : r = effective resistance, representing the power or rate of energy consumption depending upon the current, tfr; or the power component of the e.m.f. consumed in the circuit, that is, with an alternating current, the voltage, ir, in phase with the current. L = effective inductance, representing the energy storage i2L depending upon the current, - — , as electromagnetic component & of the electric field; or the voltage generated due to the change of the c ...", "... h the current. L = effective inductance, representing the energy storage i2L depending upon the current, - — , as electromagnetic component & of the electric field; or the voltage generated due to the change of the current, L — , that is, with an alternating current, the at reactive voltage consumed in the circuit - jxi, where x = 2 nfL and / = frequency. g = effective (shunted) conductance, representing the power or rate of energy consumption depending upon the voltage, e*g; or the power component of the current ...", "... htning arrester circuit, or a mile in a long-distance transmission circuit or high-potential cable, or the distance of the velocity of light, 300,000 km., etc. The permanent values of current and e.m.f. in such circuits of distributed constants have, for alternating-current circuits, been investigated in Section III, where it was shown that they can be treated as transient phenomena in space, of the complex variables, current / and e.m.f. E. Transient phenomena in circuits with distributed constants, and, therefore, the ge ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-53", "section_label": "Chapter 4: Traveling Waves", "section_title": "Traveling Waves", "kind": "chapter", "sequence": 53, "number": 4, "location": "lines 30244-31450", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "snippets": [ "... nating waves, and the equations of 12 16 \\ oanfqti ^edooaqtj + 60 h ±± + 60 20 Time t =,1150 \\ LiM X Fig. 102. Passage of a traveling wave at a given point of a line. the first main wave give the equations of the alternating-current circuit with distributed r, L, g, C, which thus appear as a special case of a traveling wave. Since in this case the frequency, and therewith the value of q, are low and comparable with u and s, the approximations made TRAVELING WAVES 473 in the pre ...", "... (qt - kl) } l { (c/CY- ctC2) cos (qt + kl) hl { (c2'C4 - C2C4) cos (qt + kl) + £ c, - c23 cos $ - ; -(C/C3 + c2(73Osin(^-^)}]. (177) In these equations of current i and e.m.f. e the first term represents the usual equations of the distribution of alternating current and voltage in a long-distance transmission line, and can by the substitution of complex quantities be reduced to a form given in Section III. The second term is a transient term of the same frequency; that is, in a long-distance transmission line or oth ...", "... d can by the substitution of complex quantities be reduced to a form given in Section III. The second term is a transient term of the same frequency; that is, in a long-distance transmission line or other circuit of distributed r, L, gt C, when carrying alternating current under an alternating impressed e.m.f., at a change of circuit conditions, a transient term of fundamental frequency may appear which has the time decrement, that is, dies out at the rate In this decrement the factor 474 TRANSIENT PHENOMENA is the u ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-05", "section_label": "Lecture 5: Single-Energy Tra.Nsient Of Ironclad Circuit", "section_title": "Single-Energy Tra.Nsient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3387-3720", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-05/", "snippets": [ "... uctance L is not constant, but varies w^ith the current, or the capacity is not constant, but varies with the voltage. The most important case is that of the ironclad magnetic cir- cuit, as it exists in one of the most important electrical apparatus, the alternating-current transformer. If the iron magnetic circuit contains an air gap of sufficient length, the magnetizing force con- sumed in the iron, below magnetic saturation, is small compared with that consumed in the air gap, and the magnetic flux, therefore, is proporti ...", "... cyclic curve of hysteresis, a mathematical calcula- tion is not feasible, but the transient has to be calculated by an 52 SINGLE-ENERGY TRANSIENT OF IRONCLAD CIRCUIT. 53 approximate step-by-step method, as illustrated for the starting transient of an alternating-current transformer in '' Transient Elec- tric Phenomena and Oscillations/' Section I, Chapter XII. Such methods are very cumbersome and applicable only to numerical instances. An approximate calculation, giving an idea of the shape of the transient of the iron ...", "... ere magnetic sat- uration is reached, but the current change is slower in the range of medium magnetic densities. Thus, in ironclad transients very high-current values of short duration may occur, and such transients, as those of the starting current of alternating-current transformers, may therefore be of serious importance by their excessive current values. An oscillogram of the voltage and current waves in an 11,000-kw. high-voltage 60-cycle three-phase transformer, when switching onto the generating station near the mo ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-05", "section_label": "Lecture 5: Single-Energy Transient Of Ironclad Circuit", "section_title": "Single-Energy Transient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2972-3286", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "snippets": [ "... ductance L is not constant, but varies with the current, or the capacity is not constant, but varies with the voltage. The most important case is that of the ironclad magnetic cir- cuit, as it exists in one of the most important electrical apparatus, the alternating-current transformer. If the iron magnetic circuit contains an air gap of sufficient length, the magnetizing force con- sumed in the iron, below magnetic saturation, is small compared with that consumed in the air gap, and the magnetic flux, therefore, is proporti ...", "... sis, a mathematical calcula- tion is not feasible,, but the transient has to be calculated by an '^''\"r '*_/ ? :,\": \\ : 52 SINGLE-ENERGY TRANSIENT OF IRONCLAD CIRCUIT. 53 approximate step-by-step method, as illustrated for the starting transient of an alternating-current transformer in \"Transient Elec- tric Phenomena and Oscillations,\" Section I, Chapter XII. Such methods are very cumbersome and applicable only to numerical instances. An approximate calculation, giving an idea of the shape of the transient of the ironcl ...", "... nts, where magnetic sat- uration is reached, but the current is slower in the range of medium magnetic densities. Thus, in ironclad transients very high-current values of short duration may occur, and such transients, as those of the starting current of alternating-current transformers, may therefore be of serious importance by their excessive current values. An oscillogram of the voltage and current waves in an 11,000-kw. high-voltage 60-cycle three-phase transformer, when switching onto the generating station near the mo ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-04", "section_label": "Chapter 5: Methods Of Approximation", "section_title": "Methods Of Approximation", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 15156-16482", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-04/", "snippets": [ "... es the result correct within the limits of accuracy required in engineer- ing, which usually, depending on the nature of the problem, is not greater than from 0.1 per cent to 1 per cent^;^ Thus, for instance, the voltage consumed by the resistance of an alternating-current transformer is at full load current only a small fraction of the supply voltage, and the exciting current of the transformer is only a small fraction of the full load current, and, therefore, the voltage consumed by the exciting current in the resistance ...", "... +j-y =40,400; 29.92 = 302(l-3i3)^900(l-j^^)=000-6 = 894; vmS = 10\\/l-0.02 = 10(1 -0.02)2 =10(1-0.01) = 9.99; 1 1 1 XOS (1+0.03)1/2 1.015 = 0.985; etc. METHODS OF APPROXIMATION. 195 130. Example i. If r is the resistance, x the reactance of an alternating-current circuit with impressed voltage e, the current is 1 = r2+x2 If the reactance x is small compared with the resistance r, as is the case in an incandescent lamp circuit, then, ._ _ _ _ef /xV] ~2 m i^' e r If the resistance is small comp ...", "... /2 (^1 - ^y ^' = ai/2 (1 - ^) ; 204 ENGINEERING MATHEMATICS. hence, F = ^i/2xa3/4(l+|il)x4(l-|82)xaV4x(l+2^)(l-2j) (1 _ \\4a2 a a J a3/2(l-3s2+2-- + S2--) \\ a a / \\ 4 a. a J 138. As further example may be considered the equations of an alternating-current electric circuit, containing distributed resistance, inductance, capacity, and shunted conductance, for instance, a long-distance transmission line or an underground high-potential cable. Equations of the Transmission Line. Let I be the distance along ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-04", "section_label": "Lecture 4: The Characteristics Of Space A. The Geometry Of The Gravitational Field", "section_title": "The Characteristics Of Space A. The Geometry Of The Gravitational Field", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3595-6820", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-04/", "snippets": [ "... hile usually considered as metric and introduced as such, in its nature is not a metric relation but a positional relation. 110 RELATIVITY AND SPACE 4. If we have, in Fig. 31, four points a, b, c, d, in a plane, and draw the six Unes through them, ah, ac, ad, he, bd, cd, and denote the three additional points of intersection of these six lines by e = ah, cd;f = ac, hd; g = ad, he, and Fig. 31. draw the three additional lines ef, eg and fg, we get a total of nine lines and four points on each of these ...", "... relation. 110 RELATIVITY AND SPACE 4. If we have, in Fig. 31, four points a, b, c, d, in a plane, and draw the six Unes through them, ah, ac, ad, he, bd, cd, and denote the three additional points of intersection of these six lines by e = ah, cd;f = ac, hd; g = ad, he, and Fig. 31. draw the three additional lines ef, eg and fg, we get a total of nine lines and four points on each of these nine lines. Each of these nine groups of points is composed of four harmonic points. This shows the positional ...", "... re that the electromagnetic energy and the electromagnetic field do not yet satisfactorily fit into it. INDEX Aberration of light, 15 Absolute number, meaning, 38 Accelerated motion, and gravitation, 52 Acceleration, 9, 47 Action at distance, 19 Alternating current, 14 dielectric field, 20 Analogue, 2 dimensional, of uni- verse, 119 Axioms of mathematics, 70 metric, of space, 95, 110 B Beltrami's pseudosphere, 91 Bending of space, 88 Betel geuse, 67 Bolyai, 71 Bullet velocity, 13 C Capacity and wa ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-11", "section_label": "Lecture 11: Lightning Protection", "section_title": "Lightning Protection", "kind": "lecture", "sequence": 11, "number": 11, "location": "lines 4931-5294", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-11/", "snippets": [ "... d by the magnetic blow-out, which is still used to a large extent on 500 volt railway circuits; by the horn gap arrester — a gap between two horn-shaped terminals, between which the arc rises, and so lengthens itself until it blows out ; and later on, for alternating current, the multi-gap between non-arcing metal cylinders, a number of small spark gaps in series with each other, between line and ground, over which the lightning discharges to ground — the machine cur- rent following as arc, but stopped at the end of the half ...", "... ti-gap between non-arcing metal cylinders, a number of small spark gaps in series with each other, between line and ground, over which the lightning discharges to ground — the machine cur- rent following as arc, but stopped at the end of the half wave of alternating current; but not starting at the next half wave, due to the property of these \"non-arcing\" metals (usually zinc-copper alloys), to carry an arc in one direction, but requir- ing an extremely high voltage to start a reverse arc. These lightning arresters operated ...", "... the magnetic blow- out 500 volt railway arrester is still in use to a large extent, but is beginning to be superseded by the aluminum cell. The multi-gap, being based on the non-arcing or rectifying prop- erty of the metal cylinders which exists only with alternating current, is not suitable for direct current circuits. In arc light circuits, that is, constant current circuits, horn gap arresters with series resistance are generally used, especially on direct current arc circuits, in which the multi-gap is not permissible. In ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-12", "section_label": "Lecture 12: Electric Railway", "section_title": "Electric Railway", "kind": "lecture", "sequence": 12, "number": 12, "location": "lines 5295-7123", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-12/", "snippets": [ "... per second, until at D, where the coast- ing line cuts the braking line bB, (which also is drawn at the slope of two miles per hour per second), the brakes are applied and the car comes to rest, at B. As the distance traveled is speed times time, the area A C D B so represents the distance traveled, that is, the distance between the two stations, and all speed time curves of the same type therefore must give the same area. During acceleration, energy is put into the car, and stored by its momentum, which is pr ...", "... d by the speed at the point B, where the brakes are applied. The lower therefore this point B is, the less power is destroyed by the brakes, and the more efficient is the run. More accurately, by pro- longing C D to E so that area D E G = B P G, the area A C E F also is the distance between the stations, and E F so would be the speed at which the car arrives at the next station, if no brakes were applied, and the energy correspond- ing thereto has to be destroyed by the brakes ; that is, represents the energy ...", "... rain is proportional ito the speed, and therefore is very low at low speeds. Or in other words, the motor during constant acceler- ation, consumes power corresponding to maximum speed, while the useful power corresponds to the average speed, which during A C is only half the maximum ; and so only half the available power is put into the car, the other half being wasted in the resistance, and the motor efficiency during constant acceleration therefore must be less than 50%. Constant acceleration up to maximum ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-08", "section_label": "Theory Section 8: Power in Alternating-current Circuits", "section_title": "Power in Alternating-current Circuits", "kind": "theory-section", "sequence": 8, "number": 8, "location": "lines 2718-2864", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-08/", "snippets": [ "8. POWER IN ALTERNATING-CURRENT CIRCUITS of effective value I = —7=-, in a circuit of resistance r and reac- V2 39. The power consumed by alternating current i = I0 sin 0, effective value I tance x = 2 nfL, is p = ei, where e = z!Q sin ( ...", "8. POWER IN ALTERNATING-CURRENT CIRCUITS of effective value I = —7=-, in a circuit of resistance r and reac- V2 39. The power consumed by alternating current i = I0 sin 0, effective value I tance x = 2 nfL, is p = ei, where e = z!Q sin (0 + 00) is the impressed e.m.f., consisting of the components ei = r/0 sin 0, the e.m.f. consumed by resistance and 62 = x ...", "... he sum of instantaneous values of the power and reactive components of the current equals the instantaneous value of the total current, ii + iz = i, while their effective values have the relation i = V77+772. Thus an alternating current can be resolved in two com- ponents, the power component, in phase with the e.m.f., and the wattless or reactive component, in quadrature with the e.m.f. An alternating e.m.f. can be resolved in two components: the power ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-10", "section_label": "Theory Section 10: Hysteresis and Effective Resistance", "section_title": "Hysteresis and Effective Resistance", "kind": "theory-section", "sequence": 10, "number": 10, "location": "lines 3234-3585", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-10/", "snippets": [ "10. HYSTERESIS AND EFFECTIVE RESISTANCE 46. If an alternating current 01 = I, in Fig. 21, exists in a circuit of reactance x = 2 irfL and of negligible resistance, the HYSTERESIS AND EFFECTIVE RESISTANCE 49 magnetic flux produced by the current, 0$ = $, is in phase with the curre ...", "... cuit contains iron or other magnetic mate- rial, energy is consumed in the magnetic circuit by a frictional resistance of the material against a change of magnetism, which is called molecular magnetic friction. If the alternating current is the only avail- able source of energy in the magnetic cir- cuit, the expenditure of energy by molec- ular magnetic friction appears as a lag of the magnetism behind the m.m.f. of the Q| r >i current, that is, a ...", "... ucault currents are proportional to the frequency, their effective resistance varies with the square of the frequency, while that of hysteresis varies only proportionally to the frequency. The total effective resistance of an alternating-current circuit increases with the frequency, but is approximately constant, within a limited range, at constant frequency, decreasing some- what with the increase of magnetism. EXAMPLES 50. A reactive coil shall give 100 volts e.m. ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-101", "section_label": "Apparatus Section 4: Alternating-current Transformer: Regulation", "section_title": "Alternating-current Transformer: Regulation", "kind": "apparatus-section", "sequence": 101, "number": 4, "location": "lines 17538-18397", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-101/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-101/", "snippets": [ "... the binomial, and dropping the higher terms: R = PP + \\ P2? = 0.02 p + 0.0002 p2 = P (P + \\ P?} = 0.02 p (1 + 0.01 p) As curves I, II, III in Fig. 157 are shown the regulation curves of three transformers: ALTERNATING-CURRENT TRANSFORMER 289 I: 2 per cent, resistance and 2 per cent, reactance. II : 1 per cent, resistance and 4 per cent, reactance. Ill : 1 per cent, resistance and 8 per cent, reactance. FIG. 158. — Vector diagram of ...", "... o and —ir sin co in quadrature with e. The former thus directly subtract, and the latter subtract by A/difference of squares, thus giving as resultant voltage : — (ix cos co — ir sin co) 2 — (ir cos co + ix sin co) ALTERNATING-CURRENT TRANSFORMER 291 or, since ir at full load as fraction of e is p, and ix as fraction of 6 is £; at the fraction p of the load: ir = pp, ix = p£, the re- sultant voltage is: \\/l — p2 (^ cos co — p sin co ...", "... s, so that the leakage flux of each path is due to a small part of the total m.m.f. of primary or secondary only, as shown in Figs. 161 and 162. In Fig. 162 the m.m.f. of each of the four leakage paths is due to ALTERNATING-CURRENT TRANSFORMER 293 one-fourth of the m.m.f. as in Fig. 161, and the leakage flux density thus reduced to one-fourth of what it is in Fig. 161. As furthermore the section of each leakage flux in Fig. 162 is materially ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-14", "section_label": "Theory Section 14: Rectangular Coordinates", "section_title": "Rectangular Coordinates", "kind": "theory-section", "sequence": 14, "number": 14, "location": "lines 5264-5831", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-14/", "snippets": [ "14. RECTANGULAR COORDINATES 64. The vector diagram of sine waves gives the best insight into the mutual relations of alternating currents and e.m.fs. For numerical calculation from the vector diagram either the trigonometric method or the method of rectangular components is used. The method of rectangular components, as explained in the above paragraphs, is u ...", "... primary impressed e.m.f. has the intensity (ai'2+flf)J (20) and the phase tan 0o = -1 + r0 (aii + h) + X0 (aiz + flf) This symbolism of rectangular components is the quickest and simplest method of dealing with alternating-current phenom- ena, and is in many more complicated cases the only method which can solve the problem at all, and therefore the reader must become fully familiar with this method. EXAMPLES 67. (1) In a 20-kw. transformer the r ...", "... «!s 32 i • t*» s§ + + I II OS §2 o •* • d § 111 + 3\" O O (NO d«o CO CO ^ «° » 1 fe : + : £ ^J- f 11 + « ^ a l' ^ E 8 *• & S ill!! i •D a c S D. g .S : s z » 1 & So. : : S t> ' « £ : tf • 05 n s s 'N o. -S V 3 3 « « & ** 03 T3 S fl 'E -*• As the reciprocal of the complex quantity, Z = r —jx, the admittance is a complex quantity also, or Y = g+jb; 54 ALTERNATING-CURRENT PHENOMENA. it consists of the component g, which represents the co- efficient of current in phase with the E.M.F., or energy current, gEt in the equation of Ohm's law, — and the component b, which represents the coefficient of current in quadrature wi ...", "... of parallel-connected admit- tances, if expressed in complex quantities, is equal to the sum of the individual admittances. In diagrammatic represen- tation, combination by the parallelogram law takes the place of addition of the complex quantities. 58 ALTERNATING-CURRENT PHENOMENA." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-25", "section_label": "Chapter 25: General Polyphase Systems", "section_title": "General Polyphase Systems", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 23643-23780", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-25/", "snippets": [ "CHAPTER XXV. GENERAL POLYPHASE SYSTEMS. 260. A polyphase system is an alternating-current sys- tem in which several E.M.Fs. of the same frequency, but displaced in phase from each other, produce several currents of equal frequency, but displaced phases. Thus any polyphase system can be considered as con- sisting of a number of single circuit ...", "... e polyphase system is called an independent system, in the latter case an inter- linked system. The three-phase system with star-connected or ring-con- nected generator, as shown diagrammatically in Figs. 181 and 182, is an interlinked system. 432 ALTERNATING-CURRENT PHENOMENA. The four-phase system as derived by connecting four equidistant points of a continuous-current armature with four collector rings, as shown diagrammatically in Fig. 183, Fig. 183. is an interlinked system also. The four-wire quarter-phase ...", "... phase system by transformation with two transformers, of which the secondary of one is reversed with regard to its primary (thus changing the phase difference from 120° to 180° - 120° = 60°), finds a limited application in low tension distribution. 434 ALTERNATING-CURRENT PHENOMENA." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-01", "section_label": "Chapter 1: Electric Conduction. Soled And Liquid", "section_title": "Electric Conduction. Soled And Liquid", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 959-3894", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-01/", "snippets": [ "... it from oxidizing — ^thus finds a use as series resistance for current limitation in vacuum arc circuits, etc. Electrolytic Conductors 4. The conductors of the second class are the electrolytic conductors. Their characteristic is that the conduction is ac- companied by chemical action. The specific resistance of elec- trolytic conductors in general is about a miUion times higher than that of ihe metallic conductors. They are either fused compounds, or solutions of compounds in solvents, ranging in resistiv ...", "... ent with alternating im- pressed voltage. Thus, when an alternating voltage, of a maxi- e ^-- ^ V. \"^7 y\"\"\"^^ eo ( • ' % Fia. 3. mum value lower than the polarization voltage, is impressed upon an electrolytic cell, an alternating current flows through the cell, which produces the hydrogen and oxygen films which hold back the current flow by their counter e.m.f. The current thus flows ahead of the voltage or counter e.m.f. which it produces, as a leading current, and the polarization cell ...", "... park, a wireless wave, etc., also is exhibited by some pyroelectric conductors. 13. Operation of pyroelectric conductors on a constant- voltage circuit, and in the unstable branch (3), is possible by the insertion of a series resistance (or reactance, in alternating-current circuits) of such value, that the resultant volt-ampere characteristic is stable, that is, rises with increase of current. Thus, the con- ductor in Fig. 4, shown as / in Fig. 11, in series with the metalUc resistance giving characteristic Ay gives the res ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-03", "section_label": "Chapter 3: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 5445-6941", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-03/", "snippets": [ "... ' / ,- /e i' ' '■ / • f' ./ B. -^ 7 A.^ -T' - / / ; ,.-- '' / ' / / ,/ * ■\" --^ ^' ■^ ' _ -' '^ t^^ -' 1. L •= -- \" or using an alternating current for field excitation, and observing the induced alternating voltage, preferably by oscillograph to eliminate wave-shape error. This \"alternating magnetic characteristic\" is the one which is ■^ consequence in the design of alternating-current apparatus. ...", "... or using an alternating current for field excitation, and observing the induced alternating voltage, preferably by oscillograph to eliminate wave-shape error. This \"alternating magnetic characteristic\" is the one which is ■^ consequence in the design of alternating-current apparatus. \" differs from the \"rising magnetic characteristic,\" B\\ by giving lowervalueaof B, forthesame/f,materiallysoat low values of ^, It shows the inward bend at low fields still more pronounced than fiidoes. It is shown as curve Bs in Fig. 27, and i ...", "... e of a condition of magnetic instability, just as remanent and permanent magnetism are. In approaching stable conditions by the superposition of an alternating field, this field can be applied at right angles to the unidirectional field, as by passing an alternating current length- wise, that is, in the direction of the lines of magnetic force, through the material of the magnetic circuit. This superimposes a cir- cular alternating flux upon the continuous-length flux, and per- mits observations while the circular alternatin ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-09", "section_label": "Chapter 9: Wave Screens. Even Harmonics", "section_title": "Wave Screens. Even Harmonics", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 16964-17631", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-09/", "snippets": [ "... the maximum of the fundamental. That is, in the last case the voltage is practically a perfect sine wave. 78. By \"wave screens\" the separation of pulsating currents into their alternating and their continuous component, or the separa- tion of complex alternating currents — and thus voltages — into their constituent har- monics can be accomplished, and inversely, the combination of alternating and continuous currents or vol- tages into resultant complex alternating or pulsating currents. The simplest arrangement of such a ...", "... produced by it divides, as the continuous component can not pass through the condenser, C, and the alternating component is barred by the inductance, L, the more completely, the higher this inductance. Thus the current, ti, in the apparatus. A, is a true alternating current, while the current, to, in the apparatus, C, is a slightly pulsating direct current. Inversely, by placing a source of alternating voltage, such as an alternator or the secondary of a transformer, at A, and a source of continuous voltage, such as a stora ...", "... inusoidally pulsating mag- netic flux density. Taking from curve J, Fig. 64, the values of H corresponding to the values in curve B, Fig. 77, gives curve H, This, resolved (\"Engineering Mathematics,'' paragraph 92) gives the constant term Zo = 36, and the alternating current, i. The latter is unsymmetrical, having one short half- wave of a peak value 64, and one long half-wave of maximum value 26. It thus resolves into the odd harmonics, f i, alternating between ±45, and the even harmonics, mainly the second harmonic, alterna ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-37", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 37, "number": 1, "location": "lines 15354-15625", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "snippets": [ "... very small compared with the transient term. 4. Periodic transient phenomena are of engineering impor- tance mainly in three cases: (1) in the control of electric circuits; (2) in the production of high frequency currents, and (3) in the rectification of alternating currents. 1. In controlling electric circuits, etc., by some operating mechanism, as a potential magnet increasing and decreasing the resistance of the circuit, or a clutch shifting brushes, etc., the main objections are due to the excess of the friction of rest ...", "... auto- matic potential regulators. 2. Production of high frequency oscillating currents by period- ically recurring condenser discharges has been discussed under \" oscillating current generator,\" in Section I, paragraph 44. Non-sinusoidal high frequency alternating currents are pro- duced by an arc, when made unstable by shunting it with a condenser, as discussed before. The Ruhmkorff coil or inductorium also represents an appli- cation of periodically recurring transient phenomena, as also does Prof. E. Thomson's dynamost ...", "... wave taken from the one source, and sent into the receiver circuit, the other half wave taken from the other source, and sent into the receiver circuit in the same direction as the first half wave. The latter arrangement has the disadvantage of using the alternating current supply source less economically, but has the advantage that no reversal, but only an opening and closing of connections, is required, and is therefore the method commonly applied in stationary rectify- ing apparatus. 6. In rectifying alternating voltage ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-56", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit", "section_title": "Power And Energy Of The Complex Circuit", "kind": "chapter", "sequence": 56, "number": 7, "location": "lines 33528-34202", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "snippets": [ "... s (310) + e~2sA [C cos q (X + 0 + D sin 0 (4 + Of - 2 [A cos q (A - 0 + B sin 0 (4 - 0] [C cos q (A + 0 + D sin 0 (J + 01} + [e+2«*(Aa -£2) cos 2 g (A -0 + fi-^C8- D2) cos 2 ^ (4 + 0] + 2 [A£e+2sA sin 2 0 (4 - 0 + CDe~2sX sin 2 g (4 + 0] - 2 [(AC - BD) cos 2 04 + (AD + BC) sin 2 g/l] - 2 [(AC + £D) cos 2qt+ (AD - BC) sin 2qt]}. (311) Integrating over a complete period in time gives the effective energy stored in the magnetic field at point A as a w j j. i*u/j 7 7T == ^ I — TT~ Ctfr (A - ...", "... 4 + Of - 2 [A cos q (A - 0 + B sin 0 (4 - 0] [C cos q (A + 0 + D sin 0 (J + 01} + [e+2«*(Aa -£2) cos 2 g (A -0 + fi-^C8- D2) cos 2 ^ (4 + 0] + 2 [A£e+2sA sin 2 0 (4 - 0 + CDe~2sX sin 2 g (4 + 0] - 2 [(AC - BD) cos 2 04 + (AD + BC) sin 2 g/l] - 2 [(AC + £D) cos 2qt+ (AD - BC) sin 2qt]}. (311) Integrating over a complete period in time gives the effective energy stored in the magnetic field at point A as a w j j. i*u/j 7 7T == ^ I — TT~ Ctfr (A - 2 [(AC - BD) cos 2qX+ (AD + BC) sin 2 ql]}, (312) ...", "... ) cos 2 04 + (AD + BC) sin 2 g/l] - 2 [(AC + £D) cos 2qt+ (AD - BC) sin 2qt]}. (311) Integrating over a complete period in time gives the effective energy stored in the magnetic field at point A as a w j j. i*u/j 7 7T == ^ I — TT~ Ctfr (A - 2 [(AC - BD) cos 2qX+ (AD + BC) sin 2 ql]}, (312) POWER AND ENERGY OF THE COMPLEX CIRCUIT 517 and integrating over one complete period of distance A, or one complete wave length, this gives (313) The energy stored by the inductance L, or in the magnetic f ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-17", "section_label": "Chapter 16: The Future Corporation", "section_title": "The Future Corporation", "kind": "chapter", "sequence": 17, "number": 16, "location": "lines 6975-7567", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-17/", "snippets": [ "... just — sensitivity of the cus- tomer, while in the latter letter often no thought is given to this feature of form, but it is assumed that the employees should be thankful. But it is the corporation which introduces social ac- tivities to establish co-operation, as it is the corporation which, from its broader view, sees the necessity of greater co-operation, while the employees do not see it yet, but suspect the new movement as hostile to their ...", "... ially in a rapidly growing democratic nation, it is not reasonable to expect anybody to go to special pains to find out what others do, but everybody, to be judged fairly, must come out before the public and explain his ac- tions and their reason, must be ready to defend himself. This the corporations have not done, and their enemies have done it for them, with the results seen to-day. In the last years a change has come and more and mor ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-05", "section_label": "Chapter 6: Empirical Curves", "section_title": "Empirical Curves", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 16483-21988", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-05/", "snippets": [ "... ter III. The resolution of a periodic function thus consists in the determination of the higher harmonics, which are super- imposed on the fundamental wave. As periodic curves are of the greatest importance in elec- trical engineering, in the theory of alternating-current phe- nomena, a familiarity with the wave shapes produced by the different harmonics is desirable. This familiarity should be sufficient to enable one to judge immediately from the shape of the wave, as given by oscillograph, etc., which harmonics are pre ...", "... h harmonics are present. The effect of the lower harmonics, such as the third, fifth, seventh, etc. (or the second, fourth, etc., where present), is to change the shape of the wave, make it differ from sine shape, and in the '' Theory and Calculation of Alternating- current Phenomena,\" 4th. Ed., Chapter XXX, a number of characteristic distortions, such as the flat top, peaked wave, saw tooth, double and triple peaked, sharp zero, flat zero, etc., have been discussed with regard to the harmonics that enter into their composit ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-04", "section_label": "Lecture 4: Load Factor And Cost Of Power", "section_title": "Load Factor And Cost Of Power", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 1527-2561", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-04/", "snippets": [ "... ifferent uses must be different if the load factors are different, and the higher the cost, the lower the load factor. Electrochemical work gives the highest load factor, frequently some 90%, while a lighting system shows the poorest load factor — in an alternating current system without motor load occasionally it is as low as 10 to 20%. Defining the load factor as the ratio of the average to the maximum load, it is necessary to state over how long a time the average is extended ; that is, whether daily, monthly or yearly ...", "... ximum demand meter would discriminate against the former. By a careful development of summer lighting loads and motor day loads, the load factors of direct current distribution systems have been raised to very high values, 50 to 60% ; but in the average alternating current system, the failure of developing a motor load frequently results in very unsatisfac- tory yearly load factors. \" \" 0 (\\ V J 3 t *f r 1 J 1 1 f \\ 1 \\ . '^i J / \\j \\ f r f 5 i s / S V / \\, ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-05", "section_label": "Lecture 5: Long Distance Transmission", "section_title": "Long Distance Transmission", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2562-3132", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-05/", "snippets": [ "... ulty of generation and utilization, it is not probable that it will find any extended use, so that it does not need to be considered. FREQUENCY The frequency depends to a great extent on the character of the load, that is, whether the power is used for alternating current distribution — 60 cycles^-or for conversion to direct current — 25 cycles. For the transmission line, 25 cycles has the advantage that the charging current is less and the inductive drop is less, because charging current and inductance voltage are proport ...", "... break- downs may occur, either from mechanical accidents or by high voltages appearing in the line. ^^ GENERAL LECTURES HIGH VOLTAGE DISTURBANCES IN TRANSMISSION LINES These may be: A. Of fundamental frequency, that is, the same frequency as the alternating current machine circuit. B. Some higher harmonic of the generator wave, that is, some odd multiple of the generator frequency. C. Of frequencies entirely independent of the generator, or of a frequency which originates in the circuit, that is, high frequency o ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-11", "section_label": "Lecture 11: Light Intensity And Illumination", "section_title": "Light Intensity And Illumination", "kind": "lecture", "sequence": 11, "number": 11, "location": "lines 12574-16484", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-11/", "snippets": [ "... ved by adding the illumination ia, ib, ic, id of the four lamps a, 6, c, d, taken from curve in Fig. Ill for the horizontal distances of point P from the lamps : lhg, lhb, lhc, lhd. These component illuminations are plotted in Figs. 112 to 115; as A , Ab, Ac, Ad in Fig. 112; as Ba, Bb in Fig. 113, etc., and their numerical values, in thousandths of candle feet, recorded in Table VI. In Fig. 116 are shown the four curves of the resultant direct illumination, superim- posed upon each other. 107. To this direc ...", "... le co varies, and averages 30 deg. for that half of the circumference, PQR (Fig. 110), at which the walls are nearest, and 60 deg. for that half, RSTUP, for which the walls are farthest, from the lamp. Hence the 1.0 0.8 0.6 0.4 0.2 Act Ac 12 10 0.8 B 0.6 0.4 G 0,2 BaScd BbStc 6 *c B B G Bfc&c Bakd X x- — ** -^ -^ -* ^» -•>s X / \\ -*- ^^ ^^** >J ^ _ ~~ _ - —. •— , — • - — - -, ~- .. •• — 4 8 12 18 20 2* FIGS. 112, 113. ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-09", "section_label": "Theory Section 9: Vector Diagrams", "section_title": "Vector Diagrams", "kind": "theory-section", "sequence": 9, "number": 9, "location": "lines 2865-3233", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-09/", "snippets": [ "9. VECTOR DIAGRAMS 42. The best way of graphically representing alternating-cur- rent phenomena is by a vector diagram. The most frequently used vector diagram is the crank diagram. In this, sine waves of alternating currents, voltages, etc., are represented as projec- tions of a revolving vector on the horizontal. That is, a vector equal in length to the maximum value of the alternating wave is assumed to revolve at uniform speed so as to ...", "... thus the resultant e.m.f . ; that is, graphically alternating sine waves of voltage, current, etc., are combined and resolved by the parallelo- gram or polygon of sine waves. FIG. 18. — Vector diagram. 43. The sine wave of alternating current i = I0 sin 0 is repre- sented by a vector equal in length, 01 0, to the maximum value 70 of the wave, and located so that at time zero 0=0, its projec- tion on the horizontal, is zero, and at times 0 > 0, but < TT ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-104", "section_label": "Apparatus Section 7: Alternating-current Transformer: Types of Transformers", "section_title": "Alternating-current Transformer: Types of Transformers", "kind": "apparatus-section", "sequence": 104, "number": 7, "location": "lines 18521-18665", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-104/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-104/", "snippets": [ "... S intermixed with each other. Core-type transformers are shown in section in Figs. 166 and 167, the former with one, the latter with two cores, and with two different coil arrangements, the intermixed and the concentric. ALTERNATING-CURRENT TRANSFORMER 297 For the transformation of three-phase circuits, three separate single-phase transformers may be used, and their primaries and FIG. 165. — Shell type transformer. FIG. 166. — Single-coil core type transf ...", "... it. Where the circuit conditions and connections are such as to give a triple harmonic — as with YY connection — the shell-type three-phase transformer may produce triple frequency voltages, resulting from the triple frequency ALTERNATING-CURRENT TRANSFORMER 299 flux, and under unfavorable conditions, as when connecting to a system of high capacity — which intensifies these voltages — this may lead to destructive voltages, and YY connections with shell-type three-p ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-106", "section_label": "Apparatus Section 9: Alternating-current Transformer: Reactors", "section_title": "Alternating-current Transformer: Reactors", "kind": "apparatus-section", "sequence": 106, "number": 9, "location": "lines 18813-18948", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-106/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-106/", "snippets": [ "... od, in the conventional definition : T^C • 1°SS Efficiency = 1 — -. — input and the input is given in total volt-amperes, the loss in energy volt-amperes, that is, watts. The efficiency then is 1 — power- factor. ALTERNATING-CURRENT TRANSFORMER 303 The transformer at open circuit is a reactor, but a very poor one, as its power-factor is high, that is, the efficiency low. In the transformer, the exciting ampere-turns are the (vector) difference b ...", "... speed turbo-alternators ca- pable of momentarily giving very high short-circuit currents, the amount of power, which can be developed momentarily by a short circuit in the system near the generating station, has reached such ALTERNATING-CURRENT TRANSFORMER 305 destructive values, that a limitation of this power has become necessary, and as economy of operation forbids sectionalizing the system into a number of smaller units, this has led to the exten- sive us ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-108", "section_label": "Apparatus Section 2: Induction Machines: Polyphase Induction Motor", "section_title": "Induction Machines: Polyphase Induction Motor", "kind": "apparatus-section", "sequence": 108, "number": 2, "location": "lines 19166-20427", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-108/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-108/", "snippets": [ "... + r0) + j (xi + XQ). Thus the characteristic behavior of the induction motor de- pends upon two complex imaginary constants, Y and Z, or four real constants, g, 6, r, x, the same terms which characterize the stationary alternating-current transformer on non-inductive load. Instead of conductance g, susceptance 6, resistance r, and react- ance x, as characteristic constants may be chosen: the absolute exciting admittance y = \\/g2 -f- &2; the absolute self-induc ...", "... G But even at its best value, the torque efficiency available with capacity in the secondary is below that available with resistance. For further discussion of the polyphase inductance motor, see \"Theory and Calculation of Alternating-current Phenomena.\"" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-109", "section_label": "Apparatus Section 3: Induction Machines: Single -phase Induction Motor", "section_title": "Induction Machines: Single -phase Induction Motor", "kind": "apparatus-section", "sequence": 109, "number": 3, "location": "lines 20428-21157", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-109/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-109/", "snippets": [ "... etic disposition thus the same as that of the polyphase induction motor. Leaving out of consideration starting by mechanical means and starting by converting the motor into a series or shunt motor, that is, by passing the alternating current by means of commutator and brushes through both elements of the motor, the following methods of starting single-phase motors are left: 1st. Shifting of the axis of armature or secondary polarization against the axis of gen ...", "... the motor thus gives approximately unity power-factor. For further discussion of this subject the reader is referred to the paper on \" Single-phase Induction Motors,\" mentioned above, and to the \" Theory and Calculation of Alternating-current Phe- nomena\" and \"Theory and Calculation of Electrical Apparatus.\" 4. ACCELERATION WITH STARTING DEVICE 152. The torque of the single-phase induction motor (without a starting device) is proportional to the product of main f ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-110", "section_label": "Apparatus Section 4: Induction Machines: Induction Generator", "section_title": "Induction Machines: Induction Generator", "kind": "apparatus-section", "sequence": 110, "number": 4, "location": "lines 21158-21588", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-110/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-110/", "snippets": [ "... s for its operation a circuit with leading current varying with the load in the manner de- termined by the internal constants of the motor, to make an induction or asynchronous generator suitable for operation on a general alternating-current circuit, it is necessary to have a syn- chronous machine as exciter in the circuit consuming leading current, that is, supplying the required lagging or magnetizing current to the induction generator; and in this case the v ...", "... size running light can be used herefor as exciter of the induction generator, or the exciting current of the induction generator may be derived from synchronous motors or converters in the same system, or from synchronous alternating- current generators operated in parallel with the induction gen- erator, in which latter case, however, these currents can be said to come from the synchronous alternator as lagging currents. Electrostatic condensers, as an underground ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-111", "section_label": "Apparatus Section 5: Induction Machines: Induction Booster", "section_title": "Induction Machines: Induction Booster", "kind": "apparatus-section", "sequence": 111, "number": 5, "location": "lines 21589-21646", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-111/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-111/", "snippets": [ "... . Induction Booster 157. In the induction machine, at a given slip s, current and terminal voltage are proportional to each other and of constant phase relation, and their ratio is a constant. Thus when con- nected in an alternating-current circuit, whether in shunt or in series, and held at a speed giving a constant and definite slip s, either positive or negative, the induction machine acts like a constant impedance. 350 ELEMENTS OF ELECTRICAL ENGINEERI ...", "... CHINES 351 machine behaves as an impedance of negative resistance, that is, adding a power e.m.f. into the circuit proportional to the current. As may be seen herefrom, the induction machine when inserted in series in an alternating-current circuit can be used as a booster, that is, as an apparatus to generate and insert in the circuit an e.m.f. proportional to the current, and the amount of the boosting effect can be varied by varying the speed, that is, ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-12", "section_label": "Theory Section 12: Impedance of Transmission Lines", "section_title": "Impedance of Transmission Lines", "kind": "theory-section", "sequence": 12, "number": 12, "location": "lines 3761-4464", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-12/", "snippets": [ "... rent. The same investigation as made here on long-distance trans- mission applies also to distribution lines, reactive coils, trans- formers, or any other apparatus containing resistance and reactance inserted in series into an alternating-current circuit. EXAMPLES 58. (1) An induction motor has 2000 volts impressed upon its terminals; the current and the power-factor, that is, the cosine of the angle of lag, are given as functions of the output in Fig. 31. The ...", "... general equation of the transmission line is £o = V (e H- iir -f izx) = V(2000 + 2n + hence, substituting the value of z*2, (2*2 - e0 = V(2120 - 0.4 n)2 + (40 - 6.8ti)a = V4,496,000 + 46.4 if - 2240 ^. ALTERNATING-CURRENT TRANSFORMER 67 Substituting successive numerical values for ii gives the values recorded in the following table and plotted in Fig. 33. ii eo 0 '2120 20 2114 40 2116 60 2126 80 2148 100 2176 120 2 ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-18", "section_label": "Theory Section 18: Equivalent Sine Waves", "section_title": "Equivalent Sine Waves", "kind": "theory-section", "sequence": 18, "number": 18, "location": "lines 7381-7736", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-18/", "snippets": [ "... fective value or intensity and the same power or effect, it follows that in regard to inten- sity and effect the general alternating waves can be represented by their equivalent sine waves. Considering in the preceding the alternating currents as equiva- lent sine waves representing general alternating waves, the investigation becomes applicable to any alternating circuit irrespective of the wave shape. The use of the terms reactance, impedance, etc., implies that a ...", "... nstruments of alternating waves (with exception of instantaneous methods) as ammsters, volt- meters, wattmeters, etc., give not general alternating waves but their corresponding equivalent sine waves. EXAMPLES 88. In a 25-cycle alternating-current transformer, at 1000 volts primary impressed e.m.f., of a wave shape as shown in 108 ELEMENTS OF ELECTRICAL ENGINEERING e §M »OCOOI>.C^O5(NCOOOOi'— l i— 1 CO CO CO »H i— 1 • OQ ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-22", "section_label": "Apparatus Section 1: Synchronous Machines: General", "section_title": "Synchronous Machines: General", "kind": "apparatus-section", "sequence": 22, "number": 1, "location": "lines 8518-8657", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-22/", "snippets": [ "I. General 3. The most important class of alternating-current apparatus consists of the synchronous machines. They comprise the alternating-current generators, single-phase and polyphase, the synchronous motors, the phase compensators, the phase con- verters, the phase balancers, the synchron ...", "I. General 3. The most important class of alternating-current apparatus consists of the synchronous machines. They comprise the alternating-current generators, single-phase and polyphase, the synchronous motors, the phase compensators, the phase con- verters, the phase balancers, the synchronous boosters and the exciters of induction generators, that is, synchronous machines ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-24", "section_label": "Apparatus Section 3: Synchronous Machines: Armature Reaction", "section_title": "Synchronous Machines: Armature Reaction", "kind": "apparatus-section", "sequence": 24, "number": 3, "location": "lines 8741-8906", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-24/", "snippets": [ "... e.m.f., it reaches its maximum in the same position A, A' of armature coil as the nominal generated e.m.f., and thus magnetizes the preceding, demagnetizes the following magnet pole (in the di- rection of rotation) in an. alternating-current generator A] magnetizes the following and demagnetizes the preceding mag- net pole in a synchronous motor A' (since in a generator the rotation is against, in a synchronous motor with the magnetic attractions and repulsions ...", "... in Fig. 48, C and C\", and thus mag- netizes the field in a generator, Fig. 48, C, and demagnetizes it in a syn- chronous motor C'. With non-inductive load, or with the current in phase with the ter- minal voltage of an alternating- current generator, the current lags behind the nominal generated e.m.f., due to armature reaction and self- inductance, and thus partly de- magnetizes; that is, the voltage is lower under load than at no load with the same field e ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-28", "section_label": "Apparatus Section 7: Synchronous Machines: Synchronous Motor", "section_title": "Synchronous Machines: Synchronous Motor", "kind": "apparatus-section", "sequence": 28, "number": 7, "location": "lines 9292-9398", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-28/", "snippets": [ "VII. Synchronous Motor 16. As seen in the preceding, in an alternating-current gen- erator the field excitation required for a given terminal voltage and current depends upon the phase relation of the external circuit or the load. Inversely, in a synchronous motor the phase relation of the current int ...", "... d E' FIG. 62. — Vector diagram of synchronous motor. FIG. 63. — Vector diagram of synchronous motor. 0=0 ing and lower with lagging current in a synchronous motor, while the opposite is the case in an alternating-current generator. In symbolic representation, by resolving all e.m.fs. into power components in phase with the current and wattless components in quadrature with the current i, we have: the terminal voltage, E = E cos 6 + jE s ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-70", "section_label": "Apparatus Subsection 70: Direct-current Commutating Machines: C. Commutating Machines", "section_title": "Direct-current Commutating Machines: C. Commutating Machines", "kind": "apparatus-subsection", "sequence": 70, "number": null, "location": "lines 12319-12398", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-70/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-70/", "snippets": [ "... uration curves. general shape as the magnetic flux density curve, except that the knee or bend is less sharp, due to the different parts of the magnetic circuit saturation successively. Thus, in order to generate voltage ac the field excitation oc is required. Subtracting from ac in a generator, Fig. 109, or adding in a motor, Fig. 110, the value ab = ir, the voltage con- sumed by the resistance of the armature, commutator, etc., gives the ...", "... ty curve, except that the knee or bend is less sharp, due to the different parts of the magnetic circuit saturation successively. Thus, in order to generate voltage ac the field excitation oc is required. Subtracting from ac in a generator, Fig. 109, or adding in a motor, Fig. 110, the value ab = ir, the voltage con- sumed by the resistance of the armature, commutator, etc., gives the terminal voltage be at current i, and adding to oc the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-78", "section_label": "Apparatus Section 15: Direct-current Commutating Machines: Appendix Alternating-current Commutator Motor", "section_title": "Direct-current Commutating Machines: Appendix Alternating-current Commutator Motor", "kind": "apparatus-section", "sequence": 78, "number": 15, "location": "lines 13008-13018", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-78/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-78/", "snippets": [ "XV. APPENDIX ALTERNATING-CURRENT COMMUTATOR MOTOR 78. Since in the series motor and in the shunt motor the direction of the rotation remains the same at a reversal of the impressed voltage, these motors can be operated by an alternat- ing voltage, as ...", "... OMMUTATOR MOTOR 78. Since in the series motor and in the shunt motor the direction of the rotation remains the same at a reversal of the impressed voltage, these motors can be operated by an alternat- ing voltage, as alternating-current motors, by making such changes in the materials, proportioning and design, as the al- ternating nature of the current requires." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-86", "section_label": "Apparatus Section 7: Synchronous Converters: Variable Ratio Converters (\"split Pole\" Converters)", "section_title": "Synchronous Converters: Variable Ratio Converters (\"split Pole\" Converters)", "kind": "apparatus-section", "sequence": 86, "number": 7, "location": "lines 15586-15734", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-86/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-86/", "snippets": [ "... the field poles, secondary currents in the latter contribute to the starting torque, but at the same time reduce the magnetic starting flux by their demagnetizing effect. The torque is produced by the attraction between the alternating currents of the successive phases upon the remanent magnetism and secondary currents produced by the preceding phase. It is necessarily comparatively weak, and from full-load to twice full-load current at from one-third to one-half of ...", "... requently preferable to run the converter up to or beyond synchronism by direct current, then cut off from the direct current, open the field circuit and connect it to the alternating system, thus bringing it into step by alternating current. If starting from the alternating side is to be avoided, and direct current not always available, as when starting the first converter, a small induction motor (of less poles than the con- verter) is used as starting moto ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-90", "section_label": "Apparatus Section 12: Synchronous Converters: Conclusion", "section_title": "Synchronous Converters: Conclusion", "kind": "apparatus-section", "sequence": 90, "number": 12, "location": "lines 15983-16064", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-90/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-90/", "snippets": [ "... r and with synchronous motors, alternators, direct-current motors and generators. Thus, for instance, a converter can be used to supply a certain amount of mechanical power as synchronous motor. In this case the alternating current is increased beyond the value corresponding to the direct current by the amount of current giving the mechanical power, and the armature reactions do not neutralize each other, but the reaction of the alternating current ex ...", "... e alternating current is increased beyond the value corresponding to the direct current by the amount of current giving the mechanical power, and the armature reactions do not neutralize each other, but the reaction of the alternating current exceeds that of the direct current by the amount corresponding to the mechanical load. In the same way the current heating of the armature is in- creased. An inverted converter can also be used to supply some mechanical ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-95", "section_label": "Apparatus Section 1: Alternating-current Transformer: General", "section_title": "Alternating-current Transformer: General", "kind": "apparatus-section", "sequence": 95, "number": 1, "location": "lines 16804-16911", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-95/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-95/", "snippets": [ "I. General 110. The alternating-current transformer consists of a magnetic circuit interlinked with two electric circuits, the primary, which receives power, and the secondary, which gives out power. Since the same magnetic flux interlinks primary and second- ary t ...", "... formers may be potential transformers — connected across the constant voltage circuit, or current transformers — connected in series into the circuit, for the supply of meters, the opera- tion of overload circuit breakers, etc. ALTERNATING-CURRENT TRANSFORMER 279 • Where not expressly stated otherwise, in general a constant potential transformer is understood." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-34", "section_label": "Chapter 34: Metering Of Polyphase Circuit", "section_title": "Metering Of Polyphase Circuit", "kind": "chapter", "sequence": 34, "number": 34, "location": "lines 37128-37452", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-34/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-34/", "snippets": [ "... ranch circuits, then is; n n p = ^i 2^- p., 1 1 n n = Si Sa; [Bi — Bx, iik] (7) 1 1 where the double summation sign indicates that the summation is to be carried out for all values of k, from 1 to n, and for all values of i, from 1 to n. 444 ALTERNATING-CURRENT PHENOMENA As the term Ci — Cx in (7) does not contain the index k, it is the same for all values of k, thus can be taken out from the second summation sign, that is: P = 2i 1 However: e, - Sx, Xk iik 1 (8) 2*^ iik is the sum of all the cur ...", "... ecting then the current coils of the two wattmeters into the lines a and h, and the voltage coils between a respectively h, and c, the two wattmeter readings are: and: [-Ei,h-h] = [Ei,h] - [Ei,h] [E,, h - h] = [E^, h] - [^3, h] (13) (14) 446 ALTERNATING-CURRENT PHENOMENA and their sum is: P = [E,, h] - [E,, h] - [Es, h] + [^3, /3]^ = [ii, ii] - [E^ + E„ h] + [^3, h] and since by (12) : El -\\- Es — — E2, it is: P = [El, I,] + [E2, h] + [Es, Is] that is, the total power of the three-phase system is the s ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-36", "section_label": "Chapter 36: Three-Phase System", "section_title": "Three-Phase System", "kind": "chapter", "sequence": 36, "number": 36, "location": "lines 37958-38392", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-36/", "snippets": [ "... Ix + h + h = 0. (1) If, I'l, I'l, I's = currents through the admittances, Fi, ¥2, Y3, ' from 2 to 3, 3 to 1, 1 to 2, it is, h = // - /'2, or, h + /'2 - /'a = 0 'h = I'l - 'I'z, or, 72 + I'z - /'i = 0 [ (2) 73=>2-i'x, or, /3 + h-r2 = 0 457 458 ALTERNATING-CURRENT PHENOMENA These three equations (2) added, give (1) as dependent equation. At the ends of the hnes 1, 2, 3, it is: E'l = El — Zili + ^3/3 E 1 — El — Zils + Zili E 3 = E3 — Zili + Z2/2 the differences of potential, and : I\\ = E\\Yi I i = E 2^2 ...", "... ,, 1 we have: EKi ?'- K EK2 ?'- K EK3 ^'= K YiEK T 1 f'- K Y2EK T 2 ^.'- K Y3EK3 ^'- k 1 Y3K3 - Y2K2E T ^'- K YiKi - YJCzE ^- K J. Y2K2 — YiK\\i!j (8) (9) (10) hence, E\\ + E'2 + ^'3 = 0 I (11) 460 ALTERNATING-CURRENT PHENOMENA 309. Special Cases. A. Balanced System Y,= Y,= Y,= Y Substituting this in (6), and transposing: 1 + 3FZ E\\ = E 2 = E 3 = h = h = h = iE 1 +3 FZ 2E 1 + 3 rz E 1 +3 FZ e^e - 1)EY 1 + 3 FZ (6- 1)EY 1 + 3 FZ e ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-02", "section_label": "Chapter 2: Chapter II", "section_title": "Chapter II", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 1728-1972", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-02/", "snippets": [ "CHAPTER II INSTAIfTAmiOUB VAI>nES KSD INTSaRAI. VAIiUia. 8. In a periodically varying function, as an alternating current, we have to distinguish between the instantaneous value, which varies constantly as function of the time, and the integral value, which characterizes the wave as a whole. As such integral value, almost exclusively the effective FI9. 4. mwrnaUng ■val ...", "... ariations of a sine-function are sinusoidal also, we have. Mean value of sine wave -5- maximum value = — -j- 1 IF = .63663. The quantities, \"current,\" \"E.M.F.,\" \"magnetism,\" etc., are in reality mathematical fictions only, as the components 14 ALTERNATING-CURRENT PHENOMENA. [§9 of the entities, \" energy,\" \" power,\" etc. ; that is, they have no independent existence, but appear only as squares or products. Consequently, the only integral value of an alternating wave which is of practical importance, as direc ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-07", "section_label": "Chapter 7: Admittance, Conductance, Susceftance", "section_title": "Admittance, Conductance, Susceftance", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 3546-3871", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-07/", "snippets": [ "... nnected resis- tances is equal to the sum of the individual resistances ; the § 30] ADMITTANCE, CONDUCTANCE, SUSCEPTANCE. 53 joint conductance of a number of parallel-connected conduc- tances is equal to the sum of the individual conductances, 39. In alternating-current circuits, instead of the term resistance we have the term impedance , Z = r —jx, with its two components, the resistance^ r, and the reactance^ x, in the formula of Ohm's law, E = IZ, The resistance, r, gives the component of E.M.F. in phase with the curr ...", "... rallel-connected admit- tances, if expressed in complex quantities^ is equal to the sum of the individual admittances. In diagrammatic represen- tation, combination by the parallelogram law takes the place of addition of the complex quantities. / 58 ALTERNATING-CURRENT PHENOMENA. [§§42, 43" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-17", "section_label": "Chapter 17: Synchbonizino Aiitebkatobs", "section_title": "Synchbonizino Aiitebkatobs", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 18829-19345", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-17/", "snippets": [ "CHAPTER XVII. SYNCHBONIZINO AIiTEBKATOBS. 168. All alternators, when brought to synchronism with each other, will operate in parallel more or less satisfactorily. This is due to the reversibility of the alternating-current machine ; that is, its ability to operate as synchronous motor. In consequence thereof, if the driving power of one of sev- eral parallel-operating generators is withdrawn, this gene- rator will keep revolving in synchronism as a synchronous motor ; and ...", "... ators, A / the value of synchronizing power, — ^ , in dash-dot line, Curve V. A For the condition of external circuit, g= 0, />= 0, ,1' = 0, .05, 0, .05, .08, 0, .08, .03, + .04, .05, .03, -.04, .05. 258 ' ALTERNATING-CURRENT PHENOMENA, [§177" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-24", "section_label": "Chapter 24: Symmetbicaii Polyphase Ststems", "section_title": "Symmetbicaii Polyphase Ststems", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 25271-25604", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-24/", "snippets": [ "... 4 The four E.M.Fs. of the four-phase system are: €' = E, jE, — E, —jE. They are in pairs opposite to each other : E and —E\\jE and —jE, Hence can be produced by two coils in quadrature with each other, analogous as the two-phase system, or ordinary alternating-current system, can be produced by one coil. Thus the symmetrical quarter-phase system is a four- phase system. Higher systems, as the quarter-phase or four-phase sys- tem, have not been used, and are of little practical interest. 237. A characteristic featur ...", "... oils dis- placed under the n equal angles is : 1 1 \\ « /\\ '' « / or, expanded : /=;//V2 \\ sin/J^tfcos^ — +ysin?''-*cos?^^- cos P 2lL sm — cos [-jsirr ) J . It is, however : cos\"^ f-y sm cos = J [ 1 + COS f- / sm // // // V // // 354 ALTERNATING-CURRENT PHENOMENA. [$237 . 27r/ 27r/ , . . o^tt/ j I ^ Aiiri . . 47r/\\ sm COS h / sin-* = ^ ( 1 — cos / sin \\ n n n 2\\ n n j and, since: as the sum of all the roots of Vl, it is, /= \"AI^ (sin p+J cos /3). or, /=!L^(sin)3+ycos/3) V2 = !^(sin)3 +ycos ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-02", "section_label": "Chapter 2: Instantaneous Values And Integral Values", "section_title": "Instantaneous Values And Integral Values", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 1367-1605", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-02/", "snippets": [ "CHAPTER II INSTANTANEOUS VALUES AND INTEGRAL VALUES. 8. IN a periodically varying function, as an alternating current, we have to distinguish between the instantaneous value, which varies constantly as function of the time, and the integral value, which characterizes the wave as a whole. As such integral value, almost exclusively the effective Fig. 4. Alternating Wave ...", "... B* cos ±TrNt + £s cos GTT Nt + . . we find, by squaring this expression and canceling all the products which give 0 as mean square, the effective value, — 1= V* W The mean value does not give a simple expression, and is of no general interest. 16 ALTERNATING-CURRENT PHENOMENA," ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-29", "section_label": "Chapter 29: Transformation Of Polyphase Systems", "section_title": "Transformation Of Polyphase Systems", "kind": "chapter", "sequence": 29, "number": 29, "location": "lines 24805-25135", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-29/", "snippets": [ "... ch of the secondary phases. Loading now the secondary polyphase system in any desired manner, corresponding to the secondary cur- rents, primary currents will flow in such a manner that the total flow of power in the primary polyphase system is the 4j^ ALTERNATING-CURRENT PHENOMENA. same as the total flow of power in the secondary system, plus the loss of power in the transformers. 285. As an instance may be considered the transforma- tion of the symmetrical balanced three-phase system E sin ft, E sin (ft — 120), E sin ...", "... f electric energy is mechanical momentum in revolving machinery. It has, however, the disadvantage of requiring attendance ; fairly efficient also are capacities and inductances, but, as a rule, have the disadvantage not to give constant potential. 468 ALTERNATING-CURRENT PHENOMENA." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-16", "section_label": "Chapter 18: Surging Of Synchronous Motors", "section_title": "Surging Of Synchronous Motors", "kind": "chapter", "sequence": 16, "number": 18, "location": "lines 20975-21712", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-16/", "snippets": [ "... 8 : 4 vfzMo b , «! + PpJL. (2Q) Of these two terms b represents the consumption, a the oscilla- tion of energy by the pulsation of phase angle, p. b and a thus SURGING OF SYNCHRONOUS MOTORS 295 have a similar relation as resistance and reactance in alternating- current circuits, or in the discharge of condensers, a is the same term as in paragraph 167. Differential equation (19) is integrated by: 5 = Atc', (21) which, substituted in (19), gives: aAtc* + 2 bCAf + C2Aec* - 0, a + 2 bC + C2 = 0, which equation has ...", "... gging of the pulsation of e causes a negative, leading a positive, Pt, P~, therefore, represents the power due to the pulsation of e 298 ELECTRICAL APPARATUS caused by the pulsation of the armature reaction, as discussed in \"Theory and Calculation of Alternating-Current Phenomena.\" Any appliance increasing the area of the magnetic cycle of pulsation, as short-circuits around the field poles, therefore, increases the steadiness of a steady and increases the unsteadi- ness of an unsteady synchronous motor. In self-excit ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-02", "section_label": "Chapter 2: Electric Conduction. Gas And Vapor", "section_title": "Electric Conduction. Gas And Vapor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3895-5444", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-02/", "snippets": [ "... vely used for rectification of alternating voltages. Usually vacuum arcs are employed for this purpose, mainly the mercury arc, due to its very great rectifying range of voltage. Since the arc is a unidirectional conductor, it usually can not exist with alternating currents of moderate voltage, as at the end of every half-wave the arc extinguishes. To maintain an alterna- ting arc between two terminals, a voltage is required suflBiciently high to restart the arc at every half-wave by jumping an elec- trostatic spark between ...", "... materials as carbon, which have a boiling point above this temperature. ELECTRIC CONDUCTION 33 require a lower voltage for restarting than for maintaining the arc, that is, the voltage required to maintain the arc restarts it at every half-wave of alternating current, and such materials thus give a steady alternating arc. Even materials of a somewhat lower boiling point, in which the starting voltage is not much above the running voltage of the arc, maintain a steady alter- nating arc, as in starting the voltage consu ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-08", "section_label": "Chapter 8: Shaping Of Waves By Magnetic Saturation", "section_title": "Shaping Of Waves By Magnetic Saturation", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 12962-16963", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-08/", "snippets": [ "... numerical values in Table III illustrate this. / gives the magnetic field intensity, and thus the direct current. SHAPING OF WAVES BY MAGNETIC SATURATION 133 which produces the magnetic density, B — that is, the B-H curve of the magnetic material. An alternating current of maxi- mum value, I, thus gives an alternating m^netic flux of maxi- mum flux density B. If / and B, were both sine waves, that is, if B V M 1 — . — , ^ \"^ / / / / / IV / J Y 0 0 and if r2 < — , s is imaginary, and the equations assume a C complex imaginary form. In either case they have to be rearranged to assume a form suitable for application. Three cases have thus to be distinguished : (a) r2 > — -, in which the equations of the circuit can be o used in their present form. Since the ...", "... potential is e, - 1000 { 1 - e\" 20° ' (cos 980 t + 0.21 sin 980 0 } . 62 TRANSIENT PHENOMENA 41. Since the equations of current and potential difference (42) to (47) contain trigonometric functions, the phenomena are periodic or waves, similar to alternating currents. They r differ from the latter by containing an exponential factor e 2 L , which steadily decreases with increase of t. That is, the sue- 16UUI — f ^ f N, c = « 1QOO volts L = = 1 X)mh 1 X \\ T = 40 oh, as C = = OE ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... ed, high power required for field excitation, poor regu- lation due to the massing of the conductors, which is required because of the small pitch per pole of the machine, etc., so that 1000 cycles probably is the limit of generation of constant potential alternating currents of appreciable power and at fair efficiency. For smaller powers, a few kilowatts, by using shunted capacity to assist the excitation, and not attempting to produce constant potential, single-phase alternators have been built and are in commercial service ...", "... the frequency available by electrodynamic generation. It becomes of importance, therefore, to investigate whether by the use of the condenser discharge the range of frequencies can be extended. Since the oscillating current approaches the effect of an alternating current only if the damping is small, that is, the resistance low, the condenser discharge can be used as high frequency generator only by making the circuit of as low resist- ance as possible. 67 68 TRANSIENT PHENOMENA This, however, means limited power. W ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-31", "section_label": "Chapter 9: Divided Circuit", "section_title": "Divided Circuit", "kind": "chapter", "sequence": 31, "number": 9, "location": "lines 9228-10474", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "snippets": [ "... cond, and the time effects thus are directly com- parable with the phenomena on a 60-cycle circuit. A better conception of the size or magnitude of inductance and capacity is secured. Since inductance and capacity are mostly observed and of importance in alternating-current cir- cuits, a reactor having an inductive reactance of x ohms and i amperes conveys to the engineer a more definite meaning as regards size: it has a volt-ampere capacity of tfx, that is, the approximate size of a transformer of half this capacity, or of ...", "... rmer of half this capacity, or of a ^2x — -watt transformer. A reactor having an inductance of L henrys and i amperes, however, conveys very little meaning to DIVIDED CIRCUIT 123 the engineer who is mainly familiar with the effect of inductance in alternating-current circuits. Substituting therefore (5) and (6) in equations (2), (3), (4), gives the e.m.f. in circuit 1 as dL e = rli1 + xl -r1 + a in circuit 2 as dL ' C * = r** + **-fi + *ctJi,M', (8) in circuit 3 as e = e a. r { 4. x -h. _j_ x I { ^. /Q\\ 0 ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-38", "section_label": "Chapter 2: Circuit Control By Periodic Transient Phenomena", "section_title": "Circuit Control By Periodic Transient Phenomena", "kind": "chapter", "sequence": 38, "number": 2, "location": "lines 15626-15962", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-38/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-38/", "snippets": [ "... RCUIT CONTROL BY PERIODIC TRANSIENT PHENOMENA. 6. As an example of a system of periodic transient phenomena, used for the control of electric circuits, may be considered an automatic potential regulator operating in the field circuit of the exciter of an alternating current system. Let, r0 = 40 ohms = resistance and L = 400 henrys = inductance of the exciter field circuit. A resistor, having a resistance, rl = 24 ohms, is inserted in series to r0, L in the exciter field, and a potential magnet, con- trolled by the alterna ...", "... current system. Let, r0 = 40 ohms = resistance and L = 400 henrys = inductance of the exciter field circuit. A resistor, having a resistance, rl = 24 ohms, is inserted in series to r0, L in the exciter field, and a potential magnet, con- trolled by the alternating current system, is arranged so as to short circuit resistance, rv if the alternating potential is below, to throw resistance rl into circuit again, if the potential is above normal. With a single resistance step, rv in the one position of the regulator, with rx ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-43", "section_label": "Chapter 3: The Natural Period Of The Transmission Line", "section_title": "The Natural Period Of The Transmission Line", "kind": "chapter", "sequence": 43, "number": 3, "location": "lines 21721-23178", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "snippets": [ "... latively high frequency of oscillating discharges, is small com- pared with the reactance. This assumption means that the dying out of the discharge current through the influence of the resistance of the circuit is neglected, and the current assumed as an alternating current of approximately the same frequency and the same intensity as the initial waves of the oscillating discharge current. By this means the problem is essentially simplified. 28. Let 10 = total length of a transmission line; I = the dis- tance from the begi ...", "... atmospheric electrostatic field of force. NATURAL PERIOD OF TRANSMISSION LINE 329 The fundamental frequency of the oscillating discharge of a transmission line is relatively low, and of not much higher mag- nitude than frequencies in commercial use in alternating-current circuits. Obviously, the more nearly sinoidal the distribution of potential before the discharge, tfye more the low harmonics predominate, while a very unequal distribution of potential, that is a very rapid change along the line, causes the higher har- ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-54", "section_label": "Chapter 5: Free Oscillations", "section_title": "Free Oscillations", "kind": "chapter", "sequence": 54, "number": 5, "location": "lines 31451-32708", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "snippets": [ "... ndent of the character of the wave. By the value of the acceleration constant, s, waves may be sub- divided into three classes, namely: s = 0, standing waves, as discussed in Chapter III; u > s > 0, traveling waves, as dis- cussed in Chapter IV; s = u, • alternating-current and e.m.f. waves, as discussed in Section III. The general equations contain eight integration constants C and C', which have to be determined by the terminal condi- tions of the problem. Upon the values of these integration constants C and C' largely ...", "... e determined by the terminal condi- tions of the problem. Upon the values of these integration constants C and C' largely depends the difference between the phenomena occurring in electric circuits, as those due to direct currents or pulsating currents, alternating currents, oscillating currents, inductive dis- charges, etc., and the study of the terminal conditions thus is of the foremost importance. 29. By free oscillations are understood the transient phe- nomena occurring in an electric circuit or part of the circuit to ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-04", "section_label": "Chapter 3: The Individualistic Era: From Competition to Co-operation", "section_title": "The Individualistic Era: From Competition to Co-operation", "kind": "chapter", "sequence": 4, "number": 3, "location": "lines 874-1745", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-04/", "snippets": [ "... t would be more economical to operate, selling the product below cost, at any loss up to 30 IROM COMPETITION TO CO-OPERATION 14 per cent. — although this would inevitablj'^ ruin the company — rather than close down and ac- cept the still greater toss of the entire fixed cost. But operation at a loss, though not so rapidly destructive as shut down, still means financial disaster, and when forced by unrestricted com- petition thus ends in rui ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-13", "section_label": "Chapter 12: Evolution: Political Government", "section_title": "Evolution: Political Government", "kind": "chapter", "sequence": 13, "number": 12, "location": "lines 5328-5797", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-13/", "snippets": [ "... s transportation and communication, agriculture, the animal industries, dairying, etc. — in short, all the human activities which deal directly or indirectly with the necessities of life. The economic development of the world, ac- celerated by the world's war, has made such a co-operative industrial organization of our na- tion a necessity of self-preservation. As structural foundation, on which to build such structure by evolution, in correspondence w ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-14", "section_label": "Chapter 13: Evolution: Industrial Government", "section_title": "Evolution: Industrial Government", "kind": "chapter", "sequence": 14, "number": 13, "location": "lines 5798-6232", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-14/", "snippets": [ "... the other hundred thousands or mil- lions, who have escaped this time, but have the possibility of the same fate hanging over them. Thus the assurance of work when capaljle of working, the insurance of a living in their ac- customed standard when not capable of work- ing, are the fundamental requisites to secure interest in the maintenance of existing condi- AMERICA AND THE NEW EPOCH tions witlioiit which there can be no real pa- triotism, ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-15", "section_label": "Chapter 14: Evolution: Inhibitory Power", "section_title": "Evolution: Inhibitory Power", "kind": "chapter", "sequence": 15, "number": 14, "location": "lines 6233-6597", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-15/", "snippets": [ "... that the influence of the individual on so- ciety should be proportional to his capacity — democratic; everybody has the same chance, the same right, and there is no discrimination — egalite; everybody is free to choose his ac- tivity, to develop his individuality — liberie; everybody is guaranteed in his standard of living, as a matter of necessity, as otherwise the organization would not be commensal, and could not exist, but the present indiffe ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-01-recommendations", "section_label": "Report Section 2: Recommendations", "section_title": "Recommendations", "kind": "report-section", "sequence": 2, "number": 2, "location": "PDF pages 7-12, lines 145-720", "status": "pdf-text-extracted-candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "snippets": [ "... ons, so that in case of a substation shut- ting down by trouble in the generating section feeding it, the adjacent substation can maintain service, etc. Also, the question of the control of the converters in the substations should be investigated, whether the A.C. circuit breakers might be set somewhat higher; whether the D.C. reverse current relay may not be given a time limit and its setting increased; whether a D.C. power limiting resistance might be considered, etc." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1003-1658", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-02/", "snippets": [ "... lectric gradient: F / = y ampere turns per G = J volts per cm. G = -, volts per cm. cm. Magnetic-field intensity: Dielectric-field inten- sity: JC = Airf. K = 7^109. Permeability: Permittivity or specific capacity: Conductivity: '^ ac D I , y = P mho-cm. Reluctivity: (Elastivity ?): Resistivity: P=^- 1 _^ 1 G , p = - = -rOhm-cm. ^ (B K D' 7 / Specific magnetic energy Specific dielectric energy : Specific power: ^^5 — 10~^ joules per cm^ OTT 2 ttv^KD joules ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1659-2484", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-03/", "snippets": [ "... illations appear, as in the dis- charge of the Leyden jar. Let, as represented in Fig. 10, a continuous voltage eo be im- pressed upon a wire coil of resistance r and inductance L (but A current Iq = — flows through the coil and % t 1 % io A C c c ..1. 1 Fig. 10. — Magnetic Single-energy Transient. negligible capacity), a magnetic field $0 10' Lio interlinks with the coil. Assuming now that the voltage eo is suddenly withdrawn, without changing 19 20 ELECTRIC DISCHARGE ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 6125-6803", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-09/", "snippets": [ "... 112 ELECTRIC DISCHARGES, WAVES AND IMPULSES. power a fraction is consumed in the line, the rest suppUed to the load. 40. The diagram of this transient power transfer of the system thus is very similar to that of the permanent power transmis- sion by alternating currents: a source of power, a partial con- sumption in the line, and the rest of the power consumed in the load. However, this transient power-transfer diagram does not repre- sent the entire power which is being consumed in the circuit, as power is also suppli ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 5521-6088", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "snippets": [ "... 112 ELECTRIC DISCHARGES, WAVES AND IMPULSES. power a fraction is consumed in the line, the rest supplied to the load. 40. The diagram of this transient power transfer of the system thus is very similar to that of the permanent power transmis- sion by alternating currents: a source of power, a partial con- sumption in the line, and the rest of the power consumed in the load. However, this transient power-transfer diagram does not repre- sent the entire power which is being consumed in the circuit, as power is also suppli ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-02", "section_label": "Chapter 2: Potential Series And Exponential Function", "section_title": "Potential Series And Exponential Function", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3492-6063", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-02/", "snippets": [ "... ite series frequently simplifies the calculation. Very convenient for development into an infinite series of powers or roots, is the binomial theorem, (14) X * n(n-l) _ n(n-l)(n-2) ^ If II 4 where |w«-lX2x3X. . .Xm. Thus, for instance, in an alternating-current circuit of resistance r, reactance x, and supply voltage e, the curi-ent is. ^■v^T7^ \"^) 60 ENGINEERING MATHEMATICS. If this circuit is practically non-inductive, as an incandescent lighting circuit; that is, if x is small compared with r, (15) can ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... propagation (velocity of light). Since the field intensity decreases inversely propor- tional to the distance x, it thus is proportional to y= — - — ; (41) and the total magnetic flux then is / 2= j ydx A'-l) -j^T^'i' <*2) If the current is an alternating current, that is, f (t) a trigonometric function of time, equation (42) leads to the functions, /sin ; X \"J dx: cos X ^ -ax. (43) If the current is a dh-ect current, rising as exponential function of the time, equation (42) leads to the functio ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-03", "section_label": "Lecture 3: Gravitation And The Gravitational Fleld", "section_title": "Gravitation And The Gravitational Fleld", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2389-3594", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-03/", "snippets": [ "... tan CO = v/vq. Suppose now the car C, in Fig. 16, is not moving at constant velocity, but at increasing velocity, so that when the bullet enters the car, at A, the velocity is Vi, and when it ( i ^ I B2B, B \\ — ^-a \\ \\ R •^ \\f A C \\ \\ \\ \\ Of \\ \\ >Vf Fig. 16. leaves the car, at the point B of the track, it is greater and is v^. Then the angle which the bullet makes relative to the car is tan coi = Vilv^ at the entrance of the bullet at A and is tan C02 = Vijv^ (thus bei ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-06", "section_label": "Lecture 6: Higher Harmonics Of The Generator Wave", "section_title": "Higher Harmonics Of The Generator Wave", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3133-3507", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-06/", "snippets": [ "... rcuit Short circuiting a generator harmonic, however, gives large 8o GENERAL LECTURES short circuit currents, due to the constant potential character, and is therefore dangerous. HIGHER HARMONICS OF SYNCHRONOUS MACHINES In synchronous machines, as alternating current genera- tors, the higher harmonics are : At No Load I St. The distribution of magnetism in the air gap depends on the shape of the field poles; it is not a sine wave; neither is the e. m. f . induced by it in an armature a sine wave. Since there are ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-16", "section_label": "Lecture 16: The Incandescent Lamp", "section_title": "The Incandescent Lamp", "kind": "lecture", "sequence": 16, "number": 16, "location": "lines 9687-9919", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-16/", "snippets": [ "... nt lamps are operated on constant potential ; and only for outdoor lighting, that is, for street lighting in cases where the arc lamp is too large and too expensive a unit of light for the requirements, incandescent lamps are used on a constant, direct or alternating current cir- cuit; they are then usually built for the standard arc circuits, and thus for low voltage. For general convenience the efficiency of incandescent lamps is given in watts power consumption per horizontal candle power, when operating on such a voltag ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-10", "section_label": "Lecture 10: Light Flux And Distribution", "section_title": "Light Flux And Distribution", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 9389-12573", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-10/", "snippets": [ "... letely extinguished. The shaded area of the radiator consists of two segments, of the respective radii r and r1 : S = D + Dr Let 2 co = angle subtending segment D and 2 co^ = angle subtending segment Dv and denoting the width of the segments thus w = AC, and the total width of the shaded area is p = AB2 = w + w,. (7) From Fig. 76, a = 002 = OA + J~02 - AB2 = r + r, - p; or, p = r + rt - a; hence, by (2), p = r + TI - tan 0. (8) LIGHT FLUX AND DISTRIBUTION. In A 02EO, 205 sin < sin ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-13", "section_label": "Lecture 13: Physiological Problems Of Illuminating Engineering", "section_title": "Physiological Problems Of Illuminating Engineering", "kind": "lecture", "sequence": 13, "number": 13, "location": "lines 17446-17956", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-13/", "snippets": [ "... on c (that is, in this direction it receives no light from C). Within this angle T, both sides of the plane are illuminated by A and B, which obviously is never possible by a resultant vector C. In the illumination of a plane, the differences between the ac- tual illumination by A and B and the illumination which would result, if light were a vector quantity, by (7, are only those of intensity of illumination. With an object of different shape, however, the phenomenon becomes far more complex. Thus the illu ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-06", "section_label": "Theory Section 6: Self-inductance of Continuous-current Circuits", "section_title": "Self-inductance of Continuous-current Circuits", "kind": "theory-section", "sequence": 6, "number": 6, "location": "lines 1785-2249", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-06/", "snippets": [ "... , - j- = log, (- + i) - log, c, where — log^ c = integration constant. At t = 0, i Substituting, E At t = 0, i = /, thus c = / + -; t E\\ -« E h7r \"7' Kon ,—400 1 p;nn *J*S\\J C iV10-»VOltS. And since the effective E.M.F. is given by, — 'eff. 77 —. -^'max. V2 we have E^ft, = V2ir«jyi0-8 = 4.44«*iV^10-8volts, which is tne fundamental formula of alternating-current induction by sine waves. 18 AL TERN A TING-CURRENT PHENOMENA. [§13 13. If, in a circuit of « turns, the magnetic flux, *, inclosed by the circuit is produced by the current flowing in the circuit, the ratio — flux X number of turns X 10~^ current ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-22", "section_label": "Chapter 20: Ri", "section_title": "Ri", "kind": "chapter", "sequence": 22, "number": 20, "location": "lines 24560-25119", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "snippets": [ "... of the wave-shape. In general, as conclusions may be derived that the im- portance of a proper wave-shape is generally greatly over- rated, but that in certain cases sine waves are desirable, in other cases certain distorted waves are preferable. 346 ALTERNATING-CURRENT PHENOMENA. [§§232,233" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-23", "section_label": "Chapter 23: Generaii Foiitfhase Ststems", "section_title": "Generaii Foiitfhase Ststems", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 25120-25270", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-23/", "snippets": [ "CHAPTER XXIII. GENERAIi FOIiTFHASE STSTEMS. 232. A polyphase system is an alternating-current sys- tem in which several E.M.Fs. of the same frequency, but displaced in phase from each other, produce several currents of equal frequency, but displaced phases. Thus any polyphase system can be considered as con- sisting of a number of single circuit ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-26", "section_label": "Chapter 26: Intebunkeid Foiiyfhase Systems", "section_title": "Intebunkeid Foiiyfhase Systems", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 26028-26427", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-26/", "snippets": [ "... system with equalizing return, if all the neutral points are connected with each other. 8.) The power of the polyphase system is — n -P = ^' €* Eli cos if>i at the generator 1 n n -^ = ^1 ^k Eik lijt cos if>ik in the receiving circuits. I 876 ALTERNATING-CURRENT PHENOMENA, [SS 255, 256" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-27", "section_label": "Chapter 27: Tbansfobmation Of Polyphase Systems", "section_title": "Tbansfobmation Of Polyphase Systems", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 26428-26583", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-27/", "snippets": [ "... he primary, and re- turned during the time when the primary power is below the secondary. The most efficient storing device of electric energy is mechanical momentum in revolving machinery. It has, however, the disadvantage of requiring attendance. 380 ALTERNATING-CURRENT PHENOMENA. [§259" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-03", "section_label": "Chapter 3: Law Of Electro-Magnetic Induction", "section_title": "Law Of Electro-Magnetic Induction", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 1606-1742", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-03/", "snippets": [ "... g = 4 « 4> JVW ~ 8 volts. Since the maximum E.M.F. is given by, — •^maz. = £ ^avg we have ^\"max. = 27r»7V710-8VOltS. And since the effective E.M.F. is given by, — we have £es. = = 4.44 n 4>^10- 8 volts, which is the fundamental formula of alternating-current induction by sine waves. 18 AL TERN A TING-CURRENT PHENOMENA, 13. If, in a circuit of n turns, the magnetic flux, , inclosed by the circuit is produced by the current flowing in the circuit, the ratio — flux X number of turns X 10~8 current . ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-31", "section_label": "Chapter 31: Three-Phase System", "section_title": "Three-Phase System", "kind": "chapter", "sequence": 31, "number": 31, "location": "lines 25598-25903", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-31/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-31/", "snippets": [ "... TERNA TING-CURRENT PHENOMENA. as three linear equations with the three quantities 2T/, Substituting the abbreviations : a I \\7 7 I I/\" 7 \\ I/\" 7 ~\\7 7 i ~T * 1^2 ~T *1^3)> -tZ^S) •*8^'2 I 7 V 7 /1_1_V7_1_V7N>/ ^zt y 2-^D — V*1 ~r -^s^i T *»^V / A c, F2Z3, F3Z2 a, - (1 + ^^3 + , Y,Zlt -(1 + F3Z1+F3Z2) - (1 + Y,Z2 + FiZ,), c, F3Z2 F.Z3, c2, YtZ, Y.Z,, 1, - (1 + F3ZX + F3Z2) (i + ^iz. + yiz,), F2z3, £ A = / FIZS, - (i FaZ2, F2ZX, it is: D 72 = i __ F2Z>2- hence, (8) (9) ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-01", "section_label": "Chapter 1: Speed Control Of Induction Motors", "section_title": "Speed Control Of Induction Motors", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1368-3542", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-01/", "snippets": [ "... \\ \\ V \\ LI 16 ELECTRICAL APPARATUS is calculated in the usual way as described on page 318 of \"Theoretics] Element* of Electrical Engineering.\" For any value of slip, -s, and cor responding value of torque, T, the secondary current is *'[ = c y/ac -\\- a*-. To this secondary current corre- sponds, by Fig. (j, the resistance, r, of the pyro-electric conductor, and the insertion of r thus increases the slip in proportion to the jni'iea-cil secondary resistance: ■> where ri = 0.1 in the present instan ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-02", "section_label": "Chapter 2: Multiple Squirrel-Cage Induction Motor", "section_title": "Multiple Squirrel-Cage Induction Motor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3543-5554", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-02/", "snippets": [ "... ction motors the secondary of the first motor is connected to the primary of the second motor, the second machine operates as a motor with the voltage and frequency impressed upon it by the secondary of the first machine. The first machine acts as general alternating-current transformer or frequency converter (see Chapter XII), changing^ part of the primary impressed power into secondary electrical power for the supply of the second machine, and a part into mechanical work. The frequency of the secondary voltage of the firs ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-05", "section_label": "Chapter 6: Induction-Motor Regulation And Stability", "section_title": "Induction-Motor Regulation And Stability", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 10583-12397", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-05/", "snippets": [ "... ing devices their effect with increasing speed and thus g laracteristics of forms similar to Fig. 53 iced curve as shown in Fig. 53, even at a loat torque, three speed points may exist of ne is unstable. In polyphase synchronous n rs, when starting by alternating current, t in motor, 1 as icpn- tbe form i it up io >n single- i? is nearer which de- ve motor- With a requiring which the lotors and lat is, as INDUCTION-MOTOR REGULATION 137 induction machines, the phenomenon is frequently observed that the mach ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-06", "section_label": "Chapter 7: Higher Harmonics In Induction Motors", "section_title": "Higher Harmonics In Induction Motors", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 12398-13955", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-06/", "snippets": [ "CHAPTER VII HIGHER HARMONICS IN INDUCTION MOTORS 88. The usual theory and calculation of induction motors, .■is discussed in '* Theoretical Elements of Electrical Enginccr- ing\" and in \"Theory and Calculation of Alternating-current Phenomena,\" is based on the assumption of the sine wave. That U, it is assumed that the voltage impressed upon the motor per phase, and therefore the magnetic flux and the current, KM sine waves, and it is further assumed, that the distribution of the wi ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-07", "section_label": "Chapter 8: Synchronizing Induction Motors", "section_title": "Synchronizing Induction Motors", "kind": "chapter", "sequence": 7, "number": 8, "location": "lines 13956-14465", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-07/", "snippets": [ "... same shaft or when driven by synchronous motors from the same supply. As in the induction-motor secondary an e.m.f. of definite fre- quency, that of slip, is generated by its rotation through the revolving motor field, the induction-motor secondary is an alternating-current generator, which is short-circuited at speed and loaded by the starting rheostat during acceleration, and the problem of operating two induction motors with their secondaries connected in parallel on the same external resistance is thus the same as that o ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-08", "section_label": "Chapter 9: Synchronous Induction Motor", "section_title": "Synchronous Induction Motor", "kind": "chapter", "sequence": 8, "number": 9, "location": "lines 14466-14550", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-08/", "snippets": [ "... ng to the phase displacement between ad- mittance and primary circuit; that is, the lag or lead of the maximum admittance with regard to the primary maximum. Hence an induction motor with single-armature circuit at syn- chronism acts either as motor or as alternating-current generator according to the relative position of the armature circuit with respect to the primary circuit. Thus it can be called a syn- chronous induction motor or synchronous induction generator, since it is an induction machine giving torque at synchroni ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-09", "section_label": "Chapter 10: Hysteresis Motor", "section_title": "Hysteresis Motor", "kind": "chapter", "sequence": 9, "number": 10, "location": "lines 14551-14761", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-09/", "snippets": [ "... . From the equation of torque it follows, however, that at constant impressed e.m.f., or current — that is, constant SF — the torque is constant and independent of the speed; and there- fore such a motor arrangement is suitable, and occasionally used as alternating-current meter. For s<0, we have a < 0, and the apparatus is an hysteresis generator. 99. The same result can be reached from a different point of view. In such a magnetic system, comprising a movable iron disk, 7, of uniform magnetic reluctance in a revolving ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-16", "section_label": "Chapter 16: Load Balance Of Polyphase Systems", "section_title": "Load Balance Of Polyphase Systems", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 29302-30428", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-16/", "snippets": [ "... tance, in power-factor compensation etc. — but Q is the vector resultant of the reactive powers of the individual circuits, while the total reactive power of the system is the algebraic sum of the individual reactive powers (see \"Theory and Calculation of Alternating- current Phenomena,\" Chapter XVI). Thus, for instance, in a system of balanced load, even if the load is reactive, Q = 0. Thus, Q is the unbalanced reactive 318 ELECTRIC CIRCUITS power of the system, and does not include the reactive power, which is balanced ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-25", "section_label": "Chapter 3: Inductance And Resistance In Continuous Current Circuits", "section_title": "Inductance And Resistance In Continuous Current Circuits", "kind": "chapter", "sequence": 25, "number": 3, "location": "lines 2659-3514", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-25/", "snippets": [ "... not •enter the equations of stationary condition, but, if e0 = impressed e.m.f., r = resistance, L = inductance, the permanent value of /> current is ia = — • r Therefore less care is taken in direct-current circuits to reduce the inductance than in alternating-current circuits, where the inductance usually causes a drop of voltage, and direct-current circuits as a rule have higher inductance, especially if the circuit is used for producing magnetic flux, as in solenoids, electro- magnets, machine-fields. Any change o ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-32", "section_label": "Chapter 10: Mutual Inductance", "section_title": "Mutual Inductance", "kind": "chapter", "sequence": 32, "number": 10, "location": "lines 10475-12216", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "snippets": [ "... it, shown diagrammatically in Fig. 38, we have di. di~ ~ * and e2 = r2i2 + x2— 2 + xm ^ • (6) Differentiating (6) gives de2 _ di2 d?i2 d2il ~dd~~T2dd^ x*~dF~VXm^] * See the chapters on induction machines, etc., in \" Theory and Calcula- tion of Alternating Current Phenomena.\" MUTUAL INDUCTANCE 145 from (5) follows /^ / « v* *\"~ , ^ ~^r \"' and, differentiated, fo * Substituting (8) and (9) in (7) gives del de2 _ . dil + <*,*,-*-•>£, (10) and analogously, de2 de^ + (*,*, - ^2) ^ • (ID Eq ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-33", "section_label": "Chapter 40: General System Of Circuits", "section_title": "General System Of Circuits", "kind": "chapter", "sequence": 33, "number": 40, "location": "lines 12217-12884", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-33/", "snippets": [ "... f., e0, as a battery, in series with an inductive reactance x. The transformers obviously must be such as not to be saturated magnetically by the component of continuous current which traverses them, must for instance be open core transformers. Fig. 42. Alternating-current circuit containing mutual and self-inductive reactance, resistance and continuous e.m.f. Let iv iv iw is, i4 = currents in the different circuits; then, at the dividing point P, by equation (2) we have hence, iQ = i3 — i2, leaving four independent c ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-35", "section_label": "Chapter 13: Transient Term Of The Rotating Field", "section_title": "Transient Term Of The Rotating Field", "kind": "chapter", "sequence": 35, "number": 13, "location": "lines 13936-14548", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-35/", "snippets": [ "... ntensity, and revolves at constant synchronous velocity. When acting upon a magnetic circuit of constant reluctance in all directions, such a polyphase system of m.m.fs. produces a revolving magnetic flux, or a rotating field. (\" Theory and Calculation of Alternating Current Phenomena,\" 4th edition, Chapter XXXIII, paragraph 368.) That is, if np equal mag- netizing coils are arranged under equal space angles of - np electrical degrees, and connected to a symmetrical np phase system, that is, to np equal e.m.fs. displaced i ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-36", "section_label": "Chapter 14: Short-Circuit Currents Of Alternators", "section_title": "Short-Circuit Currents Of Alternators", "kind": "chapter", "sequence": 36, "number": 14, "location": "lines 14549-15353", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "snippets": [ "... ure resistance, rv is very small compared with its self- inductive reactance, xv it can be neglected compared thereto, and the short-circuit current of the alternator, in permanent condition, thus is As shown in Chapter XXII, \"Theory and Calculation of Alternating Current Phenomena,\" the armature reaction can be represented by an equivalent, or effective reactance, z2, and the self-inductive reactance, xv and the effective reactance of 199 200 TRANSIENT PHENOMENA armature reaction, x2J combine to form the synchronous ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-46", "section_label": "Chapter 6: Alternating Magnetic Flux Distribution", "section_title": "Alternating Magnetic Flux Distribution", "kind": "chapter", "sequence": 46, "number": 6, "location": "lines 23948-24980", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "snippets": [ "... dj[- -j2^/(BlO-8. (7) 50. Differentiating (5) in respect to I, and substituting (7) therein, gives .0-8(B, (8) or, writing c2 = /a2 = 0.4 Tr2/^ 10-8, (9) a2 = 0.4 rfXn 10-8, (10) we have - This differential equation is integrated by X*}^9 (Pi ' + (xiX2-Xm*)^ (12) and del */ • , r + \"*\" ^ \" rr' + (13) 146 TRAN ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-37", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 37, "number": 1, "location": "lines 15354-15625", "status": "candidate", "occurrence_count": 29, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "snippets": [ "CHAPTER I. INTRODUCTION. 1. Whenever in an electric circuit a sudden change of the circuit conditions is produced, a transient term appears in the circuit, that is, at the moment when the change begins, the circuit quantities, as current, voltage, magnetic flux, etc., cor- respond to the circuit conditions existing before the change, but do not, in general, correspond to the circ ...", "... sting before the change, but do not, in general, correspond to the circuit conditions brought about by the change, and therefore must pass from the values corresponding to the previous condition to the values corre- sponding to the changed condition. This transient term may be a gradual approach to the final condition, or an approach by a series of oscillations of gradual decreasing intensities. Gradually — after indefinite time theoretically, after relatively short time practically — the transient term disappears, ...", "... condition. This transient term may be a gradual approach to the final condition, or an approach by a series of oscillations of gradual decreasing intensities. Gradually — after indefinite time theoretically, after relatively short time practically — the transient term disappears, and permanent conditions of current, of voltage, of magnetism, etc., are established. The numerical values of current, of voltage, etc., in the permanent state reached after the change of circuit con- ditions, in general, are different fr ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-10", "section_label": "Chapter 10: Instability Of Circuits : The Arc", "section_title": "Instability Of Circuits : The Arc", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 17632-21381", "status": "candidate", "occurrence_count": 27, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-10/", "snippets": [ "... s and arc-lighting machinery, the opinion prevailed that theoretical calculations are impossible and only design by trying, based on practical experience, feasible. The first class of imstable phenomena, which was systemat- ically investigated, were the transients, and even today it is ques- tionable whether a systematic theoretical classification and in- vestigation of the conditions of instability in electric circuits is yet feasible. Only a preliminary classification and discussion of such phenomena shall be att ...", "... he conditions of instability in electric circuits is yet feasible. Only a preliminary classification and discussion of such phenomena shall be attempted in the following. Three main types of instability in electric systems may be distinguished : I. The transients of readjustment to changed circuit con- ditions. II. Unstable electrical equilibrium, that is, the condition in which the eflfect of a cause increases the cause. III. Permanent instability resulting from a combination of circuit constants which can not ...", "... t to changed circuit con- ditions. II. Unstable electrical equilibrium, that is, the condition in which the eflfect of a cause increases the cause. III. Permanent instability resulting from a combination of circuit constants which can not coexist. I. Transients 82. Transients are the phenomena by which, at the change of circuit conditions, current, voltage, etc., readjust themselves from the values corresponding to the previous condition to the values corresponding to the new condition of the circuit. For in- ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-34", "section_label": "Chapter 12: Magnetic Saturation And Hysteresis In Alternat Ing-Current Circuits", "section_title": "Magnetic Saturation And Hysteresis In Alternat Ing-Current Circuits", "kind": "chapter", "sequence": 34, "number": 12, "location": "lines 12885-13935", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-34/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-34/", "snippets": [ "... lux produced by the current immediately assume their final or permanent values only in case the circuit is closed at that point of the e.m:f. wave at which the permanent current is zero. Closing the circuit at any other point of the e.m.f. wave produces a transient term of current and of magnetic flux. So for instance, if the circuit is closed when the current i should have its negative maximum value - 70, and therefore the magnetic flux and the magnetic flux density also be at their negative maximum value - ^>0 and ...", "... he higher the resistance. That is, starting at a value somewhat below 2 4>0, it decreases below zero, and reaches a negative value. During the third half wave the magnetic flux, starting not at zero as in the first half wave, but at a negative 179 180 TRANSIENT PHENOMENA value, thus reaches a lower positive maximum, and thus grad- ually, at a rate depending upon the resistance of the circuit, the waves of magnetic flux 4>, and thereby current i, approach their final permanent or symmetrical cycles. 100. In the precedin ...", "... hat is, the maximum magnetic flux density would not rise to 20,000, but remain considerably below this value. The maximum current, however, would be still very much greater than twice the normal maximum. That is, in an iron-clad circuit, in starting, the transient term of current may rise to values very much higher than in air magnetic circuits. While in the latter it is limited to twice the normal value, in the iron-clad circuit, if the magnetic flux density reaches into the range of magnetic saturation, very much ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-47", "section_label": "Chapter 7: Distribution Of Alternating-Current Density In Conductor", "section_title": "Distribution Of Alternating-Current Density In Conductor", "kind": "chapter", "sequence": 47, "number": 7, "location": "lines 24981-26094", "status": "candidate", "occurrence_count": 23, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "snippets": [ "... lity, as iron, to investigate this phenomenon. An approximate determination of this effect for the purpose of deciding whether the unequal current distribution is so small as to be negligible in its effect on the resistance of the conductor, 369 370 TRANSIENT PHENOMENA or whether it is sufficiently large to require calculation and methods of avoiding it, is given in \" Alternating-Current Phe- nomena,\" Chapter XIV, paragraph 133. An appreciable increase of the effective resistance over the ohmic resistance may be expe ...", "... ductor, that is, the voltage consumed per unit length in the conductor after subtracting the e.m.f. consumed by the self- inductance of the external magnetic field of the conductor; thus, if El = the total supply voltage per unit length of conductor 372 TRANSIENT PHENOMENA and E2 = the external reactance voltage, or voltage consumed by the magnetic field outside of the conductor, between the con- ductors, we have Let 7=^4- ji2 = current density in conductor element dl, & = ^ + y&2 = magnetic density in conductor eleme ...", "... 7 \"-^T^-^-f £~c(l-j}l\\. (15) Substituting e±^' = coscZ ± jsincZ (16) gives /= 45(e+^ + e-rf) coscZ - j (e+cl - e~cl) sincZj, (17) and for Z = Z0, or at the conductor surface, Iml = A{(e+cl» + e-c'») cos cZ0 - j (e+cl° - £~cl<>) sincZJ. (18) 374 TRANSIENT PHENOMENA At the conductor surface, however, no e.m.f. of self-inductance due to the internal field exists, and /o - ^o- (19) Substituting (19) in (18) gives the integration constant A, and this substituted in (17) gives the distribution of current density thr ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "LECTURE VIII. TRAVELING WAVES. 33. In a stationary oscillation of a circuit having uniformly distributed capacity and inductance, that is, the transient of a circuit storing energy in the dielectric and magnetic field, current and voltage are given by the expression i = ioe-\"^ cos ((/> T CO — 7), ^ . . e = eoe~\"' sin ((^ =F co — 7), where T co — 7), ) where 0 is the time angle, co the distance angle, u the exponential decr ...", "... f power, p0, is zero, and no power flows along the circuit, but there is a surge of power, of double frequency. That is, power flows first one way, during one-quarter cycle, and then in the opposite direction, during the next quarter- cycle, etc. Such a transient wave thus is analogous to the permanent wave of reactive power. As in a stationary wave, current and voltage are in quadrature with each other, the question then arises, whether, and what TRAVELING WAVES. 89 physical meaning a wave has, in which ...", "... d on the step-down trans- ^> Line Transformer Line Fig. 40. former, the high-tension switches are opened at the generator end of the transmission line. The energy stored magnetically and dielectrically in line and transformer then dissipates by a transient, as shown in the oscillogram Fig. 41. This gives the oscillation of a circuit consisting of 28 miles of line and 2500-kw. 100-kv. step-up and step-down transformers, and is produced by discon- necting this circuit by low-tension switches. In the transform ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-29", "section_label": "Chapter 7: Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "section_title": "Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "kind": "chapter", "sequence": 29, "number": 7, "location": "lines 6798-7825", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "snippets": [ "... n 00 -- rB sin o- + B (x — xc) cos a- = 0. Substituting — 4 tan 7 = in equations (10) gives x - xc r ± s and = 00 + ? = indefinite, and the equation of current, (9), thus is i = -cos (6 - 60 -7) + A/~ (ID (12) (13) 90 TRANSIENT PHENOMENA and, substituting (12) in (7), and rearranging, the potential difference at the condenser terminals is . (14) The two integration constants Al and A2 are given by the terminal conditions of the problem. Let, at the moment of start, 0-0, i = iQ ...", "... E where and r r-±£ Cos r+s (x - x — xc tan 7 . = - — > = Vr2 - 4 x xr (19) (ID The expressions of i and et consist of three terms each : (1) The permanent term, which is the only one remaining after some time; (2) A transient term depending upon the constants of the circuit, r, s, xci z0, x, the impressed e.m.f., E, and its phase 00 at the moment of starting, but independent of the conditions existing in the circuit before the start; and 92 TRANSIENT PHENOMENA (3) A term d ...", "... after some time; (2) A transient term depending upon the constants of the circuit, r, s, xci z0, x, the impressed e.m.f., E, and its phase 00 at the moment of starting, but independent of the conditions existing in the circuit before the start; and 92 TRANSIENT PHENOMENA (3) A term depending, besides upon the constants of the circuit, upon the instantaneous values of current and potential difference, iQ and e0, at the moment of starting the circuit, and thereby upon the electrical conditions of the circuit before impres ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-35", "section_label": "Chapter 13: Transient Term Of The Rotating Field", "section_title": "Transient Term Of The Rotating Field", "kind": "chapter", "sequence": 35, "number": 13, "location": "lines 13936-14548", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-35/", "snippets": [ "CHAPTER XIII. TRANSIENT TERM OF THE ROTATING FIELD. 106. The resultant of np equal m.m.fs. equally displaced from each other in space angle and in time-phase is constant in intensity, and revolves at constant synchronous velocity. When acting upon a magnetic circuit of constant ...", "... olving m.m.f., of intensity SF0 = — &, where $ Zi is the maximum value (hence — — the effective value) of the \\ V2 I m.m.f. of each coil. In starting, that is, when connecting such a system of mag- netizing coils to a polyphase system of e.m.fs., a transient term appears, as the resultant magnetic flux first has to rise to its constant value. This transient term of the rotating field is the resultant of the transient terms of the currents and therefore the m.m.fs. of the individual coils. 107. If, then, $ = ...", "... ue) of the \\ V2 I m.m.f. of each coil. In starting, that is, when connecting such a system of mag- netizing coils to a polyphase system of e.m.fs., a transient term appears, as the resultant magnetic flux first has to rise to its constant value. This transient term of the rotating field is the resultant of the transient terms of the currents and therefore the m.m.fs. of the individual coils. 107. If, then, $ = nl = maximum value of m.m.f. of each coil, where n = number of turns, and / = maximum value of curre ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-36", "section_label": "Chapter 14: Short-Circuit Currents Of Alternators", "section_title": "Short-Circuit Currents Of Alternators", "kind": "chapter", "sequence": 36, "number": 14, "location": "lines 14549-15353", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "snippets": [ "... As shown in Chapter XXII, \"Theory and Calculation of Alternating Current Phenomena,\" the armature reaction can be represented by an equivalent, or effective reactance, z2, and the self-inductive reactance, xv and the effective reactance of 199 200 TRANSIENT PHENOMENA armature reaction, x2J combine to form the synchronous react- ance, XQ = xl + x2, and the short-circuit current of the alterna- tor, in permanent condition, therefore can be expressed by where e0 = nominal generated e.m.f. 113. The effective reactanc ...", "... the momentary short-circuit current over the permanent short- circuit current is moderate, but may reach enormous values in machines of low self-inductance and high armature reaction, as large low frequency turbo alternators. 114. Superimposed upon this transient term, resulting from the gradual adjustment of the field flux to a change of m.m.f., is the transient term of armature reaction. In a polyphase alternator, the resultant m.m.f. of the .armature in permanent conditions is constant in intensity and revolves ...", "... ch enormous values in machines of low self-inductance and high armature reaction, as large low frequency turbo alternators. 114. Superimposed upon this transient term, resulting from the gradual adjustment of the field flux to a change of m.m.f., is the transient term of armature reaction. In a polyphase alternator, the resultant m.m.f. of the .armature in permanent conditions is constant in intensity and revolves with regard to the armature at uniform synchronous speed, hence is stationary 202 TRANSIENT PHEN ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... frequency of the impressed alternating e.m.fs., in resonance condition, is the velocity of light divided by four times the length of the line; or, in free oscillation or resonance condition, the length of the line is one quarter wave length. 279 280 TRANSIENT PHENOMENA If then I = length of line, S = speed of light, the frequency of oscillations or natural period of the line is — '• \"4? or, with I given in miles, hence S = 188,000 miles per second, it is , 47,000 /o = — j- cycles. (2) To get a resonance frequen ...", "... o- duces in all neighboring conductors secondary currents, which react upon the primary current and thereby introduce e.m.fs. of mutual inductance into the primary circuit. Mutual induc- tance is neither in phase nor in quadrature with the current, 282 TRANSIENT PHENOMENA and can therefore be resolved into a power component of mutual inductance in phase with the current, which acts as an increase of resistance, and into a reactive component in quadrature with the current, which decreases the self-inductance. This mutual ...", "... eiver circuit, and e.m.f., E0, at generator terminals are given; the current and e.m.f. at any point of circuit to be deter- mined, etc. 7. Counting- now the distance, I, from a point 0 of the line which has the e.m.f. + je,f and the current 284 TRANSIENT PHENOMENA and counting I positive in the direction of rising power and negative in the direction of decreasing power, at any point I, in the line differential dl the leakage current is Egdl and the capacity current is - jEb dl; hence, the total current consu ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-05", "section_label": "Lecture 5: Single-Energy Transient Of Ironclad Circuit", "section_title": "Single-Energy Transient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2972-3286", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "snippets": [ "LECTURE V. SINGLE-ENERGY TRANSIENT OF IRONCLAD CIRCUIT. 22. Usually in electric circuits, current, voltage, the magnetic field and the dielectric field are proportional to each other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discusse ...", "LECTURE V. SINGLE-ENERGY TRANSIENT OF IRONCLAD CIRCUIT. 22. Usually in electric circuits, current, voltage, the magnetic field and the dielectric field are proportional to each other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnetic materials, or if the dielectric field reaches de ...", "... . If the magnetic circuit is closed entirely by iron, the magnetic flux is not proportional to the current, and the inductance thus not constant, but varies over the entire range of currents, following the permeability curve of the iron. Furthermore, the transient due to a decrease of the stored magnetic energy differs in shape and in value from that due to an increase of magnetic energy, since the rising and decreasing magnetization curves differ, as shown by the hysteresis cycle. Since no satisfactory mathemati ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-05", "section_label": "Lecture 5: Single-Energy Tra.Nsient Of Ironclad Circuit", "section_title": "Single-Energy Tra.Nsient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3387-3720", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-05/", "snippets": [ "LECTURE V. SINGLE-ENERGY TRA.NSIENT OF IRONCLAD CIRCUIT. 22. Usually in electric circuits; current, voltage, the magnetic field and the dielectric field are proportional to each other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnetic materials, or if the dielectric field reaches de ...", "... . If the magnetic circuit is closed entirely by iron, the magnetic flux is not proportional to the current, and the inductance thus not constant, but varies over the entire range of currents, following the permeability curve of the iron. Furthermore, the transient due to a decrease of the stored magnetic energy differs in shape and in value from that due to an increase of magnetic energy, since the rising and decreasing magnetization curves differ, as shown by the hysteresis cycle. Since no satisfactory mathemati ...", "... gy, since the rising and decreasing magnetization curves differ, as shown by the hysteresis cycle. Since no satisfactory mathematical expression has yet been found for the cyclic curve of hysteresis, a mathematical calcula- tion is not feasible, but the transient has to be calculated by an 52 SINGLE-ENERGY TRANSIENT OF IRONCLAD CIRCUIT. 53 approximate step-by-step method, as illustrated for the starting transient of an alternating-current transformer in '' Transient Elec- tric Phenomena and Oscillations/' Sec ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-33", "section_label": "Chapter 40: General System Of Circuits", "section_title": "General System Of Circuits", "kind": "chapter", "sequence": 33, "number": 40, "location": "lines 12217-12884", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-33/", "snippets": [ "... containing resistance and inductance, but no capacity, a system of e.m.fs., ey be impressed. These e.m.fs. may be of any frequency or wave shape, or may be continuous or anything else, but are supposed to be given by their equations. They may be free of transient terms, or may contain transient terms depending upon the currents in the system. In the latter case, the dependency of the e.m.f. upon the currents must obviously be given. Then, in each branch circuit, ^5~=0, (1) where e = total impressed e.m.f.; r. ...", "... ctance, but no capacity, a system of e.m.fs., ey be impressed. These e.m.fs. may be of any frequency or wave shape, or may be continuous or anything else, but are supposed to be given by their equations. They may be free of transient terms, or may contain transient terms depending upon the currents in the system. In the latter case, the dependency of the e.m.f. upon the currents must obviously be given. Then, in each branch circuit, ^5~=0, (1) where e = total impressed e.m.f.; r. = resistance; L = induc- tance, ...", "... y value of current iK, reached for t = . Substituting (6) in (4) gives M^-^O. (7) 1 For t = oo , this equation becomes These n equations (8) determine the stationary components of the n currents, iK'. Subtracting (8) from (7) gives, for the transient components of currents iK, the n equations 170 TRANSIENT PHENOMENA Reversing the order of summation in (10) gives A-o =0- (11) The n equations (11) must be identities, that is, the coefficients of £~aJ must individually disappear. Each equat ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "LECTURE VII. LINE OSCILLATIONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy surges between magnetic — and dielectric — , and a transient component, by which the total stored energy decreases. Considering only the periodic component, the maximum value of magnetic energy must equal the maximum value of dielectric '^'^e^gy- Li„^ Ce, 0 \"^^0 (1) where Iq = maximum value of transien ...", "... ransient component, by which the total stored energy decreases. Considering only the periodic component, the maximum value of magnetic energy must equal the maximum value of dielectric '^'^e^gy- Li„^ Ce, 0 \"^^0 (1) where Iq = maximum value of transient current, 60 = maximum value of transient voltage. This gives the relation between Bq and Iq, ^^ = Jl ,^ = 1, (2) where Zq is called the natural impedance or surge impedance, 2/0 the natural or surge admittance of the circuit. As the maximum of curre ...", "... tored energy decreases. Considering only the periodic component, the maximum value of magnetic energy must equal the maximum value of dielectric '^'^e^gy- Li„^ Ce, 0 \"^^0 (1) where Iq = maximum value of transient current, 60 = maximum value of transient voltage. This gives the relation between Bq and Iq, ^^ = Jl ,^ = 1, (2) where Zq is called the natural impedance or surge impedance, 2/0 the natural or surge admittance of the circuit. As the maximum of current must coincide with the zero of voltage ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3956-4744", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "snippets": [ "LECTURE VII. LINE OSCILLATIONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy 7\" /j'2 f^ r/>2 surges between magnetic -^- and dielectric — , and a transient £i A component, by which the total stored energy decreases. Considering only the periodic component, the maximum mag- netic energy must equal the maximum dielectric energy, Lio2 _ Ceo2 \"2\" ~2~' where i0 = maximum transient current, e0 = maximum tr ...", "... and dielectric — , and a transient £i A component, by which the total stored energy decreases. Considering only the periodic component, the maximum mag- netic energy must equal the maximum dielectric energy, Lio2 _ Ceo2 \"2\" ~2~' where i0 = maximum transient current, e0 = maximum transient voltage. This gives the relation between eQ and io, e0 V/L_ 1 i-0 = \\C-ZQ-yQ' where ZQ is called the natural impedance or surge impedance, y0 the natural or surge admittance of the circuit. As the maximum of current ...", "... nt £i A component, by which the total stored energy decreases. Considering only the periodic component, the maximum mag- netic energy must equal the maximum dielectric energy, Lio2 _ Ceo2 \"2\" ~2~' where i0 = maximum transient current, e0 = maximum transient voltage. This gives the relation between eQ and io, e0 V/L_ 1 i-0 = \\C-ZQ-yQ' where ZQ is called the natural impedance or surge impedance, y0 the natural or surge admittance of the circuit. As the maximum of current must coincide with the zero of ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-31", "section_label": "Chapter 9: Divided Circuit", "section_title": "Divided Circuit", "kind": "chapter", "sequence": 31, "number": 9, "location": "lines 9228-10474", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "snippets": [ "... h circuits 1 and 2, it and i2 respectively = currents in branch circuits 1 and 2, and i3 = current in undivided part of circuit, 3. Then ia = il + i2 and e.m.f. at the terminals of circuit 1 is of circuit 2 is e = di 121 (2) (3) 122 TRANSIENT PHENOMENA and of circuit 3 is (4) Instead of the inductances, L, and capacities, C, it is usually preferable, even in direct-current circuits, to introduce the reactances, x = 2 nfL = inductive reactance, xc = = con- 2 7T/G densive reactance, referred to a ...", "... fferentiating equations (7), (8), and (9), to eliminate the integral, gives as differential equations of the divided circuit: d?ii dil . de d in din de cPt' . di~ . deQ de and + r*--- Subtracting (14) from (13) gives d\\\\ di, .\\ / d?i2 di2 124 TRANSIENT PHENOMENA Multiplying (15) by 2, and adding thereto (13) and (14), gives, by substituting (1), i3 = it + t'2, (] i fi'l (2 x0 + x,) -^ + (2 r, + r^+ (2 xco + xji, + (2 *0 + x,) J| + (2 r0 + r2) ^ + (2 *Co + xc>'2 = 2 ^ . (17) These two differential equations ...", "... | + (2 r0 + r2) ^ + (2 *Co + xc>'2 = 2 ^ . (17) These two differential equations (16) and (17) are integrated by the functions and - (18) i2 = i2' + A2e~ae, where if and i2 are the permanent values of current, and i\" = A^~a9 and i2\" = A2e~ae are the transient current terms. Substituting (18) in (16) and (17) gives /-/2/j / sl/\\ * \\Jj t/o (JLlci + A^-a9 (a\\ - ar1 + xc) - A2e~a0 (a?x2 - ar2 + xc) = 0 (19) and (Pi ' di' - (2 r0 + r,) + (2'^ + xc)i - a (2 r0 + r,) + (2 zco + xCl)} + A^-^ {a2 (2 x0 + ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-40", "section_label": "Chapter 4: Arc Rectification", "section_title": "Arc Rectification", "kind": "chapter", "sequence": 40, "number": 4, "location": "lines 17755-19259", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "snippets": [ "... s out the arc by interrupting the supply of conducting vapor, and a reversal of the arc stream means stopping the cathode blast and producing a reverse cathode blast, which, in general, requires a voltage higher than the electrostatic striking 249 250 TRANSIENT PHENOMENA voltage (at arc temperature) between the electrodes. With an alternating impressed e.m.f. the arc if established goes out at the end of the half wave, or if a cathode blast is maintained continuously by a second arc (excited by direct current or overlap ...", "... uctuation of the rectified current to the desired amount. In the constant-potential rectifier, instead of the transformer ACS and the reactive coils A a and Ba, generally a compensator or auto-transformer is used, as shown in Fig. 61, in which the 252 TRANSIENT PHENOMENA two halves of the coil, AC and BC, are made of considerable self-inductance against each other, as by their location on different magnet cores, and the reactive coil at c frequently omitted. The modification of the equations resulting herefrom is obviou ...", "... .m.f. and current waves of constant-current mercury arc rectifier. ance, following essentially the exponential curve of a starting current wave, and the energy which is thus consumed by the reactance as counter e.m.f. is returned by maintaining the 254 TRANSIENT PHENOMENA current half wave 1 beyond the e.m.f. wave, i.e., beyond 180 degrees, by 00 time-degrees, so that it overlaps the next half wave 2 by 00 time-degrees. Hereby the rectifier becomes self-exciting, i.e., each half wave of current, by overlapping with the ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-27", "section_label": "Chapter 5: Resistance, Inductance, And Capacity In Series Condenser Charge And Discharge", "section_title": "Resistance, Inductance, And Capacity In Series Condenser Charge And Discharge", "kind": "chapter", "sequence": 27, "number": 5, "location": "lines 4072-5311", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "snippets": [ "... it contain- ing resistance, inductance, and capacity in series, the stationary condition of the circuit is zero current, i = o, and the poten- tial difference at the condenser equals the impressed e.m.f., et =• e, no permanent current exists, but only the transient current of charge or discharge of the condenser. The capacity C of a condenser is defined by the equation . de that is, the current into a condenser is proportional to the rate of increase of its e.m.f. and to the capacity. It is therefore and ...", "... sed e.m.f., whether continuous, alternating, pulsating, etc.; i = current in the circuit at time t; r = resistance; L = inductance, and C = capacity; then the e.m.f. consumed by resistance r is n; the e.m.f. consumed by inductance L is di 47 48 TRANSIENT PHENOMENA and the e.m.f . consumed by capacity C is hence, the impressed e.m.f. is and herefrom the potential difference at the condenser terminals is Ci = -L Cidt = e - ri - L -*• (3) (/ «/ at Equation (2) differentiated and rearranged gives „ d?i di 1 ...", "... ential equation (5). That is, the general integral equation, or solution of differential equation (5), is i = Ai^ + Ai^ . (11) Substituting (11) and (9) in equation (3) gives the potential difference at the condenser terminals as e — (12) 50 TRANSIENT PHENOMENA 31. Equations (11) and (12) contain two indeterminate con- stants, A! and A2, which are the integration constants of the differential equation of second order, (5), and determined by the terminal conditions, the current and the potential differ- ence at ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-53", "section_label": "Chapter 4: Traveling Waves", "section_title": "Traveling Waves", "kind": "chapter", "sequence": 53, "number": 4, "location": "lines 30244-31450", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "snippets": [ "... uations (74) and (75), therefore, is that q be a large quantity compared with q0 = m. In this case — is a small quantity, and thus can usually be neglected in equations (76) and (75), except when C and C' are very different in magnitude. 467 458 TRANSIENT PHENOMENA This gives, under the limiting conditions discussed above, the general equations of the traveling wave, thus: i = £-ut { £+«('-*) [(7^ cos q (t — X) + (7/ sin q (t — X)] - £+s«+x) [C2 cos q (t + X) + C2' sin q (t + X)] + £—<«-*> [C3 cos q(t- X)+ C3' ...", "... ts of a main wave with variable (t - X) and a reflected wave of the same character but moving in opposite direction, thus with the variable (t + X), these waves may be studied separately, and afterwards the effect of their combination investigated. 460 TRANSIENT PHENOMENA Thus, considering at first one of the waves only, that with the variable (t - X), from equations 148 and 149 we have [Alcosq(t - X)+ A/singft - X)] + £-•«-*> [A3 cos q (t - X) + Az' sin q (t - X)}} e~ut { (Aie+8('-x) + A3£-S('-A)) cos q(t- X) + (A1's ...", "... crement £~uA contains only the circuit constant, but does not contain s and q or the other integration constants, resubstituting from equations (71) to (68), x = ai = i VLO, we have uX = u \\/LC I where I is measured in any desired length. 462 TRANSIENT PHENOMENA Therefore the attenuation constant of a traveling wave is }, '(155) and hence the distance decrement of the wave, depends upon the circuit constants r] L, g, C only, but does not depend upon the wave length, frequency, voltage, or current; hence, a ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-25", "section_label": "Chapter 3: Inductance And Resistance In Continuous Current Circuits", "section_title": "Inductance And Resistance In Continuous Current Circuits", "kind": "chapter", "sequence": 25, "number": 3, "location": "lines 2659-3514", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-25/", "snippets": [ "... solenoids, electro- magnets, machine-fields. Any change of the condition of a continuous-current circuit, as a change of e.m.f., of resistance, etc., which leads to a change of current from one value i0 to another value iv results in the appearance of a transient term connecting the current values i0 and iv and into the equation of the transient term enters the inductance. Count the time t from the moment when the change in the continuous-current circuit starts, and denote the impressed e.m.f. by e0, the resista ...", "... inuous-current circuit, as a change of e.m.f., of resistance, etc., which leads to a change of current from one value i0 to another value iv results in the appearance of a transient term connecting the current values i0 and iv and into the equation of the transient term enters the inductance. Count the time t from the moment when the change in the continuous-current circuit starts, and denote the impressed e.m.f. by e0, the resistance by r, and the inductance by L. p il = - = current in permanent or stationary ...", "... e current in circuit before the change, and therefore at the moment t = 0, by i the current during the change, the e.m.f. consumed by resistance r is ir, and the e.m.f. consumed by inductance L is di Ldt' where i = current in the circuit. 26 26 TRANSIENT PHENOMENA di Hence, eQ = ir + L — > (1) dt or, substituting eQ = if, and transposing, -i*-i±V This equation is integrated by - -t = log (i - ij - logc, where — log c is the integration constant, or, r i — i^ = ce L . However, for t = 0, i = iQ. Sub ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-43", "section_label": "Chapter 3: The Natural Period Of The Transmission Line", "section_title": "The Natural Period Of The Transmission Line", "kind": "chapter", "sequence": 43, "number": 3, "location": "lines 21721-23178", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "snippets": [ "... and the line equations (17) of Chapter II become / = (AA - A2) cos pi - j (Aj + A,) sin pi and E = V ^ (A, + A2)cos fl - / (4i - 42) sin pi or writing 4i ~ 42 = <7i and 4i + 42 = Q» and substituting c we have and • • l * • 2 (3) 322 TRANSIENT PHENOMENA A free oscillation of a circuit implies that energy is neither supplied to the circuit nor abstracted from it. This means that at both ends of the circuit, I = 0 and I = 1Q, the power equals zero. If this is the case, the following conditions may exist: ...", "... on (9) assumes the form (12) The fundamental frequency of oscillation of a transmission line open at one end and grounded at the other, and having a total inductance L0 and a total capacity (70, is, neglecting energy losses, fl = ~ rr-TT ' 324 TRANSIENT PHENOMENA while the frequency of oscillation of a localized inductance L0 and localized capacity (70, that is, the frequency of discharge of a condenser CQ through an inductance L0, is / = ^= • d3) The difference is due to the distributed character of L0 and C ...", "... ncy of oscillation. This form of free oscillation may be called quarter-wave oscillation. The fundamental or lowest discharge wave or oscillation of the circuit then is il = c cos (0 — fj) cos T and el = - \\ — c sin (0 — sn r. (22) 326 TRANSIENT PHENOMENA With this wave the voltage is a maximum at the open end of the line, I = Z0, and gradually decreases to zero at the other end or beginning of the line, I = 0. The current is zero at the open end of the line, and gradually increases to a maximum at I = ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-54", "section_label": "Chapter 5: Free Oscillations", "section_title": "Free Oscillations", "kind": "chapter", "sequence": 54, "number": 5, "location": "lines 31451-32708", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "snippets": [ "... its, as those due to direct currents or pulsating currents, alternating currents, oscillating currents, inductive dis- charges, etc., and the study of the terminal conditions thus is of the foremost importance. 29. By free oscillations are understood the transient phe- nomena occurring in an electric circuit or part of the circuit to which neither electric energy is supplied by some outside source nor from which electric energy is abstracted. Free oscillations thus are the transient phenomena resulting from the d ...", "... oscillations are understood the transient phe- nomena occurring in an electric circuit or part of the circuit to which neither electric energy is supplied by some outside source nor from which electric energy is abstracted. Free oscillations thus are the transient phenomena resulting from the dissipation of the energy stored in the electric field of the circuit, or inversely, the accumulation of the energy of the electric field; and their appearance therefore presupposes the possibility of energy storage in more than one for ...", "... at I = Z0. (4) i = 0 at I = 0; i = 0 at I = L. (197) Case (2) represents the same conditions as (1), merely with the distance I counting from the other end of the circuit — a line open at one end and grounded at the other end. Case (3) repre- 480 TRANSIENT PHENOMENA sents a circuit open at both ends, and case (4) a circuit grounded at both ends. 30. In either of the different cases, at the end of the circuit I = 0, either e = 0, or i = 0. Substituting I = 0 into the equations (50) and (51) gives eo = fi-<«- >'{ ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-39", "section_label": "Chapter 3: Mechanical Rectification", "section_title": "Mechanical Rectification", "kind": "chapter", "sequence": 39, "number": 3, "location": "lines 15963-17754", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-39/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-39/", "snippets": [ "... as on arc lighting machines, or in * If the circuit is reversed at the moment when the alternating current passes zero, due to self-inductance of the rectified circuit its current differs from zero, and an arc still appears at the rectifier. 229 230 TRANSIENT PHENOMENA cases where the voltage of the rectified circuit is only a small part of the total voltage, and thus the current not controlled thereby, as when rectifying for the supply of series fields of alternators. 2. r = r0 = oo , or open circuit rectification. T ...", "... r-connected three- phase constant-current alternator with rectifying commutator. The Brush arc machine is a quarter-phase machine with rectify- ing commutator. In rectification frequently the sine wave term of the current is entirely overshadowed by the transient exponential term, and thus the current in the rectified circuit is essentially of an exponential nature. As examples, three cases will be discussed: 1. Single-phase constant-current rectification; that is, a rectifier is inserted in an alternating-curr ...", "... 0 = 0, au (3) (4) which is integrated by the function : i = Ae-ae+ Bsin (6 - 8). Substituting (4) in (3) and arranging, gives : A (r + rl - ax) e~ a& + [B ( [r + rj cos d + x sin 8) - i/J sin 0 - [(r + rj sin d - x cos d] B cos 0 = 0, (5) 232 TRANSIENT PHENOMENA which equation must be an identity, thus : and and herefrom: r + rl — ax = 0, B ( [r + rj cos d + x sin d) - i0rl = 0 (r + PJL) sin d — x cos d = 0, tand = and where hence: r+r, B = i ° V(r+ rj' (6) z = V(r + r,)2 + x2; ( ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-50", "section_label": "Chapter 1: General Equations", "section_title": "General Equations", "kind": "chapter", "sequence": 50, "number": 1, "location": "lines 27761-28694", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "snippets": [ "... rostatic component of the electric field; or the current consumed by a change of the de voltage, C — , that is, with an alternating voltage, the (leading) dt reactive current consumed in the circuit - jbe, where 6 = 2 and / = frequency. 417 418 TRANSIENT PHENOMENA In the investigation of electric circuits, these four constants, r, L, g, C, usually are assumed as located separately from each other, or localized. Although this assumption can never be per- fectly correct, — for instance, every resistor has some induc ...", "... ance of the velocity of light, 300,000 km., etc. The permanent values of current and e.m.f. in such circuits of distributed constants have, for alternating-current circuits, been investigated in Section III, where it was shown that they can be treated as transient phenomena in space, of the complex variables, current / and e.m.f. E. Transient phenomena in circuits with distributed constants, and, therefore, the general investigation of such circuits, leads to transient phenomena of two independent variables, time t and spa ...", "... and e.m.f. in such circuits of distributed constants have, for alternating-current circuits, been investigated in Section III, where it was shown that they can be treated as transient phenomena in space, of the complex variables, current / and e.m.f. E. Transient phenomena in circuits with distributed constants, and, therefore, the general investigation of such circuits, leads to transient phenomena of two independent variables, time t and space or distance /; that is, these phenomena are transient in time and in space. T ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-13", "section_label": "Chapter 13: Reactance Of Synchronous Machines", "section_title": "Reactance Of Synchronous Machines", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 23466-24022", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-13/", "snippets": [ "... existence, correspond to actual magnetic fluxes, and for instance, when calculating efficiency and losses, the core loss of the machine does not correspond to eo, but corresponds to the actual or resultant magnetic flux. Fig. 112. Also, in deal- ing with transients involving the dissipation of the magnetic energy stored in the machine, the magnetic energy of the result- ant field, Fig. 112, comes into consideration, and not the — ^much REACTANCE OF SYNCHRONOUS MACHINES 237 larger — energy, which the fields corres ...", "... in the machine, the magnetic energy of the result- ant field, Fig. 112, comes into consideration, and not the — ^much REACTANCE OF SYNCHRONOUS MACHINES 237 larger — energy, which the fields corresponding to e© and Xo would have. Thus the short-circuit transient of a heavily loaded ma- chine is essentially the same as that of the same machine at no- load, with the same terminal voltage, although in the former the field excitation and the nominal induced voltage may be very much larger. The use of the term armat ...", "... ely, a decrease of armature current gives a simultaneous decrease of the self- inductive part of the flux, a in Fig. Ill, but a gradual decrease of the mutual inductive part, 6, and corresponding gradual increase of the resultant field flux, by inducing a transient voltage in the field, in opposition to the exciter voltage, and thereby decreasing the field current. Every sudden increase of the armature current thus gives an equal sudden drop of terminal voltage due to the self-inductive flux, a, produced by it (an ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-26", "section_label": "Chapter 4: Inductance And Resistance In Alternating Current Circuits", "section_title": "Inductance And Resistance In Alternating Current Circuits", "kind": "chapter", "sequence": 26, "number": 4, "location": "lines 3515-4071", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-26/", "snippets": [ "CHAPTER IV. INDUCTANCE AND RESISTANCE IN ALTERNATING- CURRENT CIRCUITS. • 26. In alternating-current circuits, the inductance L, or, as it is usually employed, the reactance x = 2 nfL, where / = fre- quency, enters the expression of the transient as well as the permanent term. At the moment 0 = 0, let the e.m.f. e = E cos (0 — 00) be impressed upon a circuit of resistance r and inductance L, thus inductive reactance x = 2 xfL; let the time 6 = 2 xft be counted from the moment of closing the circ ...", "... natural logarithms = 2.7183. Substituting (2) in (1), E cos (6 - 00) = Ir cos (6 - i) + Ars~a0 - Ix sin (d-d)- Aaxs'\"', or, rearranged: (E cos 00 - Ir cos § - Ix sin d) cos 0 + (E sin 00 - Ir sin 8 + /x cos d) sin 0 - ^e~a\" (ax - r) = 0. 41 42 TRANSIENT PHENOMENA Since this equation must be fulfilled for any value of 6, if (2) is the integral of (1), the coefficients of cos 6, sin 0, £~a9 must vanish separately. That is, E cos 00 — Ir cos d — Ix sin d = 0, E sin 00 - Ir sin d + Ix cos d = 0, and Herefro ...", "... ot zero but = iw we have, substituted in (7), A = ^--(508(0 i =-- cos (d - 60 - ^)-cos (00 + 0,)- e* . (10) 27. The equation of current (9) contains a permanent term E — cos (0 — 00 — dj, which usually is the only term considered, E -~e and a transient term — e x cos (00 + 0t). z The greater the resistance r and smaller the reactance x, the more rapidly the term :- e ;c cos (00 -f 0t) disappears. This transient term is a maximum if the circuit is closed at the moment 00 = — 6V that is, at the mome ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... ng current approaches the effect of an alternating current only if the damping is small, that is, the resistance low, the condenser discharge can be used as high frequency generator only by making the circuit of as low resist- ance as possible. 67 68 TRANSIENT PHENOMENA This, however, means limited power. When generating oscillat- ing currents by condenser discharge, the load put on the circuit, that is, the power consumed in the oscillating-current circuit, represents an effective resistance, which increases the rapidi ...", "... rent. A very large oscillating-current generator, therefore, would consist of 100-kv-amp. condenser and 100-kv-amp. reactor. 46. Assuming the condenser to be designed for 10,000 volts alternating impressed e.m.f. at 60 cycles, the 100 kv-amp. con- 70 TRANSIENT PHENOMENA denser consumes 10 amperes: its condensive reactance is F 1 xc — — = 1000 ohms, and the capacity C= — — = 2.65 mf . I 2 7tJ0Xc Designing the reactor for different currents, and therewith different voltages, gives different values of inductance L, a ...", "... e coil and 99 per cent of the condenser, gives since r = 0.05 x, r - 0.05 V x = 2 xfL, 1 and the energy of the discharge, by (65), is W = — - \\^LC = 10 6* C volt-ampere-seconds; — T thus the power factor is cos 00 = 0.05. 72 . TRANSIENT PHENOMENA Since the energy stored in the capacity is WQ = ^ joules, the critical resistance is hence, r. - „ 0 7 = 0.025, *'4 and the decrement of the oscillation is A = 0.92, that is, the decay of the wave is very slow at no load. Assuming, ho ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-55", "section_label": "Chapter 6: Transition Points And The Complex Circuit", "section_title": "Transition Points And The Complex Circuit", "kind": "chapter", "sequence": 55, "number": 6, "location": "lines 32709-33527", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "snippets": [ "... onsidered as stopping the current, in the latter case the cable considered as short-circuiting the transformer. This approximation, however, while frequently relied upon in engi- neering practice, and often permissible for the circuit section in which the transient phenomenon originates, is not permissible in considering the effect of the phenomenon on the adjacent sections of the circuit. For instance, in the first case above mentioned, a transient phenomenon in an underground cable connected to a high reactance, the current ...", "... ractice, and often permissible for the circuit section in which the transient phenomenon originates, is not permissible in considering the effect of the phenomenon on the adjacent sections of the circuit. For instance, in the first case above mentioned, a transient phenomenon in an underground cable connected to a high reactance, the current and e.m.f. in the cable may approx- imately be represented by considering the reactive coil as a reflection point, that is, an open circuit, since only a small current 498 TRANSITION P ...", "... exists in the reactive coil. Such a small current in the reactive coil may, however, give a very high and destructive voltage in the reactive coil, due to its high L, and thus in the circuit beyond the reactive coil. In the investigation of the effect of a transient phenomenon originating in one section of a complex circuit, as an oscillating arc on an underground cable, on other sections of the circuit, as the generating station, even a very great change of circuit constants cannot be considered as a reflection point. Since th ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-23", "section_label": "Chapter 1: The Constants Of The Electric Circuit", "section_title": "The Constants Of The Electric Circuit", "kind": "chapter", "sequence": 23, "number": 1, "location": "lines 1317-1992", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "snippets": [ "... xists which is called the electric field of the conductor. That is, the surrounding space is not uniform, but has different electric and magnetic properties in different directions. No power is required to maintain the electric field, but energy 3 4 TRANSIENT PHENOMENA is required to produce the electric field, and this energy is returned, more or less completely, when the electric field dis- appears by the stoppage of the flow of energy. Thus, in starting the flow of electric energy, before a perma- nent condition i ...", "... vely. As electric power P is resolved into the product of current i and voltage e, the power loss in the conductor, Ph therefore can also be resolved into a product of current i and voltage et which is consumed in the conductor. That is, P, = iet. 6 TRANSIENT PHENOMENA It is found that the voltage consumed in the conductor, eh is proportional to the factor i of the power P, that is, et = ri, (4) where r is the proportionality factor of the voltage consumed by the loss of power in the conductor, or by the power gradi ...", "... ric power P = ei (1) exists in a circuit, it is pr = tfr = power lost in the conductor, (16) WM = l— = energy stored in the magnetic field of the circuit, (9) l Ll W K = — = energy stored in the dielectric field of the cir- £t cuit, (14) 8 TRANSIENT PHENOMENA and the three circuit constants r, L, C therefore appear as the components of the energy conversion into heat, magnetism, and electric stress, respectively, in the circuit. 4. The circuit constant, resistance r, depends only on the size and material of ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-41", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 41, "number": 1, "location": "lines 19260-19338", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "snippets": [ "CHAPTER I. INTRODUCTION. 1. The preceding sections deal with transient phenomena in time, that is, phenomena occurring during the time when a change or transition takes place between one condition of a cir- cuit and .another. The time, t, then is the independent variable, electric quantities as current, e.m.f., etc., the dependent var ...", "... , phenomena occurring during the time when a change or transition takes place between one condition of a cir- cuit and .another. The time, t, then is the independent variable, electric quantities as current, e.m.f., etc., the dependent variables. Similar transient phenomena also occur in space, that is, with space, distance, length, etc., as independent variable. Such transient phenomena then connect the conditions of the electric quantities at one point in space with the electric quantities at another point in space, as, fo ...", "... nd .another. The time, t, then is the independent variable, electric quantities as current, e.m.f., etc., the dependent variables. Similar transient phenomena also occur in space, that is, with space, distance, length, etc., as independent variable. Such transient phenomena then connect the conditions of the electric quantities at one point in space with the electric quantities at another point in space, as, for instance, current and potential difference at the generator end of a transmission line with those at the receiving ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 6125-6803", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-09/", "snippets": [ "... have been shown in the previous lecture. If we have a circuit consisting of sections 1, 2, 3 . . . , of the respective lengths (in velocity measure) Xi, X2, X3 . . . , this entire circuit, when left to itself, gradually dissipates its stored energy by a transient. As function of the time, this transient must decrease at the same rate Uq throughout the entire circuit. Thus the time decrement of all the sections must be Every section, however, has a power-dissipation constant, Ui, U2, U3 . . . , which represents th ...", "... If we have a circuit consisting of sections 1, 2, 3 . . . , of the respective lengths (in velocity measure) Xi, X2, X3 . . . , this entire circuit, when left to itself, gradually dissipates its stored energy by a transient. As function of the time, this transient must decrease at the same rate Uq throughout the entire circuit. Thus the time decrement of all the sections must be Every section, however, has a power-dissipation constant, Ui, U2, U3 . . . , which represents the rate at which the stored energy of the ...", "... from the transformer over the line into the load; the transformer acts as generator of the power, and of this 112 ELECTRIC DISCHARGES, WAVES AND IMPULSES. power a fraction is consumed in the line, the rest suppUed to the load. 40. The diagram of this transient power transfer of the system thus is very similar to that of the permanent power transmis- sion by alternating currents: a source of power, a partial con- sumption in the line, and the rest of the power consumed in the load. However, this transient powe ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 5521-6088", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "snippets": [ "... have been shown in the previous lecture. If we have a circuit consisting of sections 1, 2, 3 . . . , of the respective lengths (in velocity measure) Xi, X2, X3 . . . , this entire circuit, when left to itself, gradually dissipates its stored energy by a transient. As function of the time, this transient must decrease at the same rate u0 throughout the entire circuit. Thus the time decrement of all the sections must be 6-**. Every section, however, has a power-dissipation constant, u\\t Uz, u3 . . . , which repre ...", "... If we have a circuit consisting of sections 1, 2, 3 . . . , of the respective lengths (in velocity measure) Xi, X2, X3 . . . , this entire circuit, when left to itself, gradually dissipates its stored energy by a transient. As function of the time, this transient must decrease at the same rate u0 throughout the entire circuit. Thus the time decrement of all the sections must be 6-**. Every section, however, has a power-dissipation constant, u\\t Uz, u3 . . . , which represents the rate at which the stored energy ...", "... rom the transformer over the line into the load; the transformer acts as generator of the power, and of this 112 ELECTRIC DISCHARGES, WAVES AND IMPULSES. power a fraction is consumed in the line, the rest supplied to the load. 40. The diagram of this transient power transfer of the system thus is very similar to that of the permanent power transmis- sion by alternating currents: a source of power, a partial con- sumption in the line, and the rest of the power consumed in the load. However, this transient powe ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-30", "section_label": "Chapter 8: Low Frequency Surges In High Potential Systems", "section_title": "Low Frequency Surges In High Potential Systems", "kind": "chapter", "sequence": 30, "number": 8, "location": "lines 7826-9227", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "snippets": [ "... igh power surges of the whole system, of a frequency of a few hundred cycles, frequently of destructive character, or, (6) Very high frequency low power oscillations, local in character, so called \"static,\" probably of frequencies of hundred 105 106 TRANSIENT PHENOMENA thousands of cycles, rarely directly destructive, but indirectly harmful in their weakening action on the insulation and the possibility of their starting a low frequency surge. The former ones only are considered in the present chapter. Their causes m ...", "... [e0 - J^ cos 0J cos T2re0 + 4xa:ct0 . _ 4VxZ 4 E XX, in 00) Jsin y/^-c (2 r cos 00 + 4 x sin These equations consist of three terms: x, . _ x, / I p \" -I- £ \"' • el ~ 61 Kl 1 ; . ^ ' (a ft \\ I — Sin (C7 — UQ), (5) (6) 108 TRANSIENT PHENOMENA E -~e ( = £ 2* ) cos 6, cos 00 cos V - 0 + ''cos 6> - Ee or, by dropping terms of secondary order, E - ~e — Ee 2x cos 6 n cos V/ — and: or, by dropping terms of secondary order, Vx cos x (7) (8) (9) (10) Thus t ...", "... ent of the frequency of the impressed e.m.f. Substituting 6 = 2 xfi, xc = —^ and x = 2 rfL & 7T/U in equations (8), (10), and (11), we have t sin - — y VCL (12) 1C - — t t i\" = V/F#£ 2L cos<90sin VCL t e/' =- Ee cos ^ cos--—; 110 TRANSIENT PHENOMENA r . , . ,„ t 1'\" = e VCL ==• + i0 V 7: sin — — [ ; C< T ° V /7 A //nr r > -~t ( i =-27zfCEsin(d - 60)+ £ 2L U0 cos (13) r 2L e, = E cos (d - 00)+ £ I (e0 - £ cos 00) cos 7^=- X , « ) (14) The oscillating terms of these equa ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-48", "section_label": "Chapter 8: Velocity Of Propagation Of Electric Field", "section_title": "Velocity Of Propagation Of Electric Field", "kind": "chapter", "sequence": 48, "number": 8, "location": "lines 26095-27002", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "snippets": [ "... d exists this field is practically in phase with the flow of energy in the conductor, that is, the velocity of propagation has no appreciable effect. Thus, the finite velocity of propagation of the electric field requires consideration only: 387 388 TRANSIENT PHENOMENA (a) At extremely high frequencies, hundreds of millions of cycles per second, as given by Hertzian resonators. (6) In high frequency discharges having no return circuit or no well defined return circuit, as lightning discharges. In this case the effect ...", "... n of the conductor, and for this reason in wireless teleg- raphy the vertical sending and receiving antennae are necessary, and the transmission is far more successful across the ocean than across the land, since in the latter case every tree, moun- 390 TRANSIENT PHENOMENA tain, etc., acts inductively as return conductor, and thus increases the rapidity of the decrease of the electric field. In such a case the use of high frequency and of conductors without return conductor, hence with electric fields decreasing relative ...", "... onductor at the time t — - . 71. Representing the time t by angle 6 = 2 nft, where /== the frequency of the alternating current in the conductor, and denoting 2f Q _ TCj A TL ,^_. S lw where a lw = - = the wave length of electric field, 392 TRANSIENT PHENOMENA the field at distance I and time angle 6 corresponds to time angle 6 — al, that is, lags in time behind the current in the conductor by the phase angle al Let i = I cos 6 = current, absolute units. (8) The magnetic induction at distance I then is A ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-38", "section_label": "Chapter 2: Circuit Control By Periodic Transient Phenomena", "section_title": "Circuit Control By Periodic Transient Phenomena", "kind": "chapter", "sequence": 38, "number": 2, "location": "lines 15626-15962", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-38/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-38/", "snippets": [ "CHAPTER II. CIRCUIT CONTROL BY PERIODIC TRANSIENT PHENOMENA. 6. As an example of a system of periodic transient phenomena, used for the control of electric circuits, may be considered an automatic potential regulator operating in the field circuit of the exciter of an alternating current system. Let, r0 = 40 oh ...", "CHAPTER II. CIRCUIT CONTROL BY PERIODIC TRANSIENT PHENOMENA. 6. As an example of a system of periodic transient phenomena, used for the control of electric circuits, may be considered an automatic potential regulator operating in the field circuit of the exciter of an alternating current system. Let, r0 = 40 ohms = resistance and L = 400 henrys = inductance of the exciter ...", "... a longer time in position r0, hence a shorter time in position (r0 + rt), before the rising potential throws it over into the next position; while at light load, requiring low field excitation, the duration of the period of high resistance, 223 224 TRANSIENT PHENOMENA (TO _|_ rj} is greater, and that of the period of low resistance, r0, less. 7. Let, ^ = the duration of the short circuit of resistance rx; t2 = the time during which resistance rx is in circuit, and t0 = t, + tr During each period t0, the resistan ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-46", "section_label": "Chapter 6: Alternating Magnetic Flux Distribution", "section_title": "Alternating Magnetic Flux Distribution", "kind": "chapter", "sequence": 46, "number": 6, "location": "lines 23948-24980", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "snippets": [ "... not follow a magnetic cycle. There is, however, no evidence of such a \" viscous hysteresis,\" but it is probable that iron follows magnetically even at the highest frequencies, traversing practically the same hysteresis cycle irrespective of 355 356 TRANSIENT PHENOMENA the frequency, if the true m.m.f., that is, the resultant of the impressed m.m.f. and the m.m.f. of the secondary currents in the iron, is considered. Since with increasing frequency, at constant impressed m.m.f., the resultant m.m.f. decreases, due to ...", "... ituting (7) therein, gives .0-8(B, (8) or, writing c2 = /a2 = 0.4 Tr2/^ 10-8, (9) a2 = 0.4 rfXn 10-8, (10) we have - This differential equation is integrated by /T> x » / • 1 ecl° (cos clQ — j sin clQ) = (B^-^o-^jcosc (Z0- 1) + ysinc (Z0- Z) ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-49", "section_label": "Chapter 9: High-Frequency Conductors", "section_title": "High-Frequency Conductors", "kind": "chapter", "sequence": 49, "number": 9, "location": "lines 27003-27760", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "snippets": [ "... radiation resistance. The power consumed by the radiation resistance is not converted into heat in the conductor, but is dissipated in the space surrounding the conductor, or in any other conductor on which the electric wave impinges. That is, 403 404 TRANSIENT PHENOMENA at very high frequency, the total power consumed by the effective resistance of the conductor does not appear as heating of the conductor, but a large part of it may be sent out into space as electric radiation, which accounts for the power exerted upon ...", "... + ^l 10~9 ohms; (3) or, reduced to common logarithms by dividing by log e, x0 = 2 TT/Z f4.6 log^ + |) 10~9 ohms. (4) \\ l>r ** The equivalent depth of penetration of the current into the con- ductor, from Chapter VII, (40), is 104 5030 (5) 406 TRANSIENT PHENOMENA hence, the effective resistance of unequal current distribution, or thermal resistance of the conductor, is, approximately, (6) and the effective reactance of the internal flux is 10- ohms. (7) The effective resistance resulting from the finite ve ...", "... ld of the conductor has less and less effect on its reactance. The radiation reactance, x2, increases proportionally with the frequency for moderate frequencies, but for higher fre- quencies increases at a lesser rate as soon as the negative term 408 TRANSIENT PHENOMENA in x2 becomes appreciable; it ultimately reaches a maximum and then decreases again, but the latter at such high frequencies as to be of no practical importance. Besides, for extremely high frequencies, thousands of millions of cycles, equation (12) doe ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-52", "section_label": "Chapter 3: Standing Waves", "section_title": "Standing Waves", "kind": "chapter", "sequence": 52, "number": 3, "location": "lines 29316-30243", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "snippets": [ "... qB,'} sin (qt-kl)] + [(mB2'-qB3) cos (qt + Jd)-(mB2 + qBJ) sin (qt + kl)]}. (106) Equations (105) and (106) represent a stationary electrical oscil- lation or standing wave on the circuit. B. Long waves, k2 < LCm2] (107) 444 hence, and TRANSIENT PHENOMENA R22 = LCm2 - k2, s = (108) (109) or approximately, for very small values of &, 1 r herefrom then follows (HO) ci = c2 = 0, and (m + s) L ~T~ (m — s) L (111) Substituting now h = Oand (109), (111) into (50) and (51), t ...", "... nd all the main waves and their reflected waves coincide when substituting h = 0, (116), (117) in (50) and (51). Hence, writing and gives B = C, - C2 + C3 - C, 1 B' = CY 4- C2' + C,7 + C/ J i = fi-\"1 {B cos kl - B' sin Id] (118) (119) 446 TRANSIENT PHENOMENA and e = y — £-M< {5' cos kl + B sin In the critical case, (119) and (120), the wave is distributed as a trigonometric function of the distance, but dies out as a simple exponential function of the time. 15. An electrical standing wave thus can have ...", "... case, m?LC = 0, or oscillatory phenomenon, substituting for m2, we have and r _L g c' or rC — gL = 0 (distortionless circuit). In the latter case, m2LC = oo , or non-oscillatory or exponen tial standing wave, we have r \\ — — Q\\ — =00 448 TRANSIENT PHENOMENA and since neither r, g, L, nor C can be equal infinity it fol- lows that either L = 0 or C = 0. Therefore, the standing wave in a circuit is always oscillatory, regardless of its wave length, if rC - gL = 0, (126) or - = §J (127) that is, the ra ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-51", "section_label": "Chapter 2: Discussion Of General Equations", "section_title": "Discussion Of General Equations", "kind": "chapter", "sequence": 51, "number": 2, "location": "lines 28695-29315", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "snippets": [ "... values of I, or towards decreasing I. Considering therefore iv el and i3J e3 as direct or main waves, iv e2 and i4, e4 are their return waves, or reflected waves, and iv e2 is the reflected wave of iv e^ i4, e4 is the reflected wave of iv ey 431 432 TRANSIENT PHENOMENA Obviously, i2J e2 and i^ e± may be considered as main waves, and then iv et and i3, e3 are reflected waves. Substituting ( - I) for (+ I) in equations (50) and (51), that is, looking at the circuit in the opposite direction, terms i2, e2 and iv e1 and te ...", "... —, during which the wave decreases to - = 0.3679 of its value, and hi = 1 gives the distance, over which the wave decreases to - = 0.3679 of its value; £ that is, q is the frequency constant of the wave, f - - I I: «'—'•• (62) > 2V °~' 434 TRANSIENT PHENOMENA k is the wave length constant, (63) (u - s) and (u -f s) are the time attenuation constants of the wave, 1 ) (64) U + S and h is the distance attenuation constant of the wave, L -I. (65) 9. If the frequency of the current and e.m.f ...", "... where ^ (ouyj In general, the circuit constants r, L, 0, C, per unit length, I = 1 give, per unit length, X = 1, the circuit constants L. £. £. 5 j or Vic ' VLC c VLC Substituting (290) in equation (309) ...", "... c field of circuit element dX at time t is Aw'rr 1 /7 \"~ = V £~2\"\"'{ (4(7+BI)) cos 2 9' + (^0-JSC) sin 2 qt\\, dX d^ dl dX dX 52. The energy stored in the electrostatic field of the conductor or by the capacity C is given by CV dw2 = — dl\\ 518 TRANSIENT PHENOMENA or, substituting (310), and substituting in (319) the value of e from equation (290) gives the same expression as (311) except that the sign of the last two terms is reversed ; that is, the total energy of the electro- static field of circuit element ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-57", "section_label": "Chapter 8: Reflection And Refraction At Transition Point", "section_title": "Reflection And Refraction At Transition Point", "kind": "chapter", "sequence": 57, "number": 8, "location": "lines 34203-34896", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-57/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-57/", "snippets": [ "... t ^ between section 1 and section 2 the constants change by (285) B2=£~s^l{a1e+8l*1Bl + b1e~'1*1 (Clsin2 q^l — Dlcos 2$is)} (At cos 2 <^1 + #1 sin 2 g^J } (A 1 sin 2 gAj — 5j cos 2 5^) } , where Oi = ?i_L^ and 6j = ^i_Z_^ . (286) 625 526 TRANSIENT PHENOMENA Choosing now the transition point as zero point of X, so that >l< 0 is section 1, A>0 is section 2, equations (285) assume the form A2 = B2 = C2 = D2 = blCv (349) From equations (349) and (286) it follows that c2 (A* - C22) = ct (A* - C, ...", "... tan (ij = + -~, and transmission angle, tan (i'2) Reversing the sign of ^ in the equation (355) of the reflected wave, that is, counting the distance for the reflected wave also in the direction of its propagation, and so in opposite direction as 528 TRANSIENT PHENOMENA in the main wave and the transmitted wave, equations (355) become C2+C1 (357) and then or c, 2 ' \"1 V1J (358) (1) In a single electric wave, current and e.m.f. are in phase with each other. Phase displacements between current and e ...", "... g a station from the transmission line or cable, of an impulse or a wave which in the transmission line is of relatively harmless voltage. The ratio of the transmitted to the reflected wave is given by 2 VLjC, 2 and 2c2 L2C, (359) 530 TRANSIENT PHENOMENA 60. Example: Transmission line Lt = 1.95 X 1(T3 Ct = 0.0162 X 10-' ct = 346 ^7, = 0.56 i* And in the opposite direction Transformer 0.4 X 10-6 1580 .-? \" 2'56 •J- -0.56. The ratio -^becomes a maximum, = GO, for -1 =77, but in e ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... ) %%%%%% i 1 1 ^ 106 ENGINEERING MATHEMATICS. COS )- = 2ah or \\ c^ = a--\\-h'^—2ahQosr. ah sin y (26) Area = 2 c^ sin a sin ^ sin 7- (27) B. TRIGONOMETRIC SERIES. 76. Engineering phenomena usually are either constant, transient, or periodic. Constant, for instance, is the terminal voltage of a storage-battery and the current taken from it through a constant resistance. Transient phenomena occur during a change in the condition of an electric circuit, as a change of load; or, dis ...", "... ^ sin 7- (27) B. TRIGONOMETRIC SERIES. 76. Engineering phenomena usually are either constant, transient, or periodic. Constant, for instance, is the terminal voltage of a storage-battery and the current taken from it through a constant resistance. Transient phenomena occur during a change in the condition of an electric circuit, as a change of load; or, disturbances entering the circuit from the outside or originating in it, etc. Periodic phenomena are the alternating currents and voltages, pulsating currents as those ...", "... is then inserted in series, making the total resistance of the con- denser charging circuit, r = 250 ohms. What is the maximum value of the charging current? The equation of the charging current of a condenser, through a circuit of low resistance, is {\" Transient Electric Phenomena and Oscillations,'^ p. 61) : '-ii--'**i. where and the equation of the charging current of a condenser, through a circuit of high resistance, is {\" Transient Electric Phenomena and Oscillations,\" p. 51), 5 I where =^F#■ ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-38", "section_label": "Apparatus Section 17: Synchronous Machines: Short-circuit Currents of Alternators", "section_title": "Synchronous Machines: Short-circuit Currents of Alternators", "kind": "apparatus-section", "sequence": 38, "number": 17, "location": "lines 10190-10429", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-38/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-38/", "snippets": [ "... ase short circuit on a polyphase system, destructive voltages may appear in the open-circuited phase, of saw-tooth wave shape. Upon- this double frequency pulsation of the field current during a single-phase short circuit the transient full frequency pulsation resulting from the unsymmetrical start of the armature current is superimposed and thus causes a difference in the in- tensity of successive waves of the double frequency pulsation, 164 ELEMENTS O ...", "... current is superimposed and thus causes a difference in the in- tensity of successive waves of the double frequency pulsation, 164 ELEMENTS OF ELECTRICAL ENGINEERING which gradually disappears with the dying out of the transient full frequency pulsation, and depends upon the point of the wave at which the short circuit is closed, and thus is absent, and the Armature current. Field Current FIG. 75. — Single-phase short-circuit current in ...", "... ield current shows only the double frequency pulsation due to the single-phase armature reaction. In Fig. 76 is shown another single-phase short circuit, in which the armature current wave starts unsymmetrical, thus giving a transient full frequency term in the field current. Thus in the double frequency pulsation of the field current at first large and small waves alternate, but the successive waves gradually be- come equal with the dying out of the f ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-18", "section_label": "Chapter 20: Single-Phase Commutator Motors", "section_title": "Single-Phase Commutator Motors", "kind": "chapter", "sequence": 18, "number": 20, "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "... -circuit current and thereby the commutation factor, the more, the higher the speed, and greater thereby the exponential term is. The determination of this exponential term is beyond the scope of the present work, but requires the methods of evaluation of transient or momentary electric phenomena, as discussed in \"Theory and Calculation of Transient Electric Phenomena and Oscillations.\" B. Series Repulsion Motor 219. As fuither illustration of the application of these funda- mental equations of the single-phase c ...", "... d greater thereby the exponential term is. The determination of this exponential term is beyond the scope of the present work, but requires the methods of evaluation of transient or momentary electric phenomena, as discussed in \"Theory and Calculation of Transient Electric Phenomena and Oscillations.\" B. Series Repulsion Motor 219. As fuither illustration of the application of these funda- mental equations of the single-phase commutator motor, (1) to (6), a motor may be investigated, in which the four independent ...", "... xponential term of generated e.m.f. and of short-circuit current, the change of the commutation current and commutation factor brought about thereby IBd the study of the conimutating field required to control this exponential term leads into the theory of transient phenomena. that is, phenomena temporarily occurring during and immedi- ately after a change of circuit condition.' The general conclusions are: The control of the e.m.f. of self-induction of commutsti I the single-phase commutator motor requires a COmmutatlDf ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-01", "section_label": "Chapter 1: Electric Conduction. Soled And Liquid", "section_title": "Electric Conduction. Soled And Liquid", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 959-3894", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-01/", "snippets": [ "... oltages less than the polarization ELECTRIC CONDUCTION 9 voltage, no permanent current flows through the electrolyte, or rather only a very small \"leakage'' current or \"diffusion\" cur- rent, as shown in Fig. 3. When closing the circuit, however, a transient current flows. At the moment of circuit closing, no counter e.m.f. exists, and current flows under the full impressed voltage. This current, however, electroljrtically produces a hy- drogen and an oxygen film at the electrodes, and with their grad- ual fo ...", "... s current, however, electroljrtically produces a hy- drogen and an oxygen film at the electrodes, and with their grad- ual formation, the counter e.m.f. of polarization increases and de- creases the current, until it finally stops it. The duration of this transient depends on the resistance of the electrolyte and on the surface of the electrodes, but usually is fairly short. 7. This transient becomes a permanent with alternating im- pressed voltage. Thus, when an alternating voltage, of a maxi- e ^-- ^ V ...", "... n, the counter e.m.f. of polarization increases and de- creases the current, until it finally stops it. The duration of this transient depends on the resistance of the electrolyte and on the surface of the electrodes, but usually is fairly short. 7. This transient becomes a permanent with alternating im- pressed voltage. Thus, when an alternating voltage, of a maxi- e ^-- ^ V. \"^7 y\"\"\"^^ eo ( • ' % Fia. 3. mum value lower than the polarization voltage, is impressed upon an elect ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-11", "section_label": "Chapter 11: Instability Of Circuits: Induction And Syn Chronous Motors", "section_title": "Instability Of Circuits: Induction And Syn Chronous Motors", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 21382-22633", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-11/", "snippets": [ "... y all theoretical study of the hunting of synchronous machines has been limited to the calculation of the frequency of the transi- ent oscillation of the synchronous machine, at a change of load, frequency or voltage, at synchronizing, etc. However, this transient oscillation is harmless, and becomes dangerous only if the oscillation ceases to be transient, but becomes permanent and cumulative, and the most important problem in the study of hunt- ing thus is the determination of the cause, which converts the transi ...", "... ation of the frequency of the transi- ent oscillation of the synchronous machine, at a change of load, frequency or voltage, at synchronizing, etc. However, this transient oscillation is harmless, and becomes dangerous only if the oscillation ceases to be transient, but becomes permanent and cumulative, and the most important problem in the study of hunt- ing thus is the determination of the cause, which converts the transient oscillation into a cumulative one, that is, the determina- tion of the source of the energ ...", "... nsient oscillation is harmless, and becomes dangerous only if the oscillation ceases to be transient, but becomes permanent and cumulative, and the most important problem in the study of hunt- ing thus is the determination of the cause, which converts the transient oscillation into a cumulative one, that is, the determina- tion of the source of the energy, and the mechanism of its trans- fer to the oscillating system. To design synchronous machines, so as to have no or very little tendency to hunting, obviously re- ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-01", "section_label": "Chapter 1: Introduction. 217", "section_title": "Introduction. 217", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 659-674", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-01/", "snippets": [ "CHAPTER I. INTRODUCTION. 217 1. General character of periodically recurring transient phenomena in time. 217 2. Periodic transient phenomena with single cycle. 218 3. Multi-cycle periodic transient phenomena. 218 4. Industrial importance of periodic transient phenomena: circuit control, high frequency generation, rectification. 220 5. Types of ...", "CHAPTER I. INTRODUCTION. 217 1. General character of periodically recurring transient phenomena in time. 217 2. Periodic transient phenomena with single cycle. 218 3. Multi-cycle periodic transient phenomena. 218 4. Industrial importance of periodic transient phenomena: circuit control, high frequency generation, rectification. 220 5. Types of rectifiers. Arc machines. 221" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-05", "section_label": "Chapter 1: Introduction. 277", "section_title": "Introduction. 277", "kind": "chapter", "sequence": 5, "number": 1, "location": "lines 745-754", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-05/", "snippets": [ "CHAPTER I. INTRODUCTION. 277 1. Transient phenomena in space, as periodic functions of time and transient functions of distance, represented by transient functions of complex variables. 277 2. Industrial importance of transient phenomena in space. 278" ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-01-recommendations", "section_label": "Report Section 2: Recommendations", "section_title": "Recommendations", "kind": "report-section", "sequence": 2, "number": 2, "location": "PDF pages 7-12, lines 145-720", "status": "pdf-text-extracted-candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "snippets": [ "... stigated. Similar results are given by grouping in pairs of identical cables with differential relays between them. This latter arrangement perhaps is somewhat less sensitive and reliable, since with two separate cables, no matter how identical they may be, a transient may occur in the one and not or a different transient in the other, and the sensitivity of the differential relay thus probably has to be lowered not to be affected by transients. On the other hand, the latter arrangement would not require such extensive repl ...", "... rs of identical cables with differential relays between them. This latter arrangement perhaps is somewhat less sensitive and reliable, since with two separate cables, no matter how identical they may be, a transient may occur in the one and not or a different transient in the other, and the sensitivity of the differential relay thus probably has to be lowered not to be affected by transients. On the other hand, the latter arrangement would not require such extensive replacement of cables. Systems involving the use of sheath ...", "... reliable, since with two separate cables, no matter how identical they may be, a transient may occur in the one and not or a different transient in the other, and the sensitivity of the differential relay thus probably has to be lowered not to be affected by transients. On the other hand, the latter arrangement would not require such extensive replacement of cables. Systems involving the use of sheath transformers or other schemes for tripping out on small ground currents, and still other arrangements for accomplishing the ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-13", "section_label": "Chapter 15: Synchronous Rectifier", "section_title": "Synchronous Rectifier", "kind": "chapter", "sequence": 13, "number": 15, "location": "lines 18413-19373", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-13/", "snippets": [ "... large extent on constant-current circuits; it is the method by which the Thomson- Fig. 92. — Double-brush rectifier. Houston (three-phase) and the Brush arc machine (quarter- phase) commutates. For more details on this see \"Theory and Calculations of Transient Phenomena/ ' Section II. Ficj. 93. — Volt ago waves of open -circuit rectifier charging storage battery. Open-circuit rectification has found a limited use on non-in- ductive circuits containing a counter e.m.f., that is, in charging ntoragc batteries. If, in ...", "... s the pulsation of the rectified current. The waves of currents, ih i2 and i0) as overlapped by the inductances, Xi, x* and x0, are shown in Fig. 103. Full description and discussion of the mercury-arc rectifier is contained in \"Theory and Calculation of Transient Phenomena,9' Section II, and in \"Radiation, Light and Illumination.\" 250 ELECTRICAL APPARATUS 143. To reduce the sparking at the rectifying commutator, the gap between the segments may be divided into a number of gaps, by small auxiliary segments, as shown ...", "... onstant-current) Fia. 120. — Counter e.m.f. shunting gaps of six-phase rectifier. alternators connected to rectifying commutators on the armature shaft. For a more complete discussion of the rectification of arc machine see \"Theory and Calculation of Transient Electric Phenomena,\" Section II. 145. Even with polyphase rectification, the power which can be rectified is greatly limited by the sparking caused by the dif- ferential current, that is, the difference between the rectified current, io, which never rev ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-45", "section_label": "Chapter 5: Distributed Series Capacity", "section_title": "Distributed Series Capacity", "kind": "chapter", "sequence": 45, "number": 5, "location": "lines 23586-23947", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "snippets": [ "... e required to bring the maximum potential gradient, near the line L, above the disruptive voltage, that is, to initiate the discharge. Thus such a multigap structure is discriminating regarding frequency; that is, the discharge voltage with increas- 350 TRANSIENT PHENOMENA ing frequency, does not remain constant, but decreases with increase of frequency, when the frequency becomes sufficiently high to give appreciable charging currents. Hence high fre- quency oscillations discharge over such a structure at lower voltage t ...", "... 7 (5) and . l-3^ <6> Differentiating (5) and substituting (6) therein gives (7) tM Equation (7) is integrated by where a = VYZ = a - //?, (9) « = ^\\{yz + gr — b (x — xc)} and J- (10) /? = * Section III, Chapter II, paragraph 7. 352 TRANSIENT PHENOMENA Substituting (10) in (8) and eliminating the imaginary expo- nents by the substitution of trigonometric functions, E = A,£-al (cos pi + j sin pi) + A2e+al (cos pi - j sin pi). (11) 46. However, if n = the total length of circuit from line L to ground ...", "... (23) C2j[l - (2^/ and ; = 27r/Ce'; (24) or, approximately, if r and = magnetic flux or number of lines of magnetic force, and n the number of times whic ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-05", "section_label": "Chapter 6: Empirical Curves", "section_title": "Empirical Curves", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 16483-21988", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-05/", "snippets": [ "... t and logi is shown, as II in Fig. 81, since it gives a straight line for the higher values of t. For the higher values of t, therefore, \\ogi = A~ht', or, ^ = a£~\"*; that is, it is an exponential function. 240 ENGINEERING MATHEMATICS. Table V. TRANSIENT CURRENT CHARACTERISTICS. t i log< logi i 11 = 4.94£-1.07< i' = J log i' 12 = 2.85£-3.84« V = ii — 12 1 0 2.10 — 0.322 0 4.94 2.84 0461 2.85 2. 09 -0-01 0.1 2.48 9.000 0394 0.1 4.44 1.96 0.292 ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-02", "section_label": "Lecture 2: Conclusions From The Relativity Theory", "section_title": "Conclusions From The Relativity Theory", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 736-2388", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... d distance enter the same equations, and it is therefore useful in electrical engineering, for instance, when dealing with transmission line phenomena. Thus in my paper on the \"General Equations of the Electric Circuit\" {A.I.E.E. Transactions, 1907, also \"Transient Phenomena,\" Section IV) the equa- tions contain exponential and trigonometric functions of time t and distance I, of the form cos {qt ± kl), etc. By choosing time measure for the distance (as more convenient in this case, since the time is the dominant term) : X = ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... ena in electric circuits, which are to be guarded against, and only in recent years, with the development of wireless telegraphy, some such electric waves have found a useful com- mercial application. The main object of their study — which is the study of transient electric phenomena, is still, however, to guard against their appearance in electric circuits and discharge them harmlessly when they appear. Considering the great difference which already exists between alternating currents of low frequency, 25 or 15 cy ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "... , low-volt- LUMINESCENCE. 115 age constant direct potential and high-voltage constant direct- current circuits from a source of alternating voltage. Regarding the electrical phenomena occurring in arc rectification, see \" Theory and Calculation of Transient Electric Phenomena and Oscillations/' Section II, Chapter IV. The inability of an alternating voltage to maintain an arc, I show you here on the same apparatus by connecting the two terminals (Fig. 40) A and B to the 1000-volt terminals of a transformer ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 3267-3618", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-06/", "snippets": [ "... circuit characteristics appear more or less as broken lines, due to the necessity of using finite line elements, while in reality they are smooth curves when calculated by the differential method, as explained in Section III of \"Theory and Calculation of Transient Electric Phenomena and Oscillations.\" 40, As further example may be considered a three-phase cir- cuit supplied over a long-distance transmission line of distrib- uted capacitj^, self-induction, resistance, and leakage. Let, in Fig. 33, OEi, OE2, OEz = ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-13", "section_label": "Chapter 13: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 13484-14333", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-13/", "snippets": [ "... , B = 5000, X = 10^ then / = 1.338 ampere-turns per cm.; that is, half as much as in a lamina of the thickness d. For a more complete investigation of the screening effect of eddy currents in laminated iron, see Section III of \"Theory and Calculation of Transient Electric Phenomena and Oscillations.\" 112. Besides the edd}^, or Foucault, currents proper, which exist as parasitic currents in the interior of the iron lamina or wire, under certain circumstances eddy currents also exist in larger orbits from lamina to ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "... in that the intensities of successive half-waves progressively increase or decrease with the distance. Such functions are called oscillating waves, and, as such, are beyond the scope of this book, but are more fully treated in \"Theory and Calculation of Transient Electric Phenomena and Oscillations,\" Section III. There also will be found the discussion of the phenomena of distributed capacitj^ in high-potential transformer windings, the effect of the finite velocity of propagation of the electric field, etc. For ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-02", "section_label": "Chapter 2: Electric Conduction. Gas And Vapor", "section_title": "Electric Conduction. Gas And Vapor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3895-5444", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-02/", "snippets": [ "... essential for the electrical engineer to thoroughly undeiv stand the nature of the arc, not only because of its use as illumi- nant, in arc lighting, but more still because accidental arcs are the foremost cause of instability and troubles from dangerous transients in electric circuits. \\ .^ s \\ ( m \\ \\ \\ \\ \\ \\ ™ V \\ '^ \\ s ^ ^ V ^ '.,. ■\" .^ ~~^ -i ■^ 'W \\, ~ ~~ — — - O.J «.. I.T7 ,„ ~ m « f ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... ative resistance, 191 equations, 35 as oscillator, 189 parallel operation on constant current, 175 shunted by capacity, 178, 184 and inductance, 184 by resistance on constant current, 172 singing and rasping, 188, 189 tending to unstability, 164 transient characteristic, 192 as unstable conductor, 167 Arcing ground on transmission lines, . 199 Area of BH relation, 53 Armature flux of alternator, 233 reactance flux of alternator, 232 reaction of alternator, 236 Attenuation constant, leaky con- ducto ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-02", "section_label": "Chapter 2: Circuit Control By Periodic Transient Phenom Ena. 223", "section_title": "Circuit Control By Periodic Transient Phenom Ena. 223", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 675-683", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-02/", "snippets": [ "CHAPTER II. CIRCUIT CONTROL BY PERIODIC TRANSIENT PHENOM- ENA. 223 6. Tirrill Regulator. 223 7. Equations. 224 8. Amplitude of pulsation. 226" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-13", "section_label": "Chapter 9: High-Frequency Conductors. 403", "section_title": "High-Frequency Conductors. 403", "kind": "chapter", "sequence": 13, "number": 9, "location": "lines 1014-1042", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-13/", "snippets": [ "... pipe ; tabulation and discussion of numerical values. 408 84. Continued discussion of results. • 409 85. Potential drop in conductors carrying high frequency currents. Tabulation. Effect of conductor shape and material. 412 CONTENTS. SECTION IV. TRANSIENTS IN TIME AND SPACE. PAGE" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-22", "section_label": "Chapter 9: Inductive Discharges. 535", "section_title": "Inductive Discharges. 535", "kind": "chapter", "sequence": 22, "number": 9, "location": "lines 1286-1316", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-22/", "snippets": [ "... aluation of frequency constant and resultant decrement. 538 67. The final equations, and their discussion. 540 68. Numerical example. Calculation of the first six har- monics. 542 APPENDIX: VELOCITY FUNCTIONS OF THE ELECTRIC FIELD. 545 SECTION I TRANSIENTS IN TIME TKANSIENTS IN TIME" ] } ] }, { "id": "impedance", "label": "Impedance", "aliases": [ "impedance", "impedances" ], "total_occurrences": 1324, "matching_section_count": 154, "matching_source_count": 13, "source_totals": [ { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 313, "section_count": 28 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 255, "section_count": 12 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 243, "section_count": 23 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 170, "section_count": 19 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 160, "section_count": 30 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 59, "section_count": 18 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 45, "section_count": 7 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 22, "section_count": 3 }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 22, "section_count": 2 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 14, "section_count": 4 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 13, "section_count": 4 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 7, "section_count": 3 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-17", "section_label": "Chapter 17: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16521-17716", "status": "candidate", "occurrence_count": 45, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-17/", "snippets": [ "... transformer depends upon the primary e.m.f., which dependence can be represented by an admittance, the \"primary admittance,\" Fo = g^i — jbo, of the transformer. The resistance and reactance of the primary and the secondary circuit are represented in the impedance by Zo = To + jxo, and Zi = ri + jxi. Within the limited range of variation of the magnetic density in a constant-potential transformer, admittance and impedance can usually, and with sufficient exactness, be considered as constant. Let no = number ...", "... The resistance and reactance of the primary and the secondary circuit are represented in the impedance by Zo = To + jxo, and Zi = ri + jxi. Within the limited range of variation of the magnetic density in a constant-potential transformer, admittance and impedance can usually, and with sufficient exactness, be considered as constant. Let no = number of primary turns in series; Hi = number of secondary turns in series; a = — = ratio of turns; ni ' Fo = ^0 — jho = primary admittance Exciting current Prima ...", "... = number of primary turns in series; Hi = number of secondary turns in series; a = — = ratio of turns; ni ' Fo = ^0 — jho = primary admittance Exciting current Primary induced e.m.f. ' 198 ALTERNATING-CURRENT PHENOMENA Zo = To -{■ jxo = primary impedance e.m.f. consumed in primary coil by resistance and reactance \"~ Primary current ' Zi = Ti -\\- jxi = secondary impedance e.m.f. consumed in secondary coil by resistance and reactance Secondary current ' where the reactances, Xo and Xi, refer to the tr ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-04", "section_label": "Chapter 5: Single-Phase Induction Motor", "section_title": "Single-Phase Induction Motor", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 8555-10582", "status": "candidate", "occurrence_count": 44, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-04/", "snippets": [ "... hus is proportional to the quadrature flux. At synchronism, the quadrature magnetic flux produced by the armature currents becomes equal to the main magnetic flux produced by the impressed single-phase voltage (approximately, in reality it is less by the impedance drop of the exciting current in the armature conductors) and the magnetic disposition of the single-phase induction motor thus becomes at synchronism iden- tical with that of the polyphase induction motor, and approxi- mately so near synchronism. The ma ...", "... olt-ampere excitation of the single- phase motor thus is the same as in the polyphase motor at the same induced voltage, and decreases to half this value at stand- still, where only one of the two quadrature components of magnetic flux exists. The primary impedance of the motor is that of the circuits used. The secondary impedance varies from the joint impedance of all phases, at synchronism, to twice this value at standstill, since at synchronism all the secondary circuits correspond to the one primary circuit, whi ...", "... s in the polyphase motor at the same induced voltage, and decreases to half this value at stand- still, where only one of the two quadrature components of magnetic flux exists. The primary impedance of the motor is that of the circuits used. The secondary impedance varies from the joint impedance of all phases, at synchronism, to twice this value at standstill, since at synchronism all the secondary circuits correspond to the one primary circuit, while at stand- still only their component parallel with the primary c ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "section_label": "Chapter 16: Induction Motor", "section_title": "Induction Motor", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 42, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "... em ; if r^ = secondary resistance per circuit, rt = a2 r{ = secondary resistance per circuit reduced to primary system ; if x± = secondary reactance per circuit, xt = a2 x\\ = secondary reactance per circuit reduced to primary system ; if £/ = secondary impedance per circuit, z1 = azz\\ = secondary impedance per circuit reduced to primary system ; that is, the number of secondary circuits and of turns per secondary circuit is assumed the same as in the primary system. In the following discussion, as secondary q ...", "... rt = a2 r{ = secondary resistance per circuit reduced to primary system ; if x± = secondary reactance per circuit, xt = a2 x\\ = secondary reactance per circuit reduced to primary system ; if £/ = secondary impedance per circuit, z1 = azz\\ = secondary impedance per circuit reduced to primary system ; that is, the number of secondary circuits and of turns per secondary circuit is assumed the same as in the primary system. In the following discussion, as secondary quantities, the values reduced to the primary s ...", "... ter XXV. INDUCTION MOTOR. 241 Thus, from the hysteretic loss, and the reluctance, the constants, g and b, and thus the admittance, Fare derived. Let rQ = resistance per primary circuit ; XQ = reactance per primary circuit ; thus, •^o = ro — j XQ = impedance per primary circuit; rv = resistance per secondary circuit reduced to pri- mary system ; xv = reactance per secondary circuit reduced to primary system, at full frequency, .A7\"; hence, sx! = reactance per secondary circuit at slip s; and = second ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-17", "section_label": "Chapter 19: Alternating- Current Motors In General", "section_title": "Alternating- Current Motors In General", "kind": "chapter", "sequence": 17, "number": 19, "location": "lines 21713-23905", "status": "candidate", "occurrence_count": 39, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-17/", "snippets": [ "... it, r', consumes an e.n r'(, in phase with the current, and the total or effective resistance of the circuit is, therefore, r = r' + r\", and the total e.m.f. consumed by the circuit, or the impressed e.m.f.. is: E = (r+jx)I = Z{, .where : Z = r + jx = impedance, in vector denotation, z = Vr* + i* = impedance, in absolute terms. If an electric circuit is in inductive relation to another electa circuit, it is advisable to separate the inductance, L, of the cir- ALTERNATING-CURRENT MOTORS 303 cuit in two parts ...", "... urrent, and the total or effective resistance of the circuit is, therefore, r = r' + r\", and the total e.m.f. consumed by the circuit, or the impressed e.m.f.. is: E = (r+jx)I = Z{, .where : Z = r + jx = impedance, in vector denotation, z = Vr* + i* = impedance, in absolute terms. If an electric circuit is in inductive relation to another electa circuit, it is advisable to separate the inductance, L, of the cir- ALTERNATING-CURRENT MOTORS 303 cuit in two parts — the self-inductance, S, which refers to that ...", "... tes a reactive e.m.f. and thereby causes a lag of the current, while the mutual inductive reactance transfers power into the second circuit, hence generally does the useful work of the ap- paratus. This\" leads to the distinction between the self-inductive impedance, Z0 = r0 + jx0, and the mutual inductive impedance, Z = r + jx. The same separation of the total inductive reactance into self- inductive reactance and mutual inductive reactance, represented respectively by the self-inductive or \"leakage\" impedance, and ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 37, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "... As illustration is shown in Fig. 20 the load curve of a typical 100-hp. 60-cycle 80-polar induction motor (90 revolutions per minute) of the constants: Impressed voltage: ea = 500. Primary exciting admittance: Ya = 0.02 — 0.6 j. Primary self-inductive impedance: Zu = 0.1 + 0.3j. Secondary self-inductive impedance: Zi = 0.1 + 0.3 j. INDUCTION MOTOR 53 As seen, at full-load of 75 kw. output, the efficiency is 80 per cent., which is fair for a slow-speed motor. But the power-factor is 55 per cent., the ap ...", "... typical 100-hp. 60-cycle 80-polar induction motor (90 revolutions per minute) of the constants: Impressed voltage: ea = 500. Primary exciting admittance: Ya = 0.02 — 0.6 j. Primary self-inductive impedance: Zu = 0.1 + 0.3j. Secondary self-inductive impedance: Zi = 0.1 + 0.3 j. INDUCTION MOTOR 53 As seen, at full-load of 75 kw. output, the efficiency is 80 per cent., which is fair for a slow-speed motor. But the power-factor is 55 per cent., the apparent efficiency only 44 per cent., and the exciting ...", "... her importance, as the frequency is zero. It represents t he magnetic leakage between the synchronous motor poles. r0 is the armature resistance and xa the armature self-inductive reactance of the synchronous machine. However, x0 is net the synchronous impedance, which enters the equation of the synchronous machine, but is only the self- inductive part of il, or the true armature self-induct ancc. The IXDTCTIOX MOTQSt mutual inductive part of the synchronous hapedance. or Ik* effective reactance of anaatare ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-11", "section_label": "Chapter 12: Frequency Converter Or General Alternating Current Transformer", "section_title": "Frequency Converter Or General Alternating Current Transformer", "kind": "chapter", "sequence": 11, "number": 12, "location": "lines 14897-17124", "status": "candidate", "occurrence_count": 33, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-11/", "snippets": [ "... air gap in the magnetic circuit, to permit movability between primary and secondary, and thus they require a higher magnetizing current than the closed magnetic circuit stationary transformer, and this again results in general in a higher self- inductive impedance. Thus, the frequency converter and in- duction motor magnetically represent transformers of high ex- citing admittance and high self-inductive impedance. 104. The mutual magnetic flux of the transformer is pro- duced by the resultant m.m.f. of both elect ...", "... magnetic circuit stationary transformer, and this again results in general in a higher self- inductive impedance. Thus, the frequency converter and in- duction motor magnetically represent transformers of high ex- citing admittance and high self-inductive impedance. 104. The mutual magnetic flux of the transformer is pro- duced by the resultant m.m.f. of both electric circuits. It is determined by the counter e.m.f., the number of turns, and the frequency of the electric circuit, by the equation : E = V2 rfnQ 10\" ...", "... per circuit; nx = number of secondary turns in series per circuit; a = = ratio of turns; Til Y = g — jb = primary exciting admittance per circuit; where: g = effective conductance; b = susceptance; Zq = r0 + jxo = internal primary self-inductive impedance per circuit, where: r0 = effective resistance of primary circuit; Xq = self-inductive reactance of primary circuit; Zn = n + jx\\ = internal secondary self-inductive im- pedance per circuit at standstill, or for « = 1, where: rx = effective resista ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-18", "section_label": "Chapter 20: Single-Phase Commutator Motors", "section_title": "Single-Phase Commutator Motors", "kind": "chapter", "sequence": 18, "number": 20, "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 33, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "... he secondary circuit, as shown by the transformer diagram, Fig. 166. Herefrom it follows that: In the inductively compensated series motor, 2, the quad- rature flux is very small and practically negligible, as very little voltage is consumed in the low impedance of the secondary cir- cuit, C; whatever flux there is, lags behind the main flux. 346 ELECTRICAL APPARATUS In the inductively compensated series ipotor with secondary excitation, or inverted repulsion motor, 3, the quadrature flux, $1, is quite la ...", "... he field flux, 4>, and thus approxi- mately with the current [, is proportional to tin* frequency of the 362 ELECTRICAL APPARATUS impressed voltage, /, to the field strength, 4>, and to the number of field turns, n„. «o = 2jirfn0* 10~8. (26) 3. The impedance voltage of the motor: e' = IZ (27) and: Z = r + jx, where r = total effective resistance of field coils, armature with commutator and brushes, and compensating winding, x = total self-inductive reactance, that is, reactance of the leakage flux of arm ...", "... Fia. 173. — Bingle-phase commutator-motor spoori characteristics. he voltage consumed by the resistance, r, is OE, — ir. in pi l 01; the voltage consumed by the reactance, x, is OE, = 90° ahead of 01. OE, and OE, combine to the voltage c ed by the motor impedance, OE' — iz. ombining OE' = iz, OE\\ — eit and OE0 = c0 thus gives linal voltage, OE = e, of the motor, and the phase an = e. l this diagram, and in the preceding approximate calculat magnetic flux, *, has been assumed in phase with the curren l reality, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-24", "section_label": "Chapter 24: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 25682-29374", "status": "candidate", "occurrence_count": 32, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-24/", "snippets": [ "... hod, we may in the following, as an example of the graphical method, treat the action of the synchronous motor graphically. Let an alternator of the e.m.f., Ei, be connected as synchron- ous motor with a supply circuit of e.m.f., Eo, by a circuit of the impedance, Z. If £\"0 is the e.m.f. impressed upon the motor terminals, Z is the impedance of the motor of generated e.m.f., Ei. If Eq is the e.m.f. at the generator terminals, Z is the impedance of motor and line, including transformers and other intermediate appa ...", "... ion of the synchronous motor graphically. Let an alternator of the e.m.f., Ei, be connected as synchron- ous motor with a supply circuit of e.m.f., Eo, by a circuit of the impedance, Z. If £\"0 is the e.m.f. impressed upon the motor terminals, Z is the impedance of the motor of generated e.m.f., Ei. If Eq is the e.m.f. at the generator terminals, Z is the impedance of motor and line, including transformers and other intermediate apparatus. If Eq is the generated e.m.f. of the generator, Z is the sum of the impeda ...", "... - ous motor with a supply circuit of e.m.f., Eo, by a circuit of the impedance, Z. If £\"0 is the e.m.f. impressed upon the motor terminals, Z is the impedance of the motor of generated e.m.f., Ei. If Eq is the e.m.f. at the generator terminals, Z is the impedance of motor and line, including transformers and other intermediate apparatus. If Eq is the generated e.m.f. of the generator, Z is the sum of the impedances of motor, line, and generator, and thus we have the problem, generator of generated e.m.f., Eo, and ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-14", "section_label": "Chapter 14: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 11605-12682", "status": "candidate", "occurrence_count": 32, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "snippets": [ "... transformer depends upon the primary E.M.F., which dependance can be rep- resented by an admittance, the \" primary admittance,\" °f tne transformer. Fig. 105. The resistance and reactance of the primary and the secondary circuit are represented in the impedance by Z0=r0- jx0, and Zl=rl- j xl . Within the limited range of variation of the magnetic density in a constant potential transformer, admittance and impedance can usually, and with sufficient .exactness, be considered as constant. Let n0 = number of ...", "... The resistance and reactance of the primary and the secondary circuit are represented in the impedance by Z0=r0- jx0, and Zl=rl- j xl . Within the limited range of variation of the magnetic density in a constant potential transformer, admittance and impedance can usually, and with sufficient .exactness, be considered as constant. Let n0 = number of primary turns in series ; #1 = number of secondary turns in series ; a = — = ratio of turns ; Y0 = g0 4- jb0 = primary admittance Exciting current . ~i I P ...", "... in series ; #1 = number of secondary turns in series ; a = — = ratio of turns ; Y0 = g0 4- jb0 = primary admittance Exciting current . ~i I Primary counter E.M.F. ' .VVWvVl rw^ww ALTERNATING-CURRENT TRANSFORMER. 205 Z0 = r0 — j x0 = primary impedance 7. — — E.M.F. consumed in primary coil by resistance and reactance. ^ -n-f '\" ' j**/\\. Primary current ~ / Z± = r± —jx1= secondary impedance __ E.M.F. consumed in secondary coil by resistance and reactance . Secondary current where the reactances, ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-109", "section_label": "Apparatus Section 3: Induction Machines: Single -phase Induction Motor", "section_title": "Induction Machines: Single -phase Induction Motor", "kind": "apparatus-section", "sequence": 109, "number": 3, "location": "lines 20428-21157", "status": "candidate", "occurrence_count": 27, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-109/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-109/", "snippets": [ "... main magnetic flux plus the current producing in the secondary the exciting current of the cross magnetic flux. In reality it is slightly less, especially in small motors, due to the drop of voltage in the self-inductive impedance and the drop of quadrature mag- netic flux below the impressed primary magnetic flux caused thereby. In the secondary at synchronism this secondary exciting current is a current of twice the primary frequency; at any other ...", "... )262a!. Since in the single-phase motor only one primary circuit but a multiplicity of secondary circuits exist, all secondary circuits are to be considered as corresponding to the same primary cir- cuit, and thus the joint impedance of all secondary circuits must be used as the secondary impedance, at least at or near syn- chronism. Thus, if the armature has a quarter-phase winding of impedance Zi per circuit, the resultant secondary impedance is r? ...", "... ut a multiplicity of secondary circuits exist, all secondary circuits are to be considered as corresponding to the same primary cir- cuit, and thus the joint impedance of all secondary circuits must be used as the secondary impedance, at least at or near syn- chronism. Thus, if the armature has a quarter-phase winding of impedance Zi per circuit, the resultant secondary impedance is r? sr; if it contains a three-phase winding of impedance Zi per a ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-13", "section_label": "Chapter 13: Ths Alternating^Cnrrent Traxsfobmer", "section_title": "Ths Alternating^Cnrrent Traxsfobmer", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 12673-14088", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "snippets": [ "... s upon the primary K.M.K., which dcpendance can be rc|> resented by an admittance, the \" primary admittance,\" Y^=^ g^ ■\\- j b^, of the transformer. rig. 9B. The resistance and reactance of the primary and the secondary circuit are represented in the impedance by ^u = r^ —j^ut and Z| = r, —Jx\\- Within the limited range of variation of the magnetic density in a constant [iotential transformer, admittance and impedance can usually, and with sufficient exactness, be considered as constant. Let «„ = number of pr ...", "... The resistance and reactance of the primary and the secondary circuit are represented in the impedance by ^u = r^ —j^ut and Z| = r, —Jx\\- Within the limited range of variation of the magnetic density in a constant [iotential transformer, admittance and impedance can usually, and with sufficient exactness, be considered as constant. Let «„ = number of primary turns in series; t, = number of secondary turns in series; a ^ -^ = ratio of turns; ^« =K\" — /''.. = primary admittance ~ i'riiMIJ cuunltF K.M.k!' § ...", "... ant. Let «„ = number of primary turns in series; t, = number of secondary turns in series; a ^ -^ = ratio of turns; ^« =K\" — /''.. = primary admittance ~ i'riiMIJ cuunltF K.M.k!' § 124] ALTERNATING-CURRENT TRANSFORMER. 179 Zo = ro — jxo = primary impedance K^I .F. cons umed in primary coil by resistance and reactance . Primary current Zi = ri — yji*, = secondary impedance E.M.F. consumed in secondary coil by resistance a nd reacta nce . Secondary current where the reactances, x^ and Xy^, refer to th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-19", "section_label": "Chapter 19: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 18053-19457", "status": "candidate", "occurrence_count": 25, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "snippets": [ "... we may in the following, as an instance of the graphical method, treat the action of the synchronous motor diagrammatically. Let an alternator of the E.M.F., E±, be connected as synchronous motor with a supply circuit of E.M.F., EQ, by a circuit of the impedance Z. If E0 is the E.M.F. impressed upon the motor termi- nals, Z is the impedance of the motor of induced E.M.F., E±. If E0 is the E.M.F. at the generator terminals, Z is the impedance of motor and line, including transformers and other intermediate appar ...", "... of the synchronous motor diagrammatically. Let an alternator of the E.M.F., E±, be connected as synchronous motor with a supply circuit of E.M.F., EQ, by a circuit of the impedance Z. If E0 is the E.M.F. impressed upon the motor termi- nals, Z is the impedance of the motor of induced E.M.F., E±. If E0 is the E.M.F. at the generator terminals, Z is the impedance of motor and line, including transformers and other intermediate apparatus. If EQ is the induced E.M.F. of the generator, Z is the sum of the impedances ...", "... hronous motor with a supply circuit of E.M.F., EQ, by a circuit of the impedance Z. If E0 is the E.M.F. impressed upon the motor termi- nals, Z is the impedance of the motor of induced E.M.F., E±. If E0 is the E.M.F. at the generator terminals, Z is the impedance of motor and line, including transformers and other intermediate apparatus. If EQ is the induced E.M.F. of the generator, Z is the sum of the impedances of motor, line, and generator, and thus we have the prob- lem, generator of induced E.M.F. EQ, and mot ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-18", "section_label": "Chapter 16: Il", "section_title": "Il", "kind": "chapter", "sequence": 18, "number": 16, "location": "lines 19346-21338", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-18/", "snippets": [ "... we may in the following, as an instance of the graphical method, treat the action of the synchronous motor diagrammatically. Let an alternator of the E.M.F., E^, be connected as synchronous motor w^ith a supply circuit of E.M.F., E^y by a circuit of the impedance Z, If E^ is the E.M.F. impressed upon the motor termi- nals, Z is the impedance of the motor of induced E.M.F., E^. If E^ is the E.M.F. at the generator terminals, Z is the impedance of motor and line, including transformers and other intermediate appar ...", "... of the synchronous motor diagrammatically. Let an alternator of the E.M.F., E^, be connected as synchronous motor w^ith a supply circuit of E.M.F., E^y by a circuit of the impedance Z, If E^ is the E.M.F. impressed upon the motor termi- nals, Z is the impedance of the motor of induced E.M.F., E^. If E^ is the E.M.F. at the generator terminals, Z is the impedance of motor and line, including transformers and other intermediate apparatus. If E^ is the induced E.M.F. of J:he generator, Z is the sum of the impedance ...", "... ronous motor w^ith a supply circuit of E.M.F., E^y by a circuit of the impedance Z, If E^ is the E.M.F. impressed upon the motor termi- nals, Z is the impedance of the motor of induced E.M.F., E^. If E^ is the E.M.F. at the generator terminals, Z is the impedance of motor and line, including transformers and other intermediate apparatus. If E^ is the induced E.M.F. of J:he generator, Z is the sum of the impedances of motor, line, and generator, and thus we have the prob- lem, generator of induced E.M.F. E^y and mo ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-05", "section_label": "Chapter 6: Induction-Motor Regulation And Stability", "section_title": "Induction-Motor Regulation And Stability", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 10583-12397", "status": "candidate", "occurrence_count": 23, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-05/", "snippets": [ "... us, if the voltage at the primary terminals of the motor transformer is constant, and such as to give the rated motor voltage at full-load, at no- load the voltage at the motor terminals is higher, but at overload lower by the voltage drop in the internal impedance of the trans- formers. If the voltage is kept constant in the center of distri- bution, the drop of voltage in the line adds itself to the imped- ance drop in the transformers, and the motor supply voltage thus varies still more between no-load and overlo ...", "... terminals, assuming the cir- cuit such as to give the rated motor voltage at full-load, the voltage at no-load and thus the exciting current is higher, the voltage at overload and thus the maximum output and maximum torque of the motor, and also the motor impedance current, that is, current consumed by the motor at standstill, and thereby the starting torque of the motor, are lower than on a constant-poten- tial supply. Hereby then the margin of overload capacity of the motor is reduced, and the characteristic const ...", "... e inferior to that given at constant voltage supply, the more so the higher the voltage drop in the supply circuit. Assuming then a three-phase motor having the following con- stants: primary exciting admittance, Y = 0.01 — 0.1 j; primary self-inductive impedance, Z0 = 0.1 + 0.3 j; secondary self -induc- 123 124 ELECTRICAL APPARATUS tive impedance, Z, = 0.1 + 0.3 j; supply voltage, e0 = 110 volts, and rated output, 5000 waits per phase. Assuming this motor to be operated: 1. By transformers of about 2 p ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-appendix-01-synchronous-operation", "section_label": "Mathematical Appendix 5: Appendix: Synchronous Operation", "section_title": "Appendix: Synchronous Operation", "kind": "mathematical-appendix", "sequence": 5, "number": 5, "location": "PDF pages 27-68, lines 2165-5013", "status": "pdf-text-extracted-candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "snippets": [ "... / (1) and the resultant voltage in the circuit between the alternators then is : e = ei e 2 = E cos \\ ( co) cos (+ co) [ = 2E sin co sin (2) and the interchange currentwbeteen the alternators is: 2E . i = sin co sin ( a) (3) where: z = r2+x 2 is the impedance of the circuit between the two alternators, and the phase angle a is given by: x tan a = - r and: r= resistance x = reactance of the circuit between the alternators (including their internal resistances and reactances). [[END_PDF_PAGE:28]] [[PDF_PAGE:29]] Re ...", "... other machine, and which gives an induction motor torque, tending to pull the machines together into synch- ronism. D Consider two alternators or groups of alternators such as station sections of the same terminal voltage, connected with each other through an impedance z, and in synchronism with each other. If then the load distribution between the alternators differs from the distribution of their driving power, electric power is transferred over the impedance z, current flows and a phase displacement 2co occurs between th ...", "... the same terminal voltage, connected with each other through an impedance z, and in synchronism with each other. If then the load distribution between the alternators differs from the distribution of their driving power, electric power is transferred over the impedance z, current flows and a phase displacement 2co occurs between the two sides of the reactor z. In this case, the phase angle w is constant, and not periodically fluctuating as in A, but varies with changes of distribution of load ; the equations, however, are t ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-20", "section_label": "Chapter 20: Single-Phase Induction Motors", "section_title": "Single-Phase Induction Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 21538-22301", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-20/", "snippets": [ "... duced either by some outside e.m.f., as in the monocyclic starting device, or by displacing the circuits of two or more primary coils from each other, either by mutual induc- tion between the coils — that is, by using one as secondary to the other — or by impedances of different inductance factors connected with the different primary coils. 178. The starting devices of the single-phase induction motor by producing a quadrature magnetic flux can be subdivided into three classes: 1. Phase-Splitting Devices. Two or m ...", "... flux can be subdivided into three classes: 1. Phase-Splitting Devices. Two or more primary circuits are used, displaced in position from each other, and either in series or in shunt with each other, or in any other way related, as by transformation. The impedances of these circuits are made different from each other as much as possible to produce a phase displacement between them. This can be done either by inserting external impedances in the circuits, as a condenser and a reactive coil, or by making the internal ...", "... n shunt with each other, or in any other way related, as by transformation. The impedances of these circuits are made different from each other as much as possible to produce a phase displacement between them. This can be done either by inserting external impedances in the circuits, as a condenser and a reactive coil, or by making the internal impedances of the motor circuits different, as by making one coil of high and the other of low resistance. 2. Inductive Devices. The different primary circuits of the motor a ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-35", "section_label": "Chapter 35: Balanced Symmetrical Polyphase Systems", "section_title": "Balanced Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 35, "number": 35, "location": "lines 37453-37957", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-35/", "snippets": [ "... ms, each e.m.f. and its current can be considered separately as constituting a single-phase system, that is, the polyphase system can be resolved into n equal single-phase systems, each of which consists of one conductor of the polyphase system, with zero impedance as return circuit. Hereby the investigation of the polyphase system resolves itself into that of its constituent single-phase system. So, for instance, the polyphase system shown in Fig. 208, at balanced load, can be considered as consisting of the equal ...", "... ts of one conductor, 1, 2, 3, . . . n, and the return conductor, 0. Since the sum of all the currents equals 0, there is no current in conductor 0, that is, no voltage is consumed in this conductor; this is equivalent to assuming this conductor as of zero impedance. This common return conductor, 0, since it carries no current, can be omitted, as is usually the case. With star connection of an apparatus into a polyphase system, as in Fig. 200, the impedance of the equivalent single-phase system is the impedance of on ...", "... or; this is equivalent to assuming this conductor as of zero impedance. This common return conductor, 0, since it carries no current, can be omitted, as is usually the case. With star connection of an apparatus into a polyphase system, as in Fig. 200, the impedance of the equivalent single-phase system is the impedance of one conductor or circuit; if, however, the appa- ratus is ring connected, as shown diagrammatically in Fig. 201, the impedance of the ring-connected part of the circuit has to be reduced to star co ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-17", "section_label": "Theory Section 17: Impedance and Admittance", "section_title": "Impedance and Admittance", "kind": "theory-section", "sequence": 17, "number": 17, "location": "lines 6814-7380", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-17/", "snippets": [ "17. IMPEDANCE AND ADMITTANCE 82. In direct-current circuits the most important law is Ohm's law, e -i or e r ir, or r = -.> where e is the e.m.f. impressed upon resistance r to produce current i therein. Since ...", "... produce current i therein. Since in alternating-current circuits a current i through a resistance r may produce additional e.m.fs. therein, when apply- a ing Ohm's law, i — - to alternating-current circuits, e is the IMPEDANCE AND ADMITTANCE ' 99 total e.m.f. resulting from the impressed e.m.f. and all e.m.fs. produced by the current i in the circuit. Such counter e.m.fs. may be due to inductance, as self-induc- tance, or mutual inductance, to ...", "... s as resistance, and measured in ohms: reactance x. The e.m.f. consumed by reactance x is in quadrature with the current, that consumed by resistance r in phase with the current. Reactance and resistance combined give the impedance, + x2; or, in symbolic or vector representation, Z = r + jx. In general in an alternating-current circuit of current i, the e.m.f. e can be resolved in two components, a power component ei in phase with the current, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-08", "section_label": "Chapter 8: Admittance, Conductance, Susceptance", "section_title": "Admittance, Conductance, Susceptance", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 4088-4673", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-08/", "snippets": [ "... joint conduct- ance of a number of parallel-connected conductances is equal to the sum of the individual conductances. 64 ADMITTANCE, CONDUCTANCE, SUSCEPTANCE 55 49. In alternating-current circuits, instead of the term resist- ance we have the term impedance, Z = r -\\- jx, with its two components, the resistance, r, and the reactance, x, in the formula of Ohm's law, E = IZ. The resistance, r, gives the component of e.m.f. in phase with the current, or the power component of the e.m.f., Ir; the reactance, x, g ...", "... ance, x, gives the component of the e.m.f. in quadrature with the current, or the wattless component of e.m.f., Ix; both combined give the total e.m.f., Iz = iVr^ + x^. Since e.m.fs. are combined by adding their complex expressions, we have: The joint impedance of a number of series-connected impedances is the sum of the individual impedances, when expressed in com- plex quantities. In graphical representation impedances have not to be added, but are combined in their proper phase by the law of parallelo- gram ...", "... . in quadrature with the current, or the wattless component of e.m.f., Ix; both combined give the total e.m.f., Iz = iVr^ + x^. Since e.m.fs. are combined by adding their complex expressions, we have: The joint impedance of a number of series-connected impedances is the sum of the individual impedances, when expressed in com- plex quantities. In graphical representation impedances have not to be added, but are combined in their proper phase by the law of parallelo- gram in the same manner as the e.m.fs. correspo ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-09", "section_label": "Chapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "section_title": "Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 4674-6992", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-09/", "snippets": [ "... - fore only some of the more common or more interesting combina- tions will here be considered. 1. Resistance in Series with a Circuit 54. In a constant-potential system with impressed e.m.f., Eo = eo-\\- je'o, Eo = V^TT^ let the receiving circuit of impedance, Z = r -\\- jx, z = y/f^ -\\- x^, be connected in series with a resistance, Tq. 60 CIRCUITS CONTAINING RESISTANCE 61 The total impedance of the circuit is then Z + ro = r -\\- ro -{- jx; hence the current is _ -go _ Eo _ Eo(r + ro - jx) _ . ~ Z ...", "... n a constant-potential system with impressed e.m.f., Eo = eo-\\- je'o, Eo = V^TT^ let the receiving circuit of impedance, Z = r -\\- jx, z = y/f^ -\\- x^, be connected in series with a resistance, Tq. 60 CIRCUITS CONTAINING RESISTANCE 61 The total impedance of the circuit is then Z + ro = r -\\- ro -{- jx; hence the current is _ -go _ Eo _ Eo(r + ro - jx) _ . ~ Z + To \" r + To -\\- jx \" (r + ro)2 + x^ ' and the e.m.f. of the receiving circuit becomes Eo{r + jx) Eo { r(r + ro) -\\- x^ -\\- jrpx} E ^ IZ ...", "... ame value when X is negative as when x is positive; or, in other words, series resistance acts upon a circuit with leading current, or in a condenser circuit, in the same way as upon a circuit with lag- ging current, or an inductive circuit. For a given impedance, z, of the receiver circuit, the current, /, and e.m.f., E, are smaller the larger the value of r; that is, the less the difference of phase in the receiver circuit. IMPRESSED E. M.F. CONSTANT, ^0-- lOO 100 90 IMPEDANCE OF RECEIVER CIRCUIT C ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-27", "section_label": "Chapter 27: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 33011-34776", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-27/", "snippets": [ "... braically identical, physically represent different frequencies, and thus cannot be combined. The general wave of e.m.f. is thus represented by E = 2:2n-i(e„i4-j„e„ii), 1 the general wave of current by 1 If Zi = r -^ j (x„, -{- xo -\\- Xc) is the impedance of the fundamental harmonic, where Xm is that part of the reactance which is proportional to the frequency (inductance, etc.), ^ Xo is that part of the reactance which is independent of the frequency (mutual inductance, synchronous motion, etc.). Xc i ...", "... uency (inductance, etc.), ^ Xo is that part of the reactance which is independent of the frequency (mutual inductance, synchronous motion, etc.). Xc is that part of the reactance which is inversely propor- tional to the frequency (capacity, etc.). The impedance for the nth harmonic is + jn (nxr^ + a^o + -^ ) This term can be considered as the general symbolic expression of the impedance of a circuit of general wave-shape. Ohm's law, in symbolic expression, assumes for the general alternating wave the form ...", "... otion, etc.). Xc is that part of the reactance which is inversely propor- tional to the frequency (capacity, etc.). The impedance for the nth harmonic is + jn (nxr^ + a^o + -^ ) This term can be considered as the general symbolic expression of the impedance of a circuit of general wave-shape. Ohm's law, in symbolic expression, assumes for the general alternating wave the form 7 = ^or, S2n-i(t„i +j„^„ii) = Ssn-i E r -{- Jn [^nxm + Xo + — j = IZ or, 22n-i (e„i -\\-jner}^) = S2n-i l^r + jn {rixm + 3^0 + ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-12", "section_label": "Chapter 14: Phase Conversion And Single-Phase Generation", "section_title": "Phase Conversion And Single-Phase Generation", "kind": "chapter", "sequence": 12, "number": 14, "location": "lines 17125-18412", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-12/", "snippets": [ "... ch the flow of energy is essentially single- phase. For instance, if, as shown diagrammatic ally in Fig. 67, we connect, between single-phase mains, AB, two pairs of non-in- ductive resistances, r, and inductive reactances, x (or in general, two pairs of impedances of different inductance factors), such that t = x, consuming the voltages E\\ and Et respectively, then the voltage e» = CD is in quadrature with, and equal to, the voltage e = AB, and the two voltages, e and eo, constitute a monocyclic system of quarter-p ...", "... the size of the device, and making it (hereby economically feasible with the use of the rather expen- sive energy-storing devices of inductance (and capacity) used in this case. The simplest and most generally used monocyclic device con- si sis of I wo impedances, Z, and Z«,ot different inductance factors (resistance and inductance, or inductance and capacity), con- nected aiTuss the single-phase mains, .4 ami li. The common connection, C, between the two impedances, Z, and Z>. then is dis- placed in phase from th ...", "... rally used monocyclic device con- si sis of I wo impedances, Z, and Z«,ot different inductance factors (resistance and inductance, or inductance and capacity), con- nected aiTuss the single-phase mains, .4 ami li. The common connection, C, between the two impedances, Z, and Z>. then is dis- placed in phase from the single-phase supply voltage. A and B, and gives with the same a system of out-of-phase voltages, AC, Cli and .4 if, or a — more or less unsymmetrical — three-phase Iriaiude. Or, between this common connect ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-108", "section_label": "Apparatus Section 2: Induction Machines: Polyphase Induction Motor", "section_title": "Induction Machines: Polyphase Induction Motor", "kind": "apparatus-section", "sequence": 108, "number": 2, "location": "lines 19166-20427", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-108/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-108/", "snippets": [ "... tance of the primary circuit with open secondary circuit; that is, ge = magnetic power current, be = wattless magnetizing current, where e = counter-generated e.m.f. of the motor; ZQ = r0 + jxQ = primary self -inductive impedance, and Zi = 7*1 + jxi = secondary self-inductive impedance, reduced to the primary by the ratio of turns.1 All these quantities refer to one primary circuit and one corre- sponding secondary circuit. Thus in a three-phas ...", "... is, ge = magnetic power current, be = wattless magnetizing current, where e = counter-generated e.m.f. of the motor; ZQ = r0 + jxQ = primary self -inductive impedance, and Zi = 7*1 + jxi = secondary self-inductive impedance, reduced to the primary by the ratio of turns.1 All these quantities refer to one primary circuit and one corre- sponding secondary circuit. Thus in a three-phase induction motor the total power, etc., is three times that ...", "... s to that flux which surrounds one of the electric circuits only, without being interlinked with the other circuits. 312 ELEMENTS OF ELECTRICAL ENGINEERING hence, . se = e.m.f. generated in the secondary. The actual impedance of the secondary circuit at the frequency sf is Zi8 = 7*1 +jsxi; hence, the secondary current is se se where the primary exciting current is /oo =eY = e[g — jb], and the total primary current is /o = e I (ai ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-18", "section_label": "Chapter 18: Polyphase Induction Motors", "section_title": "Polyphase Induction Motors", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17717-20445", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-18/", "snippets": [ "... r'l = secondary resistance per circuit, Vi = a-hr'i = secondary resistance per circuit reduced to pri- mary system; if x'l = secondary reactance per circuit, Xi = a^bx'i = secondary reactance per circuit reduced to pri- mary system; if z'l = secondary impedance per circuit, 2i = a^hz'i = secondary impedance per circuit reduced to pri- mary system; that is, the number of secondary circuits and of turns per sec- ondary circuit is assumed the same as in the primary system. In the following discussion, as second ...", "... hr'i = secondary resistance per circuit reduced to pri- mary system; if x'l = secondary reactance per circuit, Xi = a^bx'i = secondary reactance per circuit reduced to pri- mary system; if z'l = secondary impedance per circuit, 2i = a^hz'i = secondary impedance per circuit reduced to pri- mary system; that is, the number of secondary circuits and of turns per sec- ondary circuit is assumed the same as in the primary system. In the following discussion, as secondary quantities, the values reduced to the primar ...", "... ed in Chapter XII, it is V2 Thus, from the hysteretic loss, and the reluctance, the con- stants, g and h and thus the admittance, Y, are derived. Let To = resistance per primary circuit; Xo = reactance per primary circuit; thus, Zo = To -}- jxo = impedance per primary circuit; ri = resistance per secondary circuit reduced to primary system; Xi = reactance per secondary circuit reduced to primary system, at full frequency/; 1 Complete discussion hereof, see Chapter XXXIII. 212 ALTERNATING-CURRENT PHEN ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-08", "section_label": "Chapter 8: Circuits Containing Resistance, Inductance, And Capacity", "section_title": "Circuits Containing Resistance, Inductance, And Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3577-5333", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "snippets": [ "... being also the fundamental laws of alternating-current circuits, when expressed in their com- plex form, E = ZS, or, / = YE, and *%E = 0 in a closed circuit, S/ = 0 at a distributing point, where E, I, Z, Y, are the expressions of E.M.F., current, impedance, and admittance in complex quantities, — these values representing not only the intensity, but also the phase, of the alternating wave, — we can now — by application of these laws, and in the same manner as with continuous- current circuits, keeping in mi ...", "... mon or more . interesting combinations will here be considered. 1.) Resistance in series with a circuit. 43. In a constant-potential system with impressed E.M.F., o = e. +/V, E. = RESISTANCE, INDUCTANCE, CAPACITY. 59 let the receiving circuit of impedance Z = r —jx, z = Vr2 + x'2, be connected in series with a resistance, r0 . The total impedance of the circuit is then Z + r0 = r + r0—jx\\ hence the current is ____ •\" Z + r0 r+r0 -jx (r + r0)2 -f *2 ' and the E.M.F. of the receiving circuit, becom ...", "... circuit. 43. In a constant-potential system with impressed E.M.F., o = e. +/V, E. = RESISTANCE, INDUCTANCE, CAPACITY. 59 let the receiving circuit of impedance Z = r —jx, z = Vr2 + x'2, be connected in series with a resistance, r0 . The total impedance of the circuit is then Z + r0 = r + r0—jx\\ hence the current is ____ •\" Z + r0 r+r0 -jx (r + r0)2 -f *2 ' and the E.M.F. of the receiving circuit, becomes E = IZ = ^° (r ~J^ = ^° or, in absolute values we have the following : — Impressed E.M.F., ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-07", "section_label": "Chapter 7: Admittance, Conductance, Susceftance", "section_title": "Admittance, Conductance, Susceftance", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 3546-3871", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-07/", "snippets": [ "... § 30] ADMITTANCE, CONDUCTANCE, SUSCEPTANCE. 53 joint conductance of a number of parallel-connected conduc- tances is equal to the sum of the individual conductances, 39. In alternating-current circuits, instead of the term resistance we have the term impedance , Z = r —jx, with its two components, the resistance^ r, and the reactance^ x, in the formula of Ohm's law, E = IZ, The resistance, r, gives the component of E.M.F. in phase with the current, or the energy component of the E.M.F., Ir\\ the reactance, Xy g ...", "... y gives the component of the E.M.F. in quadrature with the current, or the wattless component of E.M.F., Ix\\ both combined give the total E.M.F., — Iz = lWr' + x\\ Since E.M.Fs. are combined by adding their complex ex- pressions, we have : The joint impedance of a number of series-connected impe- dances is the sum of the individual impedances , when expressed in complex quantities. In graphical representation impedances have not to be added, but are combined in their proper phase by the law of parallelogram ...", "... component of E.M.F., Ix\\ both combined give the total E.M.F., — Iz = lWr' + x\\ Since E.M.Fs. are combined by adding their complex ex- pressions, we have : The joint impedance of a number of series-connected impe- dances is the sum of the individual impedances , when expressed in complex quantities. In graphical representation impedances have not to be added, but are combined in their proper phase by the law of parallelogram in the same manner as the E.M.Fs. corre- sponding to them. The term impedance becomes ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-07", "section_label": "Chapter 7: Admittance, Conductance, Susceptance", "section_title": "Admittance, Conductance, Susceptance", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 3132-3576", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-07/", "snippets": [ "... ; the ADMITTANCE, CONDUCTANCE, SUSCEPTANCE. 53 joint conductance of a number of parallel-connected conduc~ tances is equal to the sum of the individual conductances. 39. In alternating-current circuits, instead of the term resistance we have the term impedance, Z = r —Jx, with its two components, the resistance, r, and the reactance, x, in the formula of Ohm's law, E = IZ. The resistance, r, gives the component of E.M.F. in phase with the current, or the energy component of the E.M.F., Ir; the reactance, x, gi ...", "... the reactance, x, gives the component of the E.M.F. in quadrature with the current, or the wattless component of E.M.F., Ix ; both combined give the total E.M.F., — Since E.M.Fs. are combined by adding their complex ex- pressions, we have : The joint impedance of a number of series-connected impe- dances is the sum of the individual impedances, when expressed in complex quantities. In graphical representation impedances have not to be added, but are combined in their proper phase by the law of parallelogram i ...", "... or the wattless component of E.M.F., Ix ; both combined give the total E.M.F., — Since E.M.Fs. are combined by adding their complex ex- pressions, we have : The joint impedance of a number of series-connected impe- dances is the sum of the individual impedances, when expressed in complex quantities. In graphical representation impedances have not to be added, but are combined in their proper phase by the law of parallelogram in the same manner as the E.M.Fs. corre- sponding to them. The term impedance become ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "... denotes that the/s of differ- entindices n, while algebraically identical, physically rep- resent different frequencies, and thus cannot be combined. The general wave of E.M.F. is thus represented by, the general wave of current by, if, is the impedance of the fundamental harmonic, where xm is that part of the reactance which is proportional to the frequency (inductance, etc.). x0 is that part of the reactance which is independent of the frequency (mutual induction, synchronous motion, etc.). xc is ...", "... equency (inductance, etc.). x0 is that part of the reactance which is independent of the frequency (mutual induction, synchronous motion, etc.). xc is that part of the reactance which is inversely pro- portional to the frequency (capacity, etc.). The impedance for the nth harmonic is, r —Jnn xm This term can be considered as the general symbolic expression of the impedance of a circuit of general wave shape. 412 ALTERNATING-CURRENT PHENOMENA. Ohm's law, in symbolic expression, assumes for the general ...", "... synchronous motion, etc.). xc is that part of the reactance which is inversely pro- portional to the frequency (capacity, etc.). The impedance for the nth harmonic is, r —Jnn xm This term can be considered as the general symbolic expression of the impedance of a circuit of general wave shape. 412 ALTERNATING-CURRENT PHENOMENA. Ohm's law, in symbolic expression, assumes for the general alternating wave the form, /-Jo, E = IZ or, Z = £or, Z = r -n The symbols of multiplication and division of ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-14", "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "section_title": "Constant-Potential Constant-Current Trans Formation", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "... d may be produced by the combination of inductive and condensive reactances; and the investigation of different methods of producing constant alternating current from constant alternating voltage, or inversely, constitutes a good application of the terms \"impedance,\" admittance,\" etc., and offers a large number of problems or examples for the symbolic method of dealing with alternating-current phenomena. Even outside of arc lighting, such combinations of inductance and capacity which t«nd toward constant-voltage co ...", "... sistance of the circuit is small compared with the series inductive reactance. Let ^0 = Co = constant impressed alternating voltage; r = resistance of non-inductive receiver circuit; Xo = inductive reactance inserted in series with this circuit. The impedance of this circuit then is Z = r + jxof and, absolute, and thus the current, / = ^* = -^ (1) ^ r + jxo and the absolute value is eo Co the phase angle of the supply circuit is given by (2) and the power factor. tan ^0 = - (3) T cos ...", "... rcuits, due to the inductive reactance of the regulating mechanism of the arc lamp (the effective resistance, r, and the inductive reactance, a:, in this case are both proportional to the number of lamps, hence pro- portional to each other), it is: total impedance: Z = r +j (xo + x) = r +j (xo + kr) ; or the absolute value is z = Vr^ + {xo + xy = Vr2 + {xo + kr)^; thus, the current r + j{xo + krY i *. _J_ A(^. _L hW (•) and the absolute value is i= , '\" = = '-^ -, ^ ; (8) 4' Xq Xo2 CONSTANT-CUR ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-04", "section_label": "Chapter 5: Methods Of Approximation", "section_title": "Methods Of Approximation", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 15156-16482", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-04/", "snippets": [ "... j^wli^ a greater exactness is required, by taking in the second term, ■^V T±s--ai}^-a^-^ '15) 128. Example. AVhat is the current input to an induction motor, at impressed voltage eo and slip s (given as fraction of synchronous speed) if ro — jxo is the impedance of the primary circuit of the motor, and ri — jxi the impedance of the secondary circuit of the motor at full frequency, and the exciting current of the motor is neglected; assuming s to be a small quantity; that is, the motor running at full speed? Let ...", "... term, ■^V T±s--ai}^-a^-^ '15) 128. Example. AVhat is the current input to an induction motor, at impressed voltage eo and slip s (given as fraction of synchronous speed) if ro — jxo is the impedance of the primary circuit of the motor, and ri — jxi the impedance of the secondary circuit of the motor at full frequency, and the exciting current of the motor is neglected; assuming s to be a small quantity; that is, the motor running at full speed? Let E be the e.m.f. generated by the mutual magnetic flux, that is, ...", "... G MATHEMATICS. of the primary circuit, the generated e.m.f. of the secondary circuit is sE. Since x\\ is the reactance of the secondary circuit at full frequency, at the fraction s of full frequency the reactance of the secondary circuit is sxi, and the impedance of the sec- ondary circuit at slip s, therefore, is ri — jsx\\] hence the secondary current is, • ri-]sxi If the exciting current is neglected, the primary current equals the secondary current (assuming the secondary of the same number of turns as the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-32", "section_label": "Chapter 32: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 25904-27405", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "snippets": [ "... e denoted by 1 and 2> the middle wire or common return by 0. It is then : EI = E = E.M.F. between 0 and 1 in the generator. Ez=jE = E.M.F. between 0 and 2 in the generator. Let: ./i and 72 = currents in 1 and in 2, 70 = current in 0, Z-L and Zz = impedances of lines 1 and 2, Z0 = impedance of line 0. Yl and Y2 = admittances of circuits 0 to 1, and 0 to 2, // and //= currents in circuits 0 to 1, and 0 to 2, Eia.-ndE2'= potential differences at circuit 0 to 1, and 0 to 2. it is then, 7, -f 78 + 70 = 0 ) «v ...", "... ire or common return by 0. It is then : EI = E = E.M.F. between 0 and 1 in the generator. Ez=jE = E.M.F. between 0 and 2 in the generator. Let: ./i and 72 = currents in 1 and in 2, 70 = current in 0, Z-L and Zz = impedances of lines 1 and 2, Z0 = impedance of line 0. Yl and Y2 = admittances of circuits 0 to 1, and 0 to 2, // and //= currents in circuits 0 to 1, and 0 to 2, Eia.-ndE2'= potential differences at circuit 0 to 1, and 0 to 2. it is then, 7, -f 78 + 70 = 0 ) «v or, I0 =-(/; + 72) j that is, ...", "... s of a three-wire quarter-phase system are unsymmetrical, and the leading phase 1 reacts upon the lagging phase 2 in a different manner than 2 reacts upon 1. It is thus undesirable to use a three-wire quarter-phase system, except in cases where the line impedances Z are negligible. In all other cases, the four-wire quarter-phase system is preferable, which essentially consists of two independent single-phase circuits, and is treated as such. Obviously, even in such an independent quarter-phase system, at unequa ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-02", "section_label": "Chapter 2: Multiple Squirrel-Cage Induction Motor", "section_title": "Multiple Squirrel-Cage Induction Motor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3543-5554", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-02/", "snippets": [ "... ith the mutual magnetic flux, *, or rather with the voltage induced by this flux, the mutual inductive voltage E — e, as it is most convenient, with the mutual inductive voltage, c, as starting point, to pass to the secondary current by the self-inductive impedance, to the primary current and primary impressed voltage by the primary self-inductive impedance and exciting admittance. In the calculation of multiple squirrel-cage induction motors, it is preferable to introduce the true induced voltage, that is, the vo ...", "... nductive voltage E — e, as it is most convenient, with the mutual inductive voltage, c, as starting point, to pass to the secondary current by the self-inductive impedance, to the primary current and primary impressed voltage by the primary self-inductive impedance and exciting admittance. In the calculation of multiple squirrel-cage induction motors, it is preferable to introduce the true induced voltage, that is, the voltage induced by the resultant magnetic flux interlinked with the various circuits, which is t ...", "... squirrel-cage calculation starts.1 Double Squirrel-cage Induction Motor 20. Let, in a double squirrel-cage induction motor: $2 = true induced vpltage in inner squirrel cage, reduced to full frequency, It = current, and Zi = r2 + jx2 = self-inductive impedance at full frequency, reduced to the primary circuit. #i = true induced voltage in outer squirrel cage, reduced to full frequency, /i = current, and Z\\ = t\\ + jxi = self-inductive impedance at full frequency, reduced to primary circuit. jj? = voltage i ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-14", "section_label": "Theory Section 14: Rectangular Coordinates", "section_title": "Rectangular Coordinates", "kind": "theory-section", "sequence": 14, "number": 14, "location": "lines 5264-5831", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-14/", "snippets": [ "... umed by react- ance XQ a positive horizontal component, denoted by XQ (aiz + (/)• Thus the total e.m.f. consumed by primary reactance XQ is XQ (aiz + g) + jxQ (aii + h), (11) and the total e.m.f. consumed by primary impedance is r0 (aii + A) + x0 (aiz + g) - j[rQ (aiz + g) - XQ (aii + h)]. (12) RECTANGULAR COORDINATES 79 Thus, to get from the current the e.m.f. consumed in react- ance XQ by the horizontal component of current, the coe ...", "... eactance, x, from the current, we multiply the current by jx, and substitute By defining, and substituting, j2 = — 1, jx can thus be called the reactance in the representation in rectangular coordinates and r -+- jx the impedance. The primary impedance voltage of the transformer in the preceding could thus be derived directly by multiplying the current, /o = (aii + h) - j (aii + g), (9) by the impedance, Z0 = r0 -f jxQ, which gives E'o = ...", "... urrent, we multiply the current by jx, and substitute By defining, and substituting, j2 = — 1, jx can thus be called the reactance in the representation in rectangular coordinates and r -+- jx the impedance. The primary impedance voltage of the transformer in the preceding could thus be derived directly by multiplying the current, /o = (aii + h) - j (aii + g), (9) by the impedance, Z0 = r0 -f jxQ, which gives E'o = Zo/o = (r0 + jx<>) [ ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-08", "section_label": "Chapter 8: Capacity", "section_title": "Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3872-6370", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "snippets": [ "... the fundamental laws of alternating-current circuits, or, as expressed in their com- plexform. ^ _^ ' „_ E -= ZJ^ or, / = \\Ey and S-f = in a closed circuit, 5/ = at a distributing point, where J?, /, Z^ V, are the expressions of E.M.F*., current, impedance, and admittance in complex quantities, — these laws representing not only the intensity, but also the phase, of the alternating wave, — we can now — by application of these laws, and in the same manner as with continuous- current circuits, keeping in mind ...", "... fore only some of the more common combinations will here be considered. 1.) R I sis fa nee in scries with a circuit, 43. In a constant-potential system with impressed E.M.F., ^ §43] KESISTANCEy INDUCTANCE, CAPACITY, 69 let the receiving circuit of impedance if = /• —jx^ z = V/\"*\"^ + xS be connected in series with a resistance, r^ . The total impedance of the circuit is then hence the current is /= ^o = ^o = ^oia+j'o+Jx) , Z + r^ r+ f\\, —jx (/- + r^)^ + x^ * .and the E.M.F. of the receiving circuit, ...", "... es with a circuit, 43. In a constant-potential system with impressed E.M.F., ^ §43] KESISTANCEy INDUCTANCE, CAPACITY, 69 let the receiving circuit of impedance if = /• —jx^ z = V/\"*\"^ + xS be connected in series with a resistance, r^ . The total impedance of the circuit is then hence the current is /= ^o = ^o = ^oia+j'o+Jx) , Z + r^ r+ f\\, —jx (/- + r^)^ + x^ * .and the E.M.F. of the receiving circuit, becomes r + to —jx \\r + /-„)*-» + x^ •or, in absolute values we have the following : — Impressed ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "section_label": "Chapter 30: Quartbr-Fhase System", "section_title": "Quartbr-Fhase System", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... denoted by 1 and 2, the middle wire or common return by 0. It is then : £^ = E = E.M.F. between and 1 in the generator. E2 =^ J E = E.M.F. between and 2 in the generator. • Let : Ii and I2 = currents in 1 and in 2, Iq = current in 0, Z, and Za == impedances of lines 1 and 2, Zq = impedance of line 0. K, and Y^ = admittances of circuits to 1, and to 2, // and 73'= currents in circuits to 1, and to 2, ^/and ^2'= potential differences at circuit to 1, and to 2. it is then, 7, + /a + /« = ) ^ or, /o = - (A ...", "... e or common return by 0. It is then : £^ = E = E.M.F. between and 1 in the generator. E2 =^ J E = E.M.F. between and 2 in the generator. • Let : Ii and I2 = currents in 1 and in 2, Iq = current in 0, Z, and Za == impedances of lines 1 and 2, Zq = impedance of line 0. K, and Y^ = admittances of circuits to 1, and to 2, // and 73'= currents in circuits to 1, and to 2, ^/and ^2'= potential differences at circuit to 1, and to 2. it is then, 7, + /a + /« = ) ^ or, /o = - (A + ^2) i ^ ^ that is, lo is comm ...", "... s of a three-wire quarter-phase system are unsymmetrical, and the leading phase 1 reacts upon the lagging phase 2 in a different manner than 2 reacts upon 1. It is thus undesirable to use a three-wire quarter-phase system, except in cases where the line impedances Z are negligible. In all other cases, the four-wire quarter-phase system is preferable, which essentially consists of two independent single-phase circuits, and is treated as such. Obviously, even in such an independent quarter-phase system, at unequa ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-15", "section_label": "Chapter 15: The General Alternating-Current Transformer Or Frequency Converter", "section_title": "The General Alternating-Current Transformer Or Frequency Converter", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 12683-13648", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "snippets": [ "... ; /?! = number of secondary turns in series per circuit ; a = — = ratio of turns ; «i Y0 =£\"0 H~./A) = primary exciting admittance per circuit; where gQ = effective conductance ; b0 = susceptance ; Z0 = r0 —jx0 = internal primary self-inductive impedance per circuit, where r0 = effective resistance of primary circuit ; jr0 = reactance of primary circuit ; Zu = TI — jxv = internal secondary self -inductive impedance per circuit at standstill, or for s = 1, where rj = effective resistance of secon ...", "... ve conductance ; b0 = susceptance ; Z0 = r0 —jx0 = internal primary self-inductive impedance per circuit, where r0 = effective resistance of primary circuit ; jr0 = reactance of primary circuit ; Zu = TI — jxv = internal secondary self -inductive impedance per circuit at standstill, or for s = 1, where rj = effective resistance of secondary coil ; Xl — reactance of secondary coil at standstill, or full fre- quency, s = 1. Since the reactance is proportional to the frequency, at the slip s, or the seco ...", "... s = 1, where rj = effective resistance of secondary coil ; Xl — reactance of secondary coil at standstill, or full fre- quency, s = 1. Since the reactance is proportional to the frequency, at the slip s, or the secondary frequency s N, the secondary impedance is : Zl = r1-jsxl. Let the secondary circuit be closed by an external re- sistance r, and an external reactance, and denote the latter ALTERNATING-CURRENT TRANSFORMER, 223 by x at frequency N, then at frequency s N, or slip s, it will be = s x, and ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-10", "section_label": "Chapter 10: Resistance And Reactance Of Transmission", "section_title": "Resistance And Reactance Of Transmission", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6993-9766", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-10/", "snippets": [ "... e the effect of either resolution into components is the same so far as the line is concerned, we need not make any assumption as to whether the wattless part of the . receiver circuit is in shunt, or in series, to the power part. Let Zo = To -{- jxo = impedance of the line; Zo = V ro^ + Xo^', Y = g — jb = admittance of receiver circuit; y = ^g' + b'; Eo = Co -{- je'o = impressed voltage at generator end of line ; Eo - Veo' + eo'2; E ^ e -\\- je' = voltage at receiver end of line; E = Ve2 + e'2. h = H + j ...", "... + xo^}' and ratio of e.m.f. at receiver and at generator end of line, _ E^ ^m 771 IJO #+i-:)' efficiency, : — = — -. — ■' That is: The output which can he transmitted over an inductive line of resistance, ro, and reactance, Xo — that is, of impedance, Zo — into a TRANSMISSION LINES 81 non-inductive receiver circuit, is a maximum if the resistance of the receiver circuit equals the impedance of the line, r — Zo, and is P -— ^?1_. ^'^ 2 (ro + Zo) The output is transmitted at the efficiency o ...", "... output which can he transmitted over an inductive line of resistance, ro, and reactance, Xo — that is, of impedance, Zo — into a TRANSMISSION LINES 81 non-inductive receiver circuit, is a maximum if the resistance of the receiver circuit equals the impedance of the line, r — Zo, and is P -— ^?1_. ^'^ 2 (ro + Zo) The output is transmitted at the efficiency of Zo ro + Zo and with a ratio of e.m.fs. of #+:-:) NON-INDUCTI SUPPLIED OVER IN VE RECEIVER CIRCUIT DUCTIVE LINE O.\" IMPEDANCE ■OD' ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-11", "section_label": "Chapter 11: Phase Control", "section_title": "Phase Control", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 9767-10717", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-11/", "snippets": [ "... r converter, quadrature components of current can be produced at will, proportional to the variation of the field excitation from the value that gives a magnetic flux, which at synchronous speed just consumes the impressed voltage (after allowing for the impedance of the motor). Phase control of transmission lines is especially suited for circuits supplying synchronous motors or converters; since such machines, in addition to their mechanical or electrical load, can with a moderate increase of capacity carry or pr ...", "... to suit the requirements of regulation, and is considered positive when lagging, negative when leading. E^ = e'a — jcq\" = voltage impressed upon the system at the generator end, or supply voltage, and the absolute value is Co = VevTTv. Z = r -\\- jx — impedance of the circuit between voltage e and voltage eo, and the absolute value is z = v r^ + x^- If e = terminal voltage of receiving station, eo = terniinal voltage of generating station, Z = impedance of transmission line; if e = nominal induced e.m.f. of rec ...", "... , and the absolute value is Co = VevTTv. Z = r -\\- jx — impedance of the circuit between voltage e and voltage eo, and the absolute value is z = v r^ + x^- If e = terminal voltage of receiving station, eo = terniinal voltage of generating station, Z = impedance of transmission line; if e = nominal induced e.m.f. of receiving synchronous machine, that is, voltage corresponding to its field excitation, and eo = nominal induced e.m.f. of generator, Z also includes the synchronous impedance of both machines, and of ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... be denoted by 1 and 2, the middle wire or common return by 0. It is then, El = E = e.m.f. between 0 and 1 in the generator. Ei = jE = e.m.f. between 0 and 2 in the generator. Let 1 1 and 1 2 = currents in 1 and in 2, 7o = current in 0, Z] and Z2 = impedances of lines 1 and 2, Zo = impedance of line 0, Yi and F2 = admittances of circuits 0 to 1, and 0 to 2, /'i and /'2 = currents in circuits 0 to 1, and 0 to 2, E\\ and E'2 = potential differences at circuit 0 to 1, and 0 to 2. it is then, Ii -\\- h -\\- h = ...", "... ire or common return by 0. It is then, El = E = e.m.f. between 0 and 1 in the generator. Ei = jE = e.m.f. between 0 and 2 in the generator. Let 1 1 and 1 2 = currents in 1 and in 2, 7o = current in 0, Z] and Z2 = impedances of lines 1 and 2, Zo = impedance of line 0, Yi and F2 = admittances of circuits 0 to 1, and 0 to 2, /'i and /'2 = currents in circuits 0 to 1, and 0 to 2, E\\ and E'2 = potential differences at circuit 0 to 1, and 0 to 2. it is then, Ii -\\- h -\\- h = 0, or, lo = — {Ii + ^2); that ...", "... ystem are QUARTER-PHASE SYSTEM 465 unsymmetrical, and the leading phase, 1, reacts upon the lagging phase, 2, in a different manner than 2 reacts upon 1. It is thus undesirable to use a three-wire, quarter-phase system, except in cases where the line impedances, Z, are negligible. In all other cases, the four-wire, quarter-phase system is pref- erable, which essentially consists of two independent single-phase circuits, and is treated as such. Obviously, even in such an independent quarter-phase system, at un ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-15", "section_label": "Chapter 15: Induction Motob", "section_title": "Induction Motob", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 14919-17024", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "snippets": [ "... rcuit, r, = a^ r^ = secondary resistance per circuit reduced to pri- mary system ; if Xx =- secondary reactance per circuit, Xi = a^ Xi^ = secondary reactance per circuit reduced to pri- mary system ; I 142] INDUCTION MOTOR. 209 if 0/ = secondary impedance per circuit, z^ = a^ z^ = secondary impedance per circuit reduced to pri- mary system ; that is, the number of secondary circuits and of turns per secondary circuit is assumed the same as in the primary system. In the following discussion, as seconda ...", "... ircuit reduced to pri- mary system ; if Xx =- secondary reactance per circuit, Xi = a^ Xi^ = secondary reactance per circuit reduced to pri- mary system ; I 142] INDUCTION MOTOR. 209 if 0/ = secondary impedance per circuit, z^ = a^ z^ = secondary impedance per circuit reduced to pri- mary system ; that is, the number of secondary circuits and of turns per secondary circuit is assumed the same as in the primary system. In the following discussion, as secondary quantities ex- clusively, the values reduced ...", "... X., it is V2 nbe = (R<^. Thus, from the hysteretic loss, and the reluctance, the constants, g and b, and thus the admittance, K are derived. Let r = resistance per primary circuit ; z = reactance per primary circuit ; thus, Z '=^ r — y .r = impedance per primary circuit ; * Complete discussion hereof, see Chapter XXIII. § 143J INDUCTION MOTOR, 211 ri = resistance per secondary circuit reduced to primary sys- tem; Xi = reactance per secondary circuit reduced to primary system, at full frequency, ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-15", "section_label": "Theory Section 15: Load Characteristic of Transmission Line", "section_title": "Load Characteristic of Transmission Line", "kind": "theory-section", "sequence": 15, "number": 15, "location": "lines 5832-6221", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-15/", "snippets": [ "... e is the curve of volts and watts at the receiving end of the line as function of the amperes, and at constant e.m.f . impressed upon the generator end of the line. Let r = resistance, x = reactance of the line. Its impedance z = -y/r2 + x2 can be denoted symbolically by Z = r + jx. Let EQ = e.m.f. impressed upon the line. Choosing the e.m.f. at the end of the line as horizontal com- ponent in the vector diagram, it can be denoted by ...", "... he vector diagram, it can be denoted by E = e. 86 ELEMENTS OF ELECTRICAL ENGINEERING At non-inductive load the line current is in phase with the e.m.f. e, thus denoted by 7 = i. The e.m.f. consumed by the line impedance Z — r + jx is E! = ZI = (r + jx) i = ri+jxi. (1) Thus the impressed voltage, ' Eo = E + Ei = e + ri + ja». (2) or, reduced, #o = V(e + n)2 + z2*2, (3) and _ 6 = ^o2 - z2*2 - n, the e.m.f. (4 ...", "... ower is delivered into a non- LOAD CHARACTERISTIC OF TRANSMISSION LINE 87 inductive receiving circuit over an inductive line upon which is impressed a constant e.m.f., if the resistance of the receiving circuit equals the impedance of the line, TI = z. In this case the total impedance of the system is Z0 = Z + n = r + z + jx, (10) or, zo = V(r + z)2 + z2. (11) Thus the current is *o V(r + z)2 + x2 and the power transmitted ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-09", "section_label": "Chapter 9: Resistance And Reactance Of Transmission Lines", "section_title": "Resistance And Reactance Of Transmission Lines", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 5334-6956", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "snippets": [ "... the effect of either resolution into components is the same so far as the line is concerned, we need not make any assump- tion as to whether the wattless part of the receiver circuit is in shunt, or in series, to the energy part. Let— Z0 = r0 —,jx0 = impedance of the line ; z0 = Vr02 + ^2; Y = g -\\-jb = admittance of receiver circuit; y = VFTT2; E0 = e0 -f /^, where : At = — /ti) Zit = ^tiJ it is £a = Za/if If 7,^ denotes the current passing from terminal t to a ground or neutral point, and Z,^ is the impedance of this circuit between terminal / and ne ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-28", "section_label": "Chapter 28: Interlinked Polyphase Systems", "section_title": "Interlinked Polyphase Systems", "kind": "chapter", "sequence": 28, "number": 28, "location": "lines 24489-24804", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-28/", "snippets": [ "... current. In the generator of a symmetrical polyphase system, if : c'' E are the E.M.Fs. between the n terminals and the neutral point, or star E.M.Fs., INTERLINKED POLYPHASE SYSTEMS. 457 If = the currents issuing from terminal i over a line of the impedance Z{ (including generator impedance in star connection), we have : Potential at end of line i : Difference of potential between terminals k and i : where /,. is the star current of the system, Zt the star im- pedance. The ring potential at the end o ...", "... symmetrical polyphase system, if : c'' E are the E.M.Fs. between the n terminals and the neutral point, or star E.M.Fs., INTERLINKED POLYPHASE SYSTEMS. 457 If = the currents issuing from terminal i over a line of the impedance Z{ (including generator impedance in star connection), we have : Potential at end of line i : Difference of potential between terminals k and i : where /,. is the star current of the system, Zt the star im- pedance. The ring potential at the end of the line between ter- minals i ...", "... here /,. is the star current of the system, Zt the star im- pedance. The ring potential at the end of the line between ter- minals i and k is Eik, and it is : Eile = — Eti. If now Iik denotes the current passing from terminal i to terminal k, and Zik impedance of the circuit between ter- minal i and terminal k, where : fit = ~ /*,, Zt* = Zti, it is Eik = ZitIik. If Iio denotes the current passing from terminal i to a ground or neutral point, and Zio is the impedance of this circuit between terminal i and ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-01", "section_label": "Chapter 1: Speed Control Of Induction Motors", "section_title": "Speed Control Of Induction Motors", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1368-3542", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-01/", "snippets": [ "... an admittance, F', is connected in series into the secondary circuit of the induction motor,* for the pur- pose of using the effective resistance of hysteresis, which in- creases with the frequency, to control the motor torque curve. The total secondary impedance then is: 1 Y - {» + Q + * (* + J) • « Z i — Z\\ + v/ where: Y = g — jb is the admittance of the magnetic circuit at full frequency,, and 5. For illustration, assume that in the induction motor of the constants: 6o = 100; Y0 = 0.02 - 0.2 j; Z ...", "... n motor with hysteresis starting device. p represents the power-factor, tj the efficiency, y the apparent efficiency, V the torque efficiency and y' the apparent torque efficiency. However, T corresponds to a motor of twice the admittance and half the impedance of 7\". That is, to get approximately the same output, with the hysteresis device inserted, as without it, requires a rewinding of the motor for higher magnetic density, the same as would be produced in 7\" by increasing the voltage y/2 times. It is inter ...", "... rrents in permanent closed circuits), of negligible hysteresis loss, thus is represented, as function of the slip, by the expression: Y'-g-j-- (11) © Connecting such an admittance in series to the induction- motor secondary, gives the total secondary impedance: Z J = Z\\ + y, = Ai + — ^-i-A + 3 /«»i + -™-nr Y (12) r^t) Assuming: g = b. (13) That is, 45° phase angle of the exciting circuit of the magnetic circuit at full frequency — which corresponds to complete screen- ing of the center of the magnet ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-12", "section_label": "Chapter 12: Reactance Of Induction Apparatus", "section_title": "Reactance Of Induction Apparatus", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 22634-23465", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-12/", "snippets": [ "... rnal circuit. For convenience, we may assune the secondary circuit as re- duced to the primary circuit by the ratio of turns, that is, assume ratio of turns 1 -^ 1. Let Fo = 17 - j6 = primary exciting admittance; Zo = ro+ jxo = primary self-inductive impedance; Zi = ri + jxi = secondary self-inductive impedance (reduced to the primary). The transformer thus comprises three magnetic fluxes: the mutual magnetic flux, $, which, being interlinked with primary and secondary, transforms the power from primary to s ...", "... ondary circuit as re- duced to the primary circuit by the ratio of turns, that is, assume ratio of turns 1 -^ 1. Let Fo = 17 - j6 = primary exciting admittance; Zo = ro+ jxo = primary self-inductive impedance; Zi = ri + jxi = secondary self-inductive impedance (reduced to the primary). The transformer thus comprises three magnetic fluxes: the mutual magnetic flux, $, which, being interlinked with primary and secondary, transforms the power from primary to secondary, and is due to the resultant m.m.f of primar ...", "... , since ii practically equals io, Co' = to^ [(ro + ri)2 + x^], and inversely, impressing a voltage upon coil, «, and short-cir- cuiting the coil p, gives the leakage reactance, x', for s as primary, ei' = ii^ [(ro + ri)2 + a/\")]. Thus, the so-called \"impedance test\" of the transformer gives the total leakage reactance Xq + xi, for that coil as primary, which is used as such in the impedance test. Where an appreciable difference of the total leakage flux is expected when using the one coil as primary, as when u ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-36", "section_label": "Chapter 14: Short-Circuit Currents Of Alternators", "section_title": "Short-Circuit Currents Of Alternators", "kind": "chapter", "sequence": 36, "number": 14, "location": "lines 14549-15353", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "snippets": [ "... rmature iron and pole- faces which does not interlink with the field coils, but is a true self-inductive flux, and therefore is represented by a reactance xr Combined with the effective resistance, rv of the armature winding, this gives the self-inductive impedance Zl = rl — or zt = Vr* + x*. Vectorially subtracted from the virtual generated e.m.f., ev the voltage consumed by the armature current in the self-inductive impedance Zl then gives the ter- minal voltage, e. At short circuit, the virtual generated e.m. ...", "... ith the effective resistance, rv of the armature winding, this gives the self-inductive impedance Zl = rl — or zt = Vr* + x*. Vectorially subtracted from the virtual generated e.m.f., ev the voltage consumed by the armature current in the self-inductive impedance Zl then gives the ter- minal voltage, e. At short circuit, the virtual generated e.m.f., ev is consumed by the armature self-inductive impedance, zr As the effective armature resistance, rv is very small compared with its self- inductive reactance, xv i ...", "... ted from the virtual generated e.m.f., ev the voltage consumed by the armature current in the self-inductive impedance Zl then gives the ter- minal voltage, e. At short circuit, the virtual generated e.m.f., ev is consumed by the armature self-inductive impedance, zr As the effective armature resistance, rv is very small compared with its self- inductive reactance, xv it can be neglected compared thereto, and the short-circuit current of the alternator, in permanent condition, thus is As shown in Chapter XXII, ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-01", "section_label": "Chapter 1: The General Number", "section_title": "The General Number", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 915-3491", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-01/", "snippets": [ "... it carries out the operation of rotating the direction and changing the length of the multiplicand. 26. In multiplication, division and , other algebraic opera- tions with the representations of physical quantities (as alter- nating currents, voltages, impedances, etc.) by mathematical symbols, whether ordinary numbers or general numbers, it is necessary to consider whether the result of the algebraic operation, for instance, the product of two factors, has a physical meaning, and if it has a physical meaning, whe ...", "... iod of the alternating current. This vector 01 can be represented by a general number, where ii is the horizontal, 12 the vertical component of the current vector 01. i. ^l 1 ■^E ij ''y^ 0 2N. X 1 ^f Fig. 21.. Current, E.M.F. and Impedance Vector Diagram. In the same manner an alternating E.M.F. of the same fre- quency can be represented by a vector OE in the same Fig. 21, and denoted by a general number, E = ei+je2, An impedance can be represented by a general number, Z = r—jx, whe ...", "... y^ 0 2N. X 1 ^f Fig. 21.. Current, E.M.F. and Impedance Vector Diagram. In the same manner an alternating E.M.F. of the same fre- quency can be represented by a vector OE in the same Fig. 21, and denoted by a general number, E = ei+je2, An impedance can be represented by a general number, Z = r—jx, where r is the resistance and x the reactance. If now we have two impedances, OZi and OZ2, Zi =ri —jxi and Z2 = r2—jx2, their product Zi Z^ can be formed mathema - ically, but it has no physical meanin ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-16", "section_label": "Theory Section 16: Phase Control of Transmission Lines", "section_title": "Phase Control of Transmission Lines", "kind": "theory-section", "sequence": 16, "number": 16, "location": "lines 6222-6813", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-16/", "snippets": [ "... reactive current produced in the system for controlling the voltage. i\\ shall be considered positive as lagging, negative as leading current. Then the total current, in symbolic representation, is / = i - jii; the line impedance is Z = r + jx, and thus the e.m.f. consumed by the line impedance is Ei = ZI = (r + jx) (i - jii) = ri + jrii + jxi - J2xii; and substituting f — — 1, Ei = (ri + xii) - j (rii - xi). Hence the voltage ...", "... shall be considered positive as lagging, negative as leading current. Then the total current, in symbolic representation, is / = i - jii; the line impedance is Z = r + jx, and thus the e.m.f. consumed by the line impedance is Ei = ZI = (r + jx) (i - jii) = ri + jrii + jxi - J2xii; and substituting f — — 1, Ei = (ri + xii) - j (rii - xi). Hence the voltage impressed upon the line Eo = e 4- Ei = (e + ri + xii) - j (rii ...", "... > e, a smaller amount of power if eQ < e. In the latter case ii is always leading; in the former case i\\ is lagging at no load, becomes zero at some intermediate load, and leading at higher load. 77. If the line impedance Z — r + fa and the received voltage e is given, and the power current ^o at which the reactive current shall be zero, the voltage at the generator end of the line is determined hereby from the equation (2) : eQ = ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-04", "section_label": "Chapter 4: Vector Representation", "section_title": "Vector Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2149-2759", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-04/", "snippets": [ "... ce voltage 90° ahead of the current. The voltage of the generator, Eo, has to give the three voltages E, Ei, E^, hence it is determined as their resultant. Combining by the parallelo- gram law, OEi and OE2, give OEz, the voltage required to over- come the impedance of the line, and similarly OEz and OE give OEa, the voltage required at the generator side of the line, to yield the voltage, E, at the receiving end of the line. Algebraic- ally, we get from Fig. 12 E, = V{E + Iry + {IxY or E = VEo' - {Ixy - Ir. ...", "... e as a counter e.m.f., E'l =Ir, in opposition to the current, as is done in Fig. 13; and combine the three voltages Eq, E\\, E'2, to form a resultant voltage E, which is left at the end of the line. E\\ and E'2 combine to form E'3, the counter e.m.f. of impedance; and since £\"3 and Eo must combine to form E, Eq is found as the side of a parallelogram, OEqEE's, whose other side, OE's, and diagonal QE, are given. Or we may say (Fig. 14), that to overcome the counter e.m.f. 24 ALTERNATING-CURRENT PHENOMENA ...", "... d since £\"3 and Eo must combine to form E, Eq is found as the side of a parallelogram, OEqEE's, whose other side, OE's, and diagonal QE, are given. Or we may say (Fig. 14), that to overcome the counter e.m.f. 24 ALTERNATING-CURRENT PHENOMENA of impedance, OE'^, of the line, the component, OEz, of the impressed voltage is required which, with the other component, OE, must give the impressed voltage, OEq. As shown, we can represent the voltages produced in a circuit in two ways — either as counter e.m.fs., ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "section_label": "Chapter 14: Dielectric Losses", "section_title": "Dielectric Losses", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "... ectric conductance kA C = -J- = electrostatic capacity of the layer of dielectric, hence: 2 irfk A b = 2irfC = — J — = capacity susceptance, and (1) 154 AL TERN A TING-C URREN T PHENOMENA Y = g -\\- jh = admittance, thus : Z =y = r — jx = impedance, where: 9 r = ^ = vector resistance (not ohmic resistance, but energy component of impedance, T see paragraph 89.) X = r = vector reactance, and (2) y = y/g^ + &^ = absolute admittance, (z = -y/r^ -\\- x^ = absohite impedance.) If then. ...", "... 2 irfk A b = 2irfC = — J — = capacity susceptance, and (1) 154 AL TERN A TING-C URREN T PHENOMENA Y = g -\\- jh = admittance, thus : Z =y = r — jx = impedance, where: 9 r = ^ = vector resistance (not ohmic resistance, but energy component of impedance, T see paragraph 89.) X = r = vector reactance, and (2) y = y/g^ + &^ = absolute admittance, (z = -y/r^ -\\- x^ = absohite impedance.) If then. El = potential drop across the first, E^ = potential drop across the second layer of dielectric, ...", "... y = r — jx = impedance, where: 9 r = ^ = vector resistance (not ohmic resistance, but energy component of impedance, T see paragraph 89.) X = r = vector reactance, and (2) y = y/g^ + &^ = absolute admittance, (z = -y/r^ -\\- x^ = absohite impedance.) If then. El = potential drop across the first, E^ = potential drop across the second layer of dielectric, E = El -\\- Eo = voltage impressed upon the dielectric. (3) The current i, which traverses the dielectric, partly by con- duction through its res ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "... ll enough to be represented by the approximation of one; or, three condensers shunted across the line. 130. {A) Line capacity represented hy one condenser shunted across middle of line. Let Y = g — jh = admittance of receiving circuit; Z = r -\\- jx = impedance of line; he = condenser susceptance of line. iEo Fig. 101. Denoting in Fig. 101. the e.m.f., and current in receiving circuit by E, 7, the e.m.f. at middle of line by E' , the e.m.f., and current at generator by Ea, h; we have, I = E(g-jh); ...", "... etc. For most purposes, however, in calculating long-distance transmission lines and other circuits of distributed constants, the following approximate solutions of the general differential equation of the circuit offers sufficient exactness. 133. The impedance of an element, dl, of the line is: Zdl and the voltage, dE, consumed by the current, /, in this line ele- ment dl: JE7 VTJ7 dE = Zldl The admittance of the line element, dl, is: Ydl hence the current, dl, consumed by the voltage, dE, of this line ...", "... APACITY 111 Substituting in (7) for the exponential function tlie infinite series: ^^ryyi , , ZYX\" , ZYVZYI^ , Z-^YH\" , ±VzH _ 1 + VZFZ + TT,- ± h, V -r-A V ■■■ e gives: 134. If then : I = k is the total length of line, and Zo = loZ — total line impedance, Fo = loY = total line admittance, the equations of voltage Ei and current Ii at the end k of the line are given by substituting I = lo into equations (8), as: (8) ^x = ^0 j 1 + ^ + . . . } + Zo7o { H- ^'p + . . . /x- /o { 1 + ^ + . . . } + Foi^o { ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-19", "section_label": "Chapter 19: Induction Generators", "section_title": "Induction Generators", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 20446-21537", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-19/", "snippets": [ "... rator, due regard has to be taken of the decrease of frequency with increase of load, or what may be called the slip of frequency, s. Let, in an induction generator, Yo = go — jho = primary exciting admittance, Zo = To -\\- jxo = primary self-inductive impedance, Zi = ri + jxi = secondary self-inductive impedance, reduced to primary, all these quantities being reduced to the frequency of synchronism with the speed of the machine, /. Let e = generated em.f., reduced to full frequency. s = slip of frequency, t ...", "... frequency with increase of load, or what may be called the slip of frequency, s. Let, in an induction generator, Yo = go — jho = primary exciting admittance, Zo = To -\\- jxo = primary self-inductive impedance, Zi = ri + jxi = secondary self-inductive impedance, reduced to primary, all these quantities being reduced to the frequency of synchronism with the speed of the machine, /. Let e = generated em.f., reduced to full frequency. s = slip of frequency, thus: (1 — s) / = frequency generated by machine. We ...", "... re, , S'Xi ai = —^—, — ^ — ^ and 02 = the primary exciting current, ioo = EY^ = e {go - j6o), 240 ALTERNATING-CURRENT PHENOMENA thus, the total primary current, /o = /] + /oo ^ e{bi - J62), where, &]=«! + go and 62= 02 + i>o; the primary impedance voltage, E' = /o(ro+j[l - s]xo); the primary generated e.m.f. is, e(l - s). Thus, primary terminal voltage, ^0 = e(l - s) - 7o(ro +i[l - &]:ro) = e(ci - jcz), whei'e, Ci = 1 — 5 — ro6i — (1 — s)a;o62 and Ca = (1 — s)xo6i — ro62, hence, the abso ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-04", "section_label": "Chapter 4: Graphic Befrisxintation", "section_title": "Graphic Befrisxintation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2122-2743", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "snippets": [ "... e an E.M.F. 90° ahead of the current. The E.M.F. of the generator, E^y has to give the three RM.Fs., Ey E^f and E^y hence it is determined as their resultant. Combining by the parallelogram law, OE,. and OEj^, give OEgy the E.M.F. required to overcome the impedance of the line, and similarly OE^ and OE give OE^, the E.M.F. required at the generator side of the line, to yield the E.M.F. E at the receiving end of the line. Algebraically, we get from Fig. 12 — or, E = -s/EJ\" — {IxY - Ir. In this instance we have co ...", "... sition to the current, as is done in Fig. 18 ; and combine the three E.M.Fs. E^j if/, EJ, to form a resultant E.M.F., /:, which is left at the end of the line. 118] GRAPHIC REPRESENTATIO^r, 2& E^ and E^ combine to form E^y the counter E.M.F. of impedance; and since E^ and E^ must combine to form Ey E^ is found as the side of a parallelogram, OE^EJ, whose other side, OEJy and diagonal, OE, are given. Or we may say (Fig. 14), that to overcome the counter E.M.F. of impedance, OE^y of the line, the component ...", "... form E^y the counter E.M.F. of impedance; and since E^ and E^ must combine to form Ey E^ is found as the side of a parallelogram, OE^EJ, whose other side, OEJy and diagonal, OE, are given. Or we may say (Fig. 14), that to overcome the counter E.M.F. of impedance, OE^y of the line, the component, OE^y of the impressed E.M.F., together with the other component OEy must give the impressed E.M.F., OE^, As shown, we can represent the E.M.Fs. produced in a circuit in two ways — either as counter E.M.Fs., which com- b ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-09", "section_label": "Chapter 9: Kbsistanci: And Kbactance Of Transmission Iine8", "section_title": "Kbsistanci: And Kbactance Of Transmission Iine8", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 6371-8268", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "snippets": [ "... he effect of either resolution -into components is the same so far as the line is concerned, we need not make any assump- tion as to whether the wattless part of the receiver circuit is in shunt, or in series, to the energy part. Let — ^u = ^o — j^o = impedance of the line ; y = ^ -^-j'b = admittance of receiver circuit ; jE^ = ^^ +j^/ = impressed E.M.F. at generator end of line ; E —, c '\\-jt'' — K.M.F. at receiver end of line; E = V^-'' + e'^\\ I,, == /p +yV = current in the line ; /^ = V/V^ + //*''. T ...", "... t, /*»» = ^ ~ ** and — ratio of E.M.F. at receiver and at generator end of line. ^1* rt v/- (' + 5) efficiency, m *'o That is, the output which can be transmitted over an inductive line of resistance, r^, and reactance, x^, — that is, of impedance, ^^ , — into a non-inductive receiver circuit, is a maximum, if the resistance of the receiver circuit equals the impedance of the line, r = s^, and is — E^ •* m — 2 (r, + z:) The output is transmitted at the efficiency of and with a ratio of E.M ...", "... m *'o That is, the output which can be transmitted over an inductive line of resistance, r^, and reactance, x^, — that is, of impedance, ^^ , — into a non-inductive receiver circuit, is a maximum, if the resistance of the receiver circuit equals the impedance of the line, r = s^, and is — E^ •* m — 2 (r, + z:) The output is transmitted at the efficiency of and with a ratio of E.M.Fs. of 1 fi... 59. We see from this, that the maximum output which can be delivered over an inductive line is less t ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-16", "section_label": "Chapter 16: Aiitebnatingh-Current Osnebator", "section_title": "Aiitebnatingh-Current Osnebator", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 17025-18828", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "snippets": [ "... Then e^ = -s/^icnN Ml^'^-, where // = total number of turns in series on the armature, N = frequency, J/ = total magnetic ffux per field pole. Let Xo = synchronous reactance, To = internal resistance of alternator ; then Zo = ^o — j x^ = internal impedance. If the circuit of the alternator is closed by the external impedance, and cinrcnt 7 = Zo + Z (,-,+ r)->(a', + ^)' or, j^ Eo . and, tcnninal voltage^ E = IZ = Eo- IZo Eo(r —jx) (ro-\\r r) -j{Xo+ xY or. ^^ ^oVr'l_+.v! = ^, V(r ...", "... on the armature, N = frequency, J/ = total magnetic ffux per field pole. Let Xo = synchronous reactance, To = internal resistance of alternator ; then Zo = ^o — j x^ = internal impedance. If the circuit of the alternator is closed by the external impedance, and cinrcnt 7 = Zo + Z (,-,+ r)->(a', + ^)' or, j^ Eo . and, tcnninal voltage^ E = IZ = Eo- IZo Eo(r —jx) (ro-\\r r) -j{Xo+ xY or. ^^ ^oVr'l_+.v! = ^, V(r, + rf 4- {x, + xf 1 /■« . O ^o ^ T\" •^o •^ I ^o \"f~ ^o V ^-^ r^ + ...", "... As shown, the terminal voltage varies with the condi- tions of the external circuit. 164. As an instance, in Figs. 118-118, at constant induced, the E.M.F., Eo = 2500 ; 240 ALTERNATINC-CURKENT PHENOMENA. [S164 and the values of the internal impedance, Z, = r„ ~jx^ = 1 - 10/ With the current / as abscissa:, the terminal voltages E as ordinates in drawn line, and the kilowatts output, = P r, in dotted lines, the kilovolt-amperes output, = I E, in. dash- 1 ,' '■ N ,_^ / ' \\ •^ ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 963-1366", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "snippets": [ "... h is larger than the undivided current, etc. 2. In place of the above-mentioned fundamental laws of continuous currents, we find in alternating-current circuits the following : Ohm's law assumes the form, i = e ] s, where z, the apparent resistance, or impedance, is no longer a constant of the circuit, but depends upon the frequency of the cur- rents ; and in circuits containing iron, etc., also upon the E.M.F. Impedance, z, is, in the system of absolute units, of the same dimensions as resistance (that is, of ...", "... e following : Ohm's law assumes the form, i = e ] s, where z, the apparent resistance, or impedance, is no longer a constant of the circuit, but depends upon the frequency of the cur- rents ; and in circuits containing iron, etc., also upon the E.M.F. Impedance, z, is, in the system of absolute units, of the same dimensions as resistance (that is, of the dimension LT~l = velocity), and is expressed in ohms. It consists of two components, the resistance, r, and the reactance, x, or — , 0= Vr2 + Ar2. The res ...", "... root of mean squares), if i = effective value of alternating current, e = 2 TT NLi is the effective value of E.M.F. of self-inductance, and the ratio, e I i — 2 TT NL, is the magnetic reactance : xm = 2 TT NL. Thus, \\ir— resistance, xm = reactance, z = impedance,— the E.M.F. consumed by resistance is : el = ir ; the E.M.F. consumed by reactance is : , Zo-MOj, E, xko \\ I , 1 1 1 1 \\ 1 ± 20 10 60 80 100 180 140 160 18P 2 X) 2 0 210 2 0 Fig. 129. Field Characteristic of Alternator on Non-inductive Load. ' + and the values of the internal impedance, z0 = r0 -jXo = i - ioy. With the current / as abscissae, the terminal voltages E as ordinates in drawn line, and the kilowatts output, = /2 r, in dotted lines, the kilovolt-amperes output, = / £, in dash- 304 AL TEKNA TING-CURRENT PHENOMENA. d ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-15", "section_label": "Chapter 15: Constant-Voltage Series Operation", "section_title": "Constant-Voltage Series Operation", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 27996-29301", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-15/", "snippets": [ "... ient way is to represent ro, Xo and x by their equivalent in lamps or reactors. The admittance of each eon- sumption device, comprising lamp and reactor or autotrans- former, is CONSTANT-VOLTAGE SERIES OPERATION 307 Yi = g - jbi = g(l - jc), thus the impedance, 1 1 1 + ic Zi = Yi gd - jc) (7(1 + cr and by (23), _ 1+jc If, then, we add to the resistance tq a part ctq of the reactance, we get an impedance, Z = ro(l+jc), which has the same phase angle as Zi, and thus can be expressed as a multiple ...", "... otrans- former, is CONSTANT-VOLTAGE SERIES OPERATION 307 Yi = g - jbi = g(l - jc), thus the impedance, 1 1 1 + ic Zi = Yi gd - jc) (7(1 + cr and by (23), _ 1+jc If, then, we add to the resistance tq a part ctq of the reactance, we get an impedance, Z = ro(l+jc), which has the same phase angle as Zi, and thus can be expressed as a multiple of Zi, Z = UlZly where ni = |-^ = royVT+T' (36) thus is the \"lamp equivalent\" of the line resistance ro plus the part CTo of the reactance. This leaves ...", "... ctance Xi can be expressed as multiple of Xj, Xi = 712^2 __ !^ where n2 = a;i62 = &2 [iCo + n(l — p)x — cro] (37) thus is the *'lamp equivalent\" of the line reactance xo and leakage reactances Xi in burned-out lamps. Thus the addition of the line impedance r© + jxoj and the leakage reactances x, is represented by ni lamps with reactors, and 112 burned-out lamps, or a total of rii + n2 lamps. Thus the circuit can carry rii — {n\\ -I- n^ lamps, and its regula- tion curve starts at the point v = — and ends at ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-40", "section_label": "Chapter 4: Arc Rectification", "section_title": "Arc Rectification", "kind": "chapter", "sequence": 40, "number": 4, "location": "lines 17755-19259", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "snippets": [ "... 2 e sin 6 = total secondary generated e.m.f. of the constant-current transformer; Z1 = r1 -- jx1 = imped- ance of the reactive coil in each anode circuit of the rectifier (\" alternating- current reactive coil\")? inclusive of the internal self-inductive impedance be- tween the two halves of the transformer secondary coil; t\\ and i2 = anode cur- rents, counted in the direction from anode to cathode; ea = counter e.m.f. Fig. 64. Constant-current of rectifying arc, which is constant; Z0 = mercury arc rectifier. r0 ...", "... een the two halves of the transformer secondary coil; t\\ and i2 = anode cur- rents, counted in the direction from anode to cathode; ea = counter e.m.f. Fig. 64. Constant-current of rectifying arc, which is constant; Z0 = mercury arc rectifier. r0 — jx0 = impedance of reactive coil in rectified circuit (\" direct-current re- active coil\"); Z2 = r2 ~ JX2 = impedance of load or arc-lamp circuit; e/ = counter e.m.f. in rectified circuit, which is con- ARC RECTIFICATION 257 stant (equal to the sum of the counter e.m. ...", "... rection from anode to cathode; ea = counter e.m.f. Fig. 64. Constant-current of rectifying arc, which is constant; Z0 = mercury arc rectifier. r0 — jx0 = impedance of reactive coil in rectified circuit (\" direct-current re- active coil\"); Z2 = r2 ~ JX2 = impedance of load or arc-lamp circuit; e/ = counter e.m.f. in rectified circuit, which is con- ARC RECTIFICATION 257 stant (equal to the sum of the counter e.m.fs. of the arcs in the lamp circuit) ; #0 = angle of overlap of the two rectifying arcs, or overlap o ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... y arc rectifier 251 rectification 221, 230 INDEX 563 PAGE Control of circuits by periodic transient phenomena 220 Conversion by quarter-wave circuits 313 Copper, effective penetration of alternating currents 378 ribbon, effective high frequency impedance 408 wire, effective high frequency impedance 408 Cosine wave, traveling 434 Critical case of condenser charge and discharge 53 resistance of condenser oscillation 66 start of condenser on alternating voltage 95 Current density, in alternating-curr ...", "... INDEX 563 PAGE Control of circuits by periodic transient phenomena 220 Conversion by quarter-wave circuits 313 Copper, effective penetration of alternating currents 378 ribbon, effective high frequency impedance 408 wire, effective high frequency impedance 408 Cosine wave, traveling 434 Critical case of condenser charge and discharge 53 resistance of condenser oscillation 66 start of condenser on alternating voltage 95 Current density, in alternating-current conductor 372 effective, of oscillating-c ...", "... denser oscillation 71 electromagnetic induction 67 INDEX 565 PAGE Full-wave oscillation of complex circuit 508 transmission line 330 Fundamental frequency of oscillation, cables and transmission lines 103, 105 Gas pipe, effective high frequency impedance 408 General circuits with inductance and capacity 174 without capacity 168 equations of electric circuit 428 Generator, direct-current over-compounded, building up 149 self-excitation 32 oscillating current 74 German silver, effective penetratio ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "... maximum value of dielectric '^'^e^gy- Li„^ Ce, 0 \"^^0 (1) where Iq = maximum value of transient current, 60 = maximum value of transient voltage. This gives the relation between Bq and Iq, ^^ = Jl ,^ = 1, (2) where Zq is called the natural impedance or surge impedance, 2/0 the natural or surge admittance of the circuit. As the maximum of current must coincide with the zero of voltage, and inversely, if the one is represented by the cosine function, the other is the sine function; hence the periodic ...", "... ielectric '^'^e^gy- Li„^ Ce, 0 \"^^0 (1) where Iq = maximum value of transient current, 60 = maximum value of transient voltage. This gives the relation between Bq and Iq, ^^ = Jl ,^ = 1, (2) where Zq is called the natural impedance or surge impedance, 2/0 the natural or surge admittance of the circuit. As the maximum of current must coincide with the zero of voltage, and inversely, if the one is represented by the cosine function, the other is the sine function; hence the periodic com- ponents of th ...", "... the investigation is thereby greatly simplified. 84 ELECTRIC DISCHARGES, WAVES AND IMPULSES. Substituting o-q = 1 in equations (30) and (31) gives ^0 = Xo, / = 1 To' 4> = 2Tft = 2'Kt CO = 2irf\\-- 2 7rX Xo (40) and the natural impedance of the line then becomes, in velocity measure, Zq =v/ Co L - ^ - ^ Co 2/0 (41) where eo = maximum voltage, io = maximum current. That is, the natural impedance is the inductance, and the natural admittance is the capacity, per velocity ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3956-4744", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "snippets": [ "... netic energy must equal the maximum dielectric energy, Lio2 _ Ceo2 \"2\" ~2~' where i0 = maximum transient current, e0 = maximum transient voltage. This gives the relation between eQ and io, e0 V/L_ 1 i-0 = \\C-ZQ-yQ' where ZQ is called the natural impedance or surge impedance, y0 the natural or surge admittance of the circuit. As the maximum of current must coincide with the zero of voltage, and inversely, if the one is represented by the cosine function, the other is the sine function; hence the periodic c ...", "... equal the maximum dielectric energy, Lio2 _ Ceo2 \"2\" ~2~' where i0 = maximum transient current, e0 = maximum transient voltage. This gives the relation between eQ and io, e0 V/L_ 1 i-0 = \\C-ZQ-yQ' where ZQ is called the natural impedance or surge impedance, y0 the natural or surge admittance of the circuit. As the maximum of current must coincide with the zero of voltage, and inversely, if the one is represented by the cosine function, the other is the sine function; hence the periodic com- ponents of the ...", "... all these circuit sections, and the investigation is thereby greatly simplified. 84 ELECTRIC DISCHARGES, WAVES AND IMPULSES. Substituting O-Q = 1 in equations (30) and (31) gives ^o = Ao> O ^ 27rX CO = 2 7T/X = — — ; AO (40) and the natural impedance of the line then becomes, in velocity measure, 4 / LQ T 1 1 ^O /A1\\ z° = V r = L° = T = ?T = T (41) ^o ^o 2/o ^o where e0 = maximum voltage, i0 = maximum current. That is, the natural impedance is the inductance, and the natural admittance is the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-07", "section_label": "Theory Section 7: Inductance in Alternating-current Circuits", "section_title": "Inductance in Alternating-current Circuits", "kind": "theory-section", "sequence": 7, "number": 7, "location": "lines 2250-2717", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-07/", "snippets": [ "... he zero value of e is ahead of the zero value of current by the time angle 0o, or the current lags behind the impressed e.m.f. by the angle 00. 0o is called the angle of lag of the current, and z = \\A\"2 + x2 the impedance of the circuit, e is called the e.m.f. consumed by impedance, e' the counter e.m.f. of impedance. ALTERNATING-CURRENT CIRCUITS 35 Since Ei = rl is the e.m.f. consumed by resistance, Ez = xl is the e.m.f. consumed by r ...", "... the time angle 0o, or the current lags behind the impressed e.m.f. by the angle 00. 0o is called the angle of lag of the current, and z = \\A\"2 + x2 the impedance of the circuit, e is called the e.m.f. consumed by impedance, e' the counter e.m.f. of impedance. ALTERNATING-CURRENT CIRCUITS 35 Since Ei = rl is the e.m.f. consumed by resistance, Ez = xl is the e.m.f. consumed by reactance, and E = zl = \\/r2 + x2 1 is the e.m.f. c ...", "... lags behind the impressed e.m.f. by the angle 00. 0o is called the angle of lag of the current, and z = \\A\"2 + x2 the impedance of the circuit, e is called the e.m.f. consumed by impedance, e' the counter e.m.f. of impedance. ALTERNATING-CURRENT CIRCUITS 35 Since Ei = rl is the e.m.f. consumed by resistance, Ez = xl is the e.m.f. consumed by reactance, and E = zl = \\/r2 + x2 1 is the e.m.f. consumed by impe- dance, we have E ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-05", "section_label": "Chapter 5: Symbolic Method", "section_title": "Symbolic Method", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2760-3266", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-05/", "snippets": [ "... expressed, the current lags 90° behind the e.m.f.), and represented by the expression jxl = jxi — xi' . Hence, the voltage required to overcome the resistance, r, and the reactance, x, is {r -\\- jx)I; that is, Z = r •\\- jx is the expression of the impedance of t he circuit in complex quantities. Hence, if / = ^ + ji' is the current, the voltage required to overcome the impedance, Z = r -\\- jx, is E ^ ZI = {r+ jx) {i + ji') = {ri + j^xi') -\\- j{ri' + xi) ; hence, since j^ = — 1 E = (ri — xi') + j(ri' + ...", "... required to overcome the resistance, r, and the reactance, x, is {r -\\- jx)I; that is, Z = r •\\- jx is the expression of the impedance of t he circuit in complex quantities. Hence, if / = ^ + ji' is the current, the voltage required to overcome the impedance, Z = r -\\- jx, is E ^ ZI = {r+ jx) {i + ji') = {ri + j^xi') -\\- j{ri' + xi) ; hence, since j^ = — 1 E = (ri — xi') + j(ri' + xi) ; or, ii E = e -\\- je' is the impressed voltage and Z = r -\\- jx the impedance, the current through the circuit is I _^ ...", "... rent, the voltage required to overcome the impedance, Z = r -\\- jx, is E ^ ZI = {r+ jx) {i + ji') = {ri + j^xi') -\\- j{ri' + xi) ; hence, since j^ = — 1 E = (ri — xi') + j(ri' + xi) ; or, ii E = e -\\- je' is the impressed voltage and Z = r -\\- jx the impedance, the current through the circuit is I _^ _e^je'_ Z r + jx' or, multiplying numerator and denominator by (r — jx) to eliminate the imaginary from the denominator, we have Y _ (e -\\- je') (r — jx) _er -\\- e'x . e'r — ex ^ or, if £\" = e + je' is the im ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-21", "section_label": "Chapter 21: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 22302-23970", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-21/", "snippets": [ "... Eo = V2 7r/j/4> 10-8; where n = total number of turns in series on the armature, / = frequency, $ = total magnetic flux per field-pole. Let Xo = synchronous reactance, ro = internal resistance of the alternator; then Zo ^ To -{- jxo = internal impedance. If the circuit of the alternator is closed by the external im- pedance, Z = r + jx, the current j_ En En or, / = Zo + Z (ro -^r)-hj {xn + x) Eo Viro + r)2 -h {xo + xr' and, the terminal voltage, Eo{r + jx) E = IZ = En - IZn = {r ...", "... ive load. As shown, the terminal voltage varies with the conditions of the external circuit. 188. As an example are shown in Figs. 132-137, at constant generated e.m.f., Eo = 2500; ALTERNATING-CURRENT GENERATOR 265 and the values of the internal impedance, Zo = To + jXo = 1 + 10 J, with the current, I, as abscissas, the terminal voltages, E, as ordinates in full line, and the kilowatts output, = Pr, in dotted lines, the kilovolt-amperes output, = IE, in dash-dotted lines, for the following conditions of ...", "... = 2500 volts, and the currents, / = 50, 100, 150, 200, 250 amp., the terminal voltages, E, as ordinates, with the inductance factor of the external circuit X ■y/r^ -{■ x^ as abscissas. ALTERNATING-CURRENT GENERATOR 267 190. If the internal impedance is negligible compared with the external impedance, then, approximately, E Eq Vr^ + x^ = Eo; that is, an alternator with small internal resistance and syn- chronous reactance tends to regulate for constant-terminal voltage. VOLTS 3600 320 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-22", "section_label": "Chapter 22: Armature Reactions Of Alternators", "section_title": "Armature Reactions Of Alternators", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 23971-25134", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-22/", "snippets": [ "... he actual flux existing in the machine — that is, if the magnetic characteristic would continue in a straight line passing through the origin when prolonged. The equation (17) may also be written E = 60- Zol; (20) where, Zo = r + jxo = synchronous impedance of the alternator. / = ii - jii, or, more generally E = Eo- Zol, (22) and so is the equation of a circuit, supplied by the e.m.f., Eo, with the current, /, over the impedance, Zo, as has been discussed in the chapter on resistance, inductive reactanc ...", "... ay also be written E = 60- Zol; (20) where, Zo = r + jxo = synchronous impedance of the alternator. / = ii - jii, or, more generally E = Eo- Zol, (22) and so is the equation of a circuit, supplied by the e.m.f., Eo, with the current, /, over the impedance, Zo, as has been discussed in the chapter on resistance, inductive reactance and conden- sive reactance. 278 ALTERNATING-CURRENT PHENOMENA An alternator so is equivalent to an e.m.f., Ea, the nominal generated e.m.f., supplying current over an impedan ...", "... pedance, Zo, as has been discussed in the chapter on resistance, inductive reactance and conden- sive reactance. 278 ALTERNATING-CURRENT PHENOMENA An alternator so is equivalent to an e.m.f., Ea, the nominal generated e.m.f., supplying current over an impedance, Zo, the synchronous impedance. 196. In theoretical investigations of alternators, the syn- chronous reactance, Xo, is usually assumed as constant, and has been assumed so in the preceding. In reality, however, this is not exactly, and frequently not ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1224-1727", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "snippets": [ "... e following : Ohm's law assumes the form, i = c j Sy where r, the apparent resistance, or impcdaiue^ is no longer a constant of the circuit, but depends upon the frequency of the cur- rents ; and in circuits containing iron, etc., also upon the E.M.F. Impedance, ^, is, in the system of absolute units, of the same dimensions as resistance (that is, of the dimension L T~ * = velocity), and is expressed in ohms. It consists of two components, the resistance, r, and the reactance, x, or — , The resistance, r, in ...", "... ues (square root of mean squares), if i = effective value of alternating current, c = 2ir NLi is the effective value of E.M.F. of self-inductance, and the ratio, e I i = 2 ir A^Ly is the magnetic reactance : Thus, if r = resistance, x,,^ — reactance, c = impedance, — the E.M.F. consumed by resistance is: fi = ir ; the E.M.F. consumed by reactance is : t\\ = Lv ; 1 4] INTRODUCTION, 5 and, since both E.M.Fs. are in quadrature to each other, the total E.M.F. is — that is, the impedance, ^, takes in alternating- ...", "... ce, x,,^ — reactance, c = impedance, — the E.M.F. consumed by resistance is: fi = ir ; the E.M.F. consumed by reactance is : t\\ = Lv ; 1 4] INTRODUCTION, 5 and, since both E.M.Fs. are in quadrature to each other, the total E.M.F. is — that is, the impedance, ^, takes in alternating-current cir- cuits the place of the resistance, r, in continuous-current •circuits. CAPACITY. 4. If upon a condenser of capacity, C, an E.M.F., e, is impressed, the condenser receives the electrostatic charge, Ce. If the E.M. ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-05", "section_label": "Chapter 5: Symbouc Mbthod", "section_title": "Symbouc Mbthod", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2744-3229", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "snippets": [ "... xpressed, the current lags 90° behind the E.M.F.), and represented by the expression — — ylr/= — Jxi + xi\\ Hence, the E.M.F. required to overcome the resistance,, r, and the reactance, jr, is — (r~»/; that is — Z = r —jx is the expression of the impedance of the cir- cuity in complex quantities. Hence, li I = i +ji' is the current, the E.M.F. required to overcome the impedance, Z = r — jxy is — hence, since y^ = — 1 £ = (ri -|- xi') + J (ri' — xi) ; or, if ^ = ^ +je' is the impressed E.M.F., and Z = ...", "... .F. required to overcome the resistance,, r, and the reactance, jr, is — (r~»/; that is — Z = r —jx is the expression of the impedance of the cir- cuity in complex quantities. Hence, li I = i +ji' is the current, the E.M.F. required to overcome the impedance, Z = r — jxy is — hence, since y^ = — 1 £ = (ri -|- xi') + J (ri' — xi) ; or, if ^ = ^ +je' is the impressed E.M.F., and Z = r —jx the impedance, the current flowing through the circuit is : — Z r — jx or, multiplying numerator and denominator by ( ...", "... - cuity in complex quantities. Hence, li I = i +ji' is the current, the E.M.F. required to overcome the impedance, Z = r — jxy is — hence, since y^ = — 1 £ = (ri -|- xi') + J (ri' — xi) ; or, if ^ = ^ +je' is the impressed E.M.F., and Z = r —jx the impedance, the current flowing through the circuit is : — Z r — jx or, multiplying numerator and denominator by (r+jx) to eliminate the imaginary from the denominator, we have — 7 ^ (^+J^(^+Jx) ^ er — /x , . /r + » sin a + jy cos a. z z The quantities, xr, r, ;r, and y^ gy 6, are, however, not ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "section_title": "Dibtbisnted Capacity, Inductance, Besistance, And", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "... be represented by the approx- imation of one ; viz., three condensers shunted across the line. 104. A.) Line capacity represented by one condetiser shunted across middle of line. Let — Y == g -{- j'b = admittance of receiving circuit; z =i r — j X = impedance of line ; be = condenser susceptance of line. §105] DISTRIBUTED CAPACITY. 15S Denoting, in Fig. 84, the E.M.F., viz., current in receiving circuit by E^ /, the E.M.F. at middle of line by E\\ the E.M.F., viz., current at generator by EoyJo\\ t ...", "... E.M.F. and current (differing in phase by any desired angle) may be given at the terminals of receiving cir- cuit. To be determined are the E.M.F. and current at any point of the line ; for instance, at the generator terminals. Or, Zi = ri — y xi ; the impedance of receiver circuit, or admittance, and E.M.F\"., E^, at generator terminals iare given. Current and E.M.F\\ at any point of circuit to be determined, etc. 109. Counting now the distance, x, from a point, 0, of the line which has the E.M.F., ^\\ = ^1 +/^ ...", "... ei + je( is the H by substituting (15) in (14), we get : 2 ^ = {(a /\\ + p //) + (^r^i + K O} 2 ^ = {(a/\\ + iS/i') - (^^1 + K^x)) + >{(«// ~iS A) -(^.'I'-^.^IJ a and j3 being determined by equations (11). (16) (16) 112. li Z = R — j X is the impedance of the receiver circuit, E^ = c^ -\\- J c^ is the E.M.F. at dynamo terminals (17), and / = length of line, we get at hence or At X = /, X = 0, j^ A + B E^d^'^-, ^ ^E ^ A — B a —jp /~A + B g-Jb/' A - B ^ j} S- J be A+B a-jP (18) — ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "section_label": "Chapter 10: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "... etc.). This method gives what may be called the true ohmic resistance of the circuit. 2.) By the ratio : Volts consumed in circuit Amperes in circuit In an alternating-current circuit, this method gives, not the resistance of the circuit, but the impedance, 3.) By the ratio : r__ Power consumed . (Current)2 where, however, the \"power\" does not include the work done by the circuit, and the counter E.M.Fs. representing it, as, for instance, in the case of the counter E.M.F. of a motor. In alternatin ...", "... / cos a, which is called the mag- netizing current. Or, conversely, the E.M.F. consists of an energy component, E sin a, the Jiysteretic energy E.M.F., and a wattless component, E cos a, the E.M.F. of self- induction. Denoting the absolute value of the impedance of the 116 A L TERNA TING-CURRENT PHENOMENA . circuit, E 1 1, by s, — where s is determined by the mag- netic characteristic of the iron, and the shape of the magnetic and electric circuits, — the impedance is repre- sented, in phase and intensity, by ...", "... duction. Denoting the absolute value of the impedance of the 116 A L TERNA TING-CURRENT PHENOMENA . circuit, E 1 1, by s, — where s is determined by the mag- netic characteristic of the iron, and the shape of the magnetic and electric circuits, — the impedance is repre- sented, in phase and intensity, by the symbolic expression, Z = r — jx = z sin a — jz cos a ; and the admittance by, Y = g + j b = - sin a -j- j - cos a = y sin a -f- jy cos a. z z The quantities, z, r, x, and y, g, b, are, however, not c ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "... h to be represented by the approx- imation of one ; viz., three condensers shunted across the line. 109. A.} Line capacity represented by one condenser shunted across middle of line. Let — Y = g + j b = admittance of receiving circuit ; z = r — j x = impedance of line ; be = condenser susceptance of line. DISTRIBUTED CAPACITY. 161 Denoting, in Fig. 84, the E.M.F., viz., current in receiving circuit by £, It the E.M.F. at middle of line by £', the E.M.F., viz., current at generator by E0)I0\\ If ...", "... , an E.M.F, and current (differing in phase by any desired angle) may be given at the terminals of receiving cir- cuit. To be determined are the E.M.F. and current at any point of the line ; for instance, at the generator terminals. Or, Zl=rl— JXl ; the impedance of receiver circuit, or admittance, and E.M.F., E0, at generator terminals are given. Current and E.M.F. at any point of circuit to be determined, etc. 114. Counting now the distance, x, from a point, 0, of the line which has the E.M.F., •Ei = e\\ + J ...", "... 0 ALTERNATING-CURRENT PHENOMENA. by substituting (15) in (14), we get : 2 A = {(a t\\ + ft //) + (gev + bc ^') (16) 2 B = {(a /! + /? //) - (ge, + /;c ,/)} + /{(«//- 0/0 -(^I'-^ a and ft being determined by equations (11). 117. H Z — R — j X is the impedance of the receiver circuit, E0 = e0 + j >0' is the E.M.F. at dynamo terminals (17), and / = length of line, we get at hence g — jbc or a-; ft At X = /, E0 sin/?/}. (19) Equations (18) and (19) determine the constants A and B, which, subst ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-07", "section_label": "Chapter 8: Synchronizing Induction Motors", "section_title": "Synchronizing Induction Motors", "kind": "chapter", "sequence": 7, "number": 8, "location": "lines 13956-14465", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-07/", "snippets": [ "... equal induction motors with their primaries connected to the same voltage, supply and with llieir seeondarioi connected in multiple with each other to a common resistance, r, and neglecting for simplicity the exciting current and the vol- tage drop in the impedance of the motor primaries as not mate- rially affecting the synchronizing power. Let Zi — n + ./j-t = secondary self-inductive impedance at full frequency; s = slip of the two motors, as fraction of syn- chronism; Co = absolute value of impressed voltage an ...", "... h each other to a common resistance, r, and neglecting for simplicity the exciting current and the vol- tage drop in the impedance of the motor primaries as not mate- rially affecting the synchronizing power. Let Zi — n + ./j-t = secondary self-inductive impedance at full frequency; s = slip of the two motors, as fraction of syn- chronism; Co = absolute value of impressed voltage and thus, when neglecting the primary impedance, of the voltage generated iu the primary by the rotating field. If then Ihe two motor s ...", "... rially affecting the synchronizing power. Let Zi — n + ./j-t = secondary self-inductive impedance at full frequency; s = slip of the two motors, as fraction of syn- chronism; Co = absolute value of impressed voltage and thus, when neglecting the primary impedance, of the voltage generated iu the primary by the rotating field. If then Ihe two motor secondaries are oul of phase with each • if her by angle 2 r, ami the secondary of I he motor 1 is behind in the direction of rotation mid the secondary of the motor 2 ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-06", "section_label": "Lecture 6: Higher Harmonics Of The Generator Wave", "section_title": "Higher Harmonics Of The Generator Wave", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3133-3507", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-06/", "snippets": [ "... er of the generator delta, and the sum of voltages of the three third harmonics can be measured by putting a voltmeter in a corner of the generator delta. This local current in the generator winding is the triple frequency voltage divided by the generator impedance (the stationary impedance, at triple frequency, but not the syn- chronous impedance, since the latter includes armature reac- tion). In generators of low impedance or close regulation, as turbine alternators, this local current may be far more than full ...", "... and the sum of voltages of the three third harmonics can be measured by putting a voltmeter in a corner of the generator delta. This local current in the generator winding is the triple frequency voltage divided by the generator impedance (the stationary impedance, at triple frequency, but not the syn- chronous impedance, since the latter includes armature reac- tion). In generators of low impedance or close regulation, as turbine alternators, this local current may be far more than full load current ; delta connec ...", "... e measured by putting a voltmeter in a corner of the generator delta. This local current in the generator winding is the triple frequency voltage divided by the generator impedance (the stationary impedance, at triple frequency, but not the syn- chronous impedance, since the latter includes armature reac- tion). In generators of low impedance or close regulation, as turbine alternators, this local current may be far more than full load current ; delta connection of generator windings there- fore is unsafe. As a res ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 3267-3618", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-06/", "snippets": [ "... SYSTEtif NON-INDUCTIVE LOAD Fig. 29. Fig. 30. these currents are represented in Fig. 29 by the vectors 01 1 = 01 2 = 01 3 = I, lagging behind the voltages by angles EiOIi = £20/2 = EsOh = d. Let the three-phase circuit be supplied over a line of impedance, Zi = ri -{- jxi, from a generator of internal impedance, Zo = ro + jxo. In phase OEi the voltage consumed by resistance ri is repre- sented by the distance, EiEi^ = Iri, in phase, that is, parallel with current OIi. The voltage consumed by reactance Xi ...", "... ese currents are represented in Fig. 29 by the vectors 01 1 = 01 2 = 01 3 = I, lagging behind the voltages by angles EiOIi = £20/2 = EsOh = d. Let the three-phase circuit be supplied over a line of impedance, Zi = ri -{- jxi, from a generator of internal impedance, Zo = ro + jxo. In phase OEi the voltage consumed by resistance ri is repre- sented by the distance, EiEi^ = Iri, in phase, that is, parallel with current OIi. The voltage consumed by reactance Xi is represented by Ei^Ei^^ = Ixi, 90° ahead of current OT ...", "... ws that to produce the voltage triangle, E1E2E3, at the terminals of the consumer's circuit, the voltage triangle, Ei^^Ez^^Ea^^, is required at the generator terminals. 42 ALTERNATING-CURRENT PHENOMENA Repeating the same operation for the internal impedance of the generator, we get E^^E^^^ = /ro, and parallel to OTi, W^^'^ = Ixo, and 90° ahead of OIi, and thus as triangle of (nominal) gen- erated e.m.fs. of the generator, Ei^E2°Ez^. In Fig. 29 the diagram is shown for 45° lag, in Fig. 30 for non- inductive ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... cuit. That is, an e.m.f. and current (differing in phase by any desired angle) may be given at the terminals of the receiving circuit. To be determined are the e.m.f. and current at any point of the line, for instance, at the generator terminals; or the impedance, Zt = rl - jxv or admittance, Yl = g1 + jblt of the receiver circuit, and e.m.f., E0, at generator terminals are given; the current and e.m.f. at any point of circuit to be deter- mined, etc. 7. Counting- now the distance, I, from a point 0 of the line ...", "... n, such as current and voltage at one point of the circuit, as at the generator or at the receiving end; or current at one point, voltage at the other; or voltage at one point, as at the generator, and ratio of voltage and current at the other end, as the impedance of the receiving circuit. Let the current and voltage (in intensity as well as phase, that is, as complex quantities) be given at one point of the circuit, and counting the distance Z from this point, the terminal con- ditions are 2-0, r- '{• - s' + ...", "... E = 0 and / = 0; •hence, substituting in (23) gives and A2= 0 hence, fy I = E0 V 77£~al (cos pi + j sin pi) (51) and E = E^-*1 (cos pi + j sin pi). From (51) it follows that 7 Y' that is, an infinitely long conductor acts like an impedance, Z.-V/^-r,-/*,, and the current at every point of the conductor thus has the same space-phase angle to the voltage, tan «, = -1 - T< 306 TRANSIENT PHENOMENA The equivalent impedance of the infinite conductor is 7 a - //? z, YY~g-jb .flg ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-48", "section_label": "Chapter 8: Velocity Of Propagation Of Electric Field", "section_title": "Velocity Of Propagation Of Electric Field", "kind": "chapter", "sequence": 48, "number": 8, "location": "lines 26095-27002", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "snippets": [ "... l 40^ < 0.01805, - 0.01805 < col 40 < -- 0.01725. As seen, for larger values of al sil al has the same sign as the sine function, col al the same sign as the cosine function. 73. From equations (20) and (21) then follow, for I = lr, the self-inductive impedance and the self-inductance of the con- ductor, where lr = the radius of sending conductor, and since lr 396 ' TRANSIENT PHENOMENA is very small compared with the wave length lw, the values (23) can be used, and give Self -inductive impedance : Z = 4 7r ...", "... lf-inductive impedance and the self-inductance of the con- ductor, where lr = the radius of sending conductor, and since lr 396 ' TRANSIENT PHENOMENA is very small compared with the wave length lw, the values (23) can be used, and give Self -inductive impedance : Z = 4 7r//0 ^ - j (log 4 - 0.5772) j 1(T9 ohms, (25) ( A alr and effective self-inductance: L = 2 I, \\ log-i- - 0.5772 + j^ \\ 1(T9 henrys. (26) ( alr 2 ) As an example let a current of i= 100 amperes be impressed upon a sending antenna of /0 = 1 ...", "... ry component of self-inductance L, that is, the term in L which represents the power radiation, is Z0?r 10~9 henrys; (29) hence independent of conductor size, shape, and material, of fre- quency, current, etc. The imaginary or reactive component of the impedance, x = 4 nfllog- - 0.5772 10~9 ohms, \\ Cwj* / is approximately, neglecting 0.5772 against log — , and substitut- ed,. ing equation (7), o x = 4 7r/70log — ^— 10~9 ohms j- -log/) nir i 10~9 ohms. (30) Hence, with increasing frequency /, ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 6125-6803", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-09/", "snippets": [ "... Z2 y c,L2 el = !l!, Zl Zl ' (5) (6) (7) That is, in the same oscillating circuit, the maximum voltages eo in the different sections are proportional to, and the maximum currents Iq inversely proportional to, the square root of the natural impedances Zq of the sections, that is, to the fourth root of the ratios of inductance to capacity y^ • At every transition point between successive sections traversed by a traveling wave, as those of an oscillating system, a trans- formation of voltage and of cur ...", "... voltage and of current occurs, by a transformation ratio which is the square root of the ratio of the natural imped- ances, ^0 = V PT , of the two respective sections. ^ Co When passing from a section of high capacity and low induc- tance, that is, low impedance Zq, to a section of low capacity and high inductance, that is, high impedance Zq, as when passing from a transmission line into a transformer, or from a cable into a trans- mission line, the voltage thus is transformed up, and the current transformed down ...", "... root of the ratio of the natural imped- ances, ^0 = V PT , of the two respective sections. ^ Co When passing from a section of high capacity and low induc- tance, that is, low impedance Zq, to a section of low capacity and high inductance, that is, high impedance Zq, as when passing from a transmission line into a transformer, or from a cable into a trans- mission line, the voltage thus is transformed up, and the current transformed down, and inversely, Avith a wave passing in opposite direction. A low-voltage h ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3287-3955", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "snippets": [ "... stored energy which alternately appears as magnetic and as dielectric energy, it obviously is W _ Ceo2 ~2~ ~2\" This gives a relation between the maximum transient current and the maximum transient voltage: v/: -^ therefore is of the nature of an impedance z0, and is called the natural impedance, or the surge impedance, of the circuit ; and fc its reciprocal, V/y = yo, is the natural admittance, or the surge T J j admittance, of the circuit. 62 ELECTRIC DISCHARGES, WAVES AND IMPULSES. The maximum ...", "... as magnetic and as dielectric energy, it obviously is W _ Ceo2 ~2~ ~2\" This gives a relation between the maximum transient current and the maximum transient voltage: v/: -^ therefore is of the nature of an impedance z0, and is called the natural impedance, or the surge impedance, of the circuit ; and fc its reciprocal, V/y = yo, is the natural admittance, or the surge T J j admittance, of the circuit. 62 ELECTRIC DISCHARGES, WAVES AND IMPULSES. The maximum transient voltage can thus be calculated ...", "... ectric energy, it obviously is W _ Ceo2 ~2~ ~2\" This gives a relation between the maximum transient current and the maximum transient voltage: v/: -^ therefore is of the nature of an impedance z0, and is called the natural impedance, or the surge impedance, of the circuit ; and fc its reciprocal, V/y = yo, is the natural admittance, or the surge T J j admittance, of the circuit. 62 ELECTRIC DISCHARGES, WAVES AND IMPULSES. The maximum transient voltage can thus be calculated from the maximum transi ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 5521-6088", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "snippets": [ "... I ^ into (4) gives or and z2 or fz» /ON That is, in the same oscillating circuit, the maximum voltages 60 in the different sections are proportional to, and the maximum currents i0 inversely proportional to, the square root of the natural impedances z0 of the sections, that is, to the fourth root of the ratios of inductance to capacity -^ • to At every transition point between successive sections traversed by a traveling wave, as those of an oscillating system, a trans- formation of voltage and o ...", "... voltage and of current occurs, by a transformation ratio which is the square root of the ratio of the natural imped- ances, ZQ = V TT > of the two respective sections. * Co When passing from a section of high capacity and low induc- tance, that is, low impedance z0, to a section of low capacity and high inductance, that is, high impedance z0, as when passing from a transmission line into a transformer, or from a cable into a trans- mission line, the voltage thus is transformed up, and the current transformed down ...", "... root of the ratio of the natural imped- ances, ZQ = V TT > of the two respective sections. * Co When passing from a section of high capacity and low induc- tance, that is, low impedance z0, to a section of low capacity and high inductance, that is, high impedance z0, as when passing from a transmission line into a transformer, or from a cable into a trans- mission line, the voltage thus is transformed up, and the current transformed down, and inversely, with a wave passing in opposite direction. A low-voltage hi ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-09", "section_label": "Theory Section 9: Vector Diagrams", "section_title": "Vector Diagrams", "kind": "theory-section", "sequence": 9, "number": 9, "location": "lines 2865-3233", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-09/", "snippets": [ "... — e!Q sin 0, is represented by vector OEi equal to r/0, and located on the nega- VECTOR DIAGRAMS 45 tive vertical, and the counter e.m.f. of resistance by vector OE'i on the positive vertical. The counter e.m.f. of impedance: — (r/o sin 0 + x!Q cos 0) - ?Jn sin (ft -\\- fi»} sin (6 + 00) then is represented graphically as the resultant, by the parallelo- gram of sine waves of OE\\ and OE'2} that is, by a vector OE', equal in leng ...", "... sin (6 + 00) then is represented graphically as the resultant, by the parallelo- gram of sine waves of OE\\ and OE'2} that is, by a vector OE', equal in length to z!0, and of phase 90 + 00. The voltage consumed by impedance, or the impressed voltage, is represented by the vector OE, equal and opposite in direction to the vector OE' . This vector is the resultant of OEi and OE2 and has the phase 00 — 90, or — (90 — 00), as shown in Fig. ...", "... 1. VECTOR DIAGRAMS 47 Thus the e.m.f. consumed by resist ance_,j9£'i = rl, is in phase with 7,the e.m.f. consumed by reactance, OEz = xl, is 90 degrees ahead of /, and their resultant is OE3, the e.m.f. consumed by impedance. OW3 combined with 0#, the receiver voltage, gives the genera- tor voltage OE0. FIG. 20. — Vector diagram of e.m.f. and current in transmission line. Cur- rent lagging. Resolving all e.m.fs. and currents into components ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-110", "section_label": "Apparatus Section 4: Induction Machines: Induction Generator", "section_title": "Induction Machines: Induction Generator", "kind": "apparatus-section", "sequence": 110, "number": 4, "location": "lines 21158-21588", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-110/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-110/", "snippets": [ "... ly on circuits with lead- ing current or circuits of negative effective reactance. 344 ELEMENTS OF ELECTRICAL ENGINEERING In Fig. 188 are given for the constant-speed induction gen- erator in Fig. 230 as function of the impedance of the external circuit z = -?• as abscissas (where eQ = terminal voltage, iQ = 2o current in external circuit), the leading power-factor p = cos 6 required in the load, the inductance factor q = sin 6, and the fr ...", "... (where eQ = terminal voltage, iQ = 2o current in external circuit), the leading power-factor p = cos 6 required in the load, the inductance factor q = sin 6, and the frequency. Hence, when connected to a circuit of impedance z this induc- tion generator can operate only if the power-factor of its circuit is p', and if this is the case the voltage is indefinite, that is, the circuit unstable, even neglecting the impossibility of securing exact ...", "... atter the 01 02 0,3 04 05 06 017 0.8 019 IjO 11. 12 13 14 lf.5 FIG. 190. — Induction generator and synchronous converter, phase control, no line impedance. voltage of the induction generator rises until it is as much below the counter e.m.f. of the synchronous motor as required to give the leading current corresponding to the power-factor of the generator. Thus a system con ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-16", "section_label": "Chapter 16: Power, And Double-Frequency Quantities In", "section_title": "Power, And Double-Frequency Quantities In", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 16077-16520", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-16/", "snippets": [ "... enting the absolute values of potential (with regard to any reference point chosen as coordi- nate center), and their connection the difference of potential in phase and intensity. Algebraically these vectors are represented by complex quan- tities. The impedance, admittance, etc., of the circuit is a com- plex quantity also, in symbolic denotation. Thus current, voltage, impedance, and admittance are related by multiplication and division of complex quantities in the same way as current, voltage, resistance, and ...", "... ection the difference of potential in phase and intensity. Algebraically these vectors are represented by complex quan- tities. The impedance, admittance, etc., of the circuit is a com- plex quantity also, in symbolic denotation. Thus current, voltage, impedance, and admittance are related by multiplication and division of complex quantities in the same way as current, voltage, resistance, and conductance are related by Ohm's law in direct-current circuits. In direct-current circuits, power is the product of cur ...", "... t circuits. In direct-current circuits, power is the product of current into voltage. In alternating-current circuits, if the product, is not the power; that is, multiplication and division, which are correct in the inter-relation of current, voltage, impedance, do not give a correct result in the inter-relation of voltage, current, power. The reason is, that E and / are vectors of the same fre- quency, and Z a constant numerical factor or \"operator,\" which thus does not change the frequency. 179 180 ALTERN ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-23", "section_label": "Chapter 23: Synchronizing Alternators", "section_title": "Synchronizing Alternators", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 25135-25681", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-23/", "snippets": [ "... t the voltage at the common busbars be assumed as zero line, or real axis of coordinates of the complex representation; and let e = difference of potential at the common busbars of the two alternators; SYNCHRONIZING ALTERNATORS 295 Z = r -^ jx = impedance of the external circuit; Y = 9 ~ jb == admittance of the external circuit; hence, the current in the external circuit is e I = r -\\-jx = e(g - jh). Let El = ei -\\- je'i = ai(cos di + j sin di) = generated e.m.f. of first machine; E2 = 6 ...", "... + j sin di) = generated e.m.f. of first machine; E2 = 62 -{- je'i ^ a2(cos 02. + j sin ^2) = generated e.m.f. of second machine; /i ^ ii — ji'i = current of the first machine; Jg = 12 — ji'2 = current of the second machine; Zi == ri + jxi = internal impedance, and Yi = Qi — jh\\ = inter- nal admittance of the first machine; ^2 = ^2 + jxi = internal impedance, and Y2 = ^2 — i&2 = inter- nal admittance of the second machine. Fig. 144. Then, er + e'r = al^• 62^ + e'2^ --^ a2^; Ex = e ■\\- hZi, or ei -\\- je ...", "... ed e.m.f. of second machine; /i ^ ii — ji'i = current of the first machine; Jg = 12 — ji'2 = current of the second machine; Zi == ri + jxi = internal impedance, and Yi = Qi — jh\\ = inter- nal admittance of the first machine; ^2 = ^2 + jxi = internal impedance, and Y2 = ^2 — i&2 = inter- nal admittance of the second machine. Fig. 144. Then, er + e'r = al^• 62^ + e'2^ --^ a2^; Ex = e ■\\- hZi, or ei -\\- je\\ = (e + iiVi + i'lXi) -f j(iiXi — i'\\r^; E2 = e -{- I2Z2, or 62 + je'2 = (e + ^'2^2 + ^'2a;2) + j(i2X ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-17", "section_label": "Chapter 17: Synchbonizino Aiitebkatobs", "section_title": "Synchbonizino Aiitebkatobs", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 18829-19345", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-17/", "snippets": [ "... mmon bus bars be assumed Fig, 121. as zero line, or real axis of coordinates of the complex method ; and let — 252 AL TERN A TING-CURRENT PHENOMENA, [§ 1 74 e = difference of potential at the common bus bars of the two alternators, Z ^= r — jx = impedance of external circuit, K=s^»--|-y^ = admittance of external circuit; hence, the current in external circuit is /- —JX Let £i = fi —/ ^1 = ^1 = 1 — j sin £>i) = induced E.M.F. of first machine ; £2 = e.2 — _/>•/ = a2 (cos w2 — j sin w2) = induced E.M ...", "... u>1 — j sin £>i) = induced E.M.F. of first machine ; £2 = e.2 — _/>•/ = a2 (cos w2 — j sin w2) = induced E.M.F. of sec- ond machine ; /! = /! -f-//i' = current of first machine ; /2 = /2 -j-yY2' = current of second machine ; Z^ = T! — jxi = internal impedance, and Yv = gi -\\- jbl = inter- nal admittance, of first machine ; Z2 = r2 — jxz = internal impedance, and K2 =gz ~\\~ jb, the primary induced E.M.F., E = — e, the secondary induced E.M.F., £1 = — e {sin X +j\"k cos X|; hence, if Zl = r1—jx1= secondary impedance reduced to primary circuit, Z = r — jx = primary impedance, Y = g —jb = exciting admittance, we have, & sin X -f- jk cos A secondary current, 7X = — L = - e - _ - , primary exciting current, I0 = eY= e (g +jb}, hence, total primary current, Pr ...", "... alue of rising magnetism, the mag- netism is represented by /4>, the primary induced E.M.F., E = — e, the secondary induced E.M.F., £1 = — e {sin X +j\"k cos X|; hence, if Zl = r1—jx1= secondary impedance reduced to primary circuit, Z = r — jx = primary impedance, Y = g —jb = exciting admittance, we have, & sin X -f- jk cos A secondary current, 7X = — L = - e - _ - , primary exciting current, I0 = eY= e (g +jb}, hence, total primary current, Primary impressed E.M.F., E0= — E + IZ\\ = e 1 + (sinX Negle ...", "... X)2 + (xt + x sin X — kr cos X)2 or T= V27r^lO-8 [/! sin X 7X cos A]' = [^/! cos X}> _ ^ cos X (xl sin X + r^k cos X) r2 + x2 The stationary torque is, k = 0, _ ifo2^ sin X cos X 0 = (rx + r sin X)2 + (^ + * sin X)2 ' and neglecting the primary impedance, r = 0 = x, _ e^x^ sin X cos X _ (fo2^ sin2 X which is a maximum at X = 45°. At speed k, neglecting r = 0 = x, I = 71? — current of second phase produced by phase Zr T Z»o converter, E — IZ = „ . „ = - — ;=- = ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-13", "section_label": "Theory Section 13: Alternating-current Transformer", "section_title": "Alternating-current Transformer", "kind": "theory-section", "sequence": 13, "number": 13, "location": "lines 4465-5263", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-13/", "snippets": [ "... nsumed by the secondary resistance 7*1 is OE'i = E'i = Iiri in phase with /i. The e.m.f. consumed by the secondary reactance Xi is OE\"\\ = E'\\ = I&i, 90 degrees ahead of /i. Thus the e.m.f. con- sumed by the secondary impedance z\\ = Vn2 + Xi2 is the resultant of OE'i and OE\"i, or OE\"\\ = E\"\\ =JiZi. OE'\"\\ combined with the terminal voltage OE = E gives the secondary e.m.f. OEi = E\\. Proportional thereto by the ratio of turns and in phase t ...", "... the primary is OE'Q = E'Q = /Or0 in phase with /0. The e.m.f. consumed by the primary reactance is OE\"o = E\"Q = /0£o, 90 degrees ahead of O/o. OE'Q and OE\"o combined gives OE'\"Q, the e.m.f. consumed by the primary impedance. FIG. 35. — Vector diagram of transformer with lagging load current. Equal and opposite to the primary counter-generated e.m.f. OEi is the component of primary e.m.f., OEf, consumed thereby. OE' combined with OE\"'Q gives O ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-28", "section_label": "Apparatus Section 7: Synchronous Machines: Synchronous Motor", "section_title": "Synchronous Machines: Synchronous Motor", "kind": "apparatus-section", "sequence": 28, "number": 7, "location": "lines 9292-9398", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-28/", "snippets": [ "... . consumed by resistance isj9#'i = Ir. The e.m.f. consumed by synchronous reactance, OE'o = IxQ. Thus, com- 142 ELEMENTS OF ELECTRICAL ENGINEERING bining OE'i and OE'o gives OE', the e.m.f. consumed by the synchronous impedance. The e.m.f. consumed by the synchro- nous impedance OE' and the e.m.f. consumed by the nominal generated or counter e.m.f. of the synchronous motor OEo, combined, give the impressed e.m.f. OE. Hence OEo is one side of a p ...", "... consumed by synchronous reactance, OE'o = IxQ. Thus, com- 142 ELEMENTS OF ELECTRICAL ENGINEERING bining OE'i and OE'o gives OE', the e.m.f. consumed by the synchronous impedance. The e.m.f. consumed by the synchro- nous impedance OE' and the e.m.f. consumed by the nominal generated or counter e.m.f. of the synchronous motor OEo, combined, give the impressed e.m.f. OE. Hence OEo is one side of a parallelogram, with OE' as the other side, and OE a ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-30", "section_label": "Apparatus Section 9: Synchronous Machines: Magnetic Characteristic or Saturation Curve", "section_title": "Synchronous Machines: Magnetic Characteristic or Saturation Curve", "kind": "apparatus-section", "sequence": 30, "number": 9, "location": "lines 9554-9650", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-30/", "snippets": [ "... parallel to the no-load saturation curve, but starting at a definite value of field excitation for zero terminal voltage, the field excitation required to maintain full-load current through the armature against its synchronous impedance. dF dE The ratio -«• -=- ~FT r Hi is called the saturation factor s of the machine. It gives the ratio of the proportional change of field excitation required for a change of voltage. The quantity 5 = 1 is ...", "... increase of density is required in the field magnetic circuit under load. In consequence thereof, at high saturation the load saturation curve differs more from the no-load saturation curve than corresponds to the synchronous impedance of the machine. SYNCHRONOUS MACHINES 149 The regulation becomes better by saturation; that is, the increase of voltage from full load to no load at constant field excitation is reduced, the voltage being limited by sa ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-36", "section_label": "Apparatus Section 15: Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "section_title": "Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "kind": "apparatus-section", "sequence": 36, "number": 15, "location": "lines 9918-10123", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-36/", "snippets": [ "... - nism with each other, especially when the conditions are favorable to a cumulative increase of this effect by what may be called mechanical resonance (hunting) of the engine governors, etc. They depend upon the synchronous impedance of the alternators and upon their phase difference, that is, the number of poles and the fluctuation of speed, and are specially objectionable when operating synchronous apparatus in the system. 28. Thus, for instance, if ...", "... he alternator e.m.fs. is 18 electrical time degrees; that is, the alternator e.m.fs. are represented by OEi and OEZ in Fig. 71, and when running in parallel the e.m.f. OEf = E\\E^ is short circuited through the synchronous impedance of the two alternators. . Since E' = OE\\ = 2 EI sin 9 deg. the maximum cross current is ffisin9deg. 0.156 ffi 1 = = = U.loo 1 o, 20 20 ET where IQ = -- = short-circuit current of the alternator at full- ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-38", "section_label": "Apparatus Section 17: Synchronous Machines: Short-circuit Currents of Alternators", "section_title": "Synchronous Machines: Short-circuit Currents of Alternators", "kind": "apparatus-section", "sequence": 38, "number": 17, "location": "lines 10190-10429", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-38/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-38/", "snippets": [ "... arma- ture reaction and armature self-inductance. In the first moment after short circuiting, however, the current frequently is many times larger than the permanent short- circuit current, that is, where z = self-inductive impedance of the alternator. That is, in the first moment after short circuiting the poly- phase alternator the armature current is limited only by the arma- ture self-inductance, and not by the armature reaction, and some appreciable ...", "... demagnetizing action of the armature current, and the gen- SYNCHRONOUS MACHINES 161 erated e.m.f. thereby reduced from the nominal value EQ to the virtual value Ez; the latter is consumed by the armature self- inductive impedance z, or self-inductive reactance, which is practically the same in most cases. The armature self-inductance is instantaneous, since the magnetic field rises simultaneously with the armature current which produces it; armature re ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-07", "section_label": "Chapter 7: Polar Coordinates And Polar Diagrams", "section_title": "Polar Coordinates And Polar Diagrams", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 3619-4087", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-07/", "snippets": [ "... and can 62 ALTERNATING-CURRENT PHENOMENA be transformed into it by reversing right and left, or top and bottom. So the crank diagram, Fig. 47, is the image of the polar diagram, Fig. 46. In symbolic representation, based upon the crank diagram, the impedance was denoted by Z = r -\\- jx, where x == inductive reactance. In the polar diagram, the impedance thus is denoted by: Z = r — jx since the latter is the mirror image of the crank diagram, that is, differs from it symbolically by the interchange of + ...", "... top and bottom. So the crank diagram, Fig. 47, is the image of the polar diagram, Fig. 46. In symbolic representation, based upon the crank diagram, the impedance was denoted by Z = r -\\- jx, where x == inductive reactance. In the polar diagram, the impedance thus is denoted by: Z = r — jx since the latter is the mirror image of the crank diagram, that is, differs from it symbolically by the interchange of + j and — j. A treatise written in the symbolic repre- sentation by the polar diagram, thus can be tr ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-25", "section_label": "Chapter 25: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 29375-32539", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-25/", "snippets": [ "... l wave 9.91 .Effective value of its fundamental sine wave ... 8 . 25 Effective value of the sum of all its higher harmonics 5 . 48 that is, the effective value of all the higher harmonics is 55.3 per cent, of the effective value of the total wave. The impedance of this iron-clad reactance, with a sine wave current of 7.07 effective, so is 9 91 ' = 7:07 = l-^O' while the same reactance, with a sine wave e.m.f. of 7.07 effective, in A, gives the impedance. The conclusion is that an iron-clad magnetic circuit ...", "... r cent, of the effective value of the total wave. The impedance of this iron-clad reactance, with a sine wave current of 7.07 effective, so is 9 91 ' = 7:07 = l-^O' while the same reactance, with a sine wave e.m.f. of 7.07 effective, in A, gives the impedance. The conclusion is that an iron-clad magnetic circuit is not suitable for a reactor, since even below saturation (as above assumed) it produces very great wave-shape distortion. As discussed before, the insertion of even a small air-gap into the magnet ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... due to dielectric hysteresis, is a constant. This I found proved by experiment. This would mean that the dielectric hysteretic admit- tance of a condenser, where g = hysteretic conductance, y = hysteretic susceptance ; and the dielectric hysteretic impedance of a condenser, where : r = hysteretic resistance, .T<. = hysteretic condensance ; and the angle of dielectric hysteretic lag, tan a c = n are constants of the circuit, independent of E.M.F. and fre- quency. The E.M.F. is obviously inversely p ...", "... ircuit, independent of E.M.F. and fre- quency. The E.M.F. is obviously inversely proportional to the frequency. The true static dielectric hysteresis, observed by Arno as proportional to the 1.6*** power of the density, will enter the admittance and the impedance as a term variable and dependent upon E.M.F. and frequency, in the same manner as discussed in the chapter on magnetic hysteresis. To the magnetic hysteresis corresponds, in the electro- static field, the static component of dielectric hysteresis, follo ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-19", "section_label": "Chapter 19: Commutatob Motobs", "section_title": "Commutatob Motobs", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 21339-22387", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "snippets": [ "... . Introducing now complex quantities, and counting the time from the zero value of rising magnetism, the mag- netism is represented by the primary induced E.M.P\\, E =^ — e\\ the secondary induced E.M.F. : hence, if V2 Zi = /*! — j Xx = secondary impedance reduced to primary circuit, Z =^ r — j X = primary impedance, Y = g -\\- jb = primary admittance, it is, secondary current, r _ E, _ e 1_±j±. -'i — — : — f primary exciting current, 298 AL TERN A TING-CURRENT PHENOMENA. [ § 198 hence, total p ...", "... m the zero value of rising magnetism, the mag- netism is represented by the primary induced E.M.P\\, E =^ — e\\ the secondary induced E.M.F. : hence, if V2 Zi = /*! — j Xx = secondary impedance reduced to primary circuit, Z =^ r — j X = primary impedance, Y = g -\\- jb = primary admittance, it is, secondary current, r _ E, _ e 1_±j±. -'i — — : — f primary exciting current, 298 AL TERN A TING-CURRENT PHENOMENA. [ § 198 hence, total primary current, Primary impressed E.M.F., or Neglecting i ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "... tric hysteresis, is a constant. This I found proved by experiment. This would mean that the dielectric hysteretic admittance of a condenser, Y=g+jb=g-jb', where : g = hysteretic conductance, b' = hysteretic suscep- tance ; and the dielectric hysteretic impedance of a con- denser, „ . . . Z = r — jx — r +jxc, where : r = hysteretic resistance, xc — hysteretic condens- ance ; and the angle of dielectric hysteretic lag, tan a = b' / g = xc / r, are constants of the circuit, independent of E.M.F. and frequency. T ...", "... circuit, independent of E.M.F. and frequency. The E.M.F. is obviously inversely propor- tional to the frequency. The true static dielectric hysteresis, observed by Arno as proportional to the 1.6th power of the density, will enter the admittance and the impedance as a term variable and dependent upon E.M.F. and frequency, in the same manner as discussed in the chapter on magnetic hysteresis. To the magnetic hysteresis corresponds, in the electro- static field, the static component of dielectric hysteresis, follo ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-12", "section_label": "Chapter 12: Power, And Double Frequency Quantities In General", "section_title": "Power, And Double Frequency Quantities In General", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 9381-9740", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "snippets": [ "... enting the abso- lute values of potential (with regard to any reference point chosen as co-ordinate center) and their connection the dif- ference of potential in phase and intensity. Algebraically these vectors are represented by complex quantities. The impedance, admittance, etc., of the circuit is a complex quantity also, in symbolic denotation. Thus current, E.M.F., impedance, and admittance are related by multiplication and division of complex quantities similar as current, E.M.F., resistance, and conductance ...", "... onnection the dif- ference of potential in phase and intensity. Algebraically these vectors are represented by complex quantities. The impedance, admittance, etc., of the circuit is a complex quantity also, in symbolic denotation. Thus current, E.M.F., impedance, and admittance are related by multiplication and division of complex quantities similar as current, E.M.F., resistance, and conductance are related by Ohms law in direct current circuits. In direct current circuits, power is the product of cur- rent in ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-07", "section_label": "Chapter 7: Shaping Of Waves : General", "section_title": "Shaping Of Waves : General", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 12222-12961", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-07/", "snippets": [ "... er having a specified amount of non-inductive resistance in series. Thus for instance, if x = 1000 ohms = capacity reactance of the condenser, at fundamental frequency, r = 100 ohms = re- 122 ELECTRIC CIRCUITS sistance in series to the condenser, the impedance of this circuit, for the n*^ harmonic, would be rz -^ inrk 1000. .-V Z„ = r-j- = 100--^j (7) or, absolute, the impedance. Zn = 1000^^ + 0.01 (8) and, the admittance, _ 0.001 n . . ^'^ \"\" Vl + 0.01 n^ ^ ^ and therefore, the multiplying factor ...", "... of the condenser, at fundamental frequency, r = 100 ohms = re- 122 ELECTRIC CIRCUITS sistance in series to the condenser, the impedance of this circuit, for the n*^ harmonic, would be rz -^ inrk 1000. .-V Z„ = r-j- = 100--^j (7) or, absolute, the impedance. Zn = 1000^^ + 0.01 (8) and, the admittance, _ 0.001 n . . ^'^ \"\" Vl + 0.01 n^ ^ ^ and therefore, the multiplying factor, ^ _yn _ 1.005 n . J — yi Vl + 0.01 n« this gives, for n f n / 1 1.0 13 8.0 3 2. ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-12", "section_label": "Chapter 8: Velocity Of Propagation Op Electric Field. 387", "section_title": "Velocity Of Propagation Op Electric Field. 387", "kind": "chapter", "sequence": 12, "number": 8, "location": "lines 972-1013", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-12/", "snippets": [ "... nce. 388 69. Effect of return conductor on distance decrement of field. 389 70. Inductance of length I of infinitely long conductor with- out return conductor. 390 71. Equations of magnetic flux, effective resistance of radia- tion, inductance and impedance. 391 72. Evaluation of functions sil al and col al. 394 73. Self-inductive impedance, and numerical example. 395 74. Discussion of effective resistance and radiated power, as function of frequency. 396 75. Mutual inductance of two distant conductors ...", "... uctance of length I of infinitely long conductor with- out return conductor. 390 71. Equations of magnetic flux, effective resistance of radia- tion, inductance and impedance. 391 72. Evaluation of functions sil al and col al. 394 73. Self-inductive impedance, and numerical example. 395 74. Discussion of effective resistance and radiated power, as function of frequency. 396 75. Mutual inductance of two distant conductors of finite length. 398 76. Example. 399 77. Capacity of a sphere in space. 400 78 ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-44", "section_label": "Chapter 4: Distributed Capacity Of High-Potential Transformers", "section_title": "Distributed Capacity Of High-Potential Transformers", "kind": "chapter", "sequence": 44, "number": 4, "location": "lines 23179-23585", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "snippets": [ "... her frequencies, extending over sections of the circuit, and of lesser power. 41. Let then, in the high-potential coil of a high- voltage trans- former, e = the e.m.f. generated per unit length of conductor, as, for instance, per turn; Z = r — ' jx = the impedance per unit length; Y = g — jb = the capacity admittance against ground per unit length of conductor, and Y' = pY= the capacity admittance, per unit length of conductor, between conductor elements distant from each other by unit length, as admittance betwee ...", "... tance I is counted from the point of the con- ductor, which is at ground potential, YEdl = the charging cur- rent of one conductor element against ground, and ^Idl is the total current consumed by a conductor element. However, the e.m.f. consumed by impedance equals the e.m.f. consumed per conductor element; thus dE = Zldl This gives the two differential equations : and e - - = ZI. (2) Differentiating (2) and substituting in (1) gives transposing, - E dP 1 ' (3) P ZY ffE or — = - a*E, (4) ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-53", "section_label": "Chapter 4: Traveling Waves", "section_title": "Traveling Waves", "kind": "chapter", "sequence": 53, "number": 4, "location": "lines 30244-31450", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "snippets": [ "... n q (t - X)}} e~ut { (Aie+8('-x) + A3£-S('-A)) cos q(t- X) + (A1's+a('-A) + A8'e — ('-A)) sin £ (t - X)} (150) and that is, in a single traveling wave current and voltage are in phase with each other, and proportional to each other with an effective impedance (152) This proportionality between e and i and coincidence of phase obviously no longer exist in the combination of main waves and reflected waves, since in reflection the current reverses with the reversal of the direction of propagation, while the v ...", "... 2 TT/L/Z, rk — xh h2 + k2 = h2 + k2 ' where x = 2 TT/L = reactance per unit length. From equation (54), R2 = V(s2 + q2 - m2)2 + 4 80 j»fe 79 X sil|s=(-l) + 1 2~2 INDEX PAGE Acceleration constant of traveling wave 466 Air blast, action in oscillating-current generator 75 pressure required in oscillating-current generator 75 Alternating-current circuit and transient term of fundamental frequency 473 distribution in conductor 369 transformer operating oscillating-current generator 87 transmission, ...", "... 08 267 + .008 057 1 1 80 + .007 957 1 81 - .007 858 0 x> 80 j»fe 79 X sil|s=(-l) + 1 2~2 INDEX PAGE Acceleration constant of traveling wave 466 Air blast, action in oscillating-current generator 75 pressure required in oscillating-current generator 75 Alternating-current circuit and transient term of fundamental frequency 473 distribution in conductor 369 transformer operating oscillating-current generator 87 transmission, equations of traveling wave 477 wave as traveling wav ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-32", "section_label": "Chapter 32: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 25904-27405", "status": "candidate", "occurrence_count": 58, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "snippets": [ "... epresented by the points of half axis OB upwards ; the negative imaginary numbers are represented by the points of half axis OB' downwards ; the complex imaginary numbers are represented by the points outside of the coordinate axes. APPENDIX II. OSCILLATING CURRENTS. INTRODUCTION. 308. An electric current varying periodically between constant maximum and minimum values, — that is, in equal time intervals repeating the same values, — is called an alternating current if the arithmetic mean value equals zer ...", "... rents in which the amplitude of each following wave bears to that of the preceding wave a constant ratio. Such currents consist of a series of waves of constant length, decreasing in amplitude, that is in strength, in constant proportion. They are called oscillating currents in analogy with mechanical oscillations, — for instance of the pendu- lum,— in which the amplitude of the vibration decreases in constant proportion. Since the amplitude of the oscillating current varies, constantly decreasing, the oscillating ...", "... ave bears to that of the preceding wave a constant ratio. Such currents consist of a series of waves of constant length, decreasing in amplitude, that is in strength, in constant proportion. They are called oscillating currents in analogy with mechanical oscillations, — for instance of the pendu- lum,— in which the amplitude of the vibration decreases in constant proportion. Since the amplitude of the oscillating current varies, constantly decreasing, the oscillating current differs from 497 498 APPENDIX II. ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "section_label": "Chapter 30: Quartbr-Fhase System", "section_title": "Quartbr-Fhase System", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 55, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... represented by the points of half axis OB upwards ; the negative imaginary numbers are represented by the points of half axis OB downwards ; the complex imaginary numbers are represented by the points outside of the coordinate axes. APPENDIX II. OSCILLATING CURRENTS. INTBODUCnON. 279. An electric current varying periodically between constant maximum and minimum values, — that is, in equal time intervals repeating the same values, — is called an alternating current if the arithmetic mean value equals zero ...", "... rents in which the amplitude of each following wave bears to that of the preceding wave a constant ratio. Such currents consist of a series of waves of constant length, decreasing in amplitude, that is in strength, in constant proportion. They are called oscillating currents in analogy with mechanical oscillations, — for instance of the pendu- lum, — in which the amplitude of the vibration decreases in constant proportion. Since the amplitude of the oscillating current varies, constantly decreasing, the oscillating ...", "... ave bears to that of the preceding wave a constant ratio. Such currents consist of a series of waves of constant length, decreasing in amplitude, that is in strength, in constant proportion. They are called oscillating currents in analogy with mechanical oscillations, — for instance of the pendu- lum, — in which the amplitude of the vibration decreases in constant proportion. Since the amplitude of the oscillating current varies, constantly decreasing, the oscillating current differs from 409 410 APPF.A'DIX / ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 51, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "LECTURE VII. LINE OSCILLATIONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy surges between magnetic — and dielectric — , and a transient component, by which the total stored energy decreases. Con ...", "... voltage, and inversely, if the one is represented by the cosine function, the other is the sine function; hence the periodic com- ponents of the transient are ii = Iq cos (0 — 7) ei = eo sm (0 — 7) ) where 0 = 2 Tft, (4) and is the frequency of oscillation. The dissipative or \" transient \" component is M = €-\"', (6) 72 LINE OSCILLATIONS. T6 where u 2 U ^ C; hence the total expression of transient current and voltage is ^ = ^oe~ \"^ cos (0 — 7) e = eoe~ ^^ sin (0 — 7) (7) (8) 7 ...", "... he sine function; hence the periodic com- ponents of the transient are ii = Iq cos (0 — 7) ei = eo sm (0 — 7) ) where 0 = 2 Tft, (4) and is the frequency of oscillation. The dissipative or \" transient \" component is M = €-\"', (6) 72 LINE OSCILLATIONS. T6 where u 2 U ^ C; hence the total expression of transient current and voltage is ^ = ^oe~ \"^ cos (0 — 7) e = eoe~ ^^ sin (0 — 7) (7) (8) 7, eo, and io follow from the initial values e' and i' of the transient, 2bt t = 0 or (t> = ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3956-4744", "status": "candidate", "occurrence_count": 51, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "snippets": [ "LECTURE VII. LINE OSCILLATIONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy 7\" /j'2 f^ r/>2 surges between magnetic -^- and dielectric — , and a transient £i A component, by which the total sto ...", "... nversely, if the one is represented by the cosine function, the other is the sine function; hence the periodic com- ponents of the transient are ii = IQ cos ( — 7) ei = e0 sin (0 — 7) l where # = 2»ft (4) and ' = 27^ (5) is the frequency of oscillation. The transient component is hk = e-*, (6) 72 LINE OSCILLATIONS. 73 where e = — €Q sin 7 hence the total expression of transient current and voltage is i = loe-^cos (0 - 7) 6 = eoe-^sinfa - 7) 7, e0, and i.Q follow from the initial values e ...", "... is the sine function; hence the periodic com- ponents of the transient are ii = IQ cos ( — 7) ei = e0 sin (0 — 7) l where # = 2»ft (4) and ' = 27^ (5) is the frequency of oscillation. The transient component is hk = e-*, (6) 72 LINE OSCILLATIONS. 73 where e = — €Q sin 7 hence the total expression of transient current and voltage is i = loe-^cos (0 - 7) 6 = eoe-^sinfa - 7) 7, e0, and i.Q follow from the initial values ef and i' of the transient, at £ = Oor 0 = 0: hence The preceding ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-30", "section_label": "Chapter 8: Low Frequency Surges In High Potential Systems", "section_title": "Low Frequency Surges In High Potential Systems", "kind": "chapter", "sequence": 30, "number": 8, "location": "lines 7826-9227", "status": "candidate", "occurrence_count": 49, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "snippets": [ "... NTIAL SYSTEMS. 64. In electric circuits of considerable capacity, that is, in extended high potential systems, as long distance transmission lines and underground cable systems, occasionally destructive high potential low frequency surges occur; that is, oscillations of the whole system, of the same character as in the case of localized capacity and inductance discussed in the preceding chapter. While a system of distributed capacity has an infinite number of frequencies, which usually are the odd multiples of a fun ...", "... the same character as in the case of localized capacity and inductance discussed in the preceding chapter. While a system of distributed capacity has an infinite number of frequencies, which usually are the odd multiples of a funda- mental frequency of oscillation, in those cases where the fundamental frequency predominates and the effect of the higher frequencies is negligible, the oscillation can be approxi- mated by the equations of oscillation given in Chapters V and VII, which are far simpler than the equation ...", "... ibuted capacity has an infinite number of frequencies, which usually are the odd multiples of a funda- mental frequency of oscillation, in those cases where the fundamental frequency predominates and the effect of the higher frequencies is negligible, the oscillation can be approxi- mated by the equations of oscillation given in Chapters V and VII, which are far simpler than the equations of an oscillation of a system of distributed capacity. Such low frequency surges comprise the total system, not only the transmis ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 33, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "LECTURE VIII. TRAVELING WAVES. 33. In a stationary oscillation of a circuit having uniformly distributed capacity and inductance, that is, the transient of a circuit storing energy in the dielectric and magnetic field, current and voltage are given by the expression i = ioe-\"^ cos ((/> T CO — 7), ^ . . e = eoe~\"' ...", "... , that is, at any dis- tance angle co, and at any time t, that is, time angle 0, then is p = ei, = eo^e~2\"* cos (0 =F co — 7) sin (0 =F co — 7), = ^6-^«'sin2(0Ta>-7), (2) and the average power flow is Po = avg p, (3) = 0. Hence, in a stationary oscillation, or standing wave of a uni- form circuit, the average flow of power, po, is zero, and no power flows along the circuit, but there is a surge of power, of double frequency. That is, power flows first one way, during one-quarter cycle, and then in the oppos ...", "... 40. former, the high-tension switches are opened at the generator end of the transmission line. The energy stored magnetically and dielectrically in line and transformer then dissipates by a transient, as shown in the oscillogram Fig. 41. This gives the oscillation of a circuit consisting of 28 miles of line and 2500-kw. 100-kv. step-up and step-down transformers, and is produced by discon- necting this circuit by low-tension switches. In the transformer, the duration of the transient would be very great, possibly s ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 4745-5520", "status": "candidate", "occurrence_count": 33, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "snippets": [ "LECTURE VIII. TRAVELING WAVES. 33. In a stationary oscillation of a circuit having uniformly distributed capacity and inductance, that is, the transient of a circuit storing energy in the dielectric and magnetic field, current and voltage are given ^by the expression i = iQe~ut cos (0 T co - 7), ) e = e0e~ut sin (< ...", "... is, at any dis- tance angle co, and at any time t, that is, time angle <£, then is p = ei, = e0ioe~2ut cos ( T co — 7) sin (0 =F co — 7), = ^|V2«=Fco-7), (2) and the average power flow is Po = avg p, (3) = 0. Hence, in a stationary oscillation, or standing wave of a uni- form circuit, the average flow of power, p0, is zero, and no power flows along the circuit, but there is a surge of power, of double frequency. That is, power flows first one way, during one-quarter cycle, and then in the oppos ...", "... 40. former, the high-tension switches are opened at the generator end of the transmission line. The energy stored magnetically and dielectrically in line and transformer then dissipates by a transient, as shown in the oscillogram Fig. 41. This gives the oscillation of a circuit consisting of 28 miles of line and 2500-kw. 100-kv. step-up and step-down transformers, and is produced by discon- necting this circuit by low-tension switches. In the transformer, the duration of the transient would be very great, possibly s ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-11", "section_label": "Chapter 11: Instability Of Circuits: Induction And Syn Chronous Motors", "section_title": "Instability Of Circuits: Induction And Syn Chronous Motors", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 21382-22633", "status": "candidate", "occurrence_count": 33, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-11/", "snippets": [ "... tion Machines. \" D. Hunting of S]rnchronous Machines 106. In induction-motor circuits, instability almost always assumes the form of a steady change, with increasing rapidity, from the unstable condition to a stable condition or to stand- still, etc. Oscillatory instability in induction-motor circuits, as the result of the relation of load to speed and electric supply, is rare. It has been observed, especially in single-phase motors, in cases of considerable oversaturation of the magnetic circuit. Oscillatory in ...", "... Oscillatory instability in induction-motor circuits, as the result of the relation of load to speed and electric supply, is rare. It has been observed, especially in single-phase motors, in cases of considerable oversaturation of the magnetic circuit. Oscillatory instability, however, is typical of the synchronous machine, and the hunting of synchronous machines has probably been the first serious problem of cimiulative oscillations in electric circuits, and for a long time has limited the industrial use of syn- c ...", "... gle-phase motors, in cases of considerable oversaturation of the magnetic circuit. Oscillatory instability, however, is typical of the synchronous machine, and the hunting of synchronous machines has probably been the first serious problem of cimiulative oscillations in electric circuits, and for a long time has limited the industrial use of syn- chronous machines, in its different forms: (a) Difficulty and failure of alternating-current generators to operate in parallel. (6) Hunting of synchronous converters. (c ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-07", "section_label": "Lecture 7: High Frequency Oscillations And Surges", "section_title": "High Frequency Oscillations And Surges", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3508-3780", "status": "candidate", "occurrence_count": 32, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-07/", "snippets": [ "SEVENTH LECTURE HIGH FREQUENCY OSCILLATIONS AND SURGES 1\"^ N an electric circuit, in addition to the power consump- tion by the resistance of the lines, an energy storage ■^ occurs as electrostatic energy, or electrostatic charge due to the voltage on the line (capacity) ; and as electromag- ne ...", "... ding change of the stored energy; that is, a readjustment of the stored energy e^C in the system, the electrostatic energy and the electro- i'L magnetic energy — — , from the previous to the changed cir- cuit conditions. This readjustment occurs by an oscillation, that is, a series of waves of voltage and of current, which gradually decreases in intensity, that is, dies out. ' These oscillating voltages and currents are the result of the readjustment of the stored energy of the circuit to a sudden change of cond ...", "... ctro- i'L magnetic energy — — , from the previous to the changed cir- cuit conditions. This readjustment occurs by an oscillation, that is, a series of waves of voltage and of current, which gradually decreases in intensity, that is, dies out. ' These oscillating voltages and currents are the result of the readjustment of the stored energy of the circuit to a sudden change of conditions, and are dependant upon the stored energy of the circuit, but not upon the generator frequency or wave shape ; therefore they occ ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-52", "section_label": "Chapter 3: Standing Waves", "section_title": "Standing Waves", "kind": "chapter", "sequence": 52, "number": 3, "location": "lines 29316-30243", "status": "candidate", "occurrence_count": 31, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "snippets": [ "... + (BlS + « - B2e~st)smkl]} Equations (113) and (114) represent a gradual or exponential circuit discharge, and the distribution still is a trigonometric function of the distance, that is, ^ wave distribution, but dies out gradually with the time, without oscillation. C. Critical case, hence, o, = 0, (115) (116) and c2 = 0, raL (117) and all the main waves and their reflected waves coincide when substituting h = 0, (116), (117) in (50) and (51). Hence, writing and gives B = C, - C2 + ...", "... n In the critical case, (119) and (120), the wave is distributed as a trigonometric function of the distance, but dies out as a simple exponential function of the time. 15. An electrical standing wave thus can have two different forms: it can be either oscillatory in time or exponential in time, that is, gradually changing. It is interesting to investigate the conditions under which these two different cases occur. The transition from gradual to oscillatory takes place at k* = m2LC; (121) for larger values of k ...", "... wave thus can have two different forms: it can be either oscillatory in time or exponential in time, that is, gradually changing. It is interesting to investigate the conditions under which these two different cases occur. The transition from gradual to oscillatory takes place at k* = m2LC; (121) for larger values of k the phenomenon is oscillatory; for smaller, exponential or gradual. Since k is the wave length constant, the wave length, at which the phenomenon ceases to be oscillatory in time and becomes a gr ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-29", "section_label": "Chapter 7: Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "section_title": "Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "kind": "chapter", "sequence": 29, "number": 7, "location": "lines 6798-7825", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "snippets": [ "... [T^ ~l fi - cos (00 + 7) - xcr sin (00 + 7) I - - 2 xc sin (0 + 7) (21) Here again three terms exist, namely: a permanent term, a transient term depending only on E and 00, and a transient term depending on iQ and e0. 57. In the trigonometric or oscillatory case, r2 < 4 a; xc, s be- comes imaginary, and equations (18) and (19) therefore contain complex imaginary exponents, which have to be eliminated, since the complex imaginary form of the equation obviously is only apparent, the phenomenon being real. Su ...", "... um value of impressed e.m.f. Then (20) and (21) give i = 4.78 cos (6 - 16°) + r°'75' (2.7 0 - 4.6) and e,= 358 sin (6 - 16°) - £-°-75'(410# - 99). Here also no value of 00 exists at which the transient term disappears. 69. The most important is the oscillating case, r2 < 4 x xc, since it is the most common in electrical circuits, as underground cable systems and overhead high potential circuits, and also is practically the only one in which excessive currents or excessive voltages, and thereby dangerous phenome ...", "... d (25), which give the current as E( . , { sm (0 — Xc f 2xTsin00cosV/-c0 L r x (26) and the potential difference at the condenser terminals as cos# cos V -H where cos xc sin , (27) xc, and 7 = - 90°. (28) In this case an oscillating term always exists whatever the value of 00, that is, the point of the wave, where the circuit is started. The frequency of oscillation therefore is /o or, approximately, 2x\" _ 4X2 (29) where/ = fundamental frequency. Substituting x = ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... r : from very low frequencies, that is only a few millions of millions of cycles per second, up to many times higher frequencies. We can get, if we desire, still very much lower fre- quencies, as electromagnetic waves, such as the radiation sent out by an oscillating current or an alternating current ; but the radiations which we get from heated bodies are all of extremely high frequency, compared with the customary frequencies of electric currents. At the same time they cover a very wide range of frequencies, many oc ...", "... ent rate of vibration of the atom, by resonance this vibration of the atom must rapidly increase in intensity until the atom breaks away from the others, or the molecule breaks up, that is, the chemical combination is split up. The inherent frequency of oscillation of the atom seems to be of about of the same magnitude as the visible radia- tion, or rather of a little higher frequency; that is, if the atoms are left to vibrate freely as under the influence of an electric current in the arc, then we get radiations of ...", "... 5 X 10* K. W. Estimating the energy of the discharge, as approximated from the photometric consideration, as 10,000 K. W. seconds, the duration of the discharge would be: 10V5 X 10* = 2 x 10\"* sec, or two-millionths of a second. The discharge probably is oscillatory. In view of the high resistance of the discharge path, the damping effect must be very great, that is, a very large part or nearly all the energy LIGHTNING AND LIGHTNING PROTECTION 269 is expended in the first half-wave ; that is, the discharge consist ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "... 118. The difference of phase, w, between current, /, and E.M.F., Ey at any point, x, of the line, is determined by DISTRIBUTED CAPACITY. 171 the equation, Z?(cos«+/sin£) =y, : \\j JsTI71 where Z> is a constant. Hence, w varies from point to point, oscillating around a medium position, wx, which it approaches at infinity. This difference of phase, C>x, towards which current and E.M.F. tend at infinity, is determined by the expression, ^(cos . .. , (/ or, substituting for E and /their values, and since e~a* ...", "... ifference and phase angle therefrom. As seen from these diagrams, for wattless receiving cir- cuit, current and E.M.F. oscillate in intensity inversely to ZJ 7 6sa 7 rig. 87. DISTRIBUTED CAPACITY. 175 each other, with an amplitude of oscillation gradually de- creasing when passing from the receiving circuit towards the generator, while the phase angle between current and E.M.F. oscillates between lag and lead with decreasing am- plitude. Approximately maxima and minima of current co- incide with ...", "... he angle between current and change of E.M.F., tan a = - = 4, and the angle 8 the angle between E.M.F. and change of current, tan 8 = - = 20 in above instance. g \\ Fig. 89. DISTRIBUTED CAPACITY. 177 With non-inductive load, Fig. 87, these oscillations of intensity have almost disappeared, and only traces of them are noticeable in the fluctuations of the phase angle and the relative values of current and E.M.F. along the line. Towards the generator end of the line, that is towards rising power, the cu ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-16", "section_label": "Chapter 18: Surging Of Synchronous Motors", "section_title": "Surging Of Synchronous Motors", "kind": "chapter", "sequence": 16, "number": 18, "location": "lines 20975-21712", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-16/", "snippets": [ "... wer, the excess of power being converted into momentum, it is: P - Po = d£ • l» and. substituting <'4> and (7) into (8) and rearranging: C*-° sin * sin (a - fi - *) + 2 t/AT 0 ™ = «• l»> 'Assuming 5 as a small angle, that is, considering only small oscillations, it is: . 6 6 Sln2 = 2 sin [a - 0 - ^ J = sin (« - £) ; hence, substituted in (18): ^ 5 sin (« - 0) + 4 ir/Af 0 jj]» - 0, (10) and, substituting: ce0«in(a-/8) m. 4 rfzMo it is: (14) 292 ELECTRICAL APPARATUS This differential eq ...", "... (12) gives: aAece + ACU™ = 0, a + C2 = 0, C = ± V- a. . 168. 1. If a <0, it is: 5 = A*+me + A*-m\\ where: / / ee0 sin (0 — a) \\ 4 tt/zA/o Since in this case, e*m9 is continually increasing, the syn- chronous motor is unstable. That is, without oscillation, the synchronous motor drops out of step, if 0 > a. 2. If a > 0, it is, denoting: , ^/- , /ee0sin (a - 0) \\ 4 TT/^Af o or, substituting for €+;n* and €+\"\"4* the trigonometric functions: 6 = (Ai + Ao) cos n0 + j (Ax — *42) sin n$t or, 5 = B cos ( ...", "... oting: , ^/- , /ee0sin (a - 0) \\ 4 TT/^Af o or, substituting for €+;n* and €+\"\"4* the trigonometric functions: 6 = (Ai + Ao) cos n0 + j (Ax — *42) sin n$t or, 5 = B cos (n0 + 7). (15) That is, the synchronous motor is in stable equilibrium, when oscillating with a constant amplitude B, depending upon the initial conditions of oscillation, and a period, which for small oscillations gives the frequency of oscillation: f „f _ //ee0 sin (a - 0) As instance, let: oo sin pc/> (5; would approximately represent the instantaneous value of the phase angle co where: pf= frequency of the beat, or the periodic variation of the phase angle. [In the derivation of equations (3) and (4), co has been assumed as ...", "... d thus also is of no further interest. The third term: p'Y=-!|cos(2a>-a) is of the low frequency of the beat, or the current fluctuation between the two alternators: pf. It thus represents the energy transfer between the two alternators, during their periodic oscillations, or, resolving the last equation: E 2 E 2 p'Y= TT sin a sin 2a> =- cos a cos w. 2z 2z The second term: E 2 p'Y'= - cos a. cos a> has the same sign for negative w, that is, when the machine is lagging, as for positive w when the machine is leading, thus it rep ...", "... a. cos a> has the same sign for negative w, that is, when the machine is lagging, as for positive w when the machine is leading, thus it represents no energy transfer between the machines. The synchronizing power, or energy transfer during the synchro- nizing oscillations of two alternators, which are out of phase but in synchronism, thus is given by the expression: E 2 P=- sin a sin 2co (6) Thus, the synchronizing power p, is a maximum, and is : _E 2 . for a = 90 degrees, that is, if the resistance r of the circuit between th ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 6125-6803", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-09/", "snippets": [ "LECTURE IX. OSCILLATIONS OF THE COMPOUND CIRCUIT. 38. The most interesting and most important application of the travehng wave is that of the stationary oscillation of a com- pound circuit, as industrial circuits are never uniform, but consist of sections of different characteri ...", "LECTURE IX. OSCILLATIONS OF THE COMPOUND CIRCUIT. 38. The most interesting and most important application of the travehng wave is that of the stationary oscillation of a com- pound circuit, as industrial circuits are never uniform, but consist of sections of different characteristics, as the generating system, transformer, line, load, etc. Oscillograms of such circuits have been shown in the previous lecture. If we ...", "... represent power dissipation, and thus represents power transfer. That is, §1 = Wo \"~ Ui, S2 = Uo — II2, (1) It thus follows that in a compound circuit, if Uo is the average exponential time decrement of the complete circuit, or the average 108 OSCILLATIONS OF THE COMPOUND CIRCUIT. 109 power-dissipation constant of the circuit, and u that of any section, this section must have a second exponential time decrement, s = Uq — u, (2) which represents power transfer from the section to other sections, or, if s ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 5521-6088", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "snippets": [ "LECTURE IX. OSCILLATIONS OF THE COMPOUND CIRCUIT. 38. The most interesting and most important application of the traveling wave is that of the stationary oscillation of a com- pound circuit, as industrial circuits are never uniform, but consist of sections of different character ...", "LECTURE IX. OSCILLATIONS OF THE COMPOUND CIRCUIT. 38. The most interesting and most important application of the traveling wave is that of the stationary oscillation of a com- pound circuit, as industrial circuits are never uniform, but consist of sections of different characteristics, as the generating system, transformer, line, load, etc. Oscillograms of such circuits have been shown in the previous lecture. If we ...", "... ot represent power dissipation, and thus represents power transfer. That is, 51 = U0 — Ui, 52 = UQ — Uz, (1) It thus follows that in a compound circuit, if u0 is the average exponential time decrement of the complete circuit, or the average 108 OSCILLATIONS OF THE COMPOUND CIRCUIT. 109 power-dissipation constant of the circuit, and u that of any section, this section must have a second exponential time decrement, S = UQ — U, (2) which represents power transfer from the section to other sections, or, if s ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-51", "section_label": "Chapter 2: Discussion Of General Equations", "section_title": "Discussion Of General Equations", "kind": "chapter", "sequence": 51, "number": 2, "location": "lines 28695-29315", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "snippets": [ "... e+w for rising, s~hl for decreasing I, but the wave dies out with the increasing time t by £-(tt+s>< = s\"\"* e~st, that is, faster than the first wave. If the amplitude of the wave remained constant throughout the circuit — as would be the case in a free oscillation of the circuit, in which the stored energy of the circuit is dissipated, but no power supplied one way or the other — that is, if h = 0, from equation (56) s = 0; that is, both waves coincide and form one, which dies out with the time by the decrement e~u ...", "... inversely in i', e'. DISCUSSION OF GENERAL EQUATIONS 433 It is interesting to note that in a circuit having resistance, inductance, and capacity, the mathematical expressions of the two cases of energy flow; that is, the gradual or exponential and the oscillatory or trigonometric, are both special cases of the equations (60) and (61), corresponding respectively to q = o, k = 0 and to h = 0, s = 0. 8. In the equations (50) and (51) qt = 2x gives the time of a complete cycle, that is, the period of the wave, a ...", "... , 1 ) (64) U + S and h is the distance attenuation constant of the wave, L -I. (65) 9. If the frequency of the current and e.m.f. is very high, thousands of cycles and more, as with traveling waves, lightning disturbances, high-frequency oscillations, etc., q is a very large quantity compared with s, u, m, h, k, and k is a large quantity compared with h, then by dropping in equations (50) to (61) the terms of secondary order the equations can be simplified. From (54), ^ = V(s2 + q2 - m2)2 + 4 q2m2 ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-09", "section_label": "Lecture 9: Hunting Of Synchronous Machines", "section_title": "Hunting Of Synchronous Machines", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 4218-4594", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-09/", "snippets": [ "... es are thrown together out of phase, or brought out of the phase by some cause (as the beat of an en- gine, or the change of load of a synchronous motor) then the two machines pull each other in phase again, oscillate a few times against each other, which oscillation gradually decreases and dies out, and the machines run steadily. If the oscillations do not decrease, but continue, the machines are said to be hunting. If the oscillation is small it may do no harm ; if it is greater, it may cause fluctuation of volta ...", "... beat of an en- gine, or the change of load of a synchronous motor) then the two machines pull each other in phase again, oscillate a few times against each other, which oscillation gradually decreases and dies out, and the machines run steadily. If the oscillations do not decrease, but continue, the machines are said to be hunting. If the oscillation is small it may do no harm ; if it is greater, it may cause fluctuation of voltage, resulting in flick- ering of lights, etc. ; if it gets very large, it may throw the ...", "... pull each other in phase again, oscillate a few times against each other, which oscillation gradually decreases and dies out, and the machines run steadily. If the oscillations do not decrease, but continue, the machines are said to be hunting. If the oscillation is small it may do no harm ; if it is greater, it may cause fluctuation of voltage, resulting in flick- ering of lights, etc. ; if it gets very large, it may throw the ma- chines out of step. Some causes of hunting are: 1st. Magnetic lag. 2nd. Pulsat ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-55", "section_label": "Chapter 6: Transition Points And The Complex Circuit", "section_title": "Transition Points And The Complex Circuit", "kind": "chapter", "sequence": 55, "number": 6, "location": "lines 32709-33527", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "snippets": [ "CHAPTER VI. TRANSITION POINTS AND THE COMPLEX CIRCUIT. 40. The discussions of standing waves and free oscillations in Chapters III and V, and traveling waves in Chapter IV, apply directly only to simple circuits, that is, circuits comprising a con- ductor of uniformly distributed constants r, L, g, and C. Indus- trial electric circuits, however, never are simple circu ...", "... owever, give a very high and destructive voltage in the reactive coil, due to its high L, and thus in the circuit beyond the reactive coil. In the investigation of the effect of a transient phenomenon originating in one section of a complex circuit, as an oscillating arc on an underground cable, on other sections of the circuit, as the generating station, even a very great change of circuit constants cannot be considered as a reflection point. Since this is the most important case met in industrial practice, as distur ...", "... ect- ively, of the section i of the circuit, per unit length, for instance, per mile, in a line, per turn in a transformer coil, etc. In a complex circuit the time variable t is the same throughout the entire circuit, or, in other words, the frequency of oscillation, as represented by q, and the rate of decay of the oscillation, as represented by the exponential function of time, must be the same throughout the entire circuit. Not so, however, with the distance variable Z; the wave length of the oscillation and its r ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-07", "section_label": "Chapter 3: The Natural Period Of The Transmission Line. 320", "section_title": "The Natural Period Of The Transmission Line. 320", "kind": "chapter", "sequence": 7, "number": 3, "location": "lines 836-874", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-07/", "snippets": [ "CHAPTER III. THE NATURAL PERIOD OF THE TRANSMISSION LINE. 320 27. The oscillation of the transmission line as condenser. 320 28. The conditions of free oscillation. 321 29. Circuit open at one end, grounded at other end. 322 30. Quarter-wave oscillation of transmission line. 323 31. Frequencies of line discharges, and complex disch ...", "CHAPTER III. THE NATURAL PERIOD OF THE TRANSMISSION LINE. 320 27. The oscillation of the transmission line as condenser. 320 28. The conditions of free oscillation. 321 29. Circuit open at one end, grounded at other end. 322 30. Quarter-wave oscillation of transmission line. 323 31. Frequencies of line discharges, and complex discharge wave. 327 32. Example of discharge of line of constant voltage and zero c ...", "CHAPTER III. THE NATURAL PERIOD OF THE TRANSMISSION LINE. 320 27. The oscillation of the transmission line as condenser. 320 28. The conditions of free oscillation. 321 29. Circuit open at one end, grounded at other end. 322 30. Quarter-wave oscillation of transmission line. 323 31. Frequencies of line discharges, and complex discharge wave. 327 32. Example of discharge of line of constant voltage and zero current. 329 33. Example of short-circuit oscillation of line. 331 34. Circuit grounded at ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-24", "section_label": "Chapter 2: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 24, "number": 2, "location": "lines 1993-2658", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "snippets": [ "... ctance of the circuit, overreaches and discharges the condenser farther than down to the impressed e.m.f. e0, so that after the discharge current stops again a charg- ing current — now less than the initial charging current - starts, and so by a series of oscillations, overcharges and under- charges, the condenser gradually charges itself, and ultimately the current dies out. Fig. 3 shows the oscillating charge of a condenser through an inductive circuit, by a continuous impressed e.m.f. e0. The current is represente ...", "... ent stops again a charg- ing current — now less than the initial charging current - starts, and so by a series of oscillations, overcharges and under- charges, the condenser gradually charges itself, and ultimately the current dies out. Fig. 3 shows the oscillating charge of a condenser through an inductive circuit, by a continuous impressed e.m.f. e0. The current is represented by i, the potential difference at the con- denser terminals by e, with the time as abscissas. The con- stants of the circuit are: r = 40 oh ...", "... zero, but a current exists immediately after closing the circuit, as a transient phenomenon; a temporary current, steadily increasing and then decreasing again to zero, or con- sisting of a number of alternations of successively decreasing amplitude : an oscillating current. If the circuit contains no resistance and inductance, the cur- rent into the condenser would theoretically be infinite. That f s N 6 1200 / A \\ \\ ^ x^ * H 4 7? 8004— f 1 \\ \\ ^\\? - — 4 oSOOJ-4 / \\ ^ x* ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-35", "section_label": "Chapter 13: Transient Term Of The Rotating Field", "section_title": "Transient Term Of The Rotating Field", "kind": "chapter", "sequence": 35, "number": 13, "location": "lines 13936-14548", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-35/", "snippets": [ "... 0 1170 1260 1350 1440 Fig. 48. Transient term of polyphase magnetomotive force. constants np =3, or a three-phase system; SF = 667, and Z = r - jx = 0.32 - 4 j ; hence, /0 - 1000 (1 - £ — 1.080 cos d), with 6 as abscissas, showing the gradual oscillatory approach to constancy. 109. The direction, 6Q = 0, is, however, not the direction in which the resultant m.m.f. in equation (8) is a maximum, but the maximum is given by df = 0, this gives hence, sin (0 - 60) + s x sin 00 = 0, cot 0n = ...", "... n 60 time-degrees — to its normal value, overreaches and exceeds it by 78 per cent, then drops down again below normal, by 60 per cent, rises 47 per cent above normal, drops 37 per cent below normal, rises 28 per cent above normal, and thus by a series of oscillations approaches the normal value. The maximum value of the resultant m.m.f. starts in position 198 TRANSIENT PHENOMENA 85 time-degrees ahead, in the direction of rotation, but has in half a period dropped back to the normal position, that is, the position ...", "... , that is, does not depend upon the point of the wave, 0 = r, at which the circuit is closed, while in all preced- ing investigations the transient term depended upon the point of the wave at which the circuit was closed, and that this tran- sient term is oscillatory. In the preceding chapter, in circuits containing only resistance and inductance, the transient term has always been gradual or logarithmic, and oscillatory phenom- ena occurred only in the presence of capacity in addition to in- ductance. In the rotating ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-40", "section_label": "Chapter 4: Arc Rectification", "section_title": "Arc Rectification", "kind": "chapter", "sequence": 40, "number": 4, "location": "lines 17755-19259", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "snippets": [ "... rent mercury arc rectifier. 24. As illustrations of the above phenomena are shown in Fig. 66 the performance curves of a small constant-current rec- tifier, and in Figs. 67 to 76 oscillograms of this rectifier. Interesting to note is the high frequency oscillation at the ter- mination of the jump of the potential difference cC (Fig. 60) which represents the transient term resulting from the electro- static capacity of the transformer. At the end of the period of overlap of the two rectifying arcs one of the anode c ...", "... ge depending upon the impressed e.m.f.; that is, the L — of the circuit. An increase of inductance L dt di increases the angle of overlap and so decreases the — , hence does CLL not greatly affect the amplitude, but decreases the frequency of this oscillation. An increase of — at constant L, as resulting dt from a decrease of the angle of overlap by delayed starting of the arc, caused by a defective rectifier, however increases the amplitude of this oscillation, and if the electrostatic capacity is high, an ...", "... mplitude, but decreases the frequency of this oscillation. An increase of — at constant L, as resulting dt from a decrease of the angle of overlap by delayed starting of the arc, caused by a defective rectifier, however increases the amplitude of this oscillation, and if the electrostatic capacity is high, and therefore the damping out of the oscillation slow, the Fig. 77. E.m.f. between rectifier anodes. oscillation may reach considerable values, as shown in oscillo- gram, Fig. 77, of the potential difference ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... = 0.0012 conden- sive susceptance, for various values of non-inductive, inductive, and condensive load. Starting with the complete equations of the long-distance transmission line, as given in \"Theory and Calculation of Transient Electric Phenomena and Oscillations,\" Section III, paragraph 9, and considering that for every one of the various power-factors, lag, and lead, a sufficient number of values 249 250 ENGINEERING MATHEMATICS. have to be calculated to give a curve, the amount of work appears hopeless ...", "... n electric systems, calculating the discharge capacity of lightning arres- ters, etc., the magnitude of the quantity is often sufficient. In 254 ^ ENGINEERING MATHEMATICS. calculating the critical speed of turbine alternators, or the natural period of oscillation of synchronous machines, the same applies, since it is of importance only to see that these speeds are sufficiently^ remote from the normal operating speed to give no trouble in operation. (b) Approximate calculation, requiring an accuracy of one or a f ...", "... alues, the time of the swing, or the period ot the pendulum, can no longer be assumed as constant and an exact calculation of the motion of the pendulum by elliptic functions becomes necessary. In electrical engineering, one has frequently to deal w^ith oscillations similar to those of the pendulum, for instance, in the hunting or surging of synchronous machines. In general, the frequency of oscillation is assumed as constant, but where, as in cumulative hunting of synchronous machines, the amplitude of the swing rea ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "... is current; if it drops below the disruptive voltage the current ceases, but begins again spontaneously as soon as, the voltage rises above the disruptive value. Disruptive conduction thus occurs equally well with unidirectional, with alternating, or with oscillating currents. It is best studied with alternating or oscillating voltage supply, as with a steady unidirectional voltage, the disruptive conduction, that is, conduction by the gas filling the space between the electrodes, tends to change to continuous conduct ...", "... ent ceases, but begins again spontaneously as soon as, the voltage rises above the disruptive value. Disruptive conduction thus occurs equally well with unidirectional, with alternating, or with oscillating currents. It is best studied with alternating or oscillating voltage supply, as with a steady unidirectional voltage, the disruptive conduction, that is, conduction by the gas filling the space between the electrodes, tends to change to continuous conduction, by vapors forming at the negative elec- trode and gradua ...", "... re (Fig. 31) the gradual change from the static spark to the Geissler tube glow: in a closed glass tube G, I have two needle-shaped terminals, 5 cm. distant from each other, and supply them with energy from a small 33, 000- volt trans- former. You see the oscillating static spark at atmospheric pressure. By now exhausting the tube, while the voltage is maintained at the terminals, you can watch the gradual change from the static spark to the Geissler tube glow. In this experi- ment, a small condenser, a Leyden jar, is ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-18", "section_label": "Chapter 5: Free Oscillations. 478", "section_title": "Free Oscillations. 478", "kind": "chapter", "sequence": 18, "number": 5, "location": "lines 1148-1186", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-18/", "snippets": [ "CHAPTER V. FREE OSCILLATIONS. 478 28. Types of waves: standing waves, traveling waves, alter- nating-current waves. 478 29. Conditions and types of free oscillations. 478 30. Terminal conditions. 480 31. Free oscillation as standing wave. 481 32. Quarter-wave and half-wave os ...", "CHAPTER V. FREE OSCILLATIONS. 478 28. Types of waves: standing waves, traveling waves, alter- nating-current waves. 478 29. Conditions and types of free oscillations. 478 30. Terminal conditions. 480 31. Free oscillation as standing wave. 481 32. Quarter-wave and half-wave oscillation, and their equa- tions. 482 33. Conditions under which a standing wave is a free oscilla- tion, and the power nodes of the free ...", "CHAPTER V. FREE OSCILLATIONS. 478 28. Types of waves: standing waves, traveling waves, alter- nating-current waves. 478 29. Conditions and types of free oscillations. 478 30. Terminal conditions. 480 31. Free oscillation as standing wave. 481 32. Quarter-wave and half-wave oscillation, and their equa- tions. 482 33. Conditions under which a standing wave is a free oscilla- tion, and the power nodes of the free oscillation. 485 34. Wave length, and angular measure of ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-03-record", "section_label": "Report Record 4: Record of Four Troubles", "section_title": "Record of Four Troubles", "kind": "report-record", "sequence": 4, "number": 4, "location": "PDF pages 16-27, lines 1139-2164", "status": "pdf-text-extracted-candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-03-record/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-03-record/", "snippets": [ "... the ma- chines thus oscillate against each other, while the interchange current between the machines fluctuates between a maximum value at maximum phase difference, and zero or a minimum value when machines are in phase. If there were no damping effects, this oscillation would con- tinue with constant amplitude. Due to the damping effects exerted mainly by the lag of the field flux behind the resultant field excitation (the armature reaction component of the synchronous impedance), the amplitude of the oscillation steadily di ...", "... fects, this oscillation would con- tinue with constant amplitude. Due to the damping effects exerted mainly by the lag of the field flux behind the resultant field excitation (the armature reaction component of the synchronous impedance), the amplitude of the oscillation steadily diminishes, until the oscillation disappears. That is, the interchange current between two alternators which are in synchronism but out of phase, pulsates, with approximate- ly constant frequency of the beat, but with an amplitude, which grad- ually ...", "... th constant amplitude. Due to the damping effects exerted mainly by the lag of the field flux behind the resultant field excitation (the armature reaction component of the synchronous impedance), the amplitude of the oscillation steadily diminishes, until the oscillation disappears. That is, the interchange current between two alternators which are in synchronism but out of phase, pulsates, with approximate- ly constant frequency of the beat, but with an amplitude, which grad- ually decreases to nothing. If the EMFs of the tw ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2485-3386", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-04/", "snippets": [ "... aches the final value by a series of oscil- lations ; that is, it first reaches beyond the permanent value, then drops below it, rises again beyond it, etc. 4 cycles Fig, 20. — Starting Transient of Rotating Field: Rectangular Form. \"^e have here an oscillatory transient, produced in a system with only one form of stored energy (magnetic energy), by the combination of several simple exponential transients. How- ever, it must be considered that, while energy can be stored in one form only, as magnetic energy, it ...", "... e point of the wave at which the circuit is closed. That is, while the individual transients of the three three-phase currents vary in shape with the point of the wave at which they start, as shown in Fig. 17, their polyphase resultant always has the same oscillating approach to a uniform rotating field, of duration T = — - r The maximum value, which the magnetic field during the transi- tion period can reach, is limited to less than double the final value, as is obvious from the construction of the field. Fig. 19. ...", "... the armature currents thus unsymmetrical, as seen in Fig. 22B, their resultant polyphase m.m.f. also shows a transient, the transient of the rotating magnetic field discussed in paragraph 18. That is, it approaches the curve F of Fig. 21 C by a series of oscillations, as indicated in Fig. 21E. Since the resultant m.m.f. of the machine, which produces the flux, is the difference of the field excitation. Fig. 2 ID and the armature reaction, then if the armature reaction shows an initial os- cillation, in Fig. 21 E, th ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2162-2971", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "snippets": [ "... ches the final value by a series of oscil- lations ; that is, it first reaches beyond the permanent value, then drops below it, rises again beyond it, etc. 3 4 cycles Fig. 20. — Starting Transient of Rotating Field: Rectangular Form. We have here an oscillatory transient, produced in a system with only one form of stored energy (magnetic energy), by the combination of several simple exponential transients. How- ever, it must be considered that, while energy can be stored in one form only, as magnetic energy, it ...", "... e point of the wave at which the circuit is closed. That is, while the individual transients of the three three-phase currents vary in shape with the point of the wave at which they start, as shown in Fig. 17, their polyphase resultant always has the same oscillating approach to a uniform rotating field, of duration T — — • r The maximum value, which the magnetic field during the transi- tion period can reach, is limited to less than double the final value, as is obvious from the construction of the 'field, Fig. 19 ...", "... the armature currents thus unsymmetrical, as seen in Fig. 225, their resultant polyphase m.m.f. also shows a transient, the transient of the rotating magnetic field discussed in paragraph 18. That is, it approaches the curve F of Fig. 21 C by a series of oscillations, as indicated in Fig. 21E. Since the resultant m.m.f. of the machine, which produces the flux, is the difference of the field excitation, Fig. 21 D and the armature reaction, then if the armature reaction shows an initial os- cillation, in Fig. 21 E, th ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... the transformer is connected to the 240-volt 60-cycle circuit through a rheostat R to limit the current. The transformer charges the condenser, and when the voltage of the condenser has risen sufficiently high it discharges through the spark gaps I by an oscillation of high frequency (about 500,000 cycles), then charges again from the transformer, discharges through the gap, etc. As several such condenser dis- charges occur during each half wave of alternating supply voltage the light given by the discharge appears c ...", "... C of the apparatus which I used for operating the ultra-violet arc, to a spark gap Gv of which the one side is con- nected to ground Bv the other side to a vertical aluminum rod Alf about 8 feet long. The charge and discharge of the aluminum rod Al by the oscillating condenser current, send out an electric wave of about 50 feet length. This wave passes through you, and when striking the aluminum rod A2 back of you, induces therein an electric charge. A2 is separated from ground B2 by a narrow spark gap G2 between grap ...", "... , as shown in Fig. 13. On these waves the velocity of propagation < EN ERGY-SU PPLY- o — ^^ — o FIG. 13. has been measured by Herz by producing standing waves by combination of main wave and reflected wave. Still much higher frequencies are the oscillations between the cylinders of multi-gap lightning arresters, and the limit of fre- quency of electric waves would probably be given by the oscilla- ting discharge of two small spheres against each other when separated by a narrow gap. It probably is at about 5 ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-84", "section_label": "Apparatus Section 5: Synchronous Converters: Armature Reaction", "section_title": "Synchronous Converters: Armature Reaction", "kind": "apparatus-section", "sequence": 84, "number": 5, "location": "lines 15161-15475", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-84/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-84/", "snippets": [ "... rnating current, and with full intensity, and since it is in quadrature with the field excitation, tends to shift the magnetic flux rapidly across the field poles, and thereby tends to cause sparking and power losses. This oscillating reaction is, however, reduced by the damping effect of the mag- netic field structure. It is somewhat less in the two-circuit single-phase converter. Since in consequence hereof the commutation of the single- phase converter ...", "... osses of power, which is in quadrature with the field excitation or distorting, but of negligible magnitude. 2. The armature reaction due to the wattless component of alternating current where such exists. 3. An effect of oscillating nature, which may be called a higher harmonic of armature reaction. The direct current, as rectangular alternating current in the armature, changes in phase from coil to coil, while the alternating current is the same in ...", "... o the time of motion of the armature through the angle between adjacent alternating leads; that is, double frequency in a single-phase converter (in which it is equal in magnitude to the direct-current reaction, and is the oscillating armature reaction discussed above), sextuple frequency in a three-phase converter, and quadruple frequency in a four- phase converter. The amplitude of this oscillation in a polyphase converter is small, arid its influence up ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... ght requires to travel four times the length of the line; in other words, the number of periods, or frequency of the impressed alternating e.m.fs., in resonance condition, is the velocity of light divided by four times the length of the line; or, in free oscillation or resonance condition, the length of the line is one quarter wave length. 279 280 TRANSIENT PHENOMENA If then I = length of line, S = speed of light, the frequency of oscillations or natural period of the line is — '• \"4? or, with I given in mi ...", "... y of light divided by four times the length of the line; or, in free oscillation or resonance condition, the length of the line is one quarter wave length. 279 280 TRANSIENT PHENOMENA If then I = length of line, S = speed of light, the frequency of oscillations or natural period of the line is — '• \"4? or, with I given in miles, hence S = 188,000 miles per second, it is , 47,000 /o = — j- cycles. (2) To get a resonance frequency as low as commercial frequencies, as 25 or 60 cycles, would require Z == 1880 ...", "... osite. 296 TRANSIENT PHENOMENA The difference of space phase T between current I and e.m.f. E at any point I of the line is determined by the equation Tjl m (cos r + j sin r) = j > (34) where w is a constant. Hence, r varies from point to point, oscillating around a medium position, r^ , which it approaches at infinity. This difference of phase, TW, towards which current and e.m.f. tend at infinity, is determined by the expression m (COST.+ /sin r J = - , M -h = oo or, substituting for E and 7 their v ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-48", "section_label": "Chapter 8: Velocity Of Propagation Of Electric Field", "section_title": "Velocity Of Propagation Of Electric Field", "kind": "chapter", "sequence": 48, "number": 8, "location": "lines 26095-27002", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "snippets": [ "... or to the point under consideration, or, in other words, the electric field lags the more, the greater the distance from the conductor. Since the velocity of propagation is very high — about 3 X 1010 centimeters per second — the wave of an alternating or oscillating current even of very high frequency is of considerable length ; at 60 cycles the wave length is 0.5 X 109 centimeters, and even at a million cycles the wave length is 30,000 centimeters, or about 1000 feet, that is, very great compared with the distance t ...", "... 1.5 X 105 = 0.94 mile, a = 4.19 X 10~5; hence, L= (57.2 + 9.4 j) 10~6 henrys, Z= (11.8 - 71.8 j) ohms, or, absolute, z = 72.8 ohms. Hence, the voltage required by i = IjOO amperes is e = 7280 volts, and the power radiated into space during the oscillation is p = tfr = 118 kilowatts. 74. Since the effective resistance of the total electromagnetic radiation, from the conductor surface to infinity, is, by (25), -9, (27) it follows that the effective resistance, of electromagnetic radia- tion of a condu ...", "... NSIENT PHENOMENA hence, approximately, sil ald = 0.1663 X 10~3, col ald = 0.1663 X 10~3, and LM = (- 0.227 + 1.026 j) 10~9 henrys, Z = (0.387 + 0.086 /) 10~3 ohms, or, absolute, Lm = 1.051 X 10-' henrys, z = 0.3964 X 10~3 ohms. Hence, with an oscillating current of 100 amperes in the sending antenna, the oscillating voltage generated in the receiving an- tenna, 100 miles distant, is e = iz = 0.03964 volts. C. Capacity of a sphere in space. 77. The electrostatic field of a sphere in free space decreas ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-49", "section_label": "Chapter 9: High-Frequency Conductors", "section_title": "High-Frequency Conductors", "kind": "chapter", "sequence": 49, "number": 9, "location": "lines 27003-27760", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "snippets": [ "CHAPTER IX. HIGH-FREQUENCY CONDUCTORS. 80. As the result of the phenomena discussed in the preceding chapters, conductors intended to convey currents of very high frequency, as lightning discharges, high frequency oscillations of transmission lines, the currents used in wireless telegraphy, etc., cannot be calculated by the use of the constants derived at low frequency, but effective resistance and inductance, and therewith the power consumed by the conductor, and the voltage d ...", "... e same current, as a copper conductor of the same circumference; that is, iron is nearly as good a con- ductor as copper, when considering a finite section of an infinitely long conductor without return conductor, that is, approximately, when dealing with oscillatory high frequency discharges, as lightning. It is interesting to note the high power component of impe- dance existing at high frequencies and mainly due to the radia- tion resistance, which causes a rapid decay of the oscillation, due to the high power fa ...", "... mately, when dealing with oscillatory high frequency discharges, as lightning. It is interesting to note the high power component of impe- dance existing at high frequencies and mainly due to the radia- tion resistance, which causes a rapid decay of the oscillation, due to the high power factor. The internal constants r1 and x1 are equal, and in the most important range of high frequencies, from 10,000 to 1,000,000 cycles, the external constants r2 and x2 are not very different from each other and their plotted curv ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-50", "section_label": "Chapter 1: General Equations", "section_title": "General Equations", "kind": "chapter", "sequence": 50, "number": 1, "location": "lines 27761-28694", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "snippets": [ "... ity, as r, L, g, C, are denoted the effec- tive resistance, inductance, conductance, and capacity, respec- tively, per unit length of circuit. The unit of length of the circuit- may be chosen as is convenient, thus : the centimeters in the high- frequency oscillation over the multigap lightning arrester circuit, or a mile in a long-distance transmission circuit or high-potential cable, or the distance of the velocity of light, 300,000 km., etc. The permanent values of current and e.m.f. in such circuits of distribute ...", "... he circuit in question, the integration con- stants in the equations also change correspondingly. Special cases of these general equations then are all the phe- nomena of direct currents, alternating currents, discharges of reactive coils, high-frequency oscillations, etc., and the difference between these different circuits is due merely to different values of the integration constants. 2. In a circuit or a section of a circuit containing distributed resistance, inductance, conductance, and capacity, as a trans- mi ...", "... t another point — voltage at the gen- amperes erator end, load at the receiving end of the circuit. Current and voltage given at one time t0 as function of the distance I — distribution of voltage and current in the circuit at the starting moment of an oscillation, etc. Other frequent terminal conditions are: Current zero at all times at one point Z0 — the open end of the circuit. Voltage zero at all times at one point 10 — the grounded or the short-circuited end of the circuit. Current and voltage, at all ti ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-02", "section_label": "Chapter 2: Potential Series And Exponential Function", "section_title": "Potential Series And Exponential Function", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3492-6063", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-02/", "snippets": [ "... = 0.02 and VC'L^IO-^; hence, i = 200 sin 1000 t and 6 = 10,000 cos 1000 t. 6 1. The discharge thus is alternating. ' In reality, due to the unavoidable resistance in the discharge path, the alterna- tions gradually die out, that is, the discharge is oscillating. The time of one complete period is given by, 1000^0=2;:; or, to=^. Hence the frenquency, /= — = —^ — = 159 cycles per second. As the circuit in addition to the inductance necessarily contains resistance r, besides the voltage consumed by the induc ...", "... larger, and current and e.m.f. are the product of an exponential term (gradually decreasing value) and a trigonometric term (alternating value) ; that is, they consist of successive alternations of gradually decreasing amplitude. Such functions are called oscillating functions. Practically all disturbances in electric circuits consist of such oscillating currents and voltages. 600^ = 2;: gives, as the time of one complete period, and the frequency is ^ = ^ = 0.0105 sec; 600 ' /=-^ = 95.3 cycles per sec. In ...", "... ng value) and a trigonometric term (alternating value) ; that is, they consist of successive alternations of gradually decreasing amplitude. Such functions are called oscillating functions. Practically all disturbances in electric circuits consist of such oscillating currents and voltages. 600^ = 2;: gives, as the time of one complete period, and the frequency is ^ = ^ = 0.0105 sec; 600 ' /=-^ = 95.3 cycles per sec. In this particular case, as the resistance is relatively high, the oscillations die out rathe ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-05", "section_label": "Lecture 5: Long Distance Transmission", "section_title": "Long Distance Transmission", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2562-3132", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-05/", "snippets": [ "... r is 2 \"> ^o corona effects occur. If now one terminal is grounded, the other terminal has 100,000 volts to ground and so at 2 \" diameter gives corona effects, that is, glow and streamers which may destroy the insulating material or produce high frequency oscillations. At very high voltages it is therefore necessary to have the system statically balanced or symmetrical, that is, have the same potential differences from all the conductors to the ground. Any electric circuit, and so also the transmission line, contai ...", "... ctance. the electrostatic energy is : e*C 2 and the electromagnetic energy : i'L 2 In a high potential transmission line both energies are of about the same magnitude, and the energy can therefore see- saw between the two forms and thereby produce oscillations and surges resulting in the production of high voltages, which are not liable to occur in circuits in which one of the forms of stored energy is small compared with the other. In distribution systems up to 2200 volts and even some- what higher, the elec ...", "... igh potential circuit Three-phase is always used in the transmission line. Some of the available transformer connections are given in Figs. 19 and 20. Grounding the neutral of the system has the advantage of maintaining static balance and so avoiding oscillations and disturbances in case of an accidental static unbalancing, as for 7© GENERAL LECTURES ^ i^i;;;;:;! /.) o£ir/i-o£irA ^) o£ir/<~ Y r-0£lTA a) r-r ^J 0£l77l*r s) rmsf-WMsr tf.j o^e/vasiTA r) Ttro^^AAse frM££'^/f ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-32", "section_label": "Chapter 10: Mutual Inductance", "section_title": "Mutual Inductance", "kind": "chapter", "sequence": 32, "number": 10, "location": "lines 10475-12216", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "snippets": [ "... iven by a quadratic equation (18). This quadratic equation (18) always has two real roots, and in this respect differs from the quadratic equation appearing in a circuit containing capacity, which latter may have two imaginary roots and so give rise to an oscillation. Mutual induction in the absence of capacity thus always gives a logarithmic transient term; thus, a = (r^2 + T^} \\ ; (T^ rf + * T^Xm • (19) •>//y«/y» /y» * \\ Z/ ^jU/2 .t/fn / As seen, the term under the radical in (19) is always positive, that i ...", "... duration, and therefore of interest — as in the transformer and the induction coil or Ruhmkorff coil, the equation (61) can be solved by a simple approximation. In this case, the roots, a, are two pairs of conjugate imaginary numbers, and the phenomenon oscillatory. The real components of the roots, a, must be positive, since the exponential s~a9 must decrease with increasing 0. The four roots thus can be written : (63) where a and /? are positive numbers. In the equation (61), the coefficients of a3 and a ...", "... 10' -sin 16.28 6 Approximately therefore we have i\\ = 9.6 £-°-073e cos 50.15 0 + 15.7 £-°-010' cos 16.28 0 ia = - 10 { £-°-0730 cos 50.15 0 - £-°mo0 cos 16.28 0 } e/ = 3850 fi-OJMO« sin 16.28 0 < - -3670 £-°010' sin 16.28 6. The two frequencies of oscillation are 3009 and 977 cycles per sec., hence rather low. The secondary terminal voltage has a maximum of nearly 4000, reduced to the primary, or 400 times as large as corre- sponds to the ratio of turns. In this particular instance, the frequency 3009 is ne ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-06", "section_label": "Lecture 6: Higher Harmonics Of The Generator Wave", "section_title": "Higher Harmonics Of The Generator Wave", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3133-3507", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-06/", "snippets": [ "... o that in case of a ground on one phase, enough current flows over the neutral to open the circuit breaker of the grounded phase. The use of a resistance in the generator neutral is very desirable also, since it eliminates the danger of a high frequency oscillation between line and ground through the generator reactance in the path of the third harmonic, by damping the oscillation in the resistance. For this reason, the resistance should be non-inductive. To ground the gener- ator neutral through a reactance is very ...", "... nded phase. The use of a resistance in the generator neutral is very desirable also, since it eliminates the danger of a high frequency oscillation between line and ground through the generator reactance in the path of the third harmonic, by damping the oscillation in the resistance. For this reason, the resistance should be non-inductive. To ground the gener- ator neutral through a reactance is very dangerous since it intensifies the danger of a resonance voltage rise. In grounding the generator neutral, special c ...", "... of a resonance voltage rise. In grounding the generator neutral, special care is neces- sary to get perfect contact, since an arc or loose contact would generate a high frequency in the circuit of the third harmonic and so may lead to a higher frequency oscillation between line and ground." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-37", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 37, "number": 1, "location": "lines 15354-15625", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "snippets": [ "... bout by the change, and therefore must pass from the values corresponding to the previous condition to the values corre- sponding to the changed condition. This transient term may be a gradual approach to the final condition, or an approach by a series of oscillations of gradual decreasing intensities. Gradually — after indefinite time theoretically, after relatively short time practically — the transient term disappears, and permanent conditions of current, of voltage, of magnetism, etc., are established. The numeric ...", "... tant inter- mediary between the two extremes can thus be produced. On this principle, for instance, operated the controlling solenoid of the Thomson-Houston arc machine, and also numerous auto- matic potential regulators. 2. Production of high frequency oscillating currents by period- ically recurring condenser discharges has been discussed under \" oscillating current generator,\" in Section I, paragraph 44. Non-sinusoidal high frequency alternating currents are pro- duced by an arc, when made unstable by shunting i ...", "... e, operated the controlling solenoid of the Thomson-Houston arc machine, and also numerous auto- matic potential regulators. 2. Production of high frequency oscillating currents by period- ically recurring condenser discharges has been discussed under \" oscillating current generator,\" in Section I, paragraph 44. Non-sinusoidal high frequency alternating currents are pro- duced by an arc, when made unstable by shunting it with a condenser, as discussed before. The Ruhmkorff coil or inductorium also represents an ap ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-46", "section_label": "Chapter 6: Alternating Magnetic Flux Distribution", "section_title": "Alternating Magnetic Flux Distribution", "kind": "chapter", "sequence": 46, "number": 6, "location": "lines 23948-24980", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "snippets": [ "... o give, at the impressed frequency, practically uniform magnetic induction throughout its section, that is, negligible secondary currents. This, however, is no longer the case, even with the thinnest possible laminations, at extremely high frequencies, as oscillating currents, lightning discharges, etc., and under these conditions the magnetic flux distribution in the iron is not uniform, but the magnetic flux density, (B, decreases rapidly, and lags in phase, with increasing depth below the surface of the lamination, ...", "... n into copper and into cast iron, the high conductivity of the former compensating for the higher permeability of the latter. 56. The wave length, lw = — , substituting for c, from equa- tion (9), is 31,600 (41) that is, the wave length of the oscillatory transmission of alter- nating magnetism in solid iron is inversely proportional to the square root of the electric conductivity, the magnetic permea- bility, and the frequency. Comparing this equation (41) of the wave length lw with equa- tion (40) of t ...", "... effect of iron in increasing the magnetic flux disappears only at 400 million cycles, and beyond this frequency iron lowers the magnetic flux. However, even at these frequencies, the presence of iron still exerts a great effect in the rapid damping of the oscillations by the lag of the mean magnetic flux by 45 degrees. Obviously, in large solid pieces of iron, the permeability // falls below that of air even at far lower frequencies. Where the penetration of the magnetic flux lp is small com- pared with the dimension ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-47", "section_label": "Chapter 7: Distribution Of Alternating-Current Density In Conductor", "section_title": "Distribution Of Alternating-Current Density In Conductor", "kind": "chapter", "sequence": 47, "number": 7, "location": "lines 24981-26094", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "snippets": [ "CHAPTER VII. DISTRIBUTION OF ALTERNATING-CURRENT DENSITY IN CONDUCTOR. 59. If the frequency of an alternating or oscillating current is high, or the section of the conductor which carries the current is very large, or its electric conductivity or its magnetic per- meability high, the current density is not uniform throughout the conductor section, but decreases towards the inte ...", "... high potential transmissions for branch lines of smaller power, or steel cables for long spans in transmission lines. (3) In the rail return of single-phase railways. (4) When carrying very high frequencies, such as lightning discharges, high frequency oscillations. In the last two cases, which probably are of the greatest impor- tance, the unequal current distribution usually is such that practically no current exists at the conductor center, and the effective resistance of the track rail even for 25-cycle alterna ...", "... ckness of conductor may be employed. 378 TRANSIENT PHENOMENA Such values may be given for 25 cycles and 60 cycles as the machine frequencies, and for 10,000 cycles and 1,000,000 cycles as the limits of frequency, between which most high frequency oscillations, lightning discharges, etc., are found, and also for 1,000,000,000 cycles as about the highest frequencies which can be produced. The depth of penetration of alternating current in centimeters is given below. Material M A Penetration in cm. at 2 ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1659-2484", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-03/", "snippets": [ "... ENTS IN CONTINUOUS- CURRENT CIRCUITS. 13. The simplest electrical transients are those in circuits in which energy can be stored in one form only, as in this case the change of stored energy can consist only of an increase or decrease ; but no surge or oscillation between several forms of energy can exist. Such circuits are most of the low- and medium-voltage circuits, — 220 volts, 600 volts, and 2200 volts. In them the capac- ity is small, due to the limited extent of the circuit, resulting from the low voltage, a ...", "... o is of very small resistance, and the momentary discharge currents may be very consider- able, so that in spite of the very small inductance, considerable magnetic-energy storage may oc- cur; that is, the system is one storing energy in two forms, and oscillations appear, as in the dis- charge of the Leyden jar. Let, as represented in Fig. 10, a continuous voltage eo be im- pressed upon a wire coil of resistance r and inductance L (but A current Iq = — flows through the coil and % t 1 % io A C c ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1531-2161", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "snippets": [ "... IENTS IN CONTINUOUS- CURRENT CIRCUITS. 13. The simplest electrical transients are those in circuits in which energy can be stored in one form only, as in this case the change of stored energy can consist only of an increase or decrease ; but no surge or oscillation between several forms of energy can exist. Such circuits are most of the low- and medium-voltage circuits, — 220 volts, 600 volts, and 2200 volts. In them the capac- ity is small, due to the limited extent of the circuit, resulting from the low voltage, a ...", "... y small resistance, and the momentary discharge currents may be very consider- able, so that in spite of the very small inductance, considerable __ magnetic-energy storage may oc- cur; that is, the system is one eo storing energy in two forms, and ^ oscillations appear, as in the dis- ' ~ charge of the Leyden jar. Fig 10._Magnetie Single.energy Let, as represented in Fig. 10, Transient, a continuous voltage e0 be im- pressed upon a wire coil of resistance r and inductance L (but negligible capacity). A c ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... g the total resistance of the con- denser charging circuit, r = 250 ohms. What is the maximum value of the charging current? The equation of the charging current of a condenser, through a circuit of low resistance, is {\" Transient Electric Phenomena and Oscillations,'^ p. 61) : '-ii--'**i. where and the equation of the charging current of a condenser, through a circuit of high resistance, is {\" Transient Electric Phenomena and Oscillations,\" p. 51), 5 I where =^F#■ Substituting the numerical values ...", "... h a circuit of low resistance, is {\" Transient Electric Phenomena and Oscillations,'^ p. 61) : '-ii--'**i. where and the equation of the charging current of a condenser, through a circuit of high resistance, is {\" Transient Electric Phenomena and Oscillations,\" p. 51), 5 I where =^F#■ Substituting the numerical values gives: (a) 1 = 10.2 £-200^ sin 980 i- {b) i = 6.667{ £-5oo«_ ,-20oo«j_ Simplified and diiferentiated, this gives : (o) 2=-^' = 4.9 cos 980^-sin 980^=0; hence tan 980^ = 4.9 980 ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-08", "section_label": "Lecture 8: Arc Lamps And Arc Lighting", "section_title": "Arc Lamps And Arc Lighting", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 7141-8510", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-08/", "snippets": [ "... and the regulator merely makes the regulation perfect. A more explicit discussion of the phenomena in the arc machine, and especially its rectification, is given in Chapter III of Section II of \"Theory and Calculation of Transient Electric Phenomena and Oscillations.\" In alternating-current circuits, approximate constant-current regulation is produced by a large reactance, that is, by self- induction, in the circuit. In transformers, the self-induction is the stray field, or the leakage flux between primary coil and ...", "... n changed to constant direct current by the mercury-arc rectifier. An explicit dis- cussion of the phenomena of the constant-current mercury arc rectifier is given in Chapter IV of Section II of \" Theory and Calculation of Transient Electric Phenomena and Oscillations.\" If the constant-current arc circuit accidentally opens, with a Brush machine as source of supply, the voltage practically vanishes, as the machine has series field excitation, and thus loses its field on open circuit. The constant-current trans- forme ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-13", "section_label": "Chapter 13: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 13484-14333", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-13/", "snippets": [ "... 38 ampere-turns per cm.; that is, half as much as in a lamina of the thickness d. For a more complete investigation of the screening effect of eddy currents in laminated iron, see Section III of \"Theory and Calculation of Transient Electric Phenomena and Oscillations.\" 112. Besides the edd}^, or Foucault, currents proper, which exist as parasitic currents in the interior of the iron lamina or wire, under certain circumstances eddy currents also exist in larger orbits from lamina to lamina through the whole magnetic ...", "... problem, as applicable to the distribution of alternating current in very large conductors, as the iron rails of the return circuit of alternating-current rail- ways, is given in Section III of \"Theory and Calculation of Tran- sient Electric Phenomena and Oscillations.\" In practice, this phenomenon is observed mainly with very high frequency currents, as lightning discharges, wireless tele- graph and lightning arrester circuits; in power-distribution cir- cuits it has to be avoided by either keeping the frequency suff ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "... Such functions of the distance, I, or position on the line, while alternating in time, differ from the true alternating waves in that the intensities of successive half-waves progressively increase or decrease with the distance. Such functions are called oscillating waves, and, as such, are beyond the scope of this book, but are more fully treated in \"Theory and Calculation of Transient Electric Phenomena and Oscillations,\" Section III. There also will be found the discussion of the phenomena of distributed capacitj^ ...", "... essive half-waves progressively increase or decrease with the distance. Such functions are called oscillating waves, and, as such, are beyond the scope of this book, but are more fully treated in \"Theory and Calculation of Transient Electric Phenomena and Oscillations,\" Section III. There also will be found the discussion of the phenomena of distributed capacitj^ in high-potential transformer windings, the effect of the finite velocity of propagation of the electric field, etc. For most purposes, however, in calculati ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-35", "section_label": "Chapter 35: Balanced Symmetrical Polyphase Systems", "section_title": "Balanced Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 35, "number": 35, "location": "lines 37453-37957", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-35/", "snippets": [ "... X = 2TrfL = 88 ohms. The capacity of the transmission line may be calculated directly, or more conveniently it may be derived from the inductance. If C is the capacity of the circuit, of which the inductance is L, then is the fundamental frequency of oscillation, or natural period, that is, the frequency which makes the length, I, of the line a quarter-wave length. Since the velocity of propagation of the electric field is the ve- ^ \"Theoretical Elements of Electrical Engineering.\" BALANCED SYMMETRICAL POLYP ...", "... ce the velocity of propagation of the electric field is the ve- ^ \"Theoretical Elements of Electrical Engineering.\" BALANCED SYMMETRICAL POLYPHASE SYSTEMS 451 locity of light, v, with a wave-length, 4 I, the number of waves per second, or frequency of oscillation of the line, is f - — and herefrom then follows: hence, for V I Vlc I = 100 miles, V = 186,000 miles per second, L = 0.23 henry, C = 1.26 mf. and the capacity susceptance, 6 = 2 tt/C = 475 X 10-«. Representing, as approximation, th ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-18", "section_label": "Chapter 20: Single-Phase Commutator Motors", "section_title": "Single-Phase Commutator Motors", "kind": "chapter", "sequence": 18, "number": 20, "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "... l term is. The determination of this exponential term is beyond the scope of the present work, but requires the methods of evaluation of transient or momentary electric phenomena, as discussed in \"Theory and Calculation of Transient Electric Phenomena and Oscillations.\" B. Series Repulsion Motor 219. As fuither illustration of the application of these funda- mental equations of the single-phase commutator motor, (1) to (6), a motor may be investigated, in which the four independent constants are chosen as follows: ...", "... and to lead above this speed, from the poatMl in quadrature behind the main field, the total GOmmutatiag field must lead this field controlling the e.m.f. of alternation, and it follows: 'See \"Theory ami Calculations of Transient Electric Phenomena and Oscillations,\" Sections I and II, SINGLE-PHASE COMMUTATOR MOTORS 421 Choosing the e.m.f., E2, impressed upon the compensating winding in phase with, and its magnetic flux, therefore in quad- rature (approximately), behind the main field, gives a com- mutation in t ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-16", "section_label": "Chapter 3: Standing Waves. 442", "section_title": "Standing Waves. 442", "kind": "chapter", "sequence": 16, "number": 3, "location": "lines 1087-1111", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-16/", "snippets": [ "CHAPTER III. STANDING WAVES. 442 14. Oscillatory, critical and gradual standing wave. 442 15. The wave length which divides the gradual from the oscillatory wave. 446 16. High-power high-potential overhead transmission line. Character of waves. Numerical example. General equations. 449 17. High-p ...", "CHAPTER III. STANDING WAVES. 442 14. Oscillatory, critical and gradual standing wave. 442 15. The wave length which divides the gradual from the oscillatory wave. 446 16. High-power high-potential overhead transmission line. Character of waves. Numerical example. General equations. 449 17. High-potential underground power cable. Character of waves. Numerical example. General equations. 452 18. Submarin ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-19", "section_label": "Chapter 6: Transition Points And The Complex Circuit. 498", "section_title": "Transition Points And The Complex Circuit. 498", "kind": "chapter", "sequence": 19, "number": 6, "location": "lines 1187-1227", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-19/", "snippets": [ "... f adjoining sections. 504 46. The energy transfer constant of the circuit section, and the transfer of power between the sections. 507 47. The final form of the general equations of the complex circuit, . 508 48. Full-wave, half-wave, quarter-wave oscillation, and gen- eral high-frequency oscillation. 509 49. Determination of the resultant time decrement of the cir- cuit. 510", "... transfer constant of the circuit section, and the transfer of power between the sections. 507 47. The final form of the general equations of the complex circuit, . 508 48. Full-wave, half-wave, quarter-wave oscillation, and gen- eral high-frequency oscillation. 509 49. Determination of the resultant time decrement of the cir- cuit. 510" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-31", "section_label": "Chapter 9: Divided Circuit", "section_title": "Divided Circuit", "kind": "chapter", "sequence": 31, "number": 9, "location": "lines 9228-10474", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "snippets": [ "... ^i = °> or ^L+i1) = 0 (58) while A. remains indefinite as integration constant. Equation (58) has three roots, av a2, and a3, which either are all three real, when the phenomenon is logarithmic, or, one real and two imaginary, when the phenomenon is oscillating. The integral equation for the current in branch 1 is *e • (59) the current in branch 2 is by (53) (60) 136 TRANSIENT PHENOMENA and the potential difference at the condenser is /dfL i2dd=rlil + z,^1 \"'. (61) In the case of an oscillatory ...", "... oscillating. The integral equation for the current in branch 1 is *e • (59) the current in branch 2 is by (53) (60) 136 TRANSIENT PHENOMENA and the potential difference at the condenser is /dfL i2dd=rlil + z,^1 \"'. (61) In the case of an oscillatory change, equations (59), (60), and (61) appear in complex imaginary form, and therefore have to be reduced to trigonometric functions. The three integration constants, Av A2, and A3, are deter- mined by the three terminal conditions, at 6 = 0, il = if, i ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-33", "section_label": "Chapter 40: General System Of Circuits", "section_title": "General System Of Circuits", "kind": "chapter", "sequence": 33, "number": 40, "location": "lines 12217-12884", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-33/", "snippets": [ "... termination of the 2 n2 constants Aft which now can easily be solved. The roots of equation (50) may either be real or may be com- plex imaginary, and in the latter case each pair of conjugate roots gives by elimination of the imaginary form an electric oscillation. That is, the solution of the problem of n independent circuits leads to n transient terms, each of which may be either an oscillation or a pair of exponential functions. 98. The preceding discussion gives the general method of the determination of the ...", "... imaginary, and in the latter case each pair of conjugate roots gives by elimination of the imaginary form an electric oscillation. That is, the solution of the problem of n independent circuits leads to n transient terms, each of which may be either an oscillation or a pair of exponential functions. 98. The preceding discussion gives the general method of the determination of the transient phenomena occurring in any system or net work of circuits containing resistances, self-indue- 178 TRANSIENT PHENOMENA tanc ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-36", "section_label": "Chapter 14: Short-Circuit Currents Of Alternators", "section_title": "Short-Circuit Currents Of Alternators", "kind": "chapter", "sequence": 36, "number": 14, "location": "lines 14549-15353", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "snippets": [ "... at uniform synchronous speed, hence is stationary 202 TRANSIENT PHENOMENA with regard to the field. In the first moment, however, the resultant armature m.m.f . is changing in intensity and in velocity, approaching its constant value by a series of oscillations, as discussed in Chapter XIII. Hence, with regard to the field, the transient term of armature reaction is pulsating in intensity and oscillating in position, and therefore generates in the field coils Field Current Armature Current Fig. 50. Three ...", "... ant armature m.m.f . is changing in intensity and in velocity, approaching its constant value by a series of oscillations, as discussed in Chapter XIII. Hence, with regard to the field, the transient term of armature reaction is pulsating in intensity and oscillating in position, and therefore generates in the field coils Field Current Armature Current Fig. 50. Three-phase short-circuit current of a turbo-alternator. an e.m.f. and causes a corresponding pulsation in the field current and field terminal voltage ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-45", "section_label": "Chapter 5: Distributed Series Capacity", "section_title": "Distributed Series Capacity", "kind": "chapter", "sequence": 45, "number": 5, "location": "lines 23586-23947", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "snippets": [ "... , the discharge voltage with increas- 350 TRANSIENT PHENOMENA ing frequency, does not remain constant, but decreases with increase of frequency, when the frequency becomes sufficiently high to give appreciable charging currents. Hence high fre- quency oscillations discharge over such a structure at lower voltage than machine frequencies. For a further discussion of the feature which makes such a multigap structure useful for lightning protection, see A. I. E. E. Transactions, 1906, pp. 431, 448, 1907, p. 425, etc. ...", "... ck of uni- formity of such condensation, due to the gusty nature of air currents, a non-uniform distribution of potential is produced between the rain drops in the cloud; and when the potential gradient somewhere in space exceeds the disruptive value, an oscillatory discharge starts between the rain drops, and grad- ually, in a number of successive discharges, traverses the cloud and equalizes the potential gradient. A study of circuits containing distributed series capacity thus leads to an under- standing of the ph ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-56", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit", "section_title": "Power And Energy Of The Complex Circuit", "kind": "chapter", "sequence": 56, "number": 7, "location": "lines 33528-34202", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "snippets": [ "CHAPTER VII. POWER AND ENERGY OF THE COMPLEX CIRCUIT. 50. The free oscillation of a complex circuit differs from that of the uniform circuit in that the former contains exponential functions of the distance A which represent the shifting or transfer of power between the sections of the circuit. Thus the general expression of one te ...", "... time this gives « 2^ = dw\" dw\"' The last two terms, — and — , thus represent the energy which is transferred, or pulsates, between the electromagnetic and the electrostatic field of the circuit; and the term — repre- sents the alternating (or rather oscillating) component of stored energy. 53. The energy stored by the electric field in a circuit section ^, between A, and A2, is given by integrating - - between A2 and AI} U/A as - (€-2«J, _ ^-2.^ (Ca + £>2) I . (323) or, substituting herein the approximat ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-02-discussion-of-recommendations", "section_label": "Report Section 3: Discussion of Recommendations", "section_title": "Discussion of Recommendations", "kind": "report-section", "sequence": 3, "number": 3, "location": "PDF pages 12-16, lines 721-1138", "status": "pdf-text-extracted-candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-02-discussion-of-recommendations/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-02-discussion-of-recommendations/", "snippets": [ "... ntil at some time they happen to drift close enough together within \\% so as to pull each other in step. The characteristic of this drift out of synchronism is that the fluctua- tions of current, etc., are constant, and not gradually decreasing, as in hunting oscillations, and the frequency or period of fluctuation is ir- regular. This seems to agree with the observations. It appears then : if a station section has dropped out of synchronism by a short circuit or other trouble, as indicated by its voltage not coming back promp ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 557-1002", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-01/", "snippets": [ "... f the weight, that part of the energy which is not dissipated again changes to potential gravitational en- ergy, at c, then back again to kinetic energy, at a; and in this manner the total stored energy is gradually dissipated, by a series of successive oscillations or changes between potential gravitational and kinetic mechanical Double-energy Transient of Pendulum. NATURE AND ORIGIN OF TRANSIENTS. 9 energy. Thus in electric circuits containing energy stored in the magnetic and in the dielectric field, the ch ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-05", "section_label": "Lecture 5: Single-Energy Tra.Nsient Of Ironclad Circuit", "section_title": "Single-Energy Tra.Nsient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3387-3720", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-05/", "snippets": [ "... but the transient has to be calculated by an 52 SINGLE-ENERGY TRANSIENT OF IRONCLAD CIRCUIT. 53 approximate step-by-step method, as illustrated for the starting transient of an alternating-current transformer in '' Transient Elec- tric Phenomena and Oscillations/' Section I, Chapter XII. Such methods are very cumbersome and applicable only to numerical instances. An approximate calculation, giving an idea of the shape of the transient of the ironclad magnetic circuit, can be made by neglect- ing the difference ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 460-882", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "snippets": [ "... f the weight, that part of the energy which is not dissipated again changes to potential gravitational en- ergy, at c, then back again to kinetic energy, at a; and in this manner the total stored energy is gradually dissipated, by a series of successive oscillations or changes between potential gravitational and kinetic mechanical Fig. 6. Double-energy Transient of Pendulum. NATURE AND ORIGIN OF TRANSIENTS. energy. Thus in electric circuits containing energy stored in the magnetic and in the dielectric fiel ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-05", "section_label": "Lecture 5: Single-Energy Transient Of Ironclad Circuit", "section_title": "Single-Energy Transient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2972-3286", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "snippets": [ "... as to be calculated by an '^''\"r '*_/ ? :,\": \\ : 52 SINGLE-ENERGY TRANSIENT OF IRONCLAD CIRCUIT. 53 approximate step-by-step method, as illustrated for the starting transient of an alternating-current transformer in \"Transient Elec- tric Phenomena and Oscillations,\" Section I, Chapter XII. Such methods are very cumbersome and applicable only to numerical instances. An approximate calculation, giving an idea of the shape of the transient of the ironclad magnetic circuit, can be made by neglect- ing the difference ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-05", "section_label": "Chapter 6: Empirical Curves", "section_title": "Empirical Curves", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 16483-21988", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-05/", "snippets": [ "... in the secondary circuit of the single-phase induction motor; two sets of currents, of the frequencies /« and (2/—/^) exist (where / is the primary frequency and /s the frequency of slip). Of this nature, frequently, is the distortion produced by surges, oscillations, arcing grounds, etc., in electric circuits; it is a combination of the natural frequency of the circuit with the impressed frequency. Telephonic currents commonly show such multiple frequencies, which are not harmonics of each other." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... heir relation to the radiator or oscillator which produces them, or to the receiver on which they impinge, and thus are treated in connection with the radiator or receiver, that is, the electric conductor, in the theory of transient electric phenomena and oscillations.* The radiation may be of a single frequency, that is, a single wave; or a mixture of different frequencies, that is, a mixture of different and frequently of an infinite number of waves. Electric radiation usually is of a single frequency, that is, of ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-06", "section_label": "Theory Section 6: Self-inductance of Continuous-current Circuits", "section_title": "Self-inductance of Continuous-current Circuits", "kind": "theory-section", "sequence": 6, "number": 6, "location": "lines 1785-2249", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-06/", "snippets": [ "... venient to denote the value Y as attenuation constant, since this value appears as one term of the more gen- eral constant of the electric circuit ( Y + ~r< ) • (Theory and Calculation of Transient Electric Phenomena and Oscillations, Section IV.) 26 ELEMENTS OF ELECTRICAL ENGINEERING Substituted in the foregoing equation this gives and ei = - = - 0.368 E. 31. Stopping of Current. In a circuit of inductance L and E resistance r, l ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-38", "section_label": "Apparatus Section 17: Synchronous Machines: Short-circuit Currents of Alternators", "section_title": "Synchronous Machines: Short-circuit Currents of Alternators", "kind": "apparatus-section", "sequence": 38, "number": 17, "location": "lines 10190-10429", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-38/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-38/", "snippets": [ "... the oscillogram is cut off by the open- ing of the circuit breaker. For further discussion, and the theoretical investigation of momentary short-circuit currents, see \"Theory and Calculation of Transient Electric Phenomena and Oscillations,\" Part I, Chapters XI and XII. For further discussion of the terms reactance, armature re- action and field excitation and their relation, see \"Theory and Calculation of Electric Circuits. \" 11 B. DIRECT-CURRENT COMMUTATIN ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 3267-3618", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-06/", "snippets": [ "... ore or less as broken lines, due to the necessity of using finite line elements, while in reality they are smooth curves when calculated by the differential method, as explained in Section III of \"Theory and Calculation of Transient Electric Phenomena and Oscillations.\" 40, As further example may be considered a three-phase cir- cuit supplied over a long-distance transmission line of distrib- uted capacitj^, self-induction, resistance, and leakage. Let, in Fig. 33, OEi, OE2, OEz = three-phase voltages at re- ceiver ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-22", "section_label": "Chapter 22: Armature Reactions Of Alternators", "section_title": "Armature Reactions Of Alternators", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 23971-25134", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-22/", "snippets": [ "... d \"nominal generated e.m.f.,\" eo, is hereby justified, when dealing with the permanent condition of the electric circuit. The case of the transient phenomena of momentary short- circuit currents, etc., is discussed in a chapter on \"Transient Phenomena and Oscillations,\" section I. It must be understood that the \"nominal generated e.m.f.,\" Co, in an actual machine, in which the magnetic characteristic bends due to the approach to magnetic saturation, is not the voltage generated by the field excitation /o at open-circu ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-23", "section_label": "Chapter 23: Synchronizing Alternators", "section_title": "Synchronizing Alternators", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 25135-25681", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-23/", "snippets": [ "... ransfer of the load from one engine to the other, which may even become so excessive as to throw the machines out of step, especially when by an ap- proximate coincidence of the period of engine impulses (or a multiple thereof), with the natural period of oscillation of the revolving structure, the effect is made cumulative. This diffi- culty as a rule does not exist with turbine or water-wheel driving, but is specially severe with gas-engine drive, and special pre- cautions are then often taken, by the use of a short ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-26", "section_label": "Chapter 26: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 32540-33010", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-26/", "snippets": [ "... maxima are very high above the effective values, as peaked waves, are objectionable by increasing the strain on the insulation. The striking-distance of an alternating voltage depends upon the maximum value, except at extremely high frequencies, such as oscillating discharges. In the latter, the very short duration of the voltage peak may reduce the disruptive strength, as dielectric disruption requires energy, that is, not only voltage, but time also." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... duction, 147 inductive reactance of line, 174 Neutral voltage of three-phase trans- former, 367 Nominal generated e.m.f. of alter- nator, 263, 276, 282 Non-inductive circuit and inductive line, 79, 81 Ohm's law, 1 Open delta transformation, 427 Oscillating waves, 175 Output, see Power of circuit with inductive line, 82, 95 in phase control, 104 Parallel connection of admittances, 59 of resistances and conduct- ances, 54 operation of alternators, 292 Parallelogram of sine waves, 22 in polar diagra ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "section_title": "Dibtbisnted Capacity, Inductance, Besistance, And", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "... and the E.M.Fs. are opposite. 113. The difference of phase, ^, between current, /, and E.M.F. , E^ at any point, x, of the line, is determined by the equation, D (cos u* + y sin u>) = -~ j where Z^ is a constant. Hence, ^ varies from point to point, oscillating around a medium position, wx, which it approaches at infinity. This difference of phase, wx, towards which current and E.M.F. tend at infinity, is determined by the expression, Z>(coswx +ysinwx) = /j2 / or, substituting for E and / their values, and s ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-18", "section_label": "Chapter 18: Synchronizing Alternators", "section_title": "Synchronizing Alternators", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17597-18052", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-18/", "snippets": [ "... transfer of the load from one engine to the other, which may even become so excessive as to throw the machines out of step, especially when by an approximate coincidence of the period of engine impulses (or a multiple thereof), with the natural period of oscillation of the revolving structure, the effect is made cumulative. This difficulty as a rule does not exist with turbine or water- wheel driving. 192. In synchronizing alternators, we have to distin- guish the phenomena taking place when throwing the ma- chine ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-22", "section_label": "Chapter 24: Conclusion", "section_title": "Conclusion", "kind": "chapter", "sequence": 22, "number": 24, "location": "lines 32820-33531", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-22/", "snippets": [ "... ase commutator motor, 336, 338 Concatenation of induction motors, 14, 40 Condenser excitation of induction motor secondary, 55, 84 singlephase induction motor, 120 speed control of induction motor, 13, 16 Contact making rectifier, 245 Cumulative oscillation of synchro- nous machine, 299 D Deep bar rotor of induction motor, 11 Delta connected roctifier, 251 Direct current in induction motor secondary, 54, 57 Disc type of unipolar machine, 454 Double squirrel cage induction motor, 29 Double synch ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-17", "section_label": "Chapter 17: Circuits With Distributed Leakage", "section_title": "Circuits With Distributed Leakage", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 30429-31656", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-17/", "snippets": [ "... ge conductors, such as transmission lines, etc., in general, capacity and inductance require consideration as well as resistance and shunted conductance. This general case is fully discussed in \"Theory and Calculation of Transient Electric Phe- nomena and Oscillations,\" and in \"Electric Discharges, Waves and Impulses,\" more particularly in the fourth section of the former book. 173, Let, then, in a conductor having uniformly distributed leakage, or in that conductor section, in which the leakage can be considered as ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-23", "section_label": "Chapter 1: The Constants Of The Electric Circuit", "section_title": "The Constants Of The Electric Circuit", "kind": "chapter", "sequence": 23, "number": 1, "location": "lines 1317-1992", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "snippets": [ "... instantly, the internal energy of the circuit adjusting itself to the changed circuit conditions by a transfer of energy between static and magnetic and inversely, that is, after the circuit conditions have been changed, a transient phenomenon, usually of oscillatory nature, occurs in the circuit by the readjustment of the stored energy. These transient phenomena of the readjustment of stored electric energy with a change of circuit conditions require careful study wherever the amount of stored energy is sufficiently ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-53", "section_label": "Chapter 4: Traveling Waves", "section_title": "Traveling Waves", "kind": "chapter", "sequence": 53, "number": 4, "location": "lines 30244-31450", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "snippets": [ "... e0 sin ( qtt + ^ = 6 cos + = e sin The first curve of Fig. 101 therefore is the beginning of Fig. 100. In waves traveling over a water surface shapes like Fig. 101 can be observed. For the purpose of illustration, however, in Figs. 100 and 101 the oscillations are shown far longer than they usually occur; the value q = 2620 corresponds to a frequency / = 418 cycles, while traveling waves of frequencies of 100 to 10,000 times as high are more common. Fig. 102 shows the beginning of a wave having ten times the ..." ] } ] }, { "id": "dielectricity", "label": "Dielectricity", "aliases": [ "dielectric", "dielectricity", "displacement", "displacement current", "electrostatic" ], "total_occurrences": 996, "matching_section_count": 139, "matching_source_count": 14, "source_totals": [ { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 218, "section_count": 21 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 138, "section_count": 8 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 133, "section_count": 8 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 112, "section_count": 19 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 101, "section_count": 19 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 99, "section_count": 17 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 86, "section_count": 19 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 26, "section_count": 9 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 20, "section_count": 4 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 19, "section_count": 6 }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 17, "section_count": 3 }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 14, "section_count": 2 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 12, "section_count": 3 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "section_label": "Chapter 14: Dielectric Losses", "section_title": "Dielectric Losses", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 111, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "CHAPTER XIV DIELECTRIC LOSSES Dielectric Hysteresis 116. Just as magnetic hysteresis and eddy currents give a power component in the inductive reactance, as \"effective resistance,\" so the energy losses in the dielectric lead to a power component in the condensive reactance, ...", "CHAPTER XIV DIELECTRIC LOSSES Dielectric Hysteresis 116. Just as magnetic hysteresis and eddy currents give a power component in the inductive reactance, as \"effective resistance,\" so the energy losses in the dielectric lead to a power component in the condensive reactance, which may be repre- ...", "CHAPTER XIV DIELECTRIC LOSSES Dielectric Hysteresis 116. Just as magnetic hysteresis and eddy currents give a power component in the inductive reactance, as \"effective resistance,\" so the energy losses in the dielectric lead to a power component in the condensive reactance, which may be repre- sented by an \"effective resistance of dielectric losses\" or an \"effective conductance of dielectric losses.\" In the alternating magnetic field, power is consumed by mag- netic hy ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1003-1658", "status": "candidate", "occurrence_count": 59, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-02/", "snippets": [ "... hile power flows through the conductors A, power is con- sumed in these conductors by JV[ conversion into heat, repre- sented by ^2r. This, however, Fig. 7. is not all, but in the space surrounding the conductor cer- tain phenomena occur: magnetic and electrostatic forces appear. Fig. 8. — Electric Field of Conductor. The conductor is surrounded by a magnetic field, or a magnetic flux, which is measured by the number of lines of magnetic force $. With a single conductor, the lines of magnetic force are concentri ...", "... wn in Fig. 8. By the return conductor, the circles 10 THE ELECTRIC FIELD. 11 are crowded together between the conductors, and the magnetic field consists of eccentric circles surrounding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from the conductors, that is, a dielectric flux passes between the conductors, which is measured by the number of lines of dielectric force ^. With a single conductor, the lines of dielectric force are ...", "... ircles 10 THE ELECTRIC FIELD. 11 are crowded together between the conductors, and the magnetic field consists of eccentric circles surrounding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from the conductors, that is, a dielectric flux passes between the conductors, which is measured by the number of lines of dielectric force ^. With a single conductor, the lines of dielectric force are radial straight lines, as shown dotted ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 883-1530", "status": "candidate", "occurrence_count": 59, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "snippets": [ "... While power flows through the conductors A, power is con- sumed in these conductors by conversion into heat, repre- sented by i?r. This, however, Fig. 7. is not all, but in the space surrounding the conductor cer- tain phenomena occur: magnetic and electrostatic forces appear. Fig. 8. — Electric Field of Conductor. The conductor is surrounded by a magnetic field, or a magnetic flux, which is measured by the number of lines of magnetic force . With a single conductor, the lines of magnetic force are concentr ...", "... wn in Fig. 8. By the return conductor, the circles 10 THE ELECTRIC FIELD. 11 are crowded together between the conductors, and the magnetic field consists of eccentric circles surrounding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from the conductors, that is, a dielectric flux passes between the conductors, which is measured by the number of lines of dielectric force ty. With a single conductor, the lines of dielectric force ar ...", "... ircles 10 THE ELECTRIC FIELD. 11 are crowded together between the conductors, and the magnetic field consists of eccentric circles surrounding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from the conductors, that is, a dielectric flux passes between the conductors, which is measured by the number of lines of dielectric force ty. With a single conductor, the lines of dielectric force are radial straight lines, as shown dotted ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-23", "section_label": "Chapter 1: The Constants Of The Electric Circuit", "section_title": "The Constants Of The Electric Circuit", "kind": "chapter", "sequence": 23, "number": 1, "location": "lines 1317-1992", "status": "candidate", "occurrence_count": 44, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "snippets": [ "... rostatic actions. The magnetic action is a maximum in the direction concen- tric, or approximately so, to the conductor. That is, a needle- shaped magnetizable body, as an iron needle, tends to set itself in a direction concentric to the conductor. The electrostatic action has a maximum in a direction radial, or approximately so, to the conductor. That is, a light needle- shaped conducting body, if the electrostatic component of the field is powerful enough, tends to set itself in a direction radial to the conductor, ...", "... etizable body, as an iron needle, tends to set itself in a direction concentric to the conductor. The electrostatic action has a maximum in a direction radial, or approximately so, to the conductor. That is, a light needle- shaped conducting body, if the electrostatic component of the field is powerful enough, tends to set itself in a direction radial to the conductor, and light bodies are attracted or repelled radially to the conductor. Thus, the electric field of a circuit over which energy flows has three main axe ...", "... light bodies are attracted or repelled radially to the conductor. Thus, the electric field of a circuit over which energy flows has three main axes which are at right angles with each other: The electromagnetic axis, concentric with the conductor. The electrostatic axis, radial to the conductor. The power gradient, parallel to the conductor. This is frequently expressed pictorially by saying that the lines of magnetic force of the circuit are concentric, the lines of electrostatic force radial to the conductor. ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-19", "section_label": "Theory Section 19: Fields of Force", "section_title": "Fields of Force", "kind": "theory-section", "sequence": 19, "number": 19, "location": "lines 7737-7990", "status": "candidate", "occurrence_count": 41, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-19/", "snippets": [ "... e earth, and water to run down hill — and this space thus is a field of gravitational force, the earth the gram- motive force. In the space surrounding conductors having a high potential difference, we observe a field of dielectric force, that is, electro- static or dielectric forces are exerted, and the potential difference between the conductors is the electromotive force of the dielectric field. The force exerted by the earth as gravimotive force, o ...", "... is space thus is a field of gravitational force, the earth the gram- motive force. In the space surrounding conductors having a high potential difference, we observe a field of dielectric force, that is, electro- static or dielectric forces are exerted, and the potential difference between the conductors is the electromotive force of the dielectric field. The force exerted by the earth as gravimotive force, on any mass in the gravitational field of the ...", "... tors having a high potential difference, we observe a field of dielectric force, that is, electro- static or dielectric forces are exerted, and the potential difference between the conductors is the electromotive force of the dielectric field. The force exerted by the earth as gravimotive force, on any mass in the gravitational field of the earth, causes the mass to move with increasing rapidity. The direction of motion then shows the direction in which ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 38, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "... mutual inductance ; ^ = effective reactance of mutual inductance. The susceptance of mutual inductance is negative, or of opposite sign from the reactance of self-inductance. Or, Mutual inductance consumes energy and decreases the self- inductance. Dielectric and Electrostatic Phenomena. 98. While magnetic hysteresis and eddy currents can be considered as the energy component of inductance, con- densance has an energy component also, namely, dielectric hysteresis. In an alternating magnetic field, energy is co ...", "... ce ; ^ = effective reactance of mutual inductance. The susceptance of mutual inductance is negative, or of opposite sign from the reactance of self-inductance. Or, Mutual inductance consumes energy and decreases the self- inductance. Dielectric and Electrostatic Phenomena. 98. While magnetic hysteresis and eddy currents can be considered as the energy component of inductance, con- densance has an energy component also, namely, dielectric hysteresis. In an alternating magnetic field, energy is con- sumed in hyste ...", "... ance consumes energy and decreases the self- inductance. Dielectric and Electrostatic Phenomena. 98. While magnetic hysteresis and eddy currents can be considered as the energy component of inductance, con- densance has an energy component also, namely, dielectric hysteresis. In an alternating magnetic field, energy is con- sumed in hysteresis due to molecular friction, and similarly, energy is also consumed in an alternating electrostatic field in the dielectric medium, in what is called electrostatic or dielectr ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 35, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... b = — ^-^^^ — ■* = effective susceptance of mutual inductance. The susceptance of mutual inductance is negative, or of opposite sign from the susceptance of self-inductance. Or, Mutual itidtutance consumes energy and decreases the self- inductatice. Dielectric and Electrostatic Phenomena, 98. While magnetic hysteresis and eddy currents can be considered as the energy component of inductance, cori- densance has an energy component also, called dielectric hysteresis. In an alternating magnetic field, energy is c ...", "... ■* = effective susceptance of mutual inductance. The susceptance of mutual inductance is negative, or of opposite sign from the susceptance of self-inductance. Or, Mutual itidtutance consumes energy and decreases the self- inductatice. Dielectric and Electrostatic Phenomena, 98. While magnetic hysteresis and eddy currents can be considered as the energy component of inductance, cori- densance has an energy component also, called dielectric hysteresis. In an alternating magnetic field, energy is con- sumed in hyst ...", "... ce consumes energy and decreases the self- inductatice. Dielectric and Electrostatic Phenomena, 98. While magnetic hysteresis and eddy currents can be considered as the energy component of inductance, cori- densance has an energy component also, called dielectric hysteresis. In an alternating magnetic field, energy is con- sumed in hysteresis due to molecular friction, and similarly, energy is also consumed in an alternating electrostatic field in the dielectric medium, in what is called dielectric hys- teresis. ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "section_label": "Lecture 10: Continual And Cumulative Oscillations", "section_title": "Continual And Cumulative Oscillations", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 32, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... enon by which the stored energy readjusts itself to a change of circuit conditions. In an oscilla- tory transient, the difference of stored energy of the previous and the after condition of the circuit, at a circuit change, oscillates between magnetic and dielectric energy. As there always must be some energy dissipation in the circuit, the oscillating energy of the transient must steadily decline, that is, the transient must die out, at a rate depending on the energy dissipation in the cir- cuit. Thus, the oscilla ...", "... hen, with an overlap of successive oscillations, no dead period occurs, during which the energy, which oscillates during the next wave train, is supplied to the line, this energy must be supplied during the oscillation, that is, there must be such a phase displacement or lag within the oscil- lation, which gives a negative energy cycle, or reversed hysteresis loop. Thus, essential for such a continual oscillation is the 124 ELECTRICAL DISCHARGES, WAVES AND IMPULSES existence of a hysteresis loop, formed by the lag o ...", "... he current through the residual vapor stream. Other hysteresis cycles than those of the arc are instrumental in the energy supply to other systems of continual oscillation. Thus, for instance, the hysteresis cycle between synchronizing force and position displacement supplies the energy of the con- tinual or cumulative oscillation, called hunting, in synchronous machines, as alternators, synchronous motors and converters. The mechanism, by which the hysteresis cycle supplies the energy of continual oscillations, has b ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-10", "section_label": "Lecture 10: Inductance And Capacity Of Round Parallel Conductors", "section_title": "Inductance And Capacity Of Round Parallel Conductors", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6089-7274", "status": "candidate", "occurrence_count": 27, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "snippets": [ "... inkages of the mag- netic flux to the current, £ = ?- (i) i/ where = magnetic flux or number of lines of magnetic force, and n the number of times which each line of magnetic force interlinks with the current i. The capacity is the ratio of the dielectric flux to the voltage, where \\f/ is the dielectric flux, or number of lines of dielectric force, and e the voltage which produces it. With a single round conductor without return conductor (as wireless antennae) or with the return conductor at infinite d ...", "... = ?- (i) i/ where = magnetic flux or number of lines of magnetic force, and n the number of times which each line of magnetic force interlinks with the current i. The capacity is the ratio of the dielectric flux to the voltage, where \\f/ is the dielectric flux, or number of lines of dielectric force, and e the voltage which produces it. With a single round conductor without return conductor (as wireless antennae) or with the return conductor at infinite dis- tance, the lines of magnetic force are concentr ...", "... ux or number of lines of magnetic force, and n the number of times which each line of magnetic force interlinks with the current i. The capacity is the ratio of the dielectric flux to the voltage, where \\f/ is the dielectric flux, or number of lines of dielectric force, and e the voltage which produces it. With a single round conductor without return conductor (as wireless antennae) or with the return conductor at infinite dis- tance, the lines of magnetic force are concentric circles, shown by drawn lines in Fi ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3721-4369", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-06/", "snippets": [ "... energy is stored by the current i, as magnetic field. To = -, (2) r where L = inductance = coefficient of energy storage by the cur- rent, r = resistance = coefficient of power dissipation by the current. If the energy is stored by the voltage e, as dielectric field, the duration of the transient would be TV - -, (3) g 59 60 ELECTRIC DISCHARGES, WAVES AND IMPULSES. where C = capacity = coefficient of energy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power co ...", "... urrent. If the energy is stored by the voltage e, as dielectric field, the duration of the transient would be TV - -, (3) g 59 60 ELECTRIC DISCHARGES, WAVES AND IMPULSES. where C = capacity = coefficient of energy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power consumption by the voltage, as leakage conductance by the voltage, corona, dielectric hysteresis, etc. Thus the transient of the spontaneous discharge of a condenser would be represented by e = eoe~'^\\ ...", "... 0 ELECTRIC DISCHARGES, WAVES AND IMPULSES. where C = capacity = coefficient of energy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power consumption by the voltage, as leakage conductance by the voltage, corona, dielectric hysteresis, etc. Thus the transient of the spontaneous discharge of a condenser would be represented by e = eoe~'^\\ (4) Similar single-energy transients may occur in other systems. For instance, the transient by which a water jet approaches con- stan ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3287-3955", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "snippets": [ "... , if energy is stored by the current i, as magnetic field, T0 = £, (2) where L = inductance = coefficient of energy storage by the cur- rent, r = resistance = coefficient of power dissipation by the current. If the energy is stored by the voltage e, as dielectric field, the duration of the transient would be TJ = -, (3) s/ 59 60 ELECTRIC DISCHARGES, WAVES AND IMPULSES. where C = capacity = coefficient of energy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power c ...", "... rrent. If the energy is stored by the voltage e, as dielectric field, the duration of the transient would be TJ = -, (3) s/ 59 60 ELECTRIC DISCHARGES, WAVES AND IMPULSES. where C = capacity = coefficient of energy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power consumption by the voltage, as leakage conductance by the voltage, corona, dielectric hysteresis, etc. Thus the transient of the spontaneous discharge of a condenser would be represented by e = e0e~£ct. ...", "... 0 ELECTRIC DISCHARGES, WAVES AND IMPULSES. where C = capacity = coefficient of energy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power consumption by the voltage, as leakage conductance by the voltage, corona, dielectric hysteresis, etc. Thus the transient of the spontaneous discharge of a condenser would be represented by e = e0e~£ct. (4) Similar single-energy transients may occur in other systems. For instance, the transient by which a water jet approaches con- sta ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 23, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... e balanced quarter-phase system with common re- turn is unbalanced with regard to voltage and phase relation, or in other words, even if in a quarter-phase system with common return both branches or phases are loaded equally, with a load of the same phase displacement, nevertheless the system becomes unbalanced, and the two e.m.fs. at the end of the hne are neither equal in magnitude, nor in quadrature with each other. B. One Branch Loaded, One Unloaded Zi = Z2 = Z, Z -^• (a) Fi = 0, F2 = F, {b) Fi = Y, Y, = 0. ...", "... ts of half-axis OB' downward; the complex imaginary or general numbers are represented by the points outside of the coordinate axes. INDEX Absolute values of complex quanti- ties, 37 Actual generated e.m.f., alternator, 272 Admittance, 55 of dielectric, 154 due to eddy currents, 137 to hysteresis, 129 Admittivity of dielectric circuit, 160 Air-gap in magnetic circuit, 119, 132 Ambiguity of vectors, 39 Amplitude, 6, 20 Apparent capacity of distorted wave, 386 efficiency of induction motor, 234 i ...", "... epresented by the points outside of the coordinate axes. INDEX Absolute values of complex quanti- ties, 37 Actual generated e.m.f., alternator, 272 Admittance, 55 of dielectric, 154 due to eddy currents, 137 to hysteresis, 129 Admittivity of dielectric circuit, 160 Air-gap in magnetic circuit, 119, 132 Ambiguity of vectors, 39 Amplitude, 6, 20 Apparent capacity of distorted wave, 386 efficiency of induction motor, 234 impedance of transformer, 201 torque efficiency of induction motor, 234 Arc c ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-24", "section_label": "Chapter 24: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 25682-29374", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-24/", "snippets": [ "... ading increases, the current within the range between 1 and 12. The condition of maximum output is 3, current in phase with impressed e.m.f. Since at constant current the loss is constant, this is at the same time the condition of maximum efficiency; no displacement of phase of the impressed e.m.f., or self-induction of the circuit compensated by the effect of the lead of the motor current. This condition of maximum efficiency of a circuit we have found already in Chapter XL 216. B. £\"0 and Ei constant, I variable. ...", "... The mechanical power delivered by the synchronous motor (including friction and core loss) is the electric power consumed by the counter e.m.f., ei; hence ■p = iei cos {i, 6]); (1) thus, cos (t, ei) = -^> lei sin a, eO = ^1 - (|-j (2) The displacement of phase between current i, and e.m.f. e = zi consumed by the impedance, z, is r cos {i, e) = ~ . X sm (i, e) - - (3) Since the three e.m.fs. acting in the closed circuit, ep = e.m.f. of generator, ei = counter e.m.f. of synchronous motor, ...", "... r; or, more generally, the maximum power which can be trans- mitted over a line of impedance. into any circuit, shunted by a condenser of suitable capacity. Substituting (21) in (19) and (20), we get, Co 2r (22) SYNCHRONOUS MOTOR 319 and the displacement of phase in the synchronous motor, hence, cos (ei, i) =-:— = -; lei z tan (ei, i) = - -, (23) that is, the angle of internal displacement in the synchronous motor is equal, but opposite to, the angle of displacement of line impedance, (ei, i) ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-18", "section_label": "Chapter 16: Il", "section_title": "Il", "kind": "chapter", "sequence": 18, "number": 16, "location": "lines 19346-21338", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-18/", "snippets": [ "... ng increases, the current within the range between 1 and 12. The condition of maximum output is 3, current in phase with impressed E.M.F. Since at constant current the loss is constant, this is at the same time the condition of max- imum efficiency : no displacement of phase of the impressed 2iW A/. TKHA-A rti\\G-CURRE.VT P//F..VO.VKXA. [| 181 Iv.M.I\"'., or Kclf-induction of the circuit compensated by the effect of the lead of the motor current. This condition of iiiiiximum t-fficiency of a circuit we have foun ...", "... rator, s = total impedance of line and motor; if ^f^ = E.M.F. of generator, that is, E.M.F. induced in generator armature by its rotation through the magnetic field, z includes the generator impedance also. f6 ALTERNATJNG-CURRENT PHENOMENA. [S 184 The displacement of phase between current i and E.M.F. = si consumed by the impedance s is : cos (*>) = sin (»>) = Since the three E.M.Fs. acting in the closed circuit: e^ = E.M.F. of generator, tx = C.E.M.F. of synchronous motor, £ =3 SI = E.M.F. consumed by imp ...", "... nductive line of resistance, r; or, more generally, the maximum power which can be transmitted over a line of impedance, into any circuit, shunted by a condenser of suitable capacity^ Substituting (21) in (19) and (20), we get, 2r J (22) and the displacement of phase in the synchronous motor. COs{c\\J) = -J^ = -; tCi ' z hence, tan(^„;) = --!^, (23) r 280 ALTERNATING-CURRENT PHENOMENA, [§ 186 that is, the angle of internal displacement in the synchron- ous motor is equal, but opposite to, the angle ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-19", "section_label": "Chapter 19: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 18053-19457", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "snippets": [ "... ng increases, the current within the range between 1 and 12. The condition of maximum output is 3, current in phase with impressed E.M.F. Since at constant current the loss is constant, this is at the same time the condition of max- imum efficiency : no displacement of phase of the impressed SYNCHRONOUS MOTOR. 329 E.M.F., or self-induction of the circuit compensated by the effect of the lead of the motor current. This condition of maximum efficiency of a circuit we have found already in the Chapter on Inducta ...", "... voltage of the generator, z = total impedance of line and motor; if t0= E.M.F. of generator, that is, E.M.F. induced in generator armature by its rotation through the magnetic field, z includes the generator impedance also. SYNCHRONOUS MOTOR. 339 The displacement of phase between current i and E.M.F. = z i consumed by the impedance z is : cos (ie) = - sin (/ ) E 2 . avg. p=^r sin a - -- =- sin a (1 cos 2a> ) 2Z 7T COo 7TCOZ where coo denotes the maximum value of co and as the du ...", "... voltage: e = 2E sinco (2 1 ) Current: 2F io= - sin w (3 1 ) z Power transfer: F 2 p= sin a sin 2co (6 l ) z Energy transfer during each half cycle of oscillation or beat: W= ^-sin a (1-cos 2 Wo ) (8 1 ) TrpfwoZ where : co=cooo sin p< (5) is the angle of phase displacement of either machine, from the average ; [[END_PDF_PAGE:31]] [[PDF_PAGE:32]] 26 Report of Charles P. Steinmetz z= Vr 2+x 2 t an a = - r r= resistance of circuit. x = reactance of circuit. p= frequency ratio of beat or oscillation, that is, pf= frequency of osci ...", "... th each other through an impedance z, and in synchronism with each other. If then the load distribution between the alternators differs from the distribution of their driving power, electric power is transferred over the impedance z, current flows and a phase displacement 2co occurs between the two sides of the reactor z. In this case, the phase angle w is constant, and not periodically fluctuating as in A, but varies with changes of distribution of load ; the equations, however, are the same as in A, except that now w is cons ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 557-1002", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-01/", "snippets": [ "... he load, we get a different current i\\ and possibly different voltages e' ', but again i' and e' are per- manent, that is, remain the same as long as the circuit remains unchanged. Let, however, in Fig. 2, a direct-current generator G be connected to an electrostatic condenser C. Before the switch S is closed, and therefore also in the moment of closing the switch, no current flows in the line A. Immediately after the switch S is closed, current begins to flow over line A into the condenser C, charging this condenser ...", "... onsideration of the electric power NATURE AND ORIGIN OF TRANSIENTS. 3 in generator, line, and load does not represent the entire phenome- non. While electric power flows over the line A, there is a magnetic field surrounding the line conductors, and an electrostatic field issuing from the line conductors. The magnetic field and the electrostatic or \" dielectric \" field represent stored energy. Thus, during the permanent conditions of the flow of power through the circuit Fig. 3, there is electric energy stored in the ...", "... ator, line, and load does not represent the entire phenome- non. While electric power flows over the line A, there is a magnetic field surrounding the line conductors, and an electrostatic field issuing from the line conductors. The magnetic field and the electrostatic or \" dielectric \" field represent stored energy. Thus, during the permanent conditions of the flow of power through the circuit Fig. 3, there is electric energy stored in the space surround- ing the line conductors. There is energy stored also in the gener ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 460-882", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "snippets": [ "... e load, we get a different current i', and possibly different voltages e1 '; but again i' and e' are per- manent, that is, remain the same as long as the circuit remains unchanged. Let, however, in Fig. 2, a direct-current generator G be connected to an electrostatic condenser C. Before the switch S is closed, and therefore also in the moment of closing the switch, no current flows in the line A. Immediately after the switch S is closed, current begins to flow over line A into the condenser C, charging this condenser ...", "... nsideration of the electric power NATURE AND ORIGIN OF TRANSIENTS. 3 in generator, line, and load does not represent the entire phenome- non. While electric power flows over the line A , there is a magnetic field surrounding the line conductors, and an electrostatic field issuing from the line conductors. The magnetic field and the electrostatic or \"dielectric \" field represent stored energy. Thus, during the permanent conditions of the flow of power through the circuit Fig. 3, there is electric energy stored in the ...", "... tor, line, and load does not represent the entire phenome- non. While electric power flows over the line A , there is a magnetic field surrounding the line conductors, and an electrostatic field issuing from the line conductors. The magnetic field and the electrostatic or \"dielectric \" field represent stored energy. Thus, during the permanent conditions of the flow of power through the circuit Fig. 3, there is electric energy stored in the space surround- ing the line conductors. There is energy stored also in the genera ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-01", "section_label": "Chapter 1: Electric Conduction. Soled And Liquid", "section_title": "Electric Conduction. Soled And Liquid", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 959-3894", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-01/", "snippets": [ "... The phenomena outside of the conductor are conditions of stress in space which are called the electric field, the two main components of the electric field being the electromagnetic component, characterized by the cir- cuit constant inductance, L, and the electrostatic component, characterized by the electric circuit constant capacity, C. Inside of the conductor we find a conversion of energy into heat; that is, electric power is consumed in the conductor by what may be considered as a kind of resistance of the conducto ...", "... current flow by their counter e.m.f. The current thus flows ahead of the voltage or counter e.m.f. which it produces, as a leading current, and the polarization cell thus acts like a condenser, and is called an \"electrolytic condenser.\" It has an enormous electrostatic capacity, or \"effective capacity,\" but can stand low voltage only — 1 volt or less — and therefore is of limited industrial value. As chemical action requires appreciable time, such electrolytic condensers show at commercial frequencies high losses of pow ...", "... , not an electrolytic condenser, and the counter e.m.f., which gives the capacity effect, is not electrolytic polarization. The aluminum cell is a true electro- static condenser, in which the film of alumina, formed on the positive aluminum plates, is the dielectric. Its characteristic is, that the condenser is self-healing; that is, a puncture of the alum- ina film causes a current to flow, which electroljrtically produces alumina at the puncture hole, and so closes it. The capacity is very high, due to the great th ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-02", "section_label": "Lecture 2: Conclusions From The Relativity Theory", "section_title": "Conclusions From The Relativity Theory", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 736-2388", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... and define the field as ''a condition of energy storage in space exerting a force on a body susceptible to this energy.'' The space surrounding a magnet is a magnetic field. If we electrify a piece of sealing wax by rubbing it, it surrounds itself by a dielectric or electrostatic field, and bodies susceptible to electrostatic forces- — such as light pieces of paper — are attracted. The earth is surrounded by a gravitational field, the lines of gravitational force CONCLUSIONS FROM RELATIVITY THEORY 19 issuing r ...", "... e field as ''a condition of energy storage in space exerting a force on a body susceptible to this energy.'' The space surrounding a magnet is a magnetic field. If we electrify a piece of sealing wax by rubbing it, it surrounds itself by a dielectric or electrostatic field, and bodies susceptible to electrostatic forces- — such as light pieces of paper — are attracted. The earth is surrounded by a gravitational field, the lines of gravitational force CONCLUSIONS FROM RELATIVITY THEORY 19 issuing radially from the ...", "... pace exerting a force on a body susceptible to this energy.'' The space surrounding a magnet is a magnetic field. If we electrify a piece of sealing wax by rubbing it, it surrounds itself by a dielectric or electrostatic field, and bodies susceptible to electrostatic forces- — such as light pieces of paper — are attracted. The earth is surrounded by a gravitational field, the lines of gravitational force CONCLUSIONS FROM RELATIVITY THEORY 19 issuing radially from the earth. If a stone falls to the earth, it is due ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "... he mechanism of light production by the firefly, etc., is still unknown. When splitting a sheet of mica, or shaking a well-exhausted tube containing mercury, flashes of light are seen in the darkness. This, however, is not real phosphorescence but due to electrostatic flashes of frictional electricity. The light given by fluorescence and phosphorescence of solids or liquids, gives a continuous spectrum, that is, is a mixture of all frequencies, just as is the case with temperature radiation; it differs, however, from ...", "... tinuous conduction, by vapors forming at the negative elec- trode and gradually bridging the space between the electrodes, and thereby replacing the gas which fills the space, by the elec- trode vapor as conductor. This is usually expressed by saying: the electrostatic spark between two terminals starts, or tends to start, an arc. Disruptive conduction, thus, does not follow Ohm's law; it is zero below the disruptive voltage, while with a supply voltage exceeding the disruptive voltage of the gas between the terminals, ...", "... n a constant potential supply of unlimited power, but requires a current limiting im- pedance in series with it, or a source of limited power, that is, a source in which the voltage drops with increase of cur- rent, as a constant current transformer or an electrostatic machine, etc. The disruptive voltage essentially depends on the gas pressure in the space between the electrodes, and also on the chemical nature, and on the temperature of the gas. It is over a wide range, directly proportional to the gas pressure. Thu ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-33", "section_label": "Chapter 33: Efficiency Of Systems", "section_title": "Efficiency Of Systems", "kind": "chapter", "sequence": 33, "number": 33, "location": "lines 36515-37127", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-33/", "snippets": [ "... um potential only, but where the limitation of potential depends upon the problem of insulating the conductors against disruptive discharge, the proper com- parison is on the basis of equality of the maximum difference of potential; that is, equal maximum dielectric strain on the insulation. In this case, the comparison voltage may be either the poten- tial difference between any two conductors of the system, or it may be the potential difference between any conductor of the system and the ground, depending on the ...", "... this case, the comparison voltage may be either the poten- tial difference between any two conductors of the system, or it may be the potential difference between any conductor of the system and the ground, depending on the character of the circuit. The dielectric stress is from conductor to conductor, or be- tween any two conductors, in a system which is insulated from the ground, as is mostly the case in medium voltage overhead transmissions, and frequently in underground cables. In an ungrounded cable system, i ...", "... NG-CURRENT PHENOMENA Hence the quarter-phase system with common return saves 2 per cent, more copper than the three-phase system, but is inferior to the single-phase three-wire system. The inverted three-phase system, consistmg of two e.m.fs. e at 60° displacement, and three equal currents iz in the three lines of equal resistance rs, gives the output 2 eis, that is, compared { with the single-phase system, is = -^- The loss in the three lines is 3 z'sVs = I ihs. Hence, to give the same loss, 2 ih, as the singl ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-48", "section_label": "Chapter 8: Velocity Of Propagation Of Electric Field", "section_title": "Velocity Of Propagation Of Electric Field", "kind": "chapter", "sequence": 48, "number": 8, "location": "lines 26095-27002", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "snippets": [ "... elocity of propagation of the electric field through space is usually not considered, but the electric field assumed as instan- taneous throughout space; that is, the electromagnetic com- ponent of the field is considered as in phase with the current, the electrostatic component as in phase with the voltage. In reality, however, the electric field starts at the conductor and propa- gates from there through space with a finite though very high velocity, the velocity of light; that is, at any point in space the electric f ...", "... able distance from the conductor is of importance as in wireless telegraphy. In wireless telegraphy the electric field of the sending antennae propagating through space impinges upon the receiving antennae and there is observed by its electromagnetic and electrostatic effect. 68. The electric field of an infinitely long conductor without return conductor decreases inversely proportionally to the dis- tance, and therefore is represented by ^r #-j, CD where ^ is the intensity of the electric field at unit distance ...", "... finite conductors without return conductors, at considerable distance from each other. ((7) The capacity of a sphere in free space. (D) The capacity of a sphere against ground, in space. Cases A and B deal with the electromagnetic, C and D with the electrostatic component of the electric field. A. Inductance of a length I of an infinitely long conductor without return conductor. 70. The inductance of a length I of a straight conductor is usually given by the equation L = 2Zlog^XlO-9, (6) lr where V = the ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-04", "section_label": "Lecture 4: The Characteristics Of Space A. The Geometry Of The Gravitational Field", "section_title": "The Characteristics Of Space A. The Geometry Of The Gravitational Field", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3595-6820", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-04/", "snippets": [ "... c energy and the electromagnetic field do not yet satisfactorily fit into it. INDEX Aberration of light, 15 Absolute number, meaning, 38 Accelerated motion, and gravitation, 52 Acceleration, 9, 47 Action at distance, 19 Alternating current, 14 dielectric field, 20 Analogue, 2 dimensional, of uni- verse, 119 Axioms of mathematics, 70 metric, of space, 95, 110 B Beltrami's pseudosphere, 91 Bending of space, 88 Betel geuse, 67 Bolyai, 71 Bullet velocity, 13 C Capacity and wave velocity, 23 ...", "... eltrami's pseudosphere, 91 Bending of space, 88 Betel geuse, 67 Bolyai, 71 Bullet velocity, 13 C Capacity and wave velocity, 23 Centrifugal field, 47 force and inertia, 49 mass, 47 Characteristic of space, 69 constant of space, 81 Charge, electrostatic, 47 Circle, in centrifugal and gravita- tional field, 62 circumference and diameter, 61 Color, relatively, 7 Combination of velocities in rela- tivity, 42 Comet, orbits, 60 velocity, 13 Completely metric space, 115 Cone, as Euclidean 2-space, 90 ...", "... ements, 92 Corpuscular theory of light, 13 Curvature of bundle as 2-space, 102 of curve, 82 of space, 80, 81, 83 Cylinder, as Euclidean 2-space, 90 D Deflection of light in gravitational field, 55 angle and equation, 59 Detonation velocity, 13 Dielectric field, 18 intensity, 47 Differential metric space, 115 Dimensions of physical space, 97 Direction of curve, 82 Distance between two events, 32 measure of time, 33 E Earth as elliptic 2-space, 75 Einstein, law of gravitation, 11 Electric field, 4 ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-07", "section_label": "Lecture 7: High Frequency Oscillations And Surges", "section_title": "High Frequency Oscillations And Surges", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3508-3780", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-07/", "snippets": [ "SEVENTH LECTURE HIGH FREQUENCY OSCILLATIONS AND SURGES 1\"^ N an electric circuit, in addition to the power consump- tion by the resistance of the lines, an energy storage ■^ occurs as electrostatic energy, or electrostatic charge due to the voltage on the line (capacity) ; and as electromag- netic energy, or magnetic field of the current in the line (inductance). In the long distance transmission line, both amounts of stored energy are very consider ...", "SEVENTH LECTURE HIGH FREQUENCY OSCILLATIONS AND SURGES 1\"^ N an electric circuit, in addition to the power consump- tion by the resistance of the lines, an energy storage ■^ occurs as electrostatic energy, or electrostatic charge due to the voltage on the line (capacity) ; and as electromag- netic energy, or magnetic field of the current in the line (inductance). In the long distance transmission line, both amounts of stored energy are very considerable, and of about equal ...", "... e line. Any change of the voltage on the line, or the current in the line, or the relation between volt- age and current, therefore requires a corresponding change of the stored energy; that is, a readjustment of the stored energy e^C in the system, the electrostatic energy and the electro- i'L magnetic energy — — , from the previous to the changed cir- cuit conditions. This readjustment occurs by an oscillation, that is, a series of waves of voltage and of current, which gradually decreases in intensity, that is, d ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... y Prof. Langley, that is, the gusty character of the air currents, results not only in an internal mechanical energy, which the bird utilizes for soaring, but also results in unequal moisture distribution, and so, when condensation occurs, in an \"internal electrostatic energy\" of the thunder cloud, which dis- charges as lightning. With an average length of the half -wave of 1000 feet, and 50,000 volts per foot as potential gradient, the potential 270 GENERAL LECTURES differences in the clouds would be of the magnit ...", "... rops in a space of two miles' length, and 200 to 400 feet diameter, can be calculated, and also their electro- static capacity. With a wave length of 2000 feet, and a potential gradient of 50,000 volts per foot, from the capacity follows the energy of the electrostatic charge, which dis- charges as lightning flash. This is found under the above assumption, as of the magnitude of 10,000 K. W. seconds, so agrees with the results derived from the photometric considera- tions. To conclude then, as approximate values of ma ...", "... nd a comparison thereof with the observed effects. In general, the high potential phenomena possible in electric circuits are the same three classes of phenomena which can occur in any medium, as a body of water, which is the seat of energy. 1. Steady electrostatic stress, that is, a gradual rise of potential of the total circuit against ground, until a discharge occurs somewhere ; just as in a body of water, as a river, the pressure, that is, the water level, may gradually rise, until it breaks through the embankme ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-83", "section_label": "Apparatus Section 4: Synchronous Converters: Armature Current and Heating", "section_title": "Synchronous Converters: Armature Current and Heating", "kind": "apparatus-section", "sequence": 83, "number": 4, "location": "lines 13889-15160", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-83/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-83/", "snippets": [ "... in phase with the rectangular current in the coil d, it becomes more and more out of phase with the rectangular current when passing from coil d toward ai or a2, as shown in Figs. 130 to 133, until the maximum phase displacement between alternating and rectangular current is reached at the alternating leads ai and a2, and is equal to -• li 89. Thus, if E = direct voltage, and I = direct current, in an armature coil displaced by angle T from ...", "... d midway between adjacent leads, Fig. 127, and the resultant current is a minimum and of the shape shown in Fig. 128, at a point of the armature winding displaced from mid position d by angle r = 0. At the leads the displacement between alternating cur- 7T • 7T rent and direct current then is not -, but - + 8 at the n n one, 6 at the other lead, and thus at the other side of the same n lead. The resultant ...", "... r lead are displaced SYNCHRONOUS CONVERTERS 239 respectively by- + & = 75 deg. and by - — d = 15 deg., and so of very different shape, as shown by Figs. 135 and 136, giving very different local heating. Phase displacement thus increases the heating at the one, decreases it at the other side of each commutator lead. Let again, I = direct current per commutator brush. The effective value of the alternating power current in the armature wi ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "section_label": "Chapter 16: Induction Motor", "section_title": "Induction Motor", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "... s, and impressed E.M.F., £0; f=^— or, /= _ j + (>i-yji _ E \" ( Neglecting, in the denominator, the small quantity F, it is Z, F 0 + r\\ or, expanded, [(j^ + A'0) + r^ -f s^ (rog - +/ [J3 (jfo+^O + r^+JT! (xtg+r^+fx^ (xj>+ xj- Hence, displacement of phase between current and E.M.F., tan , = ^(^o+^ Neglecting the exciting current, /<„ altogether, that is, setting Y = 0, We have 7= sEn^- „ S tan fj) = cos o^ We have, however, thus, «! <$ substituting these values in the equation of the torque, it is T. 248 ALTERNATING-CURRENT PHENOMENA. or, in practical (C.G.S.) units, ...", "... nces, x^ + x0. Starting Torque. 162. In the moment of starting an induction motor, the slip is hence, starting current, Oo - or, expanded, with the rejection of the last term in the denominator, as insignificant, T _io11 010,io1 . - 8 and, displacement of phase, or angle of lag, fi + r0] + *! [Jfx 4- Jf0]) - jf (r0 ^ - *0 rt) „ _ 1 W° r0) INDUCTION MOTOR. 255 Neglecting the exciting current, g = 0 = b, these equa- tions assume the form, or, eliminating imaginary quantities, and tan w0 = ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-18", "section_label": "Chapter 20: Single-Phase Commutator Motors", "section_title": "Single-Phase Commutator Motors", "kind": "chapter", "sequence": 18, "number": 20, "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "... that in 6 the armature circuit is more inductive, and the quadrature flux therefore lags less behind the main flux than in 7, and by thus using more or less of the field coil in the arma- ture circuit its inductivity can be varied, and therewith the phase displacement of the quadrature flux against, the main flux adjusted from nearly 90° lag to considerably less lag, hence not only the proper intensity but also the exact phase of the required commutating flux produced. As seen herefrom, the difference between the diff ...", "... usually is sufficiently high, such compensation is rarely needed. In motors in which some of the circuits are connected induct ively in series with the others the diagram is essentially thesame, except SINGLE-PHASE COMMUTATOR MOTORS 369 that a phase displacement exists between the secondary and the primary current. The secondary current, Ii, of the transformer lags behind the primary current, Jo, slightly less than 180° ; that is, considered in opposite direction, the secondary current leads the primary by a smal ...", "... 1\" \\ in the non-inductive resistance, gives the dia- gram Fig. 180, where a = I'iO$ = angle of lag of magnetic field. 24 370 ELECTRICAL APPARATUS 205. The action of the commutator in an alternating-eurreri motor, in permitting compensation for phase displacement iwl thus allowing a control of the power-factor, is very imn. ■-m-.- and important, and can also be used in other types of machines, as induction motors am! alternators, by supplying these machines with a commutator for phase control. A lag of the curr ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... acity, also see Condenser. and inductance, equations 48 and velocity of propagation 400, 401 distributed series 348 energy of complex circuit 517 in mutual inductive circuit 161 of electric circuit 112 range in electric circuit 13 representing electrostatic component of electric field 5 shunting direct-current circuit 133 specific, numerical values 11 suppressing pulsations in direct-current circuit 134 Cast iron, effective penetration of alternating current 378 Cathode of arcs 249 Charge of condense ...", "... r oscillation 66, 72 Decay of continuous current in inductive circuit 17 of wave of condenser oscillation 72 Decrement of condenser oscillation 65, 72 resultant time, of complex circuit 504 Destructive voltages in cables and transmission lines 120 Dielectric constant, numerical values 11 strength, numerical values 11 Dielectric also see Electrostatic. Direct-current generator, self-excitation 32 railway, transient effective resistance 379 Disappearance of transient term in alternating-current circuit 43 ...", "... of wave of condenser oscillation 72 Decrement of condenser oscillation 65, 72 resultant time, of complex circuit 504 Destructive voltages in cables and transmission lines 120 Dielectric constant, numerical values 11 strength, numerical values 11 Dielectric also see Electrostatic. Direct-current generator, self-excitation 32 railway, transient effective resistance 379 Disappearance of transient term in alternating-current circuit 43 Discharge of condenser , . 51 Geissler tube 9 inductive, as wave 535 ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-05", "section_label": "Lecture 5: Long Distance Transmission", "section_title": "Long Distance Transmission", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2562-3132", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-05/", "snippets": [ "... ential differences from all the conductors to the ground. Any electric circuit, and so also the transmission line, contains inductance and capacity, and therefore stores energy as electromagnetic energy in the magnetic field due to the cur- rent, and as electrostatic energy, or electrostatic charge, due to the voltage. LONG DISTANCE TRANSMISSION 69 If: e = voltage, C = capacity. i = current, L = inductance. the electrostatic energy is : e*C 2 and the electromagnetic energy : i'L 2 In a high potential t ...", "... ll the conductors to the ground. Any electric circuit, and so also the transmission line, contains inductance and capacity, and therefore stores energy as electromagnetic energy in the magnetic field due to the cur- rent, and as electrostatic energy, or electrostatic charge, due to the voltage. LONG DISTANCE TRANSMISSION 69 If: e = voltage, C = capacity. i = current, L = inductance. the electrostatic energy is : e*C 2 and the electromagnetic energy : i'L 2 In a high potential transmission line both ene ...", "... s energy as electromagnetic energy in the magnetic field due to the cur- rent, and as electrostatic energy, or electrostatic charge, due to the voltage. LONG DISTANCE TRANSMISSION 69 If: e = voltage, C = capacity. i = current, L = inductance. the electrostatic energy is : e*C 2 and the electromagnetic energy : i'L 2 In a high potential transmission line both energies are of about the same magnitude, and the energy can therefore see- saw between the two forms and thereby produce oscillations and surges r ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-25", "section_label": "Chapter 25: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 29375-32539", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-25/", "snippets": [ "... ntly exact in most cases, under certain circumstances the deviation of the wave from sine shape becomes of importance, and with certain distortions it may not be pos- sible to replace the distorted wave by an equivalent sine wave, since the angle of phase displacement of the equivalent sine wave becomes indefinite. Thus it becomes desirable to investi- gate the distortion of the wave, its causes and its effects. Since, as stated before, any alternating wave can be repre- sented by a series of sine functions of odd ord ...", "... magnetic saturation and hysteresis is essentially of the frequency, 2 / — that is, describes a complete cycle for each half-wave of current — this shows why the distortion of wave-shape by hysteresis consists essentially of a triple harmonic. The phase displacement between e and i, and thus the power consumed or produced in the electric circuit, depends upon the angle, 9, as discussed before. 350 ALTERNATING-CURRENT PHENOMENA 238. In case of a distortion of the wave-shape by reactance, the distorted waves can be ...", "... ed out under the assumption of sine waves, as done in the preceding chapters. Similar phenomena take place in circuits containing polari- zation cells, leaky condensers, or other apparatus representing a synchronously varying negative reactance. Possibly dielectric hysteresis in condensers causes a distortion similar to that due to magnetic hysteresis. Inversely, at very high voltages, where corona appears on the conductors, with a sine wave of impressed voltage, a distor- tion of the capacity current wave occurs, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-26", "section_label": "Chapter 26: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 32540-33010", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-26/", "snippets": [ "... ^ - 0.3 sin (3 ^ - 180°). ^^.^. 4i^ ft Fig. 186. As seen, the effect of the triple harmonic is, in the first figure, to flatten the zero values and point the maximum values of the wave, giving what is called a peaked wave. With increasing phase displacement of the triple harmonic, the flat zero rises and gradually changes to a second peak, giving ultimately a flat-top or even double-peaked wave with sharp zero. The intermediate positions represent what is called a saw-tooth wave. In Fig. 186 are shown the f ...", "... a saw-tooth wave. In Fig. 186 are shown the fundamental sine wave and the EFFECTS OF HIGHER HARMONICS 371 complex waves produced by superposition of a quintuple har- monic of 20 per cent, the amplitude of the fundamental, under the relative phase displacement of 0°, 45°, 90°, 135°, 180°, represented by the equations: sin /3 sin iS - 0.2 sin 5 jS sin ^ - 0.2 sin (5 /S - 45°) sin /3 - 0.2 sin (5 ^S - 90°) sin 13 - 0.2 sin (5 /S - 135°) sin 13 - 0.2 sin (5 i3 - 180°). Fig. 187. — Some characteristic w ...", "... sin /3 - 0.2 sin (5 ^S - 90°) sin 13 - 0.2 sin (5 /S - 135°) sin 13 - 0.2 sin (5 i3 - 180°). Fig. 187. — Some characteristic wave-shapes. The quintuple harmonic causes a flat-topped or even double- peaked wave with flat zero. With increasing phase displacement the wave becomes of the type called saw-tooth wave also. The flat zero rises and becomes a third peak, while of the two former 372 ALTERNATING-CURRENT PHENOMENA peaks, one rises, the otlier decreases, and the wave gradually changes to a triple-peaked ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-04", "section_label": "Chapter 5: Single-Phase Induction Motor", "section_title": "Single-Phase Induction Motor", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 8555-10582", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-04/", "snippets": [ "... — The primary system of the single- phase induction motor is composed of two or more circuits displaced from each other in position around the armature circumference, and combined with impedances of different in- ductance factors so as to produce a phase displacement between them. The motor circuits may be connected in series, and shunted by the impedance, or they may be connected in shunt with each other, but in series with their respective impedance, or they may be connected with each other by transformation, etc. ...", "... but in series with their respective impedance, or they may be connected with each other by transformation, etc. B. Inductive Devices. — The motor is excited by two or more circuits which are in inductive relation with each other so as to produce a phase displacement. 98 ELECTRICAL APPARATUS This inductive relation may be established outside of the motor by an external phase-splitting device, or may take place in the motor proper. C. Monocyclic Devices. — An essentially reactive quadrature voltage is produced ou ...", "... euits. lie first motor, as positive reactance in the second motor, rsely. K Higher values of starting-torque efficiency are aecurec use of capacity in the one, and inductance in the other m nit. It is obvious that by resistance and inductance al phase displacement between the two component curre thus true quarter-phase relation, can not be reached. s resistance consumes energy, the use of resistance is justi and by tor ne, its;, Bed SINGLE-PHASE INDUCTION MOTOR 107 only due to its simplicity and cheapn ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-03-record", "section_label": "Report Record 4: Record of Four Troubles", "section_title": "Record of Four Troubles", "kind": "report-record", "sequence": 4, "number": 4, "location": "PDF pages 16-27, lines 1139-2164", "status": "pdf-text-extracted-candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-03-record/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-03-record/", "snippets": [ "... chronous machines. f) Sufficiently sensitive synchronoscopes between the station sec- tions would indicate whether the station sections are in phase with each other or out of synchronism, whether they are hunting against each other, and whether and what phase displacement exists between the station sections. [[END_PDF_PAGE:21]] [[PDF_PAGE:22]] 16 Report of Charles P. Steinmetz HI OPERATION Momentum of Alternators The emergency steam cut offs of the turbo-alternators are stated to he set for an excess speed of about 10%. Consi ...", "... one alternator is increased, on the other decreased, or with the same driving power, the load on the one is increased, on the other decreased, but the terminal voltage kept the same, then current and power flows over the dividing reactor, resulting in a phase displacement between the two alternators (or station sections). This phase displacement increases with the increase of power transfer. This gives a case where current and power is carried over a reactance from one circuit to another one, without any voltage drop. It is th ...", "... ng power, the load on the one is increased, on the other decreased, but the terminal voltage kept the same, then current and power flows over the dividing reactor, resulting in a phase displacement between the two alternators (or station sections). This phase displacement increases with the increase of power transfer. This gives a case where current and power is carried over a reactance from one circuit to another one, without any voltage drop. It is this, on which the use of limiting busbar reactors is based. The power transf ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-05", "section_label": "Lecture 5: Single-Energy Tra.Nsient Of Ironclad Circuit", "section_title": "Single-Energy Tra.Nsient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3387-3720", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-05/", "snippets": [ "LECTURE V. SINGLE-ENERGY TRA.NSIENT OF IRONCLAD CIRCUIT. 22. Usually in electric circuits; current, voltage, the magnetic field and the dielectric field are proportional to each other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other ...", "... h other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnetic materials, or if the dielectric field reaches densities beyond the dielectric strength of the carrier of the field, etc.; and the proportionality between current or voltage and their respective fields, the magnetic and the dielectric, thus ceases, or, as it may be expressed, the inducta ...", "... ponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnetic materials, or if the dielectric field reaches densities beyond the dielectric strength of the carrier of the field, etc.; and the proportionality between current or voltage and their respective fields, the magnetic and the dielectric, thus ceases, or, as it may be expressed, the inductance L is not constant, but varies w^ith the cu ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-05", "section_label": "Lecture 5: Single-Energy Transient Of Ironclad Circuit", "section_title": "Single-Energy Transient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2972-3286", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "snippets": [ "LECTURE V. SINGLE-ENERGY TRANSIENT OF IRONCLAD CIRCUIT. 22. Usually in electric circuits, current, voltage, the magnetic field and the dielectric field are proportional to each other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other ...", "... h other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnetic materials, or if the dielectric field reaches densities beyond the dielectric strength of the carrier of the field, etc. ; and the proportionality between current or voltage and their respective fields, the magnetic and the dielectric, thus ceases, or, as it may be expressed, the induct ...", "... ponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnetic materials, or if the dielectric field reaches densities beyond the dielectric strength of the carrier of the field, etc. ; and the proportionality between current or voltage and their respective fields, the magnetic and the dielectric, thus ceases, or, as it may be expressed, the inductance L is not constant, but varies with the cu ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-08", "section_label": "Theory Section 8: Power in Alternating-current Circuits", "section_title": "Power in Alternating-current Circuits", "kind": "theory-section", "sequence": 8, "number": 8, "location": "lines 2718-2864", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-08/", "snippets": [ "... nce is a wattless or reactive e.m.f., while the e.m.f. of resistance is a power or active e.m.f. The wattless e.m.f. is in quadrature, the power e.m.f. in phase with the current. In general, if 0 = angle of time-phase displacement between the resultant e.m.f. and the resultant current of the circuit, / = current, E = impressed e.m.f., consisting of two com- ponents, one, EI = E cos 0, in phase with the current, the other, 1£2 = E sin 0, in quad ...", "... f transmission with non- inductive load, with 45-time-degree lagging load and 45-degree leading load? The power received per line with non-inductive load is P = El = 3170 X 44 = 139 kw. With a load of 45 degrees phase displacement, P = El cos 45° = 98 kw. The power lost per line PI = PR = 442 X 7.6 = 14.7 kw. Thus the input into the line P0 = P + PI = 151.7 kw. at non-inductive load, and = 111.7 kw. at load of 45 degrees phase ...", "... , P = El cos 45° = 98 kw. The power lost per line PI = PR = 442 X 7.6 = 14.7 kw. Thus the input into the line P0 = P + PI = 151.7 kw. at non-inductive load, and = 111.7 kw. at load of 45 degrees phase displacement. The efficiency with non-inductive load is P 14 7 Po = l - 15T7 = )0-3 p and with a load of 45 degrees phase displacement is P 14.7 ^- = 1 — 111 -, = 86.8 per cent. L Q 111./ The total output is 3 P = ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-18", "section_label": "Chapter 18: Polyphase Induction Motors", "section_title": "Polyphase Induction Motors", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17717-20445", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-18/", "snippets": [ "... + r,^ + sa^ife) — j (rib — sx^g) Eo, (ri + STo) + is (xi + a^o) or, expanded, [(sfi + sVo) + ri^g + sri (ro? — Xob) + s^a^i (a^ofi' + Xig + rofe)- , i[s- (xq + a^i) + ri^b + sri (x^g + rpb) + s^x^ (xob + a^i^- Ti^g)] {ri-hsror-hs'ixi + xor- Hence, displacement of phase between current and e.m.f., _ s^(^o + Xi) + ri-b + sr^ixog + ro6) + s~Xi{xob + a: 16 - r„g) ° ~ (sri + sVo) +ri2(/ + sr](ro<7-a:o&) +s2a;i(a;og+a;]6i-ro6) Neglecting the exciting current, h, altogether, that is, setting F= 0, We have tan do ...", "... The secondary induced e.ni.f., E), lags 90° behind the inducing magnetism, hence reaches a maximum displaced in space by 90° from the position of maximum magnetization. Thus, if the secondary current, Ii, lags l^ehind its emf., Ei, by angle, 6i, the space displacement ])etween armature current and field magnetism is ^ (/i4>) = 90° + ^1, hence sin ($/i) = cos ^i. We have, however, cos di es 10-1 e = V2 7r7?,i$/10-8, thus, el08 substituting these values in the equation of the torque, it is ^ qpisrie^ 10 ...", "... or, expanded, with the rejection of the last term in the denomi- nator, as insignificant, [(^1 + ro) + ^(ri[ri + ro] + Xifxi + Xo\\) + b{roXi - XoVi)]- j ^ i[(xi + Xo) + 6(ri[ri + ro] + Xt[xi + x^]) - g (roXi - XorQ] (ri + ro)2 + (xi + Xo)=^ •■\"' and, displacement of phase, or angle of lag, ^^^ Q ^ (xi + xo) + b (ri [ri + ro] + Xi[xi + Xp]) - gir^Xx — rcorQ ('/•i -\\- ra) + g (ri [ri + ro] + Xi{X], + Xo]) + 6(roXi - XorO' 224 ALTERNATING-CURRENT PHENOMENA Neglecting the exciting current, g = 0 = b, these equatio ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-30", "section_label": "Chapter 30: Balanced And Unbalanced Polyphase Systems", "section_title": "Balanced And Unbalanced Polyphase Systems", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 35256-35691", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-30/", "snippets": [ "... low of energy varies periodically, as in the single-phase system; and the ratio of the minimum value to the maximum value of power is called the halance-J actor of the system. Hence in a single-phase system on non-inductive circuit, that is, at no-phase displacement, the balance-factor is zero; and it is negative in a single-phase system with lagging or leading current, and becomes equal to — 1 if the phase displace- ment is 90° — that is, the circuit is wattless. 275. Obviously, in a polyphase system the balance of ...", "... distribution of load between the different branch circuits. A balanced system in particular is called a polyphase system, whose flow of energy is constant, if all the circuits are loaded equally with a load of the same character^ that is, the same phase displacement. POLYPHASE SYSTEMS 407 276. All the symmetrical systems from the three-phase system upward are balanced systems. Many unsymmetrical systems are balanced systems also. 1. Three-phase system: Let ei = E v^ sin ^, and ii = I \\/2 sin (/? - 6), 62 = ...", "... nstantaneous value of power is p = 2 EI {sin i8 sin (^ - 9) + cos /S cos (/3 - 0) } = 2 EI cos 9 = P, or constant. Hence the quarter-phase system is an unsymmetrical balanced system. 3. The symmetrical n-phase system, with equal load and equal phase-displacement in all n branches, is a balanced system. For, let e.- = E\\/2 sin I (3 ^j = e.m.f . ; ii = /\\/2 sin 1^ — 9 j = current; 408 ALTERNATING-CURRENT PHENOMENA the instantaneous value of power is p = Si Biii 1 = 2 EI h sin (p - ^~) sin (i3 - 0 ^) ' \" ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-21", "section_label": "Chapter 21: Dibtobtiox Of Wavs-Shafe And Its Causes", "section_title": "Dibtobtiox Of Wavs-Shafe And Its Causes", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 23274-24559", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "snippets": [ "... s sufficiently exact in most cases, under certain circumstances the deviation of the wave from sine shape becomes of importance, and no longer, and it may not be possible to replace the distorted wave by an equiv- alent sine wave, since the angle of phase displacement of the equivalent sine wave becomes indefinite. Thus it becomes desirable to investigate the distortion of the wave, its causes and its effects. Since, as stated before, any alternating wave can be represented by a series of sine functions of odd orders ...", "... ially of the frequency, 2N, §§218,210] DISTORTION OF WAVE-SHAPE. 329 — that is, describes a complete cycle for each half-wave of current, — this shows why the distortion of wave-shape by hysteresis consists essentially of a triple harmonic. The phase displacement between e and /, and thus the power consumed or produced in the electric circuit, depend upon the angle, w, as discussed before. 218. In case of a distortion of the wave-shape by reactance, the distorted waves can be replaced by their equivalent sine wa ...", "... ied out under the assumption of sine waves, as done in the preceding chapters. Similar phenomena take place in circuits containing polarization cells, leaky condensers, or other apparatus representing a synchronously varying negative reactance. Possibly dielectric hysteresis in condensers causes a dis- tortion similar to that due to magnetic hysteresis. Pulsation of Resistance, 219. To'a certain extent the investigation of the effect of synchronous pulsation of the resistance coincides with that of reactance ; s ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-25", "section_label": "Chapter 25: Baiianced And Unbaxiancbd Polyphase Systema", "section_title": "Baiianced And Unbaxiancbd Polyphase Systema", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 25605-26027", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-25/", "snippets": [ "... -phase sys- tem ; and the ratio of the minimum value to the maximum value of power is called the balance factor of ttie system. 358 ALTERNATIXG-CURRENT PHENOMENA. [§§241,242 Hence in a single-phase system on non-inductive circuit, that is, at no-phase displacement, the balance factor is zero ; and it is negative in a single-phase system with lagging or leading current, and becomes = — 1, if the phase displace- ment is 90° — that is, the circuit is wattless. 241. Obviously, in a polyphase systeiji the balance of t ...", "... distribution of load between the different branch circuits. A balanced system in particular is called a polyphase system, whose flow of energy is constant, if all the circuits are loaded equally with a load of the same character, that is, the same phase displacement. 242. All the symmetrical systems from the three-phase system upward are balanced systems. Many unsymmetrical systems are balanced systems also. 1.) Three-phase system : Let ^i=^V2sin)3, and /i = /V2 sin ()8 - u») ; e^ = E V2 sin ()3 - 120), i^ = I ...", "... antaneous flow of power is : / = 2 EI{s\\x\\ p sin {p - Q,) + cos fi cos (J3- «)) = 2 EI cos w = J\\ or constant. Hence the quarter-phase system is an unsymmetrical bal- anced system. 3.) The symmetrical //-phase system, with equal load and equal phase displacement in all « branches, is a bal- anced system. For, let : ^, = ^ V2 sin (p - ^^^ = E.M.F. ; /, = / V5 sin f )3 — a» — J = current the instantaneous flow of power is : n 1 = 2 EI ^tsin U - ^-^'J sin U-C^- ^^'j = E I ) ^i cos d — XT' cos j 2 )3 — (u — ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-28", "section_label": "Chapter 28: Copper Efficiency Of Systems", "section_title": "Copper Efficiency Of Systems", "kind": "chapter", "sequence": 28, "number": 28, "location": "lines 26584-27052", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-28/", "snippets": [ "... nly, but where the limitation of potential depends upon the problem of insulating the conductors against disruptive discharge, the proper comparison is on the basis of equality of the maximum difference of potential in the system ; that is, equal maximum dielectric strain on the insulation. The same consideration holds in moderate potential power circuits, in considering the danger to life from wires or high differences of potential. Thus the comparison of different systems of long-dis- tance transmission at high ...", "... single-phase system. Hence the quarter-phase system with common return saves 2 per cent more copper than the three-phase system, but is inferior to the single-phase three-wire system. The inverted three-phase system, consisting of two E.M.Fs. ^ at 60® displacement, and three equal currents /g in the three lines of equal resistance rg, gives the out- put 2^*/3, that is, compared with the single-phase system, /g = //2. The loss in the three lines is 3 i^ ^3 = 3 ^^ 's- Hence, to give the same loss 2 /^ ;- as the singl ...", "... ircuit of potential e V2, which latter requires only half the copper of the alternating system. This comparison of the alternating with the continuous*- current system is not proper however, since the continuous- current potential introduces, besides the electrostatic strain, an electrolytic strain on the dielectric which does not exist in the alternating system, and thus makes the action of the continuous-current potential on the insulation more severe than that of an equal alternating potential. Besides, at the volt ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-22", "section_label": "Chapter 22: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 21190-21982", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "snippets": [ "... iently exact in most cases, under certain circumstances the deviation of the wave from sine shape becomes of importance, and with certain distortions it may not be possible to replace the distorted wave by an equivalent sine wave, since the angle of phase displacement of the equivalent sine wave becomes indefinite. Thus it becomes desirable to investigate the distortion of the wave, its causes and its effects. Since, as stated before, any alternating wave can be represented by a series of sine functions of odd orders ...", "... is essentially of the frequency, 21V, DISTORTION OF WAVE-SHAPE. 393 — that is, describes a complete cycle for each half -wave of current, — this shows why the distortion of wave-shape by hysteresis consists essentially of a triple harmonic. The phase displacement between e and i, and thus the power consumed or produced in the electric circuit, depend \\ipon the angle, o>, as discussed before. 239. In case of a distortion of the wave-shape by reactance, the distorted waves can be replaced by their equivalent sine ...", "... ied out under the assumption of sine waves, as done in the preceding chapters. Similar phenomena take place in circuits containing polarization cells, leaky condensers, or other apparatus representing a synchronously varying negative reactance. Possibly dielectric hysteresis in condensers causes a dis- tortion similar to that due to magnetic hysteresis. Pulsation of Resistance. 240. To a certain extent the investigation of the effect of synchronous pulsation of the resistance coincides with that of reactance ; s ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-23", "section_label": "Chapter 23: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 21983-22448", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "snippets": [ "... ft - .3 sin (3 ft - 135°) sin ft — .3 sin (3/3 — 180°). • As seen, the effect of the triple harmonic is in the first figure to flatten the zero values and point the maximum values of the wave, giving what is called a peaked wave. With increasing phase displacement of the triple harmonic, the flat zero rises and gradually changes to a second peak, giving ultimately a flat-top or even double-peaked wave with sharp zero. The intermediate positions represent what is called a saw-tooth wave. In Fig. 176 are shown the ...", "... ediate positions represent what is called a saw-tooth wave. In Fig. 176 are shown the fundamental sine wave and the complex waves produced by superposition of a quintuple harmonic of 20 per cent the amplitude of the fundamental, under the relative phase displacement of 0°, 45°, 90°, 135°, 180°, represented by the equations : sin ft sin ft — .2 sin 5 ft sin/3- .2 sin (5,8-45°) sin/3- .2 sin (5/3-90°) smft- .2 sin (5/3- 135°) sin/3- .2 sin (5/8- 180°). The quintuple harmonic causes a flat -topped or even double ...", "... uations : sin ft sin ft — .2 sin 5 ft sin/3- .2 sin (5,8-45°) sin/3- .2 sin (5/3-90°) smft- .2 sin (5/3- 135°) sin/3- .2 sin (5/8- 180°). The quintuple harmonic causes a flat -topped or even double-peaked wave with flat zero. With increasing phase displacement, the wave becomes of the type called saw- tooth wave also. The flat zero rises and becomes a third peak, while of the two former peaks, one rises, the other 400 AL TERN A TING- CURRENT PHENOMENA. decreases, and the wave gradually changes to a tripl ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-27", "section_label": "Chapter 27: Balanced And Unbalanced Polyphase Systems", "section_title": "Balanced And Unbalanced Polyphase Systems", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 24054-24488", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-27/", "snippets": [ "... n the single-phase sys- tem ; and the ratio of the minimum value to the maximum value of power is called the balance factor of the system. 442 ALTERNATING-CURRENT PHENOMENA. Hence in a single-phase system on non-inductive circuit, that is, at no-phase displacement, the balance factor is zero ; and it is negative in a single-phase system with lagging or leading current, and becomes = — 1, if the phase displace- ment is 90° — that is, the circuit is wattless. 269. Obviously, in a polyphase system the balance of the ...", "... distribution of load between the different branch circuits. A balanced system in particular is called a polyphase system, whose flow of Energy is constant, if all the circuits are loaded equally with a load of the same character, that is, the same phase displacement. 270. All the symmetrical systems from the three-phase system upward are balanced systems. Many unsymmetrical systems are balanced systems also. 1.) Three-phase system : Let ^ = E V2 sin ft, and t\\ = I V2 sin (ft — w) ; ez = E V2 sin (ft - 120), /2 ...", "... stantaneous flow of power is : / = 2 £I(sm J3 sin (/? — 5) + cos ft cos (0 — £>)) = 2 £Scos w = P, or constant. Hence the quarter-phase system is an unsymmetrical bal- anced system. 3.) The symmetrical «-phase system, with equal load and equal phase displacement in all n branches, is a bal- anced system. For, let : e( = E V2 sin ( ft - — \"\\ = E.M.F. ; V » / / 2 IT A *',- = 7V2 sin O — S — = current V » V the instantaneous flow of power is : l V « 7 \\ » EI \\ yr cos a -57-035^2 /?-£- — or p = n E I ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-30", "section_label": "Chapter 30: Efficiency Of Systems", "section_title": "Efficiency Of Systems", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 25136-25597", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-30/", "snippets": [ "... ly, but where the limitation of potential depends upon the problem of insulating the conductors against disruptive discharge, the proper comparison is on the basis of equality of the maximum difference of potential in the system ; that is, •equal maximum dielectric strain on the insulation. The same consideration holds in moderate potential power circuits, in considering the danger to life from live wires entering human habitations. Thus the comparison of different systems of long-dis- tance transmission at high ...", "... single-phase system. Hence the quarter-phase system with common return saves 2 per cent more copper than the three-phase system, but is inferior to the single-phase three-wire system. The inverted three-phase system, consisting of two E.M.Fs. e at 60° displacement, and three equal currents /8 in the three lines of equal resistance r3, gives the out- put 2^z'3, that is, compared with the single-phase system, /8 = z'/2. The loss in the three lines is 3 z'32 r3 = | z2 rs. Hence, to give the same loss 2 z'2 r as the si ...", "... ircuit of potential e A/2, which latter requires only half the copper of the alternating system. This comparison of the alternating with the continuous- current system is not proper however, since the continuous- current potential introduces, besides the electrostatic strain, an electrolytic strain on the dielectric which does not exist in the alternating system, and thus makes the action of the continuous-current potential on the insulation more severe than that of an equal alternating potential. Besides, self- induc ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-40", "section_label": "Chapter 4: Arc Rectification", "section_title": "Arc Rectification", "kind": "chapter", "sequence": 40, "number": 4, "location": "lines 17755-19259", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "snippets": [ "... then by gradually withdrawing the terminals derive the energy of the arc flame by means of the current, from the electric circuit, as is done in practically all arc lamps. Or by increasing the voltage across the gap between the terminals so high that the electrostatic stress in the gap repre- sents sufficient energy to establish a path for the current, i.e., by jumping an electrostatic spark across the gap, this spark is fol- lowed by the arc flame. An arc can also be established between two terminals by supplying the ...", "... ic circuit, as is done in practically all arc lamps. Or by increasing the voltage across the gap between the terminals so high that the electrostatic stress in the gap repre- sents sufficient energy to establish a path for the current, i.e., by jumping an electrostatic spark across the gap, this spark is fol- lowed by the arc flame. An arc can also be established between two terminals by supplying the arc flame from another arc, etc. The arc therefore must be continuous at the cathode, but may be shifted from anode to ...", "... terruption of the cathode blast puts out the arc by interrupting the supply of conducting vapor, and a reversal of the arc stream means stopping the cathode blast and producing a reverse cathode blast, which, in general, requires a voltage higher than the electrostatic striking 249 250 TRANSIENT PHENOMENA voltage (at arc temperature) between the electrodes. With an alternating impressed e.m.f. the arc if established goes out at the end of the half wave, or if a cathode blast is maintained continuously by a second ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1659-2484", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-03/", "snippets": [ "... energy can exist. Such circuits are most of the low- and medium-voltage circuits, — 220 volts, 600 volts, and 2200 volts. In them the capac- ity is small, due to the limited extent of the circuit, resulting from the low voltage, and at the low voltage the dielectric energy thus is negligible, that is, the circuit stores appreciable energy only by the magnetic field. A circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectri ...", "... ielectric energy thus is negligible, that is, the circuit stores appreciable energy only by the magnetic field. A circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectric field. The usual high-voltage capacity circuit, as that of an electrostatic machine, while of very small inductance, also is of very small resistance, and the momentary discharge currents may be very consider- able, so that in spite of the very small ind ...", "... ble energy only by the magnetic field. A circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectric field. The usual high-voltage capacity circuit, as that of an electrostatic machine, while of very small inductance, also is of very small resistance, and the momentary discharge currents may be very consider- able, so that in spite of the very small inductance, considerable magnetic-energy storage may oc- cur; that is, the sys ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1531-2161", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "snippets": [ "... energy can exist. Such circuits are most of the low- and medium-voltage circuits, — 220 volts, 600 volts, and 2200 volts. In them the capac- ity is small, due to the limited extent of the circuit, resulting from the low voltage, and at the low voltage the dielectric energy thus is negligible, that is, the circuit stores appreciable energy only by the magnetic field. A circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectri ...", "... ielectric energy thus is negligible, that is, the circuit stores appreciable energy only by the magnetic field. A circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectric field. The usual high-voltage capacity circuit, as that of an electrostatic machine, while of very small inductance, also is of very small resistance, and the momentary discharge currents may be very consider- able, so that in spite of the very small in ...", "... ble energy only by the magnetic field. A circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectric field. The usual high-voltage capacity circuit, as that of an electrostatic machine, while of very small inductance, also is of very small resistance, and the momentary discharge currents may be very consider- able, so that in spite of the very small inductance, considerable __ magnetic-energy storage may oc- cur; that is, th ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-109", "section_label": "Apparatus Section 3: Induction Machines: Single -phase Induction Motor", "section_title": "Induction Machines: Single -phase Induction Motor", "kind": "apparatus-section", "sequence": 109, "number": 3, "location": "lines 20428-21157", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-109/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-109/", "snippets": [ "... cing the secondary currents, and in phase with the latter, that is, in time quadrature with the primary magnetic flux. Thus, if Fp = polarization due to the secondary currents, a = auxiliary magnetic flux, 6 = phase displacement in time between 3>a and 3>p, and T = phase displacement in space between ^a and Fp, the torque is D = Fp$a sin T cos 6. In general the starting torque, apparent torque efficiency, etc., of the single-phase induction ...", "... that is, in time quadrature with the primary magnetic flux. Thus, if Fp = polarization due to the secondary currents, a = auxiliary magnetic flux, 6 = phase displacement in time between 3>a and 3>p, and T = phase displacement in space between ^a and Fp, the torque is D = Fp$a sin T cos 6. In general the starting torque, apparent torque efficiency, etc., of the single-phase induction motor with any of these de- vices are given in per cent, ...", "... three classes. 1. Phase-splitting Devices. The primary system is composed of two or more circuits displaced from each other in position, and combined with impedances of different inductance factors so as to produce a phase displacement between them. When using two motor circuits, they can either be connected in series between the single-phase* mains, and shunted with impedances of different inductance factors, as, for instance, a INDUCTION MACHINES 335 ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-11", "section_label": "Theory Section 11: Capacity and Condensers", "section_title": "Capacity and Condensers", "kind": "theory-section", "sequence": 11, "number": 11, "location": "lines 3586-3760", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-11/", "snippets": [ "... ing, the e.m.f. of the condenser is 106/ 106 The value z0 = fn is called the condensive reactance of the ^ 7T/C condenser. 56 ELEMENTS OF ELECTRICAL ENGINEERING Due to the energy loss in the condenser by dielectric hysteresis, the current leads the e.m.f. by somewhat less than 90 time de- grees, and can be resolved into a wattless charging current and a dielectric hysteresis current, which latter, however, is generally so small as to ...", "... OF ELECTRICAL ENGINEERING Due to the energy loss in the condenser by dielectric hysteresis, the current leads the e.m.f. by somewhat less than 90 time de- grees, and can be resolved into a wattless charging current and a dielectric hysteresis current, which latter, however, is generally so small as to be negligible, though in underground cables of poor quality, it may reach as high as 50 per cent, or more of the charging or wattless current of the ...", "... a transmission line is i.nxio-6x/ . C = - — ~-i - , in mf., where Id = diameter of wire, cm.; 18 — distance of wire from return wire, cm.; I = length of wire, cm., and 1.11 X 10~6 = reduction coefficient from electrostatic units to mf . The logarithm is the natural logarithm; thus in common loga- rithms, since loge a = 2.303 logio a, the capacity is 0.24 X 10~6 X I i ^ t>s logio -7- I'd . , , in mf . The derivation of ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-36", "section_label": "Apparatus Section 15: Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "section_title": "Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "kind": "apparatus-section", "sequence": 36, "number": 15, "location": "lines 9918-10123", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-36/", "snippets": [ "... i- tion by 1/4 per cent, of 20 or 1/20 pole, that is, 180/20 = 9 elec- trical space degrees. If the armature of the other alternator at this moment is behind its average position by 9 electrical space degrees, the phase displacement between the alternator e.m.fs. is 18 electrical time degrees; that is, the alternator e.m.fs. are represented by OEi and OEZ in Fig. 71, and when running in parallel the e.m.f. OEf = E\\E^ is short circuited through the s ...", "... ulation of their prime movers, especially steam A ^^ engines. With alternators driven by gas engines, the problem of parallel operation is made more difficult by the more jerky nature of the gas-engine ^ 73._Phase displacement between impulse. In such machines, alternators to be synchronized, therefore, squirrel-cage wind- ings in the field-pole faces are commonly used, to assist synchron- izing by the currents induced in this short-circuited ...", "... lagging or demagnetizing, and in the other a leading or magnetizing, current. Hence two kinds of cross currents may exist in parallel opera- tion of alternators — currents transferring power between the machines, due to phase displacement between their e.m.fs., and wattless currents transferring magnetization between the ma- chines, due to a difference of their induced e.m.fs. In compound-wound alternators, that is, alternators in which the field excitation is ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1120-1683", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-01/", "snippets": [ "... in circuits where energy is expended only in heating the conductor, is the same as the ohmic resistance of continuous-current circuits. In circuits, however, where energy is also expended outside of the conductor by magnetic hysteresis, mutual inductance, dielectric hysteresis, etc., r is larger than the true ohmic resistance of the conductor, since it refers to the total expenditure of energy. It may be called then the effective re- sistance. It may no longer be a constant of the circuit. The reactance, x, does not ...", "... ^ = i Vr^ + x„,^ = iz; that is, the impedance, z, takes in alternating-current circuits the place of the resistance, r, in continuous-current circuits. Capacity 4. If upon a condenser of capacity C an e.m.f., e, is impressed, the condenser receives the electrostatic charge, Ce. If the e.m.f., e, alternates with the frequency, /, the average rate of charge and discharge is 4 /, and 2 irf the maximum rate of charge and discharge, sinusoidal waves supposed; hence, i = 2 irfCe, the current to the condenser, which is in ...", "... f e.m.f. to the current. Since in alternating-cur- rent circuits, in addition to the energy expended iii the ohmic re- sistance of the conductor, energy is expended, partly outside, partly inside of the conductor, by magnetic hysteresis, mutual induction, dielectric hysteresis, etc., the effective resistance, r, is in general larger than the true resistance of the conductor, sometimes many time larger, as in transformers at open sec- ondary circuit, and is no longer a constant of the circuit. It is more fully discuss ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-04", "section_label": "Chapter 4: Vector Representation", "section_title": "Vector Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2149-2759", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-04/", "snippets": [ "... in vector representation by the product of the current, I, into the projection of the e.m.f., E, upon the current, or by the e.m.f., E, into the projection of the current, I, £3 Eo upon the e.m.f., or by IE cos d, where A ^,--^^'' ^ ~ angle of phase displacement. ^J,.^--^ / 19. Suppose, as an example, that in ^^ *E ^' a line having the resistance, r, and the reactance, x = 2 irfL — where / = fre- quency and L = inductance — there p, ,r> exists a current of / amp., the line being connected to a non-inductive ...", "... mary cir- cuit is found to be 00 = EoOFo. 24. Thus, in Figs. 18 to 20, the diagram of a transformer is drawn for the same secondary e.m.f., E^, secondary current, /i, and therefore secondary m.m.f., Fi, but with different conditions of secondary phase displacement: VECTOR REPRESENTATION 29 In Fig. 18 the secondary current, /i, lags 60° behind the sec- ondary e.m.f., El. In Fig. 19, the secondary current, /i, is in phase with the sec- ondary e.m.f., El. In Fig. 20 the secondary current, /i, leads by 60° t ...", "... e see that a difference of phase existing in the secondary circuit of a transformer reappears in the primary circuit, somewhat decreased, if the current is leading, and slightly increased if lagging in phase. Later we shall see that hysteresis reduces the displacement in the primary circuit, so that, with an excessive lag in the secondary circuit, the lag in the primary circuit may be less than in the secondary. A conclusion from the foregoing is that the transformer is not suitable for producing currents of displaced ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1224-1727", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "snippets": [ "... ircuits where energy is expended only in heating the conductor, is the same as the ohmic resistance of continuous-current circuits. In circuits, how- ever, where energy is also expended outside of the con- ductor by magnetic hysteresis, mutual inductance, dielectric hysteresis, etc., r is larger than the true ohmic resistance of the conductor, since it refers to the total expenditure of energy. It may be called then the effective resistance. It is no longer a constant of the circuit. The reactance, ;r, does not rep ...", "... l E.M.F. is — that is, the impedance, ^, takes in alternating-current cir- cuits the place of the resistance, r, in continuous-current •circuits. CAPACITY. 4. If upon a condenser of capacity, C, an E.M.F., e, is impressed, the condenser receives the electrostatic charge, Ce. If the E.M.F., e, alternates with the frequency, iV, the average rate of charge and discharge is 4 A^, and 2w JV the maximum rate of charge and discharge, sinusoidal waves sup- posed, hence, i = 2ir NCe the current passing into the con- dens ...", "... the energy component of E.M.F. to the cur- rent. Since in alternating-current circuits, besides by the ohmic resistance of the conductor, energy is expended, partly outside, partly even inside, of the conductor, by magnetic hysteresis, mutual inductance, dielectric hystere- sis, etc., the effective resistance, r, is in general larger than the true resistance of the conductor, sometimes many times larger, as in transformers at open secondary circuit, and is not a constant of the circuit any more. It is more fully di ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-15", "section_label": "Chapter 15: Induction Motob", "section_title": "Induction Motob", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 14919-17024", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "snippets": [ "... j^-^i) {i + J^) Neglecting, in the denominator, the small quantity ZZiK, it is §144] INDUCTION MOTOR. 218 (n - j'sx^) + s{r- jx) ^ {s + r^^ + jJT i^ ) + j {r^g - jj:i^) ^ (ri + sr) —js{x^ + x) or, expanded, {r^ + sr)^ + s^(x, + xy Hence,displacement of phase between current and E.M.F., {sr^ + s^r) + r^^g+sr^{rg-x^)+^x^{xg+x^+^^ Neglecting the exciting current, /^, altogether, that is, setting F = 0, it is, \\r, + sry + s\\x + x,y ^ s_Eo . (r\\ + sr) - s {x + x^) ' . « s (x '\\- x^ tan Wo = — ^^ ...", "... e secondary induced E.M.F., E^^ lags 90® behind the inducing magnetism, hence reaches a maximum displaced in space by 90° from the position of maximum magnetization. Thus, if the secondary current, /, , lags behind its E.M.F., E^, by angle, cS^, the space displacement between armature current and field magnetism is ^ (/, *) = 90<'+ CO, hence, sin (<^ /,) = cos wj It is, however, cos 0*1 = n Vr,2 + ^ x^ , es thus, = — . substituting these values in the equation of the torque, it is or, in practic ...", "... (r -jx) + (/-I -jxi) (r - jx) (^ +jb) or, expanded, with the neglection of the last term in the denominator, as insignificant : l{r,+r)+g{r,lr,+r-]+x,lx^+x']) + b{rx,-xr,)'\\ + T _ j\\(x^+x)+b{r^\\_r^+r']+x^lx,+x'])-g(rx^-xr;)^ .^ . (r,+ry+(x,+xf and, displacement of phase, or angle of lag, - ^ C ^i + x)-\\-b (ri [ri + r ] + - ^1 [-^1 + x']) - g {rx^ - xr^) tan 01, (''i + r) +g{r, [ri + r'] + x^ [.Vi + x'\\) + b (rxy - xr^) Neglecting the exciting current, ^ = = ^, these equa- tions assume the form : J ^ (n ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-19", "section_label": "Chapter 19: Commutatob Motobs", "section_title": "Commutatob Motobs", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 21339-22387", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "snippets": [ "... it closed upon itself and displaced in Bg. 144. space by 45° — in a bipolar motor — from the direction of the magnetic flux, as shown diagrammatically in Fig. 144. This secondary circuit, while set in motion, still remains in the same position of 45° displacement, with the magnetic flux, or rather, what is theoretically the same, when moving out of this position, is replaced by other secondary circuits entering this position of 45° displacement. For simplicity, in the following all the secondary quan- 296 AL T ...", "... ircuit, while set in motion, still remains in the same position of 45° displacement, with the magnetic flux, or rather, what is theoretically the same, when moving out of this position, is replaced by other secondary circuits entering this position of 45° displacement. For simplicity, in the following all the secondary quan- 296 AL TERN A TJNG-CURRENT PHENOMENA. [ § 196 titles, as E.M.F., current, resistance, reactance, etc., are assumed as reduced to the primary circuit by the ratio of turns, in the same way as d ...", "... and ^» - v/(i^?2' a \\Til P\"' ,'1^^'' =v/(^^+'-+^'Y+(-^+-') a ^« =v/(r^ f ^+'- +'■■)\"+ (^•+^-^- 1*200] COMMUTATOR MOTORS, 303 200. The power output at armature shaft is, P^ EI ( ( - ^ ^ •'^ + '- + '■lY + (•* + ^.)* The displacement of phase between current and E.M.F. tan 01 = F A- F — ^^— + '^ + n ? a ^. + .+ ... TT pn N Neglecting, as approximation, the resistances r + ri, it is, tan 01 = 2 nj Ni w pn N p = -ElSL K pn N 2 «, ^ 304 AL TERN A TING^CURRENT PHENOM ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-22", "section_label": "Chapter 20: Ri", "section_title": "Ri", "kind": "chapter", "sequence": 22, "number": 20, "location": "lines 24560-25119", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "snippets": [ "... )3 n (3)3 n(3)3 n(3)3 n(3^ 45°) 90°) 135°) 180°). As seen, the effect of the triple harmonic is in the first figure to flatten the zero values and point the maximum values of the wave, giving what is called a peaked wave. With increasing phase displacement of the triple harmonic, the flat zero rises and gradually changes to a second peak, giving ultimately a flat-top or even double-peaked wave with sharp zero. The intermediate positions represent what is called a saw-tooth wave. In Fig. 160 are shown the ...", "... ediate positions represent what is called a saw-tooth wave. In Fig. 160 are shown the fundamental sine wave and the complex waves produced by superposition of a quintuple harmonic of 20 per cent the amplitude of the fundamental, under the relative phase displacement of 0°, 45°, 90°, 135°, 180°, represented by the equations : s s s s s s n)3 n)3 n)3 n)3 n)3 n)3 .2 sin 5 )5 .2 sin (5 fi .2 sin (5 fi .2 sin (5 ^ .2 sin (5 ^ 45°) 90°) 135°) 180°). The quintuple harmonic causes a flat-topped o ...", "... s s s s s n)3 n)3 n)3 n)3 n)3 n)3 .2 sin 5 )5 .2 sin (5 fi .2 sin (5 fi .2 sin (5 ^ .2 sin (5 ^ 45°) 90°) 135°) 180°). The quintuple harmonic causes a flat-topped or even double-peaked wave with flat zero. With increasing phase displacement, the wave becomes of the type called saw- tooth wave also. The flat zero rises and becomes a third peak, while of the two former peaks, one rises, the other r 336 AL TERN A TING- CURRENT PHENOMENA, [ § 223 decreases, and the wave gradually chang ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 963-1366", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "snippets": [ "... ircuits where energy is expended only in heating the conductor, is the same as the ohmic resistance of continuous-current circuits. In circuits, how- ever, where energy is also expended outside of the con- ductor by magnetic hysteresis, mutual inductance, dielectric hysteresis, etc., r is larger than the true ohmic resistance of the conductor, since it refers to the total expenditure of energy. It may be called then the effective resistance. It is no longer a constant of the circuit. The reactance, x, does not repr ...", "... .M.F. is — e that is, the impedance, z, takes in alternating-current cir- cuits the place of the resistance, r, in continuous-current circuits. CAPACITY. 4. If upon a condenser of capacity, C, an E.M.F., e, is impressed, the condenser receives the electrostatic charge, Ce. If the E.M.F., e, alternates with the frequency, N, the average rate of charge and discharge is 4 IV, and 2 TT N the maximum rate of charge and discharge, sinusoidal waves sup- posed, hence, i — 2 TT ./VCV the current passing into the con- d ...", "... the energy component of E.M.F. to the cur- rent. Since in alternating-current circuits, besides by the ohmic resistance of the conductor, energy is expended, partly outside, partly even inside, of the conductor, by magnetic hysteresis, mutual inductance, dielectric hystere- sis, etc., the effective resistance, r, is in general larger than the true resistance of the conductor, sometimes many times larger, as in transformers at open secondary circuit, and is not a constant of the circuit any more. It is more fully di ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-20", "section_label": "Chapter 20: Commutator Motors", "section_title": "Commutator Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 19458-20501", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "snippets": [ "... closed upon itself and displaced in Fig. 160. space by 45° — in a bipolar motor — from the direction of the magnetic flux, as shown diagrammatically in Fig. 160. * This secondary circuit, while set in motion, still remains in the same position of 45° displacement, with the magnetic flux, or rather, what is theoretically the same, when moving out of this position, is replaced by other secondary circuits entering this position of 45° displacement. For simplicity, in the following all the secondary quan- COMMUTAT ...", "... ircuit, while set in motion, still remains in the same position of 45° displacement, with the magnetic flux, or rather, what is theoretically the same, when moving out of this position, is replaced by other secondary circuits entering this position of 45° displacement. For simplicity, in the following all the secondary quan- COMMUTATOR MOTORS. 359 titles, as E.M.F., current, resistance, reactance, etc., are assumed as reduced to the primary circuit by the ratio of turns, in the same way as done in the chapter on I ...", "... x = 2 TT N^- = reactance of field ; (R 2-n-jV— = reactance of armature fti and / « • «, 366 AL TERNA TING-CURRENT PHENOMENA. 221. The power output at armature shaft is, J>= El \\ (R (R fi- *Ef 7T « 7V^ /2 n± N± x _j_ r _^_ The displacement of phase between current and E.M.F. tan CD = Neglecting, as approximation, the resistances r + rlf it 1 + |! lan W = ? «j ^ 7T /« 7V ^n2 1+^' ^ /« TV COMMUTATOR MOTORS. 367 hence a maximum for, 3r 7T substituting this in tan w ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "... nteresting to note the relatively great drop of speed at light-load, while at heavier load the speed remains more nearly constant. This is a general characteristic of anti-inductive im- pedance in the induction-motor secondary, and shared by the use of an electrostatic condenser in the secondary. For comparison, on Fig. 28 the curve of apparent efficiency of this motor couple is shown as CC. Induction Motor with Condenser in Secondary Circuit 66. As a condenser consumes leading, that is, produces lagging reactive cu ...", "... s very low at speed, thus a very great condenser capacity is required, far greater than would be sufficient for compensation by shunting the condenser across the primary terminals. In view of the low frequency and low voltage of the secondary circuit, the electrostatic condenser generally is at a disadvantage for this use, but the electrolytic condenser, that is, the polarization cell, appears better adapted. 56. Let then, in an induction motor, of impressed voltage, e0: Ya = g — jb — exciting admittance; Z» — H + J ...", "... pedance at full frequency; and let the secondary circuit be closed through a condenser of capacity reactance, at full frequency: Z* — U — j*h where r%, representing the energy loss in the condenser, usually is very small and can lie neglected in the electrostatic condenser, so that: Zt= - jxj. The inductive reactance, Xt, is proportional to the frequency, that is, the slip, s, and the capacity reactance, x:, inverse propor- tional thereto, and the total impedance of the secondary circuit, at slip, j*, thus is: ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-12", "section_label": "Chapter 14: Phase Conversion And Single-Phase Generation", "section_title": "Phase Conversion And Single-Phase Generation", "kind": "chapter", "sequence": 12, "number": 14, "location": "lines 17125-18412", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-12/", "snippets": [ "... e factor of the single-phase system is zero or negative, while that of the balanced polyphase system is unity. For such energy storage may be used capacity, or inductance, or momentum or a combination thereof: Energy storage by capacity, that is, in the dielectric fu Id, required per kilovolt-ampere at 60 cycles about 200O <-.•■. ol space, at a cost of about $10. Inductance, that is. energy storage by the magnetic field, requires about 1000 c.e. per kilo- volt-ampere at 60 cycles, at a cost of $1, while energy stor ...", "... a quarter of the mass of the mechanical structure (motor, etc.) is revolving, and that the energy storage takes place by a pulsation of speed of per cent., then 1 kva. at 60 cycles would require 600 c.e. of terial, at 40c, Obviously, at the limits of dielectric or magnetic field strength, or at the limits of mechanical speeds, very much larger amounts of energy per bulk could be stored. Thus for instance, at the limits of steam-turbine rotor speeds, about 400 meter-seconds, in a very heavy material as tungsten, ...", "... ly by the double transformer Fig. 69B. The only difference between Fig. 69A and 69B is, that in Fig. 69.4 the synchronous rotation of the circuit, £\\Zi, carries the cur- rent, 1 1, 90° in space to the second transformer, and thereby pro- duces a 90° time displacement. That is, primary current and voltage of the second transformer of Fig. 69/* are identical in intensity with the secondary currents and voltage of the first, transformer, but lag behind them by a quarter period in space and thus also in time. The momentum ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-17", "section_label": "Chapter 19: Alternating- Current Motors In General", "section_title": "Alternating- Current Motors In General", "kind": "chapter", "sequence": 17, "number": 19, "location": "lines 21713-23905", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-17/", "snippets": [ "... ■» position angle lwtween the stator and rotor circuits. The e.m.fH., #o and — j#0, produce the same rotating e.m.f. as two e.m.fH. of equal intensity, but dis- placed in phase and in position by angle 0O from #», and jf/l,,, and instead of considering a displacement of phase, 0,h arid a dis- placement of position, 0i, between stator and rotor circuits, we can, therefore, assume zero-phase displacement and diMplacemeut in position by angle 0O + 0i = 0. Phase diMplaecmcnf l*etween stator and rotor e.m.fH. is, therefore ...", "... ual intensity, but dis- placed in phase and in position by angle 0O from #», and jf/l,,, and instead of considering a displacement of phase, 0,h arid a dis- placement of position, 0i, between stator and rotor circuits, we can, therefore, assume zero-phase displacement and diMplacemeut in position by angle 0O + 0i = 0. Phase diMplaecmcnf l*etween stator and rotor e.m.fH. is, therefore, equivalent to n fluff of brushes, hence gives no additional feature beyond those pro- duced by a shift of the commutator bru«he*. 320 ...", "... +~z^' ( ' 9) for c = o, this gives: , _ „ *Z_+ Z\\ /0 \" *\" sZZ* + ZZ\\ + ZoZi j - v sZ ' *l-'r«0szz0-+zzl + z0zi' (74) ALTERNATING-CURRENT MOTORS 321 that is, the polyphase induction-motor equations, a = cos 0 + j sin 0 = 1» representing the displacement of position between stator and rotor currents. This shows the polyphase induction motor as a special case of the polyphase shunt motor, for c = o. The e.m.fs. of rotation are: £'i = -jSZ (- jh + h sin 0 + j/o cos 0) - SZ (*h- I i)i hence : &l ^'i ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-02", "section_label": "Chapter 2: Electric Conduction. Gas And Vapor", "section_title": "Electric Conduction. Gas And Vapor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3895-5444", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-02/", "snippets": [ "... ies resistance, but the con- duction changes to arc conduction, if sufficient current is avail- able, as from power generators, or the conduction ceases by the voltage drop of the supply source, and then starts again by the recovery of voltage, as with an electrostatic machine. Thus spark conduction also is called disruptive conduction and discon- tinuous conduction. Apparently continuous — though still interipittent — spark con- duction is produced at atmospheric pressure by capacity in series to the gaseous conducto ...", "... ating-voltage supply, as corona, and as Geissler tube conduction at a partial vacuum, by an alternating-supply voltage with considerable reactance or resistance in series, or from a direct-current source of very high voltage and very Umited current, as an electrostatic machine. In the Geissler tube or vacuum tube, on alternating-voltage supply, the effective voltage consumed by the tube, at constant temperature and constant gas pressure, is approximately con- stant and independent of the effective current, that is, the ...", "... e arc at every half-wave by jumping an elec- trostatic spark between the terminals through the hot residual vapor of the preceding half-wave. The temperature of this vapor is that of the boiling point of the electrode material. The voltage required by the electrostatic spark, that is, by disruptive conduc- tion, decreases with increase of temperature, for a 13-mm. gap about as shown by curve I in Fig. 18. The voltage required to maintain an arc, that is, the direct-current voltage, increases with increasing arc temperat ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... tance have a negative term added, which depends on the decrement a. Such a negative resistance repre- sents energy production, and its meaning in the present case is, that with the decrease of the oscillating current and voltage, their stored magnetic and dielectric energy become available. Circuits of Zero Impedance 190. In an oscillating-current circuit of decrement, a, of resistance, r, inductive reactance, x, and condensive reactance, Xc, the impedance was represented in symbolic expression by or numerically ...", "... Closed magnetic circuit, wave dis- tortion, 139 C/obalt iron alloy, magnetic, 78 magnetic properties, 80 Coefficient of hysteresis, 61 Coherer action of pyroelectric con- ductor, 19 Compensating voltage balancing un- balanced power, 320 Condenser, electrostatic, 9 power equation, 319 tending to instability, 164. See Capacity, Conductance with oscillating cur- rents, 349 Conduction, electric, 1 Conductors, mechanical magnetic forces, 106 Constant component of power in general system, 317 current arc, stab ...", "... ics, 121 Decrement of oscillating wave, 34J Demagnetization by alternating ci^ :y, rent, 54 temperature, 78 Diffusion current of polarization, S Direct current producing even har- monics, 159 Discharges, oscillating, 352 Discontinuous conduction, 29 Displacement of field poles elimmat- ing harmonics, 120 of position in synchronous ma- chme, 210 Disruptive conduction, 29, 42 Distortion of wave improving regu- lation in series circuits, 311 of voltage by bridged magnetic gap, 148 in constant potential con- st ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-24", "section_label": "Chapter 2: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 24, "number": 2, "location": "lines 1993-2658", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "snippets": [ "... us current in an inductive circuit. continuous current in an inductive circuit: the exciting current of an alternator field, or a circuit having the constants r = 12 ohms; L = 6 henrys, and eQ = 240 volts; the abscissas being seconds of time. 13. If an electrostatic condenser of capacity C is connected to a continuous e.m.f. e0, no current exists, in stationary con- dition, in this direct-current circuit (except that a very small current may leak through the insulation or the dielectric of the condenser), but the con ...", "... seconds of time. 13. If an electrostatic condenser of capacity C is connected to a continuous e.m.f. e0, no current exists, in stationary con- dition, in this direct-current circuit (except that a very small current may leak through the insulation or the dielectric of the condenser), but the condenser is charged to the potential dif- ference eo; or contains the electrostatic charge Q = to0. In the moment of closing the circuit of e.m.f. e0 upon the capacity C, the condenser contains no charge, that is, zero pote ...", "... current exists, in stationary con- dition, in this direct-current circuit (except that a very small current may leak through the insulation or the dielectric of the condenser), but the condenser is charged to the potential dif- ference eo; or contains the electrostatic charge Q = to0. In the moment of closing the circuit of e.m.f. e0 upon the capacity C, the condenser contains no charge, that is, zero potential difference exists at the condenser terminals. If there were no resistance and no inductance in the circuit ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "LECTURE VII. LINE OSCILLATIONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy surges between magnetic — and dielectric — , and a transient component, by which the total stored energy decreases. Considering only the periodic component, the maximum value of magnetic energy must equal the maximum value of dielectric '^'^e^gy- Li„^ Ce, 0 \"^^0 (1) where Iq = maxim ...", "... by which the stored energy surges between magnetic — and dielectric — , and a transient component, by which the total stored energy decreases. Considering only the periodic component, the maximum value of magnetic energy must equal the maximum value of dielectric '^'^e^gy- Li„^ Ce, 0 \"^^0 (1) where Iq = maximum value of transient current, 60 = maximum value of transient voltage. This gives the relation between Bq and Iq, ^^ = Jl ,^ = 1, (2) where Zq is called the natural impedance or surge impedance ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "LECTURE VIII. TRAVELING WAVES. 33. In a stationary oscillation of a circuit having uniformly distributed capacity and inductance, that is, the transient of a circuit storing energy in the dielectric and magnetic field, current and voltage are given by the expression i = ioe-\"^ cos ((/> T CO — 7), ^ . . e = eoe~\"' sin ((^ =F co — 7), where 2 surges between magnetic -^- and dielectric — , and a transient £i A component, by which the total stored energy decreases. Considering only the periodic component, the maximum mag- netic energy must equal the maximum dielectric energy, Lio2 _ Ceo2 \"2\" ~2~' where i0 = maximum transient curr ...", "... e stored energy 7\" /j'2 f^ r/>2 surges between magnetic -^- and dielectric — , and a transient £i A component, by which the total stored energy decreases. Considering only the periodic component, the maximum mag- netic energy must equal the maximum dielectric energy, Lio2 _ Ceo2 \"2\" ~2~' where i0 = maximum transient current, e0 = maximum transient voltage. This gives the relation between eQ and io, e0 V/L_ 1 i-0 = \\C-ZQ-yQ' where ZQ is called the natural impedance or surge impedance, y0 the natural o ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 4745-5520", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "snippets": [ "LECTURE VIII. TRAVELING WAVES. 33. In a stationary oscillation of a circuit having uniformly distributed capacity and inductance, that is, the transient of a circuit storing energy in the dielectric and magnetic field, current and voltage are given ^by the expression i = iQe~ut cos (0 T co - 7), ) e = e0e~ut sin ( T co — 7), ) where 0 is the time angle, co the distance angle, u the exponential decrement, or the \"power-dissipation constant,\" and ...", "... and a pulsation or surge, pi, of the same nature as that of the standing wave (2) : Such a flow of power along the circuit is called a traveling wave. It occurs very frequently. For instance, it may be caused if by a lightning stroke, etc., a quantity of dielectric energy is impressed A • Fig. 39. — Starting of Impulse, or Traveling Wave. upon a part of the circuit, as shown by curve A in Fig. 39, or if by a local short circuit a quantity of magnetic energy is impressed upon a part of the circuit. This energy ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-03", "section_label": "Lecture 3: Gravitation And The Gravitational Fleld", "section_title": "Gravitation And The Gravitational Fleld", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2389-3594", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-03/", "snippets": [ "... ss, the same quantity which in the days of action at a distance was called the magnetic pole strength, and which is related to the magnetic flux $ by: $ = AtP. The force exerted by an electric field on an electrified body is: F=KQ, (2) where K is the dielectric field intensity and Q the electric mass or electric quantity, also called electrostatic charge, measured in coulombs. The force exerted by a gravitational field is : F = gN, (3) where g is the gravitational field intensity and N the sus- ceptibility ...", "... ic pole strength, and which is related to the magnetic flux $ by: $ = AtP. The force exerted by an electric field on an electrified body is: F=KQ, (2) where K is the dielectric field intensity and Q the electric mass or electric quantity, also called electrostatic charge, measured in coulombs. The force exerted by a gravitational field is : F = gN, (3) where g is the gravitational field intensity and N the sus- ceptibility of the body to a gravitational field, or the gravitational mass of the body- — often sim ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... is a polarized wave: the direction parallel to the conductor is the direction of energy flow; the direction concentric to the con- ductor is the direction of the electromagnetic component, and the direction radial to the conductor is the direction of the electrostatic component of the electric field. Therefore, if light rays can be polarized, that is, made to ex- hibit different properties in two directions at right angles to each other and to the direction of wave travel, this would prove tke light wave to be a trans ...", "... The electric waves used in wireless telegraphy range in wave lengths from 100 feet or less to 10,000 feet or more, corresponding to 107 to 105 cycles per sec. Still very much longer waves are the fields of alternating cur- rent circuits: the magnetic and electrostatic field of an alterna- ting current progresses as a wave of radiation from the conductor. But as the wave length is very great, due to the low frequency, — 3 X 1010 a 60-cycle alternating current gives a wave length of ^ = 500 X 10\" cm. or 3100 miles — t ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... : S = -L= , (5) VLC where L is the inductance, C the capacity of the conductor per unit length (the length measured in the same measure as the speed S). The inductance L is proportional to the permeability /*, and the capacity C proportional to the dielectric constant, or specific capacity K of the medium surrounding the conductor, that is, the medium through which the electric wave propagates; that is, A V p* where A is a proportionality constant. The ratio of the speed of propagation of an electric wave ...", "... and « = 1; hence, (8) where Sl is the speed of propagation in the medium of constants /^ and jcr Comparing equation (8) with (4) it follows : Vl = d*-, (9) that is, the square of the refractive index d equals the product of permeability JJL and dielectric constant K. Since for most media the permeability /JL = 1, for all except e maneti mri the magnetic materials RELATION OF BODIES TO RADIATION. 25 This relation between the constant of the electric circuit K and the constant of optics d was on ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-13", "section_label": "Theory Section 13: Alternating-current Transformer", "section_title": "Alternating-current Transformer", "kind": "theory-section", "sequence": 13, "number": 13, "location": "lines 4465-5263", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-13/", "snippets": [ "... E\\OE -T- sin E\\EO = .E^n -f- EiO ALTERNATING-CURRENT TRANSFORMER 71 thus, writing £ E&E = 0\", we have sin 0\" -4- sin (0' - 0i) = hz + Ei, wherefrom we get % 6\", and £ E1OIl = 6 = 0, + 0\", the phase displacement between secondary current and secondary e.m.f. FIG. 37. — Vector diagram of transformer with leading load current. In triangle O/oo/o we have since and 0/02 = O/oo2 + /oo/o2 - 2 O/oo/oo/o COS O/oo/o, £ #i00 = 90° ...", "... £V = ^2\" + ^02^02 H COS (00 — 02). In triangle OE'EQ sin E'OEo -T- sin thus, writing we have sin Q'\\ + sin (0'0 - 02) = /o£o ^ ^0; herefrom we get ^ 0\"i, and ^ 00 = 02 + 0\"l, the phase displacement between primary current and impressed e.m.f. As seen, the trigonometric method of transformer calculation is rather complicated. 62. Somewhat simpler is the algebraic method of resolving into rectangular components. Considerin ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 3267-3618", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-06/", "snippets": [ "... ement, 90° ahead of the current, Oh, and proportional thereto. In the same Hne element we have a current, hh^, in phase with the voltage, OEi, and proportional thereto, representing 44 ALTERNATING-CURRENT PHENOMENA the loss of current by leakage, dielectric hysteresis, etc., and a current, /i^ /i^\\ 90° ahead of the voltage, 0E-[, and proportional thereto, the charging current of the line element as condenser; and in this manner passing along the line, element by element, we ultimately reach the generator ter ...", "... bscissas, counting from the receiving circuit toward the generator. As seen from Fig. 35, voltage and current periodically but alternately rise and fall, a maximum of one approximately coinciding with a minimum of the other, and with a point of zero phase displacement. The phase angle between current and e.m.f. changes from 90° lag to 72° lead, 44° lag, 34° lead, etc., gradually decreasing in the amplitude of its variation." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-12", "section_label": "Chapter 12: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 10718-13483", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-12/", "snippets": [ "... nalytically with alternating-current circuits containing iron. 90. The foremost sources of energy loss in alternating-current circuits, outside of the true ohmic resistance loss, are as follows : 1. Molecular friction, as, (a) Magnetic hysteresis; (6) Dielectric hysteresis. 2. Primary electric currents, as, (a) Leakage or escape of current through the insulation, brush discharge, corona. (6) Eddy currents in the conductor or unequal current distribution. EFFECTIVE RESISTANCE AND REACTANCE 113 -» 3. Se ...", "... currents, as, (a) Eddy or Foucault currents in surrounding magnetic materials; (b) Eddy or Foucault currents in surrounding conducting materials ; (c) Secondary currents of mutual inductance in neighboring circuits. 4. Induced electric charges, electrostatic induction or influence. While all these losses can be included in the terms effective resistance, etc., the magnetic hysteresis and the eddy currents are the most frequent and important sources of energy loss. Magnetic Hysteresis 91. In an alternating ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-20", "section_label": "Chapter 20: Single-Phase Induction Motors", "section_title": "Single-Phase Induction Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 21538-22301", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-20/", "snippets": [ "... re used, displaced in position from each other, and either in series or in shunt with each other, or in any other way related, as by transformation. The impedances of these circuits are made different from each other as much as possible to produce a phase displacement between them. This can be done either by inserting external impedances in the circuits, as a condenser and a reactive coil, or by making the internal impedances of the motor circuits different, as by making one coil of high and the other of low resistance ...", "... ternal impedances of the motor circuits different, as by making one coil of high and the other of low resistance. 2. Inductive Devices. The different primary circuits of the motor are inductively related to each other in such a way as to produce a phase displacement between them. The induct- ive relation can be outside of the motor or inside, by having the one coil submitted to the inductive action of the other; and in this latter case the current in the secondary coil may be made leading, accelerating coil, or laggi ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-21", "section_label": "Chapter 21: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 22302-23970", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-21/", "snippets": [ "... ary reaction can be neglected, and the field m.m.f. be assumed as constant. Fig. 130. The relative position of the armature m.m.f. with respect to the field m.m.f. depends upon the phase relation existing in the electric circuit. Thus, if there is no displacement of phase be- tween current and e.m.f., the current reaches its maximum at the same moment as the e.m.f. or, in the position of the armature shown in Fig. 129, midway between the field-poles. In this case the armature current tends neither to magnetize nor ...", "... ty at the leading pole corner will be less than the decrease of density at the trailing pole corner. Since the internal self-inductive reactance of the alternator itself causes a certain lag of the current behind the generated e.m.f., this condition of no displacement can exist only in a circuit with external negative reactance, as capacity, etc. ALTERNATING-CURRENT GENERATOR 2G1 If the armature current lags, it reaches the maximum later than the e.m.f.; that is, in a position where the armature-coil partly faces t ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-23", "section_label": "Chapter 23: Synchronizing Alternators", "section_title": "Synchronizing Alternators", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 25135-25681", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-23/", "snippets": [ "... ubstituting g = y cos a £\"1=01 cos di €2 = a2 cos 62 b = ^ sin a e'l = ai sin 0i e'2 = ^2 sin 02 gives g -\\- gi + gz _ aiVi cos (^i - gQ + ^2^2 cos {(X2 - 62) & + &i + 62 ~ CLiVx sin (ai — 0i) + «22/2 sin (a2 — ^2) as the equation between the phase displacement angles, di and 62, in parallel operation. The power supplied to the external circuit is, V ^ e^g, of which that supplied by the first machine is, Pi = eii] by the second machine. Pi = eii. The total electrical power of both machines is, P = P ...", "... es hence That is, and cos or, 5 = a cos € cos 5 = e ( 1 H ^ j ' Xog--rob, a sin € cos 5 — e ^ , a;og - rpb tan € = ?r— ; n — \"^ — constant. 2 -j-rog -j- xob 01 -\\- di = constant; ^ - a\\V + 2—) + 1—2^; ' a cos 5 at no-phase displacement between the alternators, or, 5 - 2 \" ^' we have a e = From the eight initial equations we get, by combination, eiro + e'ia;o = eoro + iiiro^ + a^o^), eo^o + e'2a:o = Coro + i^iro^ + Xo\"); subtracted and expanded. To (ei — 62) + rco (e'l — e'2 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-27", "section_label": "Chapter 27: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 33011-34776", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-27/", "snippets": [ "... t sine waves, from the sine wave formula, p^ + qo^ = 1, the inductance factor would be, Qo = 0.914, and the phase angle, tan d = ^ = ^-^I^ = 2.8, 6 = 65.4°, p 0.418 ' 25 386 ALTERNATING-CURRENT PHENOMENA giving apparently a very great phase displacement, while in reality, of the 41.85 amp. total current, 40 amp. (the current of the third harmonic) are in phase with their e.m.f. We thus have here a case of a circuit with complex harmonic waves which cannot be represented by their equivalent sine waves. ...", "... tive magnitudes of the different harmonics in the wave of current and of e.m.f. differ essentially, and the circuit has simultaneously a very low power-factor and a very low inductance factor; that is, a low power-factor exists without corresponding phase displacement, the circuit-factor being less than one-half. Such circuits, for instance, are those including alternating arcs, reaction machines, synchronous induction motors, react- ances with over-saturated magnetic circuit, high potential lines in which the maximu ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-35", "section_label": "Chapter 35: Balanced Symmetrical Polyphase Systems", "section_title": "Balanced Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 35, "number": 35, "location": "lines 37453-37957", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-35/", "snippets": [ "... In most applications of polyphase systems the system is a balanced symmetrical system, or as nearly balanced as possible. That is, it consists of n equal e.m.fs. displaced in phase from each other by - period, and producing equal currents of equal phase displacement against their e.m.fs. In such systems, each e.m.f. and its current can be considered separately as constituting a single-phase system, that is, the polyphase system can be resolved into n equal single-phase systems, each of which consists of one conductor ...", "... Choosing the voltage at the receiving end as zero vector, e = 46,100 volts, at 90 per cent, power-factor and therefore 43.6 per cent, induc- tance factor, the current is represented by 7 = 80 (0.9 - 0.436 j) =72-35 j. ^ Or. ii fi = permeability, k = dielectric constant of the medium sur- rounding the conductor, it is hence, V [^ I = \\W or. C = (4) 452 ALTERNATING-CURRENT PHENOMENA This gives: Voltage at receiver circuit, e = 46,100 volts; current in receiver circuit, Z = 72 — 35 j amp. ; im ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-04", "section_label": "Chapter 4: Graphic Befrisxintation", "section_title": "Graphic Befrisxintation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2122-2743", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "snippets": [ "... ^ = EjOA, 22. Thus, in Figs. 18, 19, and 20, the diagram of an ^temating-current transformer is drawn for the same sec- 122] GRAPHIC REPRESENTATION. 31 •ondary E.M.F., E^^ and secondary current, /j, but with dif- ferent conditions of secondary displacement : -. — In Fig. 18, the secondary current, f^ , lags 60° behind the sec- ondary E.M.F., Ex, In Fig. 19, the secondary current, /i, is in phase with the secondary E.M.F., Ey. In Fig. 20, the secondary current, I^ , leads by 60** the second- ary E.M.F., ...", "... e existing in the secondary circuit of a transformer reappears / V 82 AL TERNA TING-CURRENT PHENOMENA, [§ 22 in the primary circuit, somewhat decreased if leading, and slightly increased if lagging. Later we shall see that hysteresis reduces the displacement in the primary circuit, so that, with an excessive lag in the secondary circuit, the lag in the primary circuit may be less than in the secondary. A conclusion from the foregoing is that the transformer is not suitable for producing currents of displaced ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-10", "section_label": "Chapter 10: F", "section_title": "F", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 8269-10499", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "snippets": [ "... ytically with alternating-current circuits containing iron. 73. The foremost sources of energy loss in alternating- current circuits, outside of the true ohmic resistance loss, are as follows : 1.) Molecular friction, as, a.) Magnetic hysteresis; b) Dielectric hysteresis. 106 ALTERNATING-CURRENT PHENOMENA. [§ 74 2.) Primary electric currents, as, a.) Leakage or escape of current through the in- sulation, brush discharge ; b.) Eddy currents in the conductor or unequal current distribution. 3.) Secondary ...", "... currents, as, a,) Eddy or Foucault currents in surrounding mag- netic materials ; b.) Eddy or Foucault currents in surrounding con- ducting materials ; r.) Secondary currents of mutual inductance in neighboring circuits. 4.) Induced electric charges, electrostatic influence. While all these losses can be included in the terms effective resistance, etc., only the magnetic hysteresis and the eddy currents in the iron will form the subject of what follows. Magnetic Hysteresis, 74. In an alternating-current circui ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-16", "section_label": "Chapter 16: Aiitebnatingh-Current Osnebator", "section_title": "Aiitebnatingh-Current Osnebator", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 17025-18828", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "snippets": [ "... secondary reaction can be neglected, and the field M.M.F. be assumed as constant. 160. The relative position of the armature M.M.F. with respect to the field M.M.F. depends upon the phase rela- tion existing in the electric circuit. Thus, if there is no displacement of phase between current and E.M.F., the current reaches its maximum at the same moment as the E.M.F. ; or, in the position of the armature shown in Fig. 110, midway between the field poles. In this case the arma- ture current tends neither to magnetize n ...", "... s than the decrease of 236 AL TERNA TING-CURRENT PHENOMENA. [§ 160 density at the trailing-pole corner. Since the internal self- inductance of the alternator alone causes a certain lag of the current behind the induced E.M.F., this condition of no displacement can exist only in a circuit with external nega- tive reactance, as capacity, etc. If the armature current lags, it reaches the maximum later than the E.M.F. ; that is, in a position where the armature coil partly faces the following-field pole, as shown ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-17", "section_label": "Chapter 17: Synchbonizino Aiitebkatobs", "section_title": "Synchbonizino Aiitebkatobs", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 18829-19345", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-17/", "snippets": [ "... = V cos a ^1 = 2 b •=^ V sin a e( = i e^ = 02 sin (02 gives ^ + ^ 1 + ^ 2 ^ <7x g/| COS (ai — ctf|) + <72 7'2 cos (ag — a»2) ^ + ^1 + ^2 ''i ^1 sin (tti — a>i) + ' hence tan c = \"^Q*^ \"~ ^Q = constant. That is wi + aij = constant; and cos 8 = fy/^l + ^oZii^V + ^-»Xr:i<^J; rtr cos 8 or, 2 cos (a2 — a2) tfj z/! sin (ai — w^) -\\- a^Vs sin (a2 — a>2) as the equation between the phase displacement angles and oi2 in parallel operation. The power supplied to the external circuit is of which that supplied by the first machine is, /i = «\\ ; by the second machine, /2 = «a • The total electrical work done by both machines is, P = Pl + P*, of. ...", "... ng — 8 = 318 AL TERN A TING-CURRENT PHENOMENA. a cos e cos 8 = e ( 1 + rQg -\\-Xzb a sin e cos 8 = ^^ ^ hence That is -and cos 8 = - tan e = — ^ ^ — = constant. + A2 = constant; -M1*5 z±aiy , /^o^-^o^\\2. cos 8 at no-phase displacement between the alternators, or, -we have e = ^ — . V/(' + n>^ + -*o^\\2 , fxn £— r*b From the eight initial equations we get, by combina- (''o2 subtracted and expanded — .or, since T6, J and pi, the armature heating becomes a minimum. Neglecting the losse ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-11", "section_label": "Chapter 11: Instability Of Circuits: Induction And Syn Chronous Motors", "section_title": "Instability Of Circuits: Induction And Syn Chronous Motors", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 21382-22633", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-11/", "snippets": [ "... lting from the oscillation of speed (hysteresis and eddies in the pole faces, currents in damper windings), that is, the damping power, assumed as proportional to the square of the speed. If there is no lag of the synchronizing force behind the position displacement, the synchronizing force, that is, the force which tends to bring the rotor back from a position behind or ahead of the position corresponding to the load, would be — or may ap- proximately be assumed as — proportional to the position dis- placement, p, b ...", "... ronizing force behind position displace- ment p (12) and /3 = (joto (13) where ^0 = time lag of synchronizing force. (14) The synchronizing force then is F = bpoe-*'* cos (<^ - /3) (15) where 6 = — = ratio of synchronizing force to po- sition displacement, or specific synchronizing force. (16) The synchronizing power then is W2 = Fv = bcopoAe-^\"^ sin (0 + a) cos (<^ - /3). (17) The oscillating mechanical power is d mv^ dv dt e d4 = mco/Spo'^A^e-^ «* sin (0 + a) {cos {4i-\\' a) - a sin (<^ + a)} (18 ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-20", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit. 513", "section_title": "Power And Energy Of The Complex Circuit. 513", "kind": "chapter", "sequence": 20, "number": 7, "location": "lines 1228-1261", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-20/", "snippets": [ "... ntaneous power. Effective or mean power. Power transferred. 513 51. Instantaneous and effective value of energy stored in the magnetic field ; its motion along the circuit, and varia- tion with distance and with time. 513 52. The energy stored in the electrostatic field and its compo- nents. Transfer of energy between electrostatic and electromagnetic field. 517 53. Energy stored in a circuit section by the total electric field, and power supplied to the circuit by it. 518 54. Power dissipated in the resistanc ...", "... Instantaneous and effective value of energy stored in the magnetic field ; its motion along the circuit, and varia- tion with distance and with time. 513 52. The energy stored in the electrostatic field and its compo- nents. Transfer of energy between electrostatic and electromagnetic field. 517 53. Energy stored in a circuit section by the total electric field, and power supplied to the circuit by it. 518 54. Power dissipated in the resistance and the conductance of a circuit section. 519 55. Relations betwe ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-27", "section_label": "Chapter 5: Resistance, Inductance, And Capacity In Series Condenser Charge And Discharge", "section_title": "Resistance, Inductance, And Capacity In Series Condenser Charge And Discharge", "kind": "chapter", "sequence": 27, "number": 5, "location": "lines 4072-5311", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "snippets": [ "... circuit containing inductance and capac- ity two electric quantities must be given at the moment of start of the phenomenon, the current and the condenser poten- tial — representing the values of energy stored at the moment t = 0 as electromagnetic and as electrostatic energy, respec- tively — the equations must lead to two integration constants, that is, to a differential equation of second order. Let i = i0 = current and et = e0 = potential difference at condenser terminals at the moment t = 0; substituting in (11) ...", "... conditions is relatively harmless. In charging or discharging a condenser, or in general a circuit containing capacity, the insertion of a resistance in series in the circuit of such value that r2 > — therefore eliminates the C danger from abnormal electrostatic or electromagnetic stresses. In general, the higher the resistance of a circuit, compared with inductance and capacity, the more the transient term is suppressed. 54 TRANSIENT PHENOMENA 35. In a circuit containing resistance and capacity but no indu ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-29", "section_label": "Chapter 7: Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "section_title": "Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "kind": "chapter", "sequence": 29, "number": 7, "location": "lines 6798-7825", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "snippets": [ "... it conditions, is the most important, since in circuits containing capacity the transient effect is almost always oscillating. The most common examples of capacity are distributed capacity in transmission lines, cables, etc., and capacity in the form of electrostatic condensers for neutralizing lagging currents, for constant potential-constant current transformation, etc. (a) In transmission lines or cables the charging current is a fraction of full-load current i0, and the e.m.f. of self-inductance consumed by the l ...", "... very large non-inductive resistance (of such size as to cut the starting current down to less than — of full-load current). Even in this case, however, oscillations would appear by a change of load, etc., after the start of the circuit. (6) When using electrostatic condensers for producing watt- less leading currents, the resistance in series with the condensers is made as low as possible, for reasons of efficiency. Even with the extreme value of 10 per cent resistance, or r 4- xc = I -f- 10, the non-oscillating c ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-35", "section_label": "Chapter 13: Transient Term Of The Rotating Field", "section_title": "Transient Term Of The Rotating Field", "kind": "chapter", "sequence": 35, "number": 13, "location": "lines 13936-14548", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-35/", "snippets": [ "... the phases of a sym- metrical polyphase system equals zero. In the polyphase field, however, these m.m.fs. (4) do not act in the same direction, but in directions displaced from each other by a space angle — equal to the time angle of their phase np displacement. 108. The component of the m.m.f., fit acting in the direction (00 - T), thus is 27T .> // = ft cos (»„ - T - ~ i), (6) \\ nn i TRANSIENT TERM OF THE ROTATING FIELD 193 and the sum of the components of all the np m.m.fs., in the direction (00 - ...", "... after differentiating numerator and denominator twice, this value becomes definite. So = ^; (20) that is, the rotating field starts at half speed. As illustration are shown, in Fig. 49, the maximum value of the resultant polyphase m.m.f., fm, and its displacement in +40 ' ° -40 ,400 Inten'sit^/ = 1000 /\\ \\f position |(0 ili + 8il mil 2 2 2 22 Fig. 49. Start of rotating field. position from that of uniform synchronous rotation, 00— 6, for the same constants as before, namely: np ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-43", "section_label": "Chapter 3: The Natural Period Of The Transmission Line", "section_title": "The Natural Period Of The Transmission Line", "kind": "chapter", "sequence": 43, "number": 3, "location": "lines 21721-23178", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "snippets": [ "... d inductance L0 and localized capacity (70, that is, the frequency of discharge of a condenser CQ through an inductance L0, is / = ^= • d3) The difference is due to the distributed character of L0 and C0 in the transmission line and the resultant phase displacement between the elements of the line, which causes the inductance and capacity of the line elements, in their effect on the frequency, not to add but to combine to a resultant, which is the projection 2 of the elements of a quadrant, on the diameter, or - ...", "... scillations produced by sudden changes of circuit conditions are complex waves of many harmonics, which in their relative magnitude depend upon the initial charge and its distribution — that is, in the case of the lightning discharge, upon the atmospheric electrostatic field of force. NATURAL PERIOD OF TRANSMISSION LINE 329 The fundamental frequency of the oscillating discharge of a transmission line is relatively low, and of not much higher mag- nitude than frequencies in commercial use in alternating-current circ ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-50", "section_label": "Chapter 1: General Equations", "section_title": "General Equations", "kind": "chapter", "sequence": 50, "number": 1, "location": "lines 27761-28694", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "snippets": [ "... ltage, e*g; or the power component of the current consumed in the circuit, that is, with an alternating voltage, the current, eg, in phase with the voltage. C = effective capacity, representing the energy storage e*C depending upon the voltage, — , as electrostatic component of the electric field; or the current consumed by a change of the de voltage, C — , that is, with an alternating voltage, the (leading) dt reactive current consumed in the circuit - jbe, where 6 = 2 and / = frequency. 417 418 TRANSIEN ...", "... tion moves along the circuit with the speed — *., or, in other words, (15) is the speed of propagation of the electric phenomenon in the cir- cuit. (If no energy losses occur, r = 0, g = 0, in a straight con- ductor in a medium of unit magnetic and dielectric constant, that is, unit permeability and unit inductive capacity, S is the velocity of light.) 4. Since (11) is a quadratic equation, several pairs or corre- sponding values of a and b exist, which, in the most general case, are complex imaginary. The t ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-56", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit", "section_title": "Power And Energy Of The Complex Circuit", "kind": "chapter", "sequence": 56, "number": 7, "location": "lines 33528-34202", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "snippets": [ "... £ only but not of the distance ^, 1 2 (317) and the total energy of the electromagnetic field of circuit element dX at time t is Aw'rr 1 /7 \"~ = V £~2\"\"'{ (4(7+BI)) cos 2 9' + (^0-JSC) sin 2 qt\\, dX d^ dl dX dX 52. The energy stored in the electrostatic field of the conductor or by the capacity C is given by CV dw2 = — dl\\ 518 TRANSIENT PHENOMENA or, substituting (310), and substituting in (319) the value of e from equation (290) gives the same expression as (311) except that the sign of the la ...", "... ic field of the conductor, dw dw, dw2 cydw^ dw' and integrated over a complete period of time this gives « 2^ = dw\" dw\"' The last two terms, — and — , thus represent the energy which is transferred, or pulsates, between the electromagnetic and the electrostatic field of the circuit; and the term — repre- sents the alternating (or rather oscillating) component of stored energy. 53. The energy stored by the electric field in a circuit section ^, between A, and A2, is given by integrating - - between A2 and AI} ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... MATHEMATICS. f ■ . Theoretically, obviously this condition can never be perfectly attained, and frequently the deviation from sine shape is suffi- cient to require practical consideration/ especially in those cases, where the electric circuit contains electrostatic capacity, as is for instance, the case with long-distance transmission lines, underground cable systems, high potential transformers, etc. (However, no matter how much the alternating or other periodic wave differs from simple sine shape — ^that is, howe ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-09", "section_label": "Lecture 9: Hunting Of Synchronous Machines", "section_title": "Hunting Of Synchronous Machines", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 4218-4594", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-09/", "snippets": [ "... fect phase with each other, but pulsate, alter- natingly getting out of phase with each other, coming together, and getting out again in the opposite direction. If the deviation of the two engines from uniform rate of rotation is very little — the maximum displacement of the alternator from the position of uniform rotation not more than three electrical degrees — the pulsating cross currents, which flow between the alternators, are moderate, and the phenomenon harmless, as long as the oscillation is not cumulative. An ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-103", "section_label": "Apparatus Section 6: Alternating-current Transformer: Heating and Ventilation", "section_title": "Alternating-current Transformer: Heating and Ventilation", "kind": "apparatus-section", "sequence": 103, "number": 6, "location": "lines 18461-18520", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-103/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-103/", "snippets": [ "... nternal losses, by the natural ventilation of the air currents pro- duced by the centrifugal forces in rotating apparatus, and it is therefore fortunate that the transformer is the most efficient apparatus (except perhaps the electrostatic condenser) and thus has to dissipate less heat than any other apparatus of the same output. Thus in smaller transformers radiation and the natural convection from the surface are often sufficient to keep the tem- perature w ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-107", "section_label": "Apparatus Section 1: Induction Machines: General", "section_title": "Induction Machines: General", "kind": "apparatus-section", "sequence": 107, "number": 1, "location": "lines 18949-19165", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-107/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-107/", "snippets": [ "... achine then acts as a brake or induction generator. In the polyphase induction motor this magnetic field is pro- duced by a number of electric circuits relatively displaced in space, and excited by currents having the same displacement in phase as the exciting coils have in space. In the single-phase motor one of the two superimposed mag- netic quadrature fields is excited by the primary electric circuit, the other by the . secondary currents carried int ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-108", "section_label": "Apparatus Section 2: Induction Machines: Polyphase Induction Motor", "section_title": "Induction Machines: Polyphase Induction Motor", "kind": "apparatus-section", "sequence": 108, "number": 2, "location": "lines 19166-20427", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-108/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-108/", "snippets": [ "... The \"apparent efficiency\" or \"apparent power efficiency\" is the ratio of the mechanical output of the motor to the output which it would give at the same volt-ampere input if there were neither internal losses nor phase displacement in the motor. The \"torque efficiency\" is the ratio of the torque of. the motor to the torque which it would give at the same power input if there were no internal losses in the motor. The \"apparent torque efficiency\" ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-110", "section_label": "Apparatus Section 4: Induction Machines: Induction Generator", "section_title": "Induction Machines: Induction Generator", "kind": "apparatus-section", "sequence": 110, "number": 4, "location": "lines 21158-21588", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-110/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-110/", "snippets": [ "... m, or from synchronous alternating- current generators operated in parallel with the induction gen- erator, in which latter case, however, these currents can be said to come from the synchronous alternator as lagging currents. Electrostatic condensers, as an underground cable system, may also be used for excitation, but in this case besides the condensers a synchronous machine or other means is required to secure stability. The induction machine may thus be ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-12", "section_label": "Theory Section 12: Impedance of Transmission Lines", "section_title": "Impedance of Transmission Lines", "kind": "theory-section", "sequence": 12, "number": 12, "location": "lines 3761-4464", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-12/", "snippets": [ "... sending end of a line of resistance r and reactance x, delivering current / at vol- tage E} and the voltage drop in the line, do not depend upon current and line constants only, but depend also upon the angle of phase displacement of the current delivered over the line. If 0 = o, that is, non-inductive receiving circuit, FIG. 29. — Locus of the generator and receiver e.m.fs. in a transmission line with varying load phase angle. E0 = - 4 EIz ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-18", "section_label": "Theory Section 18: Equivalent Sine Waves", "section_title": "Equivalent Sine Waves", "kind": "theory-section", "sequence": 18, "number": 18, "location": "lines 7381-7736", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-18/", "snippets": [ "... ig. 42. FIG. 44. — Corresponding sine waves for e.m.f. and exciting current in Fig. 43. Since p' = i'e'Q cos 0, where e'0 and i' are the equivalent sine waves of e.m.f. and of current respectively, and 0 their phase displacement, substitut- ing these numerical values of p', er, and i', we have 264.8 = 1000 X 1.198 cos 6. hence, cos 0 = 0.221, 6 = 77.2°, 112 ELEMENTS OF ELECTRICAL ENGINEERING and the angle of hysteretic advance of phase, ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-21", "section_label": "Apparatus Introduction 21: Introduction", "section_title": "Introduction", "kind": "apparatus-introduction", "sequence": 21, "number": null, "location": "lines 8292-8517", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-21/", "snippets": [ "... circuits interlinked with two electric circuits or sets of circuits moving with regard to each other. 5th. Stationary induction apparatus, consisting of a magnetic circuit interlinked with one or more electric circuits. 6th. Electrostatic and electrolytic apparatus as condensers and polarization cells. Apparatus changing from one to a different form of electric energy have been defined as: A. Transformers, when using magnetism, and as B. Converters, when us ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-29", "section_label": "Apparatus Section 8: Synchronous Machines: Characteristic Curves of Synchronous Motor", "section_title": "Synchronous Machines: Characteristic Curves of Synchronous Motor", "kind": "apparatus-section", "sequence": 29, "number": 8, "location": "lines 9399-9553", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-29/", "snippets": [ "VIII. Characteristic Curves of Synchronous Motor 17. In Fig. 66 are shown, at constant impressed e.m.f. E, the nominal counter-generated e.m.f. EQ and thus the field excitation FQ required, 1. At no phase displacement, 6 = 0, or for the condition of minimum input; 144 ELEMENTS OF ELECTRICAL ENGINEERING 2. For 0 = + 60, or 60 deg. lag: p = 0.5, q = + 0.866, and 3. For 0 = - 60, or 60 deg. lead: p = 0.5, q = - 0.866, ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-81", "section_label": "Apparatus Section 1: Synchronous Converters: General", "section_title": "Synchronous Converters: General", "kind": "apparatus-section", "sequence": 81, "number": 1, "location": "lines 13189-13795", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-81/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-81/", "snippets": [ "... tor rings, the voltage between any collector ring and the common neutral, or star voltage, is consequently the voltage between two adjacent collector rings, or ring voltage, is s' E sin- V2 since — is the angular displacement between two adjacent col- lector rings. Herefrom the current per line, or star current, is found as 2V27 and the current from line to line, or from collector ring to ad- jacent collector ring, or ring current, is V ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-89", "section_label": "Apparatus Section 11: Synchronous Converters: Double-current Generators", "section_title": "Synchronous Converters: Double-current Generators", "kind": "apparatus-section", "sequence": 89, "number": 11, "location": "lines 15893-15982", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-89/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-89/", "snippets": [ "... current armature polarization is thus shifted against the neutral by the same angle as the brushes. The direction of the alternating-current armature polarization, however, is shifted against the neutral by the angle of phase displacement of the alternating current. In consequence thereof, the reactions upon the field of the two parts of the armature polari- zation, that due to the continuous current and that due to the alternating current, are usually diffe ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-96", "section_label": "Apparatus Section 2: Alternating-current Transformer: Excitation", "section_title": "Alternating-current Transformer: Excitation", "kind": "apparatus-section", "sequence": 96, "number": 2, "location": "lines 16912-17026", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-96/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-96/", "snippets": [ "... es, increasing with the square of the load. (c) Spurious load losses, as eddy currents in the conductors and other metal parts. With proper design these should be negligible. (d) In very high voltage transformers, electrostatic losses in the insulation appear. These usually are small in large well- designed transformers. In large transformers, the total &r loss may be less than 1 per cent., and so also the core loss, resulting in efficiencie ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-07", "section_label": "Chapter 7: Polar Coordinates And Polar Diagrams", "section_title": "Polar Coordinates And Polar Diagrams", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 3619-4087", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-07/", "snippets": [ "... t is represented in polar coordinates by the product of the current, I, into the projec- tion of the e.m.f., E, upon the current, or by the e.m.f., E, into the projection of the current, /, upon the e.m.f., or by IE cos d, where 9 = angle of time- phase displacement. 45. The instances represented by the vector representation of the crank diagram in Chapter IV as Figs. IG, 17, 18, 19, 20, ^i Fig. 41. Fig. 42. then appear in the vector representation of the time diagram or polar coordinate diagram, in the f ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-32", "section_label": "Chapter 32: Transformation Of Polyphase Systems", "section_title": "Transformation Of Polyphase Systems", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 36062-36514", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-32/", "snippets": [ "... Fig. 212. by the internal impedance of the transformers. It is convenient for small powers at moderate voltage, since it requires only two transformers, but is dangerous in high potential circuits, being liable to produce destructive voltages by its electrostatic un- balancing. 5. The main and teaser, or T connection of transformers be- tween three-phase systems, is shown in Fig. 212. One of the 428 ALTERNATING-CURRENT PHENOMENA two transformers is wound for V3 2 times the voltage of the other (the a ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-36", "section_label": "Chapter 36: Three-Phase System", "section_title": "Three-Phase System", "kind": "chapter", "sequence": 36, "number": 36, "location": "lines 37958-38392", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-36/", "snippets": [ "CHAPTER XXXVI THREE-PHASE SYSTEM 308. With equal load of the same phase displacement in all three branches, the symmetrical three-phase system offers no special featm-es over those of three equally loaded single-phase systems, and can be treated as such; since the mutual reactions between the three phases balance at equal distribution of ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-20", "section_label": "Chapter 20: Beactiox Machines", "section_title": "Beactiox Machines", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 22388-23273", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "snippets": [ "... 314 ALTERNATING-CURRENT PHENOMENA. [§ 209 current wave also. Hence the equivalent sine wave of magnetism is of equal phase with the current wave ; that is, the E.M.F. of self-induction lags 90° behind the cur- rent, or is wattless. Thus at no-phase displacement, and at 90° phase dis- placement, a reaction machine can neither produce electri- cal power nor mechanical power. 209. If, however, the current wave differs in phase from the wave of E.M.F. by less than 90°, but more than zero degrees, it is unsymmetric ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-29", "section_label": "Chapter 29: Thbkb-Fhase System", "section_title": "Thbkb-Fhase System", "kind": "chapter", "sequence": 29, "number": 29, "location": "lines 27053-27500", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-29/", "snippets": [ "CHAPTER XXIX. THBKB-FHASE SYSTEM. 263. With equal load of the same phase displacement in all three branches, the symmetrical three-phase system offers no special features over those of three equally loaded single-phase systems, and can be treated as such ; since the mutual reactions between the three-phases balance at equal distribution o ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-21", "section_label": "Chapter 21: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 20502-21189", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-21/", "snippets": [ "... symmetrical to the REACTION MACHINES. 377 current wave also. Hence the equivalent sine wave of magnetism is of equal phase with the current wave ; that is, the E.M.F. of self-induction lags 90° behind the cur- rent, or is wattless. Thus at no-phase displacement, and at 90° phase dis- placement, a reaction machine can neither produce electri- cal power nor mechanical power. 230. If, however, the current wave differs in phase from the wave of E.M.F. by less than 90°, but more than zero degrees, it is unsymmetric ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "... 3. Considering the waves as replaced by their equivalent sine waves, from the sine wave formula, f + qf = 1 the inductance factor would be, ft = -914 and the phase angle, tan a, = ^= '-^=2.8 « = 65.4° p .41o giving apparently a very great phase displacement, while in reality, of the 41.85 amperes total current, 40 amperes (the current of the third harmonic) are in phase with their E.M.F. We thus have here a case of a circuit with complex har- monic waves which cannot be represented by their equiva- lent s ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-08", "section_label": "Chapter 9: Synchronous Induction Motor", "section_title": "Synchronous Induction Motor", "kind": "chapter", "sequence": 8, "number": 9, "location": "lines 14466-14550", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-08/", "snippets": [ "... f the periodically varying admittance coincide with the SYNCHRONOUS INDUCTION MOTOR 167 and zero values of the primary circuit, but gives a definite torque if they are displaced therefrom. This torque may be positive or negative according to the phase displacement between ad- mittance and primary circuit; that is, the lag or lead of the maximum admittance with regard to the primary maximum. Hence an induction motor with single-armature circuit at syn- chronism acts either as motor or as alternating-current generato ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-14", "section_label": "Chapter 16: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 14, "number": 16, "location": "lines 19374-20293", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-14/", "snippets": [ "... wave of magnetism therefore sym- metrical to the current wave also. Hence the equivalent sine wave of magnetism is of equal phase with the current wave ; that is, the e.m.f. of self-induction lags 90° behind the current, or is wattless. Thus at no-phase displacement, and at 90° phase displace- ment, a reaction machine can neither produce electrical power nor mechanical power. If, however, the current wave differs in phase from the wave of e.m.f. by less than 90°, but more than zero degrees, it is un- symmetrical wi ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-21", "section_label": "Chapter 23: Review", "section_title": "Review", "kind": "chapter", "sequence": 21, "number": 23, "location": "lines 32138-32819", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-21/", "snippets": [ "... le-phase Induction Motor.— XI, 101 (See \"Eickemeyer Rotary Terminal Induction Motor.\") Shading Coil. — 73. A short-circuited turn surrounding i part of the pole face of a single-phase induction motor with definite poles, for the purpose of giving a phase displacement of I he flux, and therehy a starting torque. It is the simplest ;iml cheap- est single-phase motor-starting device, but gives only low start- ing torque and low torque efficiency, thus is not well suited for larger motors. It thus is very extensively used ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-09", "section_label": "Chapter 9: Wave Screens. Even Harmonics", "section_title": "Wave Screens. Even Harmonics", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 16964-17631", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-09/", "snippets": [ "... ay illustrate some of the numerous wave- shape distortions which are met in electrical engineering, their characteristics, origin, effects, use and danger. Numerous other wave distortions, such as those produced by arcs, by unidirec- tional conductors, by dielectric effects such as corona, by Y con- nection of transformers for reactors, by electrolytic polarization, by pulsating resistance or reactance, etc., are discussed in other chapters or may be studied in a similar manner. v/" ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-14", "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "section_title": "Constant-Potential Constant-Current Trans Formation", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "... us economy is ^ \" 2(r'* + xo^) ^^^ which is a maximum for r' = xo (30) /o = 1 = 0.25 (31) which is rather low: That is, non-inductive load and supply circuit do not give very high apparatus economy, but inductive reactance of the load, and phase displacement in the supply circuit, gives far higher appa- ratus economy, that is, more output with the same volt-amperes in reactance. By inserting in (23), with the quantities, Q', Q'', and Q\"\\ coefficients ni, n2, ns, which are proportional respectively to the co ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... ce equal to three times the internal resistance, that is, an elec- trical efficiency of 75 per cent, gives the total resistance as r + r' = 0.2 x\\ hence, and the decrement is A = 0.73; hence a fairly rapid decay of the wave. At high frequencies, electrostatic, inductive, and radiation losses greatly increase the resistance, thus giving lower effi- ciency and more rapid decay of the wave. 48. The frequency of oscillation does not directly depend upon the size of apparatus, that is, the kilovolt-ampere capacity ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-44", "section_label": "Chapter 4: Distributed Capacity Of High-Potential Transformers", "section_title": "Distributed Capacity Of High-Potential Transformers", "kind": "chapter", "sequence": 44, "number": 4, "location": "lines 23179-23585", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "snippets": [ "... from distributed capacity occur. In transformers for very high voltages — 100;000 volts and more, or even considerably less in small transformers — the high- potential coil contains a large number of turns, a great length of conductor, and therefore its electrostatic capacity is appreciable, and such a coil thus represents a circuit of distributed resistance, inductance, and capacity somewhat similar to a transmission line. The same applies to reactive coils, etc., wound for very high voltages, and even in smaller r ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-45", "section_label": "Chapter 5: Distributed Series Capacity", "section_title": "Distributed Series Capacity", "kind": "chapter", "sequence": 45, "number": 5, "location": "lines 23586-23947", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "snippets": [ "... uctor, as from turn to turn or layer to layer of a transformer coil. In some circuits, in addition to this shunted capacity, dis- tributed series capacity also exists, that is, the circuit is broken at frequent and regular intervals by gaps filled with a dielectric or insulator, as air, and the two faces of the conductor ends thus constitute a condenser in series with the circuit. Where the elements of the circuit are short enough so as to be represented, approximately, as conductor differentials, the circuit consti ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-51", "section_label": "Chapter 2: Discussion Of General Equations", "section_title": "Discussion Of General Equations", "kind": "chapter", "sequence": 51, "number": 2, "location": "lines 28695-29315", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "snippets": [ "... or L C r -H g = L H- C, (89) or, in words, the power coefficients of the circuit are proportional to the energy storage coefficients, or the time constant of the electromagnetic field of the circuit, — , equals the time constant L of the electrostatic field of the circuit, -^ , then u = — = — = time constant of the circuit, (90) L C and from equation (54) R* = s2 + (f, h = VWs = as, k = VWq = aq, and from equation (52) = L . /L c/ m 0, (91) and / = 0; (92) DISCUSSION OF GEN ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-52", "section_label": "Chapter 3: Standing Waves", "section_title": "Standing Waves", "kind": "chapter", "sequence": 52, "number": 3, "location": "lines 29316-30243", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "snippets": [ "... se three- conductor 12,000-volt cable. Assume the conductor as stranded and of a section equiva- lent to No. 00 B. and S. G. Calculating the constants in the same manner, except that the expression for the capacity, equation (119), multiplies with the dielectric constant or specific capacity of the cable insula- tion, and that f ig verv small, about three or less; or taking the ^r values of the circuit constants from tests of the cable, we get values of the magnitude, per mile of single conductor, r = 0.41 ohm ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-54", "section_label": "Chapter 5: Free Oscillations", "section_title": "Free Oscillations", "kind": "chapter", "sequence": 54, "number": 5, "location": "lines 31451-32708", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "snippets": [ "... rgy of the electric field; and their appearance therefore presupposes the possibility of energy storage in more than one form so as to allow 478 FREE OSCILLATIONS 479 an interchange or surge of energy between its different forms, electromagnetic and electrostatic energy. Free oscillations occur only in circuits containing both capacity C and inductance, L. The absence of energy supply or abstraction defines the free oscillations by the condition that the power p = ei at the two ends of the circuit or section of t ..." ] } ] }, { "id": "illumination", "label": "Illumination", "aliases": [ "Illumination", "candle power", "candle-power", "illuminant", "illuminants", "illuminating", "illumination" ], "total_occurrences": 983, "matching_section_count": 21, "matching_source_count": 5, "source_totals": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 805, "section_count": 13 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 170, "section_count": 4 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 5, "section_count": 1 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 2, "section_count": 2 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-12", "section_label": "Lecture 12: Illumination And Illuminating Engineering", "section_title": "Illumination And Illuminating Engineering", "kind": "lecture", "sequence": 12, "number": 12, "location": "lines 16485-17445", "status": "candidate", "occurrence_count": 242, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-12/", "snippets": [ "LECTURE XII. ILLUMINATION AND ILLUMINATING ENGINEERING. 110. Artificial light is used for the purpose of seeing and distinguishing objects clearly and comfortably when the day- light fails. The problem of artificial lighting thus comprises con- sideration of the source of light o ...", "LECTURE XII. ILLUMINATION AND ILLUMINATING ENGINEERING. 110. Artificial light is used for the purpose of seeing and distinguishing objects clearly and comfortably when the day- light fails. The problem of artificial lighting thus comprises con- sideration of the source of light or the illuminant; ...", "... LLUMINATING ENGINEERING. 110. Artificial light is used for the purpose of seeing and distinguishing objects clearly and comfortably when the day- light fails. The problem of artificial lighting thus comprises con- sideration of the source of light or the illuminant; the flux of light issuing from it; the distribution of the light flux in space, that is, the light flux density in space and more particularly at the illuminated objects; the illumination, that is, the light flux density reflected from the illuminated ob ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-11", "section_label": "Lecture 11: Light Intensity And Illumination", "section_title": "Light Intensity And Illumination", "kind": "lecture", "sequence": 11, "number": 11, "location": "lines 12574-16484", "status": "candidate", "occurrence_count": 169, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-11/", "snippets": [ "LECTURE XI. LIGHT INTENSITY AND ILLUMINATION. A. INTENSITY CURVES FOR UNIFORM ILLUMINATION. 102. The distribution of the light flux in space, and thus the illumination, depends on the location of the light sources, and on their distribution curves. The character of the required illumi- nation de ...", "LECTURE XI. LIGHT INTENSITY AND ILLUMINATION. A. INTENSITY CURVES FOR UNIFORM ILLUMINATION. 102. The distribution of the light flux in space, and thus the illumination, depends on the location of the light sources, and on their distribution curves. The character of the required illumi- nation depends on the purpose for which it is used: a gene ...", "LECTURE XI. LIGHT INTENSITY AND ILLUMINATION. A. INTENSITY CURVES FOR UNIFORM ILLUMINATION. 102. The distribution of the light flux in space, and thus the illumination, depends on the location of the light sources, and on their distribution curves. The character of the required illumi- nation depends on the purpose for which it is used: a general illumination of low and approximately uniform intensity for street lightin ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 124, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... ved. So far only three materials have been found, which in luminous arcs give efficiences vastly superior to incandescence : mercury, calcium (lime), and titanium. All (three even in moderate sized units, give efficiencies of one-half watt or better per candle power. The mercury arc has the advantage of perfect steadiness, a long life — requiring no attention for thousands of hours — ARC LIGHTING 225 and high efficiency over a fairly wide range of candle powers ; but it is seriously handicapped for many purposes ...", "... r efficiency of the latter ; and the inconvenience of daily attendance required by an open arc, and the large consumption of carbons, makes a return to this type improbable. For this reason the flame carbon lamp has not proven suitable for general outdoor illumination, as street lighting, where the cost of carbons and trimming would usually far more than ofl^set the gain in efficiency. Flame carbon lamps, however, have found a field for decora- tive lighting, for advertising purposes, etc., for which the glare of ligh ...", "... he titanium-iron spectrum as represented by the magnetite arc, the metallic oxide arc, and other types still in development. In all these long burning luminous arcs, some efficiency had to be sacrificed in developing sufficiently small units for general illumination. While the substitution of -the flame car- bon in the open arc has quadrupled the light at the same power consumption, and the substitution of the magnetite electrode for carbon at the same power consumption would in the same manner increase the light, fo ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-13", "section_label": "Lecture 13: Physiological Problems Of Illuminating Engineering", "section_title": "Physiological Problems Of Illuminating Engineering", "kind": "lecture", "sequence": 13, "number": 13, "location": "lines 17446-17956", "status": "candidate", "occurrence_count": 98, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-13/", "snippets": [ "LECTURE XIII. PHYSIOLOGICAL PROBLEMS OF ILLUMINATING ENGINEERING. 123. The design of an illumination requires the solution of physiological as well as physical problems. Physical considera- tions, for instance, are the distribution of light-flux intensity throughout the illuminated space, as related to si ...", "LECTURE XIII. PHYSIOLOGICAL PROBLEMS OF ILLUMINATING ENGINEERING. 123. The design of an illumination requires the solution of physiological as well as physical problems. Physical considera- tions, for instance, are the distribution of light-flux intensity throughout the illuminated space, as related to size, location and number of light sources, while th ...", "... physical problems. Physical considera- tions, for instance, are the distribution of light-flux intensity throughout the illuminated space, as related to size, location and number of light sources, while the relation, to the satisfac- tory character of the illumination, of the direction of the light, its subdivision and diffusion, etc., are physiological questions. Very little, however, is known on the latter, although the entire field of the physiological effects of the physical methods of illumination is still largely ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-03", "section_label": "Lecture 3: Physiological Effects Of Radiation", "section_title": "Physiological Effects Of Radiation", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2366-3638", "status": "candidate", "occurrence_count": 87, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-03/", "snippets": [ "... CTURE III. PHYSIOLOGICAL EFFECTS OF RADIATION. Visibility. 20. The most important physiological effect is the visibility of the narrow range of radiation, of less than one octave, between wave length 76 X 10~6 and 39 X 1Q-6. The range of intensity of illumination, over which the eye can see with practically equal comfort, is enormous: the average intensity of illumination at noon of a sunny day is nearly one million times greater than the illumination given by the full moon, and still we can see fairly well in eit ...", "... e visibility of the narrow range of radiation, of less than one octave, between wave length 76 X 10~6 and 39 X 1Q-6. The range of intensity of illumination, over which the eye can see with practically equal comfort, is enormous: the average intensity of illumination at noon of a sunny day is nearly one million times greater than the illumination given by the full moon, and still we can see fairly well in either case; that is, the human eye can adapt itself to enormous differences in the intensity of illumination, and ...", "... wave length 76 X 10~6 and 39 X 1Q-6. The range of intensity of illumination, over which the eye can see with practically equal comfort, is enormous: the average intensity of illumination at noon of a sunny day is nearly one million times greater than the illumination given by the full moon, and still we can see fairly well in either case; that is, the human eye can adapt itself to enormous differences in the intensity of illumination, and that so perfectly that it is difficult to realize the differences in intensity w ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-09", "section_label": "Lecture 9: Measurement Of Light And Radiation", "section_title": "Measurement Of Light And Radiation", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 8511-9388", "status": "candidate", "occurrence_count": 52, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-09/", "snippets": [ "... , in the sense in which it is con- sidered photometrically, is not power, but is the physiological effect of certain wave lengths of radiation, and therefore can- not be measured, physically, as power, but only physiologically, 168 RADIATION, LIGHT, AND ILLUMINATION. by comparison with other physiological effects of the same nature. The power of visible radiation obviously can be measured, and thus we can express the power of the visible radiation of a mercury lamp or an incandescent lamp in watts. But the power ...", "... thereof. One watt of green radiation gives many times as great a physiological effect, that is, more light, as does one watt of red or violet radiation, and, besides, gives a different kind of physiological effect: a differ- ent color. The unit in which illuminating value of light, or its intensity, is expressed as the \"candle-power,\" is, therefore, a physiological and not a physical quantity, and hence it has no direct or con- stant relation to the unit .of power, or the watt. The unit of light intensity has been ch ...", "... siological effect, that is, more light, as does one watt of red or violet radiation, and, besides, gives a different kind of physiological effect: a differ- ent color. The unit in which illuminating value of light, or its intensity, is expressed as the \"candle-power,\" is, therefore, a physiological and not a physical quantity, and hence it has no direct or con- stant relation to the unit .of power, or the watt. The unit of light intensity has been chosen by convention: as the physio- logical effect exerted on the hum ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-10", "section_label": "Lecture 10: Light Flux And Distribution", "section_title": "Light Flux And Distribution", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 9389-12573", "status": "candidate", "occurrence_count": 45, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-10/", "snippets": [ "LECTURE X. LIGHT FLUX AND DISTRIBUTION. 86. The light flux of an illuminant is its total radiation power, in physiological measure. It therefore is the useful output of the illuminant, and the efficiency of an illuminant thus is the ratio of the total light flux divided by the power input. In general, the distribution of the li ...", "LECTURE X. LIGHT FLUX AND DISTRIBUTION. 86. The light flux of an illuminant is its total radiation power, in physiological measure. It therefore is the useful output of the illuminant, and the efficiency of an illuminant thus is the ratio of the total light flux divided by the power input. In general, the distribution of the light flux throughout space is not uniform, but the light-flux density is different in different directions fr ...", "LECTURE X. LIGHT FLUX AND DISTRIBUTION. 86. The light flux of an illuminant is its total radiation power, in physiological measure. It therefore is the useful output of the illuminant, and the efficiency of an illuminant thus is the ratio of the total light flux divided by the power input. In general, the distribution of the light flux throughout space is not uniform, but the light-flux density is different in different directions from an illuminant. Unit light-flux d ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-16", "section_label": "Lecture 16: The Incandescent Lamp", "section_title": "The Incandescent Lamp", "kind": "lecture", "sequence": 16, "number": 16, "location": "lines 9687-9919", "status": "candidate", "occurrence_count": 33, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-16/", "snippets": [ "SIXTEENTH LECTURE THE INCANDESCENT LAMP mHE two main types of electric illuminants are the in- candescent lamp and the arc. In the incandescent lamp the current flows through a solid conductor, usually in a vacuum, and the heat produced in the resistance of the conductor makes it incandescent, thus giving the light. Incandescent lamps ...", "... on a constant, direct or alternating current cir- cuit; they are then usually built for the standard arc circuits, and thus for low voltage. For general convenience the efficiency of incandescent lamps is given in watts power consumption per horizontal candle power, when operating on such a voltage, that the candle power of the lamp decreases by 20% in 500 hours run- ning; and the time, in which the candle power decreases by 20% — that is, 500 hours with the present efficiency rating — is called the useful life ; si ...", "... they are then usually built for the standard arc circuits, and thus for low voltage. For general convenience the efficiency of incandescent lamps is given in watts power consumption per horizontal candle power, when operating on such a voltage, that the candle power of the lamp decreases by 20% in 500 hours run- ning; and the time, in which the candle power decreases by 20% — that is, 500 hours with the present efficiency rating — is called the useful life ; since experience has shown, that after a decrease of candle ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... cific effects of the component radiations, as the physiologically harm- ful action of an ultra-violet component of light, still remain, even if the eye does not see the components, and in the study of radia- tion for the purpose of its engineering use for illumination it is therefore necessary to analyze the mixed radiation given by a source as a lamp, by resolving it into its component waves. This is done by using some feature of the radiation which varies with the frequency. Such is the case with the velocity of pr ...", "... y space is 3 X 1010 cm. per sec. It is practically the same in air and other gases. In denser bodies, however, as water, glass, etc., the velocity of light is less and, as will be seen, is different for different frequencies. 22 RADIATION, LIGHT, AND ILLUMINATION. Assume then, in Fig. 15, a beam of light B striking under an angle the boundary between two media, as air A and water W, the vibration of the ether particles in the beam of light is at right angles to the direction of propagation BC, and successively t ...", "... m 3, dl-3 = £2_3 -*- ^_2 = refractive index of medium 1 and medium 3; that is, the refractive index between any two media is derived as the ratio of their refractive indices against a third medium, as, for instance, against air. 24 RADIATION, LIGHT, AND ILLUMINATION. 11. Incidentally, it is interesting to consider the corresponding relations in electric waves. In an electric circuit, the speed of propagation of an electric wave is, when neglecting the energy losses in and by the con- ductor: S = -L= , (5) VLC ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "... the result of slow combustion. With those substances which have an ignition point above incandes- cence, this cannot be observed, but it is observed, for instance, in carbon bisulphide, CS2, which ignites spontaneously at about 96 RADIATION, LIGHT, AND ILLUMINATION. 180 deg. cent., and a few degrees below this temperature phos- phoresces in air, by slow combustion. A biological phosphorescence is shown by many forms of life: some bacilli of putrefaction phosphoresce, and are the cause of the faint glow occasional ...", "... ight red, green, orange The spectroscope shows in every case a spectrum having a number of definite lines which are brightest and most numerous in the red for Sr, in the green for Ba, and in the orange yellow for Ca. In general, 98 RADIATION, LIGHT, AND ILLUMINATION. metal spectra show a number, frequently very many lines in the visible range. As Sr, Ba, Ca, are much less volatile than Li, Na, Tl, to get good effects in the bunsen flame, instead of the chlorides, the nitrates, or preferably the chlorates or perchl ...", "... main the same, the terminal voltage of the Geissler tube or the spark gap remains the same and independent of the current, and the current is determined by the impedance between the. Geissler tube or spark gap and the source of 100 RADIATION, LIGHT, AND ILLUMINATION. e.m.f., or by the available power of the supply source. A Geissler tube, thus, cannot be operated directly on a constant potential supply of unlimited power, but requires a current limiting im- pedance in series with it, or a source of limited power, th ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-05", "section_label": "Lecture 5: Temperature Radiation", "section_title": "Temperature Radiation", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3946-5076", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-05/", "snippets": [ "... or and thus increasing radiation power, its temperature first rises proportional to the power input and then slower and ultimately approaches proportionality with the fourth root of the power output: 4/p- T =V — • ll V kA 72 RADIATION, LIGHT, AND ILLUMINATION. In Fig. 27 is shown the radiation curve, with the temperatures T as ordinates and the radiated power Pr as abscissas, the upper curve with 100 times the scale of abscissas. Thus, to double the temperature rise from 10 deg. cent, to 20 deg. cent, requ ...", "... the power input and thereby the radi- ated power to T^ it becomes invisible, but if we move away from the lamp to 10 times the previous distance, we get only T^ the radiation reaching our eyes and still the light is very plainly 74 RADIATION, LIGHT, AND ILLUMINATION. visible. The invisibility in the former case, thus, is not due to low intensity, but to low frequency. The fraction of the total radiation, which is visible to the eye as light, thus increases with the increasing temperature, from zero at low temperat ...", "... production is rather low even at the maximum efficiency point and with the average frequency of radiation in the visible range, since this visible range is less than one octave; under these most favorable conditions the visible 76 RADIATION, LIGHT, AND ILLUMINATION. energy probably does not much exceed 20 per cent of the total radiation, the rest falls below and above the visible frequencies. 36. At the highest attainable temperature, the boiling point of carbon, the efficiency is much lower, probably below 10 per ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-08", "section_label": "Lecture 8: Arc Lamps And Arc Lighting", "section_title": "Arc Lamps And Arc Lighting", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 7141-8510", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-08/", "snippets": [ "... 25 1 0 FIG. 45. arc length, I, we get tor every value of current, i, a practically straight line, as shown for the magnetite arc in Fig. 45, for values of current of 1, 2, 4 and 8 amperes. These lines are steeper 137 138 RADIATION, LIGHT, AND ILLUMINATION. for smaller currents, that is, low-current arcs consume a higher voltage for the same length than high-current arcs, the in- crease being greater the longer the arc. These lines in Fig. 45 intersect in a point which lies at I = — 0.125 cm. = — 0.05 in. ...", "... the power is p0 = eQi, it follows that the voltage, e0, consumed at the arc terminals is constant. The power consumed in the arc stream : pl = ej,, is given off, by heat conduction, convection, and by radiation, from the sur- 140 RADIATION, LIGHT, AND ILLUMINATION. face of the arc stream, and thus, as the temperature of the arc stream is constant, and is that of the boiling point of the arc vapor, the power pl consumed in the arc stream is proportional to its surface, that is, to the product of arc diameter ld and ...", "... e arc meets only a part of this ter- minal drop e\", and, for very short arc length, only the terminal drop e0' occurs. Possibly the voltage e0' = 28 is consumed at the negative terminal in producing the conducting vapor stream, 142 RADIATION, LIGHT, AND ILLUMINATION. while the voltage e\" = 8 is consumed by the moving vapor stream in penetrating a layer of dead carbon vapor formed by heat evaporation from the positive terminal, and surrounding this terminal. Stability Curves of the Arc. 64. From the volt-ampere c ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-01", "section_label": "Lecture 1: General Review", "section_title": "General Review", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 154-565", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-01/", "snippets": [ "... rely used, but the voltages of distribution systems in this country are distributed over the whole range, so as to secure best economy of the incan- descent lamp. This condition was brought about by the close co-oper- ation, in this country, between the illuminating com- panies and the manufacturers of incandescent lamps. The constants of an incandescent lamp are the candle power — for instance t6; the economy — for instance 3.1 watts for hori- zontal candle power; and the voltage — for instance no. By careful manuf ...", "... ecure best economy of the incan- descent lamp. This condition was brought about by the close co-oper- ation, in this country, between the illuminating com- panies and the manufacturers of incandescent lamps. The constants of an incandescent lamp are the candle power — for instance t6; the economy — for instance 3.1 watts for hori- zontal candle power; and the voltage — for instance no. By careful manufacture, a lamp can be made in which the filament reaches 3.1 watts per candle power economy at 16 c. p. within one-h ...", "... e close co-oper- ation, in this country, between the illuminating com- panies and the manufacturers of incandescent lamps. The constants of an incandescent lamp are the candle power — for instance t6; the economy — for instance 3.1 watts for hori- zontal candle power; and the voltage — for instance no. By careful manufacture, a lamp can be made in which the filament reaches 3.1 watts per candle power economy at 16 c. p. within one-half candle-power: but the attempt to fulfill at the same time (the condition, that this ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-07", "section_label": "Lecture 7: Flames As Illuminants", "section_title": "Flames As Illuminants", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 6609-7140", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-07/", "snippets": [ "LECTURE VII. FLAMES AS ILLUMINANTS. 56. Two main classes of illuminants exist: those producing radiation by the conversion of the chemical energy of com- bustion— the flames — and those deriving the energy of radia- tion from electric energy — the incandescent lamp and the arc lamp, and ...", "LECTURE VII. FLAMES AS ILLUMINANTS. 56. Two main classes of illuminants exist: those producing radiation by the conversion of the chemical energy of com- bustion— the flames — and those deriving the energy of radia- tion from electric energy — the incandescent lamp and the arc lamp, and other less frequently used electric ill ...", "... nts exist: those producing radiation by the conversion of the chemical energy of com- bustion— the flames — and those deriving the energy of radia- tion from electric energy — the incandescent lamp and the arc lamp, and other less frequently used electric illuminants. Flames. To produce light from the chemical energy of combustion, almost exclusively hydrocarbon flames are used, as the gas flame, the candle, the oil lamp, the gasolene and kerosene lamp, etc.; that is, compounds of hydrogen and carbon or of hydrogen ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... y the interception of the rays of the mercury lamp or the rays of the moon. The most conspicuous form of radiation is light, and, therefore, it was in connection with this form that the laws of radiation were first studied. 1 2 RADIATION, LIGHT, AND ILLUMINATION. 2. The first calculations of the velocity of light were made by astronomers in the middle of the eighteenth century, from the observations of the eclipses of the moons of Jupiter. A number of moons revolve around the planet Jupiter, some of them so clos ...", "... passed with the disk stationary, but through the next hole H2, that is, the disk has moved a distance equal to the pitch of one hole while the light traveled 10 miles. Assume, for instance, that the disk D has 200 holes and makes 4 RADIATION, LIGHT, AND ILLUMINATION. 94 rev. per sec. at the moment when the light has again reached full brilliancy* In this case, 200 X 94 = 18,800 holes pass the telescope per second, and the time of motion by the pitch of one hole is sec., and as this is the time required by the light ...", "... c. at which the distance FIG. 4. between the two glass plates is J wave length, or j, J, etc., the two component beams of a would differ by \\, f , |, etc. wave lengths, and thus would blot each other out, producing darkness, 6 RADIATION, LIGHT, AND ILLUMINATION. while at those points where the distance between the glass plates is J, 1, lj, etc. wave lengths, and the two component beams a thus differ in phase by a full wave or a multiple thereof, they would add. If, therefore, light is a wave motion, such a stru ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-04", "section_label": "Lecture 4: Chemical And Physical Effects Of Radiation", "section_title": "Chemical And Physical Effects Of Radiation", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3639-3945", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-04/", "snippets": [ "... a sound wave of the frequency with which it can vibrate, and if the vibration of the silver atom, in response to the frequency of radiation, becomes sufficiently intense, it breaks away from the atom with which it is chemically 64 RADIATION, LIGHT, AND ILLUMINATION. combined in the compound, the silver bromide, etc., and this compound thus splits up, dissociates. The phenomenon, how- ever, must be more complex, as a simple resonance vibration would be especially pronounced at one definite frequency, the frequency ...", "... nd used as such by the animals. The radiations which supply the energy of plant life, probably are the long waves of yellow, red and ultra-red light, while the short waves of blue, violet and ultra-violet cannot be used by the 66 RADIATION, LIGHT, AND ILLUMINATION. plant, but are harmful, kill the vegetation. This can easily be understood : to the long waves of red and yellow light the atoms do not respond, but only the much heavier groups of atoms or car- bon radicals, and these thus separate and recombine and th ...", "... frequencies given by fluorescence and then looking at the fluorescent body through a glass having the same color as that given by fluorescence. Thus the least traces of red fluorescence can be discovered by looking at the body through a red glass, in the illumination given by the mer- cury lamp. As the mercury lamp contains practically no red rays, seen through a red glass everything appears nearly black or invisible except red fluorescent bodies, which appear self-lumi- nous, glowing in a light of their own, and appe ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-01", "section_label": "Chapter 1: The General Number", "section_title": "The General Number", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 915-3491", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-01/", "snippets": [ "... 5 horses -7 horses = -2 horses has no physical meaning. There exist no negative horses, and at the best we could only express the relation by saying, 5 horses -7 horses is impossible, 2 horses are missing. D THE GENERAL NUMBER. In the same way, an illumination of 5 foot-candles, lowered by 3 foot-candles, gives an illumination of 2 foot-candles, thus, . b foot-candles —3 foot-candles = 2 foot-candles. If it is tried to lower the illumination of 5 foot-candles by 7 foot-candles, it will be found impossible; th ...", "... no negative horses, and at the best we could only express the relation by saying, 5 horses -7 horses is impossible, 2 horses are missing. D THE GENERAL NUMBER. In the same way, an illumination of 5 foot-candles, lowered by 3 foot-candles, gives an illumination of 2 foot-candles, thus, . b foot-candles —3 foot-candles = 2 foot-candles. If it is tried to lower the illumination of 5 foot-candles by 7 foot-candles, it will be found impossible; there cannot be a negative illumination of 2 foot-candles ; the limit ...", "... orses are missing. D THE GENERAL NUMBER. In the same way, an illumination of 5 foot-candles, lowered by 3 foot-candles, gives an illumination of 2 foot-candles, thus, . b foot-candles —3 foot-candles = 2 foot-candles. If it is tried to lower the illumination of 5 foot-candles by 7 foot-candles, it will be found impossible; there cannot be a negative illumination of 2 foot-candles ; the limit is zero illumina- tion, or darkness. From a string of 5 feet length, we can cut off 3 feet, leaving 2 feet, but we c ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-02", "section_label": "Lecture 2: General Distribution", "section_title": "General Distribution", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 566-982", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-02/", "snippets": [ "... s very low ; and so it can be understood that in the early days, where this arrange- ment was generally used, the financial results of most alternat- ing current distributions were very discouraging. Assuming as an instance a connected load of twenty 16 candle power lamps — low efficiency lamps, of 60 watts per lamp, since (the voltage regulation cannot be very perfect — allowing then in cases of all lamps being used, an overload of 100%, which is rather beyond safe limits, and permissible only on the assumption that ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-13", "section_label": "Chapter 15: Synchronous Rectifier", "section_title": "Synchronous Rectifier", "kind": "chapter", "sequence": 13, "number": 15, "location": "lines 18413-19373", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-13/", "snippets": [ "... ih i2 and i0) as overlapped by the inductances, Xi, x* and x0, are shown in Fig. 103. Full description and discussion of the mercury-arc rectifier is contained in \"Theory and Calculation of Transient Phenomena,9' Section II, and in \"Radiation, Light and Illumination.\" 250 ELECTRICAL APPARATUS 143. To reduce the sparking at the rectifying commutator, the gap between the segments may be divided into a number of gaps, by small auxiliary segments, as shown in Fig. 104, and these then connected to intermediate po ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-01", "section_label": "Chapter 1: Electric Conduction. Soled And Liquid", "section_title": "Electric Conduction. Soled And Liquid", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 959-3894", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-01/", "snippets": [ "... current the terminal voltage decreases, is unstable on constant-potential supply. 11. An important application of pyroelectric conduction has been the glower of the Nernst lamp, which before the develop- ment of the tungsten lamp was extensively used for illumination. Pyroelectrolytes cover the widest range of conductivities; the alloys of silicon with iron and other metals give, depending on their composition, resistivities from those of the pure metals up to the lower resistivities of electrolytes: 1 ohm per cm.'; ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-15", "section_label": "Chapter 15: Constant-Voltage Series Operation", "section_title": "Constant-Voltage Series Operation", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 27996-29301", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-15/", "snippets": [ "... t., while a variation of current in the P lamp, by p per cent., gives a variation of voltage of about jr-^ per cent., and thus a variation of power of about (1 + 7r^)p = 2.67 p per cent. Thus, with the increasing use of incandescent lamps for street illumination, series operation in a constant-voltage circuit be- comes of increasing importance. If e = rated voltage, i = rated current of lamp or other con- suming device, and eo = supply voltage, n = — lamps can be op- erated in series on the constant-voltage su ..." ] } ] }, { "id": "radiation", "label": "Radiation", "aliases": [ "Radiation", "radiant energy", "radiation", "radiations" ], "total_occurrences": 931, "matching_section_count": 34, "matching_source_count": 11, "source_totals": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 785, "section_count": 13 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 85, "section_count": 1 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 36, "section_count": 8 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 7, "section_count": 2 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 5, "section_count": 2 }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 5, "section_count": 2 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 3, "section_count": 2 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 2, "section_count": 1 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 1, "section_count": 1 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 1, "section_count": 1 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-05", "section_label": "Lecture 5: Temperature Radiation", "section_title": "Temperature Radiation", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3946-5076", "status": "candidate", "occurrence_count": 233, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-05/", "snippets": [ "LECTURE V. TEMPERATURE RADIATION. 34. The most common method of producing radiation is by impressing heat energy upon a body and thereby raising its tem- perature. Up to a short time ago this was the only method avail- able for the production of artificial light. The temperature is rai ...", "LECTURE V. TEMPERATURE RADIATION. 34. The most common method of producing radiation is by impressing heat energy upon a body and thereby raising its tem- perature. Up to a short time ago this was the only method avail- able for the production of artificial light. The temperature is raised by heating a body by the transformation of chemic ...", "... . The temperature is raised by heating a body by the transformation of chemical energy, that is, by combustion, and in later years by the trans- formation of electric energy, as in the arc and incandescent lamp. With increasing temperature of a body the radiation from the body increases. Thus, also, the power which is required to main- tain the body at constant temperature increases with increase of temperature. In a vacuum (as approximately in the incandes- cent lamp) , where heat conduction and heat convection f ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-03", "section_label": "Lecture 3: Physiological Effects Of Radiation", "section_title": "Physiological Effects Of Radiation", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2366-3638", "status": "candidate", "occurrence_count": 105, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-03/", "snippets": [ "LECTURE III. PHYSIOLOGICAL EFFECTS OF RADIATION. Visibility. 20. The most important physiological effect is the visibility of the narrow range of radiation, of less than one octave, between wave length 76 X 10~6 and 39 X 1Q-6. The range of intensity of illumination, over which the eye can see with ...", "LECTURE III. PHYSIOLOGICAL EFFECTS OF RADIATION. Visibility. 20. The most important physiological effect is the visibility of the narrow range of radiation, of less than one octave, between wave length 76 X 10~6 and 39 X 1Q-6. The range of intensity of illumination, over which the eye can see with practically equal comfort, is enormous: the average intensity of illumination at noon of a sunny day is nearly ...", "... ace of the moon's disk, of one-half degree diameter, is about TffsWtf the surface of the sky, it thus follows that the daylight reflected from the sky is about 100,000 times more intense than the light of the full moon. The organ by which we perceive the radiation, the human eye (Fig. 20), contains all the elements of a modern photographic camera — an achromatic lense: the lense L, of high refractive power, enclosed between the two transparent liquids A and B which correct the color dispersion, that is, give the ac ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 89, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "LECTURE II. RELATION OF BODIES TO RADIATION. 9. For convenience, the total range of known radiations can be divided into two classes, the electric waves and the light waves, which are separated from each other by the blank space in the middle of the spectrum of radiation (Fig. 14). Under light wa ...", "LECTURE II. RELATION OF BODIES TO RADIATION. 9. For convenience, the total range of known radiations can be divided into two classes, the electric waves and the light waves, which are separated from each other by the blank space in the middle of the spectrum of radiation (Fig. 14). Under light waves we here include also the invisible ultra-red radiation ...", "... II. RELATION OF BODIES TO RADIATION. 9. For convenience, the total range of known radiations can be divided into two classes, the electric waves and the light waves, which are separated from each other by the blank space in the middle of the spectrum of radiation (Fig. 14). Under light waves we here include also the invisible ultra-red radiation and the ultra-violet radiation and the non-refrangible radiations, as X-rays, etc., separated from the latter by the second blank space of the radiation spectrum. In the ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 85, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... to do any more strictly with a problem of physics, but that we are on .the borderland between applied physics, that is engineering, and physiology. Light is not a physical quantity, but it is the physiological effeot exerted upon the human eye by certain radiations. There are different forms of energy, all convertible into each other, as magnetic energy, electric energy, heat energy, mechanical momentum, radiating energy, etc. The latter, radi- ating energy, is a vibratory motion of a hypothetical medium, the ethe ...", "... locity of about 188,000 miles per second; and it is a transverse vibration, differing from the vibratory energy of sound in this respect, that the sound waves are longitudinal, that is, the vibration is in the direction of the beam, while the vibration of radiation is transverse. Radiating energy can be derived from other forms of energy, for instance, from heat energy by raising a body to a 230 GENERAL LECTURES high temperature. Then the heat energy is converted into radi- ation and issues from the heated body ...", "... s of energy, for instance, from heat energy by raising a body to a 230 GENERAL LECTURES high temperature. Then the heat energy is converted into radi- ation and issues from the heated body, as for instance an incan- descent lamp filament, as a mass of radiations of different wave lengths, that is, different frequencies. All kinds of frequencies appear : from very low frequencies, that is only a few millions of millions of cycles per second, up to many times higher frequencies. We can get, if we desire, still very ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 84, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "LECTURE I. NATURE AND DIFFERENT FORMS OF RADIATION. 1. Radiation is a form of energy, and, as such, can be produced from other forms of energy and converted into other forms of energy. The most convenient form of energy for the production of rad- iation is heat energy, and radiation when destroyed by b ...", "LECTURE I. NATURE AND DIFFERENT FORMS OF RADIATION. 1. Radiation is a form of energy, and, as such, can be produced from other forms of energy and converted into other forms of energy. The most convenient form of energy for the production of rad- iation is heat energy, and radiation when destroyed by being intercepte ...", "... DIFFERENT FORMS OF RADIATION. 1. Radiation is a form of energy, and, as such, can be produced from other forms of energy and converted into other forms of energy. The most convenient form of energy for the production of rad- iation is heat energy, and radiation when destroyed by being intercepted by an opaque body, usuaDy is converted into heat. Thus in an incandescent lamp, the heat energy produced by the electric current in the resistance of the filament, is converted into radiation. If I hold my hand near the ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-09", "section_label": "Lecture 9: Measurement Of Light And Radiation", "section_title": "Measurement Of Light And Radiation", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 8511-9388", "status": "candidate", "occurrence_count": 70, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-09/", "snippets": [ "LECTURE IX. MEASUREMENT OF LIGHT AND RADIATION. 74. Since radiation is energy, it can be measured as such by converting the energy of radiation into some other form of energy, as, for instance, into heat, and measuring the latter. Thus a beam of radiation may be measured by having it impinge on one ...", "LECTURE IX. MEASUREMENT OF LIGHT AND RADIATION. 74. Since radiation is energy, it can be measured as such by converting the energy of radiation into some other form of energy, as, for instance, into heat, and measuring the latter. Thus a beam of radiation may be measured by having it impinge on one contact of a thermo-co ...", "LECTURE IX. MEASUREMENT OF LIGHT AND RADIATION. 74. Since radiation is energy, it can be measured as such by converting the energy of radiation into some other form of energy, as, for instance, into heat, and measuring the latter. Thus a beam of radiation may be measured by having it impinge on one contact of a thermo-couple, of which the other contact is maintained at constant temperature. A ga ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 59, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "LECTURE VI. LUMINESCENCE. 43. All methods of producing radiation, and more particularly light, other than the temperature radiation or incandescence, are generally comprised by the name luminescence. Some special cases of luminescence have already been discussed in the phe- nomena of fluorescence and phosphorescence, r ...", "LECTURE VI. LUMINESCENCE. 43. All methods of producing radiation, and more particularly light, other than the temperature radiation or incandescence, are generally comprised by the name luminescence. Some special cases of luminescence have already been discussed in the phe- nomena of fluorescence and phosphorescence, represented by the conversion of the radiation absorbed by a body in ...", "... than the temperature radiation or incandescence, are generally comprised by the name luminescence. Some special cases of luminescence have already been discussed in the phe- nomena of fluorescence and phosphorescence, represented by the conversion of the radiation absorbed by a body into radiation of a different wave length. Usually luminescence at ordinary temperature, or at moderate temperatures, that is, temperatures below incandescence, is called fluorescence or phosphorescence. Fluorescence and Phosphoresce ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-04", "section_label": "Lecture 4: Chemical And Physical Effects Of Radiation", "section_title": "Chemical And Physical Effects Of Radiation", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3639-3945", "status": "candidate", "occurrence_count": 49, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-04/", "snippets": [ "LECTURE IV. CHEMICAL AND PHYSICAL EFFECTS OF RADIATION. Chemical Effects. 31. Where intense radiation is intercepted by a body chemical action may result by the heat energy into which the radiation is converted. This, however, is not a direct chemical effect of radiation but an indirect effect, resulting f ...", "LECTURE IV. CHEMICAL AND PHYSICAL EFFECTS OF RADIATION. Chemical Effects. 31. Where intense radiation is intercepted by a body chemical action may result by the heat energy into which the radiation is converted. This, however, is not a direct chemical effect of radiation but an indirect effect, resulting from the energy of the radiation. Direct chemical ...", "LECTURE IV. CHEMICAL AND PHYSICAL EFFECTS OF RADIATION. Chemical Effects. 31. Where intense radiation is intercepted by a body chemical action may result by the heat energy into which the radiation is converted. This, however, is not a direct chemical effect of radiation but an indirect effect, resulting from the energy of the radiation. Direct chemical effects of radiation are frequent. It is such an effect on which photography is based : the dis ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-10", "section_label": "Lecture 10: Light Flux And Distribution", "section_title": "Light Flux And Distribution", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 9389-12573", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-10/", "snippets": [ "LECTURE X. LIGHT FLUX AND DISTRIBUTION. 86. The light flux of an illuminant is its total radiation power, in physiological measure. It therefore is the useful output of the illuminant, and the efficiency of an illuminant thus is the ratio of the total light flux divided by the power input. In general, the distribution of the light flux throughout spa ...", "... coordinates does not give a fair representation of the total light flux, or the mean spherical intensity of the light source, but on the contrary frequently is very misleading. When com- paring different polar curves of intensity distribution, it is 188 RADIATION, LIGHT, AND ILLUMINATION. impossible to avoid the impression of the area of the curve as representative of the light flux. The area of the polar curve, however, has no direct relation whatever to the total light flux, that is, to the output of the illumi ...", "... lux in the space from the downward direction = 0 to the angle <£ = fa against the vertical or symmetry axis, then is fc1 = 2 TT / sin dfa (3) */0 and the light flux in a zone between the angles (j)1 and fa is (4) I. DISTRIBUTION CURVES OF RADIATION. (1) Point, or Sphere, of Uniform Brilliancy. In this case, the intensity distribution is uniform, and thus, if / = intensity of light, in candles, <£= 4 nl = light flux, in lumens; (5) or, inversely: / = -. (6) The brilliancy of a radiator ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-07", "section_label": "Lecture 7: Flames As Illuminants", "section_title": "Flames As Illuminants", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 6609-7140", "status": "candidate", "occurrence_count": 23, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-07/", "snippets": [ "LECTURE VII. FLAMES AS ILLUMINANTS. 56. Two main classes of illuminants exist: those producing radiation by the conversion of the chemical energy of com- bustion— the flames — and those deriving the energy of radia- tion from electric energy — the incandescent lamp and the arc lamp, and other less frequently used electric illuminants. Flames. To produce l ...", "... carbon particles formed by this dissociation of hydrocar- bon gas float in the burning gases, that is, in the flame, and are raised to a high temperature by the heat of combustion of the gases, thereby made incandescent, and radiate light by tem- perature radiation; until ultimately, at the outer edge of the flame, they are burned by the oxygen of the air, and thus destroyed. We can see these carbon particles, which, floating 128 FLAMES AS ILLUMINANTS. 129 in the flame in anjncandescent state, give the light if ...", "... e through the luminous flame, we suddenly chill it and thereby preserve the carbon particles from combustion; they appear then on the plate as a carbon deposit, soot or lampblack. The light given by the luminous hydrocarbon flame thus is due to black-body radiation, and the flame makes its own radiator, and afterwards destroys it by combustion. To give a luminous flame, the hydrocarbon must be suffi- ciently rich in carbon to split off carbon at high temperatures. Thus methane, CH4, does not give a luminous flame, ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-49", "section_label": "Chapter 9: High-Frequency Conductors", "section_title": "High-Frequency Conductors", "kind": "chapter", "sequence": 49, "number": 9, "location": "lines 27003-27760", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "snippets": [ "... sistance and induc- tance. In conductors such as are used in the connections and the discharge path of lightning arresters and surge protectors, the unequal current distribution in the conductor (Chapter VII) and the power and voltage consumed by electric radiation, due to the finite velocity of the electric field (Chapter VIII), require con- sideration. The true ohmic resistance in high frequency conductors is usually entirely negligible compared with the effective resistance resulting from the unequal current di ...", "... e conductor. The total effective resistance, or resistance representing the power consumed by the current in the conductor, thus comprises the true ohmic resistance, the effective resistance of unequal current distribution, and the effective resistance of radiation. The power consumed by the effective resistance of unequal current distribution in the conductor is converted into heat in the conductor, and this resistance thus may be called the \" thermal resistance\" of the conductor, to distinguish it from the radia ...", "... ation. The power consumed by the effective resistance of unequal current distribution in the conductor is converted into heat in the conductor, and this resistance thus may be called the \" thermal resistance\" of the conductor, to distinguish it from the radiation resistance. The power consumed by the radiation resistance is not converted into heat in the conductor, but is dissipated in the space surrounding the conductor, or in any other conductor on which the electric wave impinges. That is, 403 404 TRANSIENT ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-08", "section_label": "Lecture 8: Arc Lamps And Arc Lighting", "section_title": "Arc Lamps And Arc Lighting", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 7141-8510", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-08/", "snippets": [ "... 0 10 I.fi6 0[5 25 1 0 FIG. 45. arc length, I, we get tor every value of current, i, a practically straight line, as shown for the magnetite arc in Fig. 45, for values of current of 1, 2, 4 and 8 amperes. These lines are steeper 137 138 RADIATION, LIGHT, AND ILLUMINATION. for smaller currents, that is, low-current arcs consume a higher voltage for the same length than high-current arcs, the in- crease being greater the longer the arc. These lines in Fig. 45 intersect in a point which lies at I = ...", "... terminal is proportional to the current, i\\ and, as the power is p0 = eQi, it follows that the voltage, e0, consumed at the arc terminals is constant. The power consumed in the arc stream : pl = ej,, is given off, by heat conduction, convection, and by radiation, from the sur- 140 RADIATION, LIGHT, AND ILLUMINATION. face of the arc stream, and thus, as the temperature of the arc stream is constant, and is that of the boiling point of the arc vapor, the power pl consumed in the arc stream is proportional to it ...", "... e current, i\\ and, as the power is p0 = eQi, it follows that the voltage, e0, consumed at the arc terminals is constant. The power consumed in the arc stream : pl = ej,, is given off, by heat conduction, convection, and by radiation, from the sur- 140 RADIATION, LIGHT, AND ILLUMINATION. face of the arc stream, and thus, as the temperature of the arc stream is constant, and is that of the boiling point of the arc vapor, the power pl consumed in the arc stream is proportional to its surface, that is, to the produ ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-11", "section_label": "Lecture 11: Light Intensity And Illumination", "section_title": "Light Intensity And Illumination", "kind": "lecture", "sequence": 11, "number": 11, "location": "lines 12574-16484", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-11/", "snippets": [ "... l illumination is l 7 cos and the vertical illumination is . 7 cos2 sin (4) (5) (6) (7) (8) where 7 is the intensity of the light source in the direc- tion . Inversely, to produce a uniform total illumination, i0, on the 228 RADIATION, LIGHT, AND ILLUMINATION. horizontal plane P, the intensity of the light source must vary with the angle according to the equation (6) : 7\" 1 2 (9) or, if we denote by 70 the vertical, or downward, intensity of the light source, A, - V,2; (10) ...", "... 087 132.00 152.0 133.00 90 0 00 00 00 103. Therefore, in the problem, as it is usually met, of pro- ducing uniform intensity i0 over a limited area, subtending angle 2 aj beneath the light source, the intensity of the light source 230 RADIATION, LIGHT, AND ILLUMINATION. FIG. 96. FIG. 97, LIGHT INTENSITY AND ILLUMINATION. 231 should follow (11) for 0 < < a>. Beyond <£ = a>, the intensity may rapidly decrease to zero — as would be most economical, if no light is required beyond the ar ...", "... = 2 tan 60 deg. = 2 V3 = 3.46. IV for a) = 75 deg.; or diameter of floor -f- height of walls = 2 tan 75 deg. = 7.46. These curves are drawn for the same total flux of light in the lower hemisphere, namely, 250 mean hemispherical candle power; 232 RADIATION, LIGHT, AND ILLUMINATION. or, 1570 lumens. The vertical or downward intensities 70 are in this case: I: aj = 30 deg.; 70 = 428 cp. II: cu = 45 deg.; 70 = 195 cp. Ill: w = 60 deg.; 70 = 95 cp. IV: aj = 75 deg.; 70 = 41.5 cp. The values are recorded ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-12", "section_label": "Lecture 12: Illumination And Illuminating Engineering", "section_title": "Illumination And Illuminating Engineering", "kind": "lecture", "sequence": 12, "number": 12, "location": "lines 16485-17445", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-12/", "snippets": [ "... ities with which we have to deal in illumi- nating engineering thus are : The intensity of the light source or the illuminant, and its brilliancy, that is, the flux density at the surface of the illuminant; The flux of light, that is, the total visible radiation issuing from the illuminant; 256 ILLUMINATION AND ILLUMINATING ENGINEERING. 257 The light flux density, that is, the distribution of the light flux in space, and The illumination, that is, the light flux density issuing from the illuminated object ...", "... ible radia- tion of the mercury lamp or a Moore tube as well as that of a point source — by adding all the flux densities intercepted by any surface enclosing the source of light. In a point source of light, the intensity, in candles, is the total 258 RADIATION, LIGHT, AND ILLUMINATION. flux of light, in lumens, divided by 4 x. In any illuminant which is not a point source, we cannot speak of an intensity, except at such distances at which the source of light can be assumed as a point; and in interior illuminat ...", "... f the light source generally is meas- ured in lumens per square centimeter, or per square millimeter. It is a quantity which is of high importance mainly in its physio- logical effect. Light intensity, brilliancy and light flux thus are character- 260 RADIATION, LIGHT, AND ILLUMINATION. istics of the illuminant, while flux density is a function of the space traversed by the light flux, but not of the source of light : with the same source of light, in the space from the surface of the illuminant to infinite dis ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-13", "section_label": "Lecture 13: Physiological Problems Of Illuminating Engineering", "section_title": "Physiological Problems Of Illuminating Engineering", "kind": "lecture", "sequence": 13, "number": 13, "location": "lines 17446-17956", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-13/", "snippets": [ "... xists to fail in their fulfillment, though it is frequently done. Such, for instance, is the requirement of low intrinsic brilliancy in the field of vision, of the color of the light, etc. Other physiological requirements are still very little 277 278 RADIATION, LIGHT, AND ILLUMINATION. understood or entirely unknown, while on others not sufficient quantitative data are available for exact engineering calculation. Thus, for instance, the usual suburban street illumination, with arcs spaced at considerable dist ...", "... ght; by attributing the results to a wrong cause, serious mistakes thus may be made in basing further work on the results. 125. In discussing diffused light, we must realize that the meaning of \" diffused light\" is to some extent indefinite. To 280 RADIATION, LIGHT, AND ILLUMINATION. define diffused light as light which traverses the space in all direc- tions and thus casts no shadow, is not correct, since even diffused daylight casts shadows. For instance, if in Fig. 122 P is the sur- M/w///^^^^^ FIG. ...", "... by two light sources, an object casts two shadows, in which the illumination is reduced to half (if the two light sources give equal illumination), but, where the shadows overlap, a perfectly black and lightless shadow is produced. The more the two 282 RADIATION, LIGHT, AND ILLUMINATION. half shadows overlap to a complete shadow, the less the combina- tion of the two light sources is equivalent to diffusion. At the same time, occasionally the existence of two or more half shadows and of their compound shadows ma ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... les and transmission lines 103, 105 power surge of low-frequency 105 stray field and starting current of transformer 189 Impact angle at transition point of wave 527 Impedance of conductor at high frequency 407 effective high frequency 408, 413 of radiation 396 traveling wave 460 Inductance and shunted capacity suppressing pulsations in direct-cur- rent circuit 134 effective, of radiation 394 energy of complex circuit 515 in telephone lines 455, 462 massed, in circuit 537 of conductor without retu ...", "... t transition point of wave 527 Impedance of conductor at high frequency 407 effective high frequency 408, 413 of radiation 396 traveling wave 460 Inductance and shunted capacity suppressing pulsations in direct-cur- rent circuit 134 effective, of radiation 394 energy of complex circuit 515 in telephone lines 455, 462 massed, in circuit 537 of conductor without return 390 electric circuit 12 range in electric circuit 13 representing magnetic component of electric field 5 566 INDEX PAGE Induc ...", "... Pyroelectrolytes, resistivities 9 Quarter-phase rectification 230 Quarter-wave circuit 313 oscillation 483, 489 of complex circuit 509 transmission line 322 transformer 312 transmission line 306, 315 Quartic equation of divided circuit 126 Radiation, effective resistance 393 power of conductor 393, 397 resistance of conductor 403 Rail, effective penetration of alternating current 378 return of single-phase system 370 transient effective resistance 379 Railway, direct-current, transient rail r ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-05", "section_label": "Chapter 6: Empirical Curves", "section_title": "Empirical Curves", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 16483-21988", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-05/", "snippets": [ "... 5r4xl0-i^ that is, the power input varies with the fourth power of the resistance. Assuming the resistance r as proportional to the absolute temperature T, and considering that the power input into the lamp is radiated from it, that is, is the power of radiation P^, the equation between p and r also is the equation between P^ and T, thus, P, = A:T4; that is, the radiation is proportional to the fourth power of the absolute temperature. This is the law of black body radiation, and above equation of the volt-am ...", "... roportional to the absolute temperature T, and considering that the power input into the lamp is radiated from it, that is, is the power of radiation P^, the equation between p and r also is the equation between P^ and T, thus, P, = A:T4; that is, the radiation is proportional to the fourth power of the absolute temperature. This is the law of black body radiation, and above equation of the volt-ampere characteristic of the tungsten lamp thus appears as a conclusion from the radiation law, that is, as a rational ...", "... d from it, that is, is the power of radiation P^, the equation between p and r also is the equation between P^ and T, thus, P, = A:T4; that is, the radiation is proportional to the fourth power of the absolute temperature. This is the law of black body radiation, and above equation of the volt-ampere characteristic of the tungsten lamp thus appears as a conclusion from the radiation law, that is, as a rational equation. 154. Example 2. In a magnetite arc, at constant arc length, the voltage consumed by the arc, ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-02", "section_label": "Chapter 2: Electric Conduction. Gas And Vapor", "section_title": "Electric Conduction. Gas And Vapor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3895-5444", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-02/", "snippets": [ "... conduc- tion, decreases with increase of temperature, for a 13-mm. gap about as shown by curve I in Fig. 18. The voltage required to maintain an arc, that is, the direct-current voltage, increases with increasing arc temperature, and therefore increasing radiation, etc., about as shown by curve II in Fig. 18. As seen, the curves I and II intersect at some very high temperature, and materials as carbon, which have a boiling point above this temperature. ELECTRIC CONDUCTION 33 require a lower voltage for rest ...", "... constant and independent of current or arc length — similar as the terminal drop at the electrodes in electro- lytic conduction is independent of the current. The power consumed in the arc stream, pi = Cii, is given off from the surface of the stream, by radiation, conduction and con- vection of heat. The temperatm-e of the arc stream is constant, as that of the boiling point of the electrode material. The power, therefore, is proportional to the surface of the arc stream, that is, proportional to the square root o ...", "... erent considerations apply. Thus, in a mercury arc in a glass tube, if the current is sufficiently large to fill the entire tube, but not so large that condensation of the mercury vapor can not freely occur in a condensing chamber, the power dissipated by radiation, etc., may be assumed as proportional to the length of the tube, and to the current p = eii = di thus, ei = d (10) that is, the stream voltage of the tube, or voltage consumed by the arc streana (exclusive terminal drop) is independent of the ELE ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-02", "section_label": "Lecture 2: Conclusions From The Relativity Theory", "section_title": "Conclusions From The Relativity Theory", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 736-2388", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... consists in the better conception of nature and its laws which it affords. Some of the most interesting illustra- tions of this will be discussed in the following pages. B. THE ETHER AND THE FIELD OF FORCE Newton's corpuscular theory of light explained radiation as a bombardment by minute particles projected at extremely high velocities, in much the same way as the alpha and the beta rays are explained today. This corpuscular theory was disproven by the phenomenon of interference, in the following manner: If the ...", "... then, is the fallacy in the wave theory of light which has led to the erroneous conception of an ether? The phenomenon of interference proves that light is a wave, a periodic phenomenon, just like an alternating current. Thus the wave theory of light and radiation stands today as unshaken as ever. However, when this theory was established, the only waves with which people were familiar were the waves in water and the sound waves, and both are wave motions. As the only known waves were wave motions, it was natural ...", "... cannot extend through space instantaneously, but must propagate through space at a finite velocity, the rate at which the power radiated by the source of the field can fill up the space with the field energy. The field energy is proportional to the energy radiation of the source of the field (transmission line, radio antenna, incandescent body) and to the electromagnetic constants of space (permeability, or specific inductance, and permittivity, or specific capac- ity), and the velocity of propagation of the electro ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-01", "section_label": "Chapter 1: Electric Conduction. Soled And Liquid", "section_title": "Electric Conduction. Soled And Liquid", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 959-3894", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-01/", "snippets": [ "... ut heat. That is, a consumption of power takes place in the metallic con- 1 2 ELECTRIC CIRCUITS ductors by conversion into heat, and into beat only. Indirectly, we may get light, if the heat produced raises the temperature high enough to get visible radiation as in the incandescent lamp filament, but this radiation is produced from heat, and directly the conversion of electric energy takes place into beat. Most of the metaUic conductors cover, as regards their specific resist- ance, a rather narrow range, betw ...", "... he metallic con- 1 2 ELECTRIC CIRCUITS ductors by conversion into heat, and into beat only. Indirectly, we may get light, if the heat produced raises the temperature high enough to get visible radiation as in the incandescent lamp filament, but this radiation is produced from heat, and directly the conversion of electric energy takes place into beat. Most of the metaUic conductors cover, as regards their specific resist- ance, a rather narrow range, between about 1.6 microhm-cm. {1.6 X 10~*) for copper, to abo ...", "... the conductor in an electric circuit by eliminating the temperature, and relating only electrical quan- tities with each other. Such volt-ampere characteristics of elec- tric conductore can easily and very accurately be determined, and, if desired, by the radiation law approximate values of the temperature be derived, and therefrom the temperature-resist- ance curve calculated, while & direct measurement of the resist- VOLT-AMPERE CHARACTERISTIC 1 PURE METALS n ALLOYS m ELECTROLYTES , / t I / ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-48", "section_label": "Chapter 8: Velocity Of Propagation Of Electric Field", "section_title": "Velocity Of Propagation Of Electric Field", "kind": "chapter", "sequence": 48, "number": 8, "location": "lines 26095-27002", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "snippets": [ "... y high frequencies, hundreds of millions of cycles per second, as given by Hertzian resonators. (6) In high frequency discharges having no return circuit or no well defined return circuit, as lightning discharges. In this case the effective resistance of radiation may be so large com- pared with the ohmic resistance, even when considering the unequal current distribution in the conductor (Chapter VII), that the effect of the conductor material practically disappears. In the conductors forming the discharge path of ...", "... or, absolute, z = 72.8 ohms. Hence, the voltage required by i = IjOO amperes is e = 7280 volts, and the power radiated into space during the oscillation is p = tfr = 118 kilowatts. 74. Since the effective resistance of the total electromagnetic radiation, from the conductor surface to infinity, is, by (25), -9, (27) it follows that the effective resistance, of electromagnetic radia- tion of a conductor is proportional to the frequency and to the length of the conductor, but independent of its size or s ...", "... nductor, the radiated power is At 60 cycles ............. 3.5 watts; At 10,000 cycles .......... 5.9 kilowatts; At 106 cycles ............ 5900 kilowatts. The imaginary component of self-inductance L, that is, the term in L which represents the power radiation, is Z0?r 10~9 henrys; (29) hence independent of conductor size, shape, and material, of fre- quency, current, etc. The imaginary or reactive component of the impedance, x = 4 nfllog- - 0.5772 10~9 ohms, \\ Cwj* / is approximately, neglecting 0.577 ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-03", "section_label": "Lecture 3: Gravitation And The Gravitational Fleld", "section_title": "Gravitation And The Gravitational Fleld", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2389-3594", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-03/", "snippets": [ "LECTURE III GRAVITATION AND THE GRAVITATIONAL FLELD A. THE IDENTITY OF GRAVITATIONAL, CENTRIFUGAL AND INERTIAL MASS As seen in the preceding lecture, the conception of the ether as the carrier of radiation had to be abandoned as incompatible with the theory of relativity; the conception of action at a distance is repugnant to our reasoning, and its place is taken by the conception of the field of force, or, more correctly, the energy field. The energy fie ...", "... ld is a storage of energy in space, character- ized by the property of exerting a force on any body susceptible to this energy — that is, a magnetic field on a magnetizable body, a gravitational field on a gravitational mass, etc. Light, or, in general, radiation, is an electromagnetic wave — ^that is, an alternation or periodic variation of the electromagnetic field^ — and the difference between the alternating fields of our transmission lines, the electro- magnetic waves of our radio stations, the waves of visib ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-103", "section_label": "Apparatus Section 6: Alternating-current Transformer: Heating and Ventilation", "section_title": "Alternating-current Transformer: Heating and Ventilation", "kind": "apparatus-section", "sequence": 103, "number": 6, "location": "lines 18461-18520", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-103/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-103/", "snippets": [ "... erefore fortunate that the transformer is the most efficient apparatus (except perhaps the electrostatic condenser) and thus has to dissipate less heat than any other apparatus of the same output. Thus in smaller transformers radiation and the natural convection from the surface are often sufficient to keep the tem- perature within safe limits. Smaller distribution transformers usually are installed out- doors, on poles, and then require protection by enclos ...", "... o keep the tem- perature within safe limits. Smaller distribution transformers usually are installed out- doors, on poles, and then require protection by enclosure in an iron case or tank. This still further reduces the heat radiation, and therefore such transformer cases are now almost always filled with oil, the oil serving to carry the heat from the transformer iron and windings to the case. Incidentally, the oil filling also protects the transformer ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "... of power, and due to: Resistance, and its increase by unequal current distri- bution; to the power component of mutual inductive reactance or to induced currents; to the power component of self-inductive reactance or to electromagnetic hysteresis, and to radiation. e.m.fs. consumed in quadrature with the current, I, and = xl, wattless, and due to: Self -inductance, and mutual inductance. Currents consumed in phase with the e.mf., E, and = g E, representing consumption of power, and due to: Leakage through the ins ...", "... e e.mf., E, and = g E, representing consumption of power, and due to: Leakage through the insulating material, including silent discharge and corona; power component of electrostatic influence; power component of capacity or dielectric hysteresis, and to radiation. Currents consumed in quadrature to the e.m.f., E, and = bE, being wattless, and due to: Capacity and electrostatic influence. Hence we get four constants: Effective resistance, r, Effective reactance, x, Effective conductance, g, Effective susceptan ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... nternal resistance, that is, an elec- trical efficiency of 75 per cent, gives the total resistance as r + r' = 0.2 x\\ hence, and the decrement is A = 0.73; hence a fairly rapid decay of the wave. At high frequencies, electrostatic, inductive, and radiation losses greatly increase the resistance, thus giving lower effi- ciency and more rapid decay of the wave. 48. The frequency of oscillation does not directly depend upon the size of apparatus, that is, the kilovolt-ampere capacity of condenser and reactor ...", "... ously higher than the highest frequencies which can be produced by electrodynamic machinery. At five billion cycles per second, the wave length is about 6 cm., that is, the frequency only a few octaves lower than the lowest frequencies observed as, heat radiation or ultra red light. The average wave length of visible light, 55 X 10~6 cm., corresponding to a frequency of 5.5 X 1014 cycles, would require spheres 10~5 cm. in diameter, that is, approaching molecular dimensions. OSCILLATING-CURRENT GENERATOR. 49. ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... power, and due to resistance, and its apparent increase by unequal current distribution; to the power component of mutual inductance: to secondary currents; to the power component of self -inductance: to electromagnetic hysteresis; and to electromagnetic radiation. E.m.fs. consumed in quadrature with the current, I, and = xl, reactive, and due to self-inductance and mutual inductance. Currents consumed in phase with the e.m.f., E, and = gE, representing consumption of power, and due to leakage through the insula ...", "... d = gE, representing consumption of power, and due to leakage through the insulating material, including brush discharge; to the power component of electrostatic influence; to the power component of capacity, or dielectric hysteresis, and to electrostatic radiation. Currents consumed in quadrature with tJw e.m.f., E, and = bE, being reactive, and due to capacity and electrostatic influence. Hence we get four constants per unit length of line, namely: Effective resistance, r; effective reactance, x; effective condu ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 557-1002", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-01/", "snippets": [ "... is, the curve is the exponential. The exponential curve thus is the expression of the simplest form of transient. This explains its common occurrence in elec- trical and other transients. Consider, for instance, the decay of radioactive substances : the radiation, which represents the decay, din is proportional to the amount of radiating material; it is -t- = cm, which leads to the same exponential function. Not all transients, however, are of this simplest form. For instance, the deceleration of a ship does n ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 460-882", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "snippets": [ "... is, the curve is the exponential. The exponential curve thus is the expression of the simplest form of transient. This explains its common occurrence in elec- trical and' other transients. Consider, for instance, the decay of radioactive substances : the radiation, which represents the decay, is proportional to the amount of radiating material; it is ~-r- = cm, Cit which leads to the same exponential function. Not all transients, however, are of this simplest form. For instance, the deceleration of a ship does ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... sin 4(^ + 8.7°) +0.91 sin 5(o\"-5.6°) +0.184 sin 6((5 + 8.65°) +0.085 sin 7(^+29.15°). (d) The periodic variation of the temperature y, as expressed iDy these equations, is a result of the periodic variation of the thermomotive force; that is, the solar radiation. This latter TRIGONOMETRIC SERIES. 133 is a minimum on Dec. 22d, that is, 9 time-degrees before the zero of 0, hence may be expressed approximately by: z = c-h cos (^+9°); or substituting /? respectively ^ for 6: z = c-h cos (/? +23.15°) = c+h sin ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... ponents of alterna- tor armature reaction and reactance, 282 INDEX 479 Quadrature flux of single-phase in- duction motor, 245 Quarter-phase system, 398 efficiency, 466 three-phase transformation, 423 Quintuple harmonic, see Fifth har- monic Radiation from line, 174 Ratio of transformer, 197 Reactance, 2, 9 effective, 112 in phase control, 103 in series with circuit, 63 in symbolic expression, 35 synchronous, of alternator, 277 Reactive component of current and voltage, 168 power, 180 with gene ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-13", "section_label": "Chapter 15: Synchronous Rectifier", "section_title": "Synchronous Rectifier", "kind": "chapter", "sequence": 13, "number": 15, "location": "lines 18413-19373", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-13/", "snippets": [ "... e waves of currents, ih i2 and i0) as overlapped by the inductances, Xi, x* and x0, are shown in Fig. 103. Full description and discussion of the mercury-arc rectifier is contained in \"Theory and Calculation of Transient Phenomena,9' Section II, and in \"Radiation, Light and Illumination.\" 250 ELECTRICAL APPARATUS 143. To reduce the sparking at the rectifying commutator, the gap between the segments may be divided into a number of gaps, by small auxiliary segments, as shown in Fig. 104, and these then conn ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-13", "section_label": "Chapter 9: High-Frequency Conductors. 403", "section_title": "High-Frequency Conductors. 403", "kind": "chapter", "sequence": 13, "number": 9, "location": "lines 1014-1042", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-13/", "snippets": [ "CHAPTER IX. HIGH-FREQUENCY CONDUCTORS. 403 80. Effect of the frequency on the constants of a conductor. 403 81. Thermal resistance and radiation resistance, internal and external reactance, as functions of the frequency. 405 82. Total impedance of high frequency conductor, and its components, discussion. 407 83. Example of copper and iron wire, copper ribbon and iron pipe ; tabulation and di ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-45", "section_label": "Chapter 5: Distributed Series Capacity", "section_title": "Distributed Series Capacity", "kind": "chapter", "sequence": 45, "number": 5, "location": "lines 23586-23947", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "snippets": [ "... ented electrically as a circuit in Fig. 91, let r = the effective resistance per unit length of circuit, or per circuit element, that is, per arrester cylinder; g = the shunt conductance per unit length, representing leakage, brush dis- charge, electrical radiation, etc.; L = the inductance per unit length of circuit; C = the series capacity per unit length of cir- cuit, or circuit element, that is, capacity between adjacent arrester cylinders, and <70 = the shunt capacity per unit length of circuit, or circuit elem ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-54", "section_label": "Chapter 5: Free Oscillations", "section_title": "Free Oscillations", "kind": "chapter", "sequence": 54, "number": 5, "location": "lines 31451-32708", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "snippets": [ "... perfectly true. At very high frequencies r increases, due to unequal current distribution in the conductor, as discussed in Section III, L slightly decreases hereby, g increases by the energy losses resulting from brush discharges and from electro- static radiation, etc., so that, in general, at very high frequency an increase of y and ^, and therewith of u, may be expected; Li C that is, very high harmonics would die out with greater rapidity, which would result in smoothing out the wave shape with increas- ing ..." ] } ] }, { "id": "power-factor", "label": "Power Factor", "aliases": [ "power factor", "power-factor", "wattless component", "wattless current" ], "total_occurrences": 671, "matching_section_count": 101, "matching_source_count": 11, "source_totals": [ { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 206, "section_count": 14 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 133, "section_count": 18 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 89, "section_count": 14 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 83, "section_count": 24 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 54, "section_count": 5 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 39, "section_count": 12 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 35, "section_count": 5 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 18, "section_count": 2 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 11, "section_count": 4 }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 2, "section_count": 2 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-18", "section_label": "Chapter 20: Single-Phase Commutator Motors", "section_title": "Single-Phase Commutator Motors", "kind": "chapter", "sequence": 18, "number": 20, "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 64, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "... resistance, which represents the power loss. In addition thereto, in the alternating-cur rent motor voltage is consumed by the inductance, which is wattless or reactive and therefore causes a lag of current behind the vol- tage, that is, a lowering of the power-factor. While in the direct- current motor good design requires the combination of a strong field and a relatively weak armature, so as to reduce the armature reaction on the field to a minimum, in the design of the alter- iiatiiig-current motor considerations o ...", "... While in the direct- current motor good design requires the combination of a strong field and a relatively weak armature, so as to reduce the armature reaction on the field to a minimum, in the design of the alter- iiatiiig-current motor considerations of power-factor predominate; that is, to secure low self-inductance and therewith a high power- factor, the combination of a strong armature and a weak field is required, and necessitates the use of methods to eliminate the harmful effects of high armature reaction. As ...", "... ield and a relatively weak armature, so as to reduce the armature reaction on the field to a minimum, in the design of the alter- iiatiiig-current motor considerations of power-factor predominate; that is, to secure low self-inductance and therewith a high power- factor, the combination of a strong armature and a weak field is required, and necessitates the use of methods to eliminate the harmful effects of high armature reaction. As the varying-speed single-phase commutator motor has found an extensive use as railway m ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 50, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "... ating magnetizing current is a wattless reactive current, the result is, that the alternating-current input into the induction motor is always lagging, the more so, the larger a part of the total current is given by the magnetizing current. To secure good power-factor in an induction motor, the magnetizing current, that i«, the current which produces the magnetic field flux, must be kept as small as possible. This means as small an air gap between stator and rotor as mechanic- ally permissible, and as large a number of ...", "... erload capacity has to be met, etc. In such motors of necessity the exciting current or current at no-load — which is practically all magnetizing current — is a very large part of full-load current, and while fair efficiencies may nevertheless be secured, power-factor and apparent efficiency necessarily are very low. As illustration is shown in Fig. 20 the load curve of a typical 100-hp. 60-cycle 80-polar induction motor (90 revolutions per minute) of the constants: Impressed voltage: ea = 500. Primary exciting ad ...", "... . Primary self-inductive impedance: Zu = 0.1 + 0.3j. Secondary self-inductive impedance: Zi = 0.1 + 0.3 j. INDUCTION MOTOR 53 As seen, at full-load of 75 kw. output, the efficiency is 80 per cent., which is fair for a slow-speed motor. But the power-factor is 55 per cent., the apparent efficiency only 44 per cent., and the exciting current is 75 per cent, of full- load current. This motor-load curve may be compared with that of a typical induction motor, of exciting admittance: Y0 = 0.01 -O.lj, given on ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-14", "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "section_title": "Constant-Potential Constant-Current Trans Formation", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 42, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "... n series with this circuit. The impedance of this circuit then is Z = r + jxof and, absolute, and thus the current, / = ^* = -^ (1) ^ r + jxo and the absolute value is eo Co the phase angle of the supply circuit is given by (2) and the power factor. tan ^0 = - (3) T cos ^0 = -• (4) z ^ ^ If in this case, r is small compared with Xq, it is ,-^£o _-l (5) Xo ' ^* xM¥\" or, expanded by the binomial theorem. V • • • \\xj hence, : (6) 6o I = — Xo 2xo2^8xo* -r . . . ...", "... l theorem. V • • • \\xj hence, : (6) 6o I = — Xo 2xo2^8xo* -r . . . that is, for small values of r, the current, z, is approximately constant, and is 6o I = — Xo CONSTANT-CURRENT TRANSFORMATION 247 For small values of r, the power-factor cosfl — - is very low, however. Allowing a variation of current of 10 per cent, from short- circuit or no-load, r = 0, to full-load, or r = ri, it is, substituted in (2): No-load current: / -: / ^ y / ^ i < \\ s 1 ...", "... -: / ^ y / ^ i < \\ s 1 / / \\ s ^ c JV N -^ \\ s / \\ \\ ^ y S 1 / ... .„. \\ Full-load current: Vn' + a Vr^~+x? and therefore, ■ ri = 0.485 x„, and the power-factor, from (4), is 0.437. That is, even allowing as large a variation of current, i, as 10 per cent., the maximum power-factor only reaches 43.7 per cent., when producing constant-current regulation by series inductance reactance. 248 ELECTRIC CIRCUITS A ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "section_label": "Chapter 16: Induction Motor", "section_title": "Induction Motor", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 28, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "... e the motor is in operation. 256 ALTERNATING-CURRENT PHENOMENA. Since, necessarily, ri<*, ''<•< and since the starting current is, approximately, 7 =f , we have, Ta < would be the theoretical torque developed at 100 per cent efficiency and power factor, by E.M.F., E0, and current, /, at synchronous speed. Thus, T0 ~IY (29) and hence, substituted in (22), / = and E = -° U~a/ (cos /?Z + y sin /?/) + Cs +aZ (cos /M - j sin /?Z) (30) 11. As an example, consider the problem of delivering, in a three-phase system, 200 amperes per phase, at 90 per cent power factor lag at 60,000 volts per phase (or between line and neutral) and 60 cycles, at the end of a transmission line 200 miles in length, consisting of two separate circuits in multiple, each consisting of number 00 B. and S. wire with 6 feet distance between the ...", "... 53 - 0.9 j) 10~3 Zi p = ^= (0.208 + 0.047 /) 10 + 3. 293 (31) Counting the distance I from the receiving end, and choosing the receiving voltage as zero vector, we have E = E0 = e0 = 60,000 volts, and the current of 200 amperes at 90 per cent power factor, 87 j, and substituting these values in equations (25) gives / = (226 + 14.4 j) e+al (cos pl-j sin pi) - (46-72.6 j) e~al (cos ftl + j sin /#), in amperes, and £\"= (46.7 + 13.3 ?>+aZ (cos pi- /sin (13.3- 13.3 j) (32) (cos /?Z + j sin / ...", "... + 18 / I =0 i = 200 amp. e = 60,000 volts I = 100 i = 178 amp. E= (66.2 - 6.9 /) 103 e = 66,400 volts Generator end of line, /= 165.7 - 56 / E= (69 - 15 /) 103 I = 200 i = 175 amp. e = 70,700 volts tan 0, = 0.483 6, = 26° 0,= 0 power factor, 0.90 lag tan 6l= + 0.102 6l = 6° tan 02 =-0.104 62 = - 6° d, - 02 =J~^ 12° power factor, cos 6 = 0.979 lag. tan0t =-0.338 0, = -19° tan 02 = - 0.218 02 = -12° Ol - 02 = 0 = - 7° power factor, cos 0 = 0.993 lead. 294 TRANSIENT PHENOMENA As seen ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-108", "section_label": "Apparatus Section 2: Induction Machines: Polyphase Induction Motor", "section_title": "Induction Machines: Polyphase Induction Motor", "kind": "apparatus-section", "sequence": 108, "number": 2, "location": "lines 19166-20427", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-108/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-108/", "snippets": [ "... im- pressed e.m.f. EQ) enters in the equation of current, magnetism, etc., as a simple factor, in the equations of torque, power input and output, and volt-ampere input as square, and cancels in the equation of efficiency, power-factor, etc., it follows that the current, magnetic flux, etc., of an induction motor are propor- tional to the impressed e.m.f., the torque, power output, power input, and volt-ampere input are proportional to the square of the i ...", "... induction motor are propor- tional to the impressed e.m.f., the torque, power output, power input, and volt-ampere input are proportional to the square of the impressed e.m.f., and the torque- and power efficiencies and the power-factor are independent of the impressed voltage. In reality, however, a slight decrease of efficiency and power- factor occurs at higher impressed voltages, due to the increase of resistance caused by the increasing temperature of ...", "... re input are proportional to the square of the impressed e.m.f., and the torque- and power efficiencies and the power-factor are independent of the impressed voltage. In reality, however, a slight decrease of efficiency and power- factor occurs at higher impressed voltages, due to the increase of resistance caused by the increasing temperature of the motor and due to the approach to magnetic saturation, and a slight decrease of efficiency occurs at lower v ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-11", "section_label": "Chapter 11: Phase Control", "section_title": "Phase Control", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 9767-10717", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-11/", "snippets": [ "... ltage, e, is greatest if the current, /, is in phase with the voltage, e — less if the current is not in phase. Inductive reactance in series with the receiving circuit, e, at constant impressed e.m.f., eo, causes the voltage, e, to drop less with a unity power-factor current, 7, but far more with a lagging current, and causes the voltage, e, to rise with a leading current. While series resistance always causes a drop of voltage, series inductive reactance, x, may cause a drop of voltage or a rise of voltage, dependi ...", "... creasing drop of voltage with increasing load, caused by the resistance, r, that is, to maintain constant voltage, or even a voltage, e, which rises with the load on the receiving circuit, at constant voltage, Co, at the generator side of the line. Or the wattless component of the current can be varied so as to maintain unity power-factor at the generator end of the line, eo, etc. This method of controlling a circuit supplied over an induc- tive line, by varying the phase relation of the current in the circuit, has been cal ...", "... r, that is, to maintain constant voltage, or even a voltage, e, which rises with the load on the receiving circuit, at constant voltage, Co, at the generator side of the line. Or the wattless component of the current can be varied so as to maintain unity power-factor at the generator end of the line, eo, etc. This method of controlling a circuit supplied over an induc- tive line, by varying the phase relation of the current in the circuit, has been called \"phase control,\" and is used to a great extent, especially in ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-19", "section_label": "Chapter 19: Induction Generators", "section_title": "Induction Generators", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 20446-21537", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-19/", "snippets": [ "... rom zero at synchronism up to a maximum point, and then decrease again, while the current constantly increases. 174. The induction generator differs essentially from the ordinary synchronous alternator in so far as the induction generator has a definite power-factor, while the synchronous alternator has not. That is, in the synchronous alternator the phase relation between current and terminal voltage entirely depends upon the condition of the external circuit. The in- duction generator, however, can operate only if ...", "... the synchronous alternator the phase relation between current and terminal voltage entirely depends upon the condition of the external circuit. The in- duction generator, however, can operate only if the phase relation of current and e.m.f., that is, the power-factor required by the external circuit, exactly coincides with the internal power-factor of the induction generator. This requires that 237 238 ALTERNATING-CURRENT PHENOMENA the power-factor either of the external circuit or of the induction generator ...", "... entirely depends upon the condition of the external circuit. The in- duction generator, however, can operate only if the phase relation of current and e.m.f., that is, the power-factor required by the external circuit, exactly coincides with the internal power-factor of the induction generator. This requires that 237 238 ALTERNATING-CURRENT PHENOMENA the power-factor either of the external circuit or of the induction generator varies with the voltage, so as to permit the generator and the external circuit to ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "... hus, regarding the wattless power as a whole, in the general alternating circuit no distinction can be made be- tween lead and lag, since some harmonics may be leading, others lagging. The apparent power, or total volt-amperes, of the circuit is, The power factor of the circuit is, The term \"inductance factor,\" however, has no mean- ing any more, since the wattless powers of the different harmonics are not directly comparable. The quantity, ,...._ ... wattless power has no physical significance, and is not ...", "... ctors qn of the individual harmonics. As a rule, if ; and therefore: Po1 = true power input; P^ ^^ 2 ^*, V wo \"^-J Z ^is 300 ^ Fio. 65. — Synchronous induction generator regulation curves. for inductive load of 80 per cent, power-factor j'i = 0.6 /, i = 0 e, = Vi X 10' - 00064/* - 2.06/; and for anti-inductive load of 80 per cent, power-factor 1 - 0.6/,* = 0.8/: -Vi X 10« -4/1 - 0.5/. As seen, due to the internal impedance, anil especially the resistance of this machine, the r ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-109", "section_label": "Apparatus Section 3: Induction Machines: Single -phase Induction Motor", "section_title": "Induction Machines: Single -phase Induction Motor", "kind": "apparatus-section", "sequence": 109, "number": 3, "location": "lines 20428-21157", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-109/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-109/", "snippets": [ "... re Fig. 181 with Fig. 176 and to note the lesser drop of speed (due to the relatively lower secondary SLIP, S\"= FIG. 182. — Three-phase induction motor on single-phase circuit, s curves. resistance) and lower power-factor and efficiencies, especially at light load. The maximum output is reduced from 3 X 7000 = 21,000 in the three-phase motor to 9100 watts in the single-phase motor. Since, however, the internal losses are less in the singl ...", "... condenser. Usually the .con- denser is left in circuit after starting, and made of such size that its leading current compensates for the lagging magnetizing current of the motor, and the motor thus gives approximately unity power-factor. For further discussion of this subject the reader is referred to the paper on \" Single-phase Induction Motors,\" mentioned above, and to the \" Theory and Calculation of Alternating-current Phe- nomena\" and \"Theory and Calcul ...", "... ue is not the sum of main and auxiliary torque, but often less, due to the interaction between the motor and the starting device. Most starting devices depend more or less upon the total admittance of the motor and its power-factor. With increasing speed, however, the total admittance of the motor decreases and its power-factor increases, and an auxiliary torque device suited for the admittance of the motor at standstill will not be suited for the cha ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... e minima, that is, the extrema of a function, frequently occurs. For instance, the output of an electric machine is to be found, at which its efficiency is a max- imum, or, it is desired to determine that load on an induction motor which gives the highest power-factor; or, that voltage Y /^ R V / 1 V. p A ^ X p ^f Q N \\ ^ ^+- ^ x \\ -^ / \\ p y y / ^4 P. / / ^ 0 / X Fig. 50. Graphic Solution of Maxima and Minima. which makes the cost of a transmissi ...", "... 149 occurs at point n^^^, for (B = 10.2 kilolines, /i = 1340, and minima at the starting-point P2, for (B = 0, ju = 370, and also for (B = oo , where by extrapolation /x = l. Example 2. Find that output of an induction motor which gives the highest power-factor. While theoretically an equation can be found relating output and power-factor of an induction motor, the equation is too compUcated for use. The most convenient way of calculating induction motors is to calculate in tabular form for different values of s ...", "... at the starting-point P2, for (B = 0, ju = 370, and also for (B = oo , where by extrapolation /x = l. Example 2. Find that output of an induction motor which gives the highest power-factor. While theoretically an equation can be found relating output and power-factor of an induction motor, the equation is too compUcated for use. The most convenient way of calculating induction motors is to calculate in tabular form for different values of slip s, the torque, output, current, power and volt -ampere input, efficiency, ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... /)J5;o+(56.8-131.8/)/o = A +5; 1 /i = (0.919 -0.036/)7o - (0.0144 +1.168/)^olO-3 = C-D. / (2> NUMERICAL CALCULATIONS, 251 i6i. Now the work of calculating a series of numerical values is continued in tabular form, as follows : 1. 100 PER CENT Power-factor. Eo=60 kv. at step-down end of line. A = (0.919-0.036/)£;o=55.1-2.2y kv. D = (0. 0 144+1. 168?) £?o 10- 3 = 0.9 + 70.1/ amp. Iq amp. Bkv. Ei = ei- -eJ2 = A+B. ei2 + g22 = g2. e — = tan e. ei 4-6. 0 0 55.1- - 2.2/ 3036+ 5 = ...", "... 100 5.7-13.2/ 60.8- -15.4/ 3697 + 237 = 3934 62.7 -0.253 -14.2 120 6.8-15.8/ 61.9- -18.0/ 3832 + 324=4156 64.5 -0.291 -16.3 h amp. , C amp. Il = tl=/t2 = C-D tl2 + t22 = i2 i *i=tam A-i 2^t- i 4-e= 4-«'* Power- factor 0 0 -0.7-90.1/ 4914+1 = 4915 70.1 + 78 + 89.1 -90.9 -88.6 0.024 20 18.4-0.7/ 17.5-70.8/ 5013+ 306= 5319 72.9 -4.04 -76.3 -71.4 0.332 40 36.8-1.4/ 35.9-71.5/ 5112 + 1289= 6401 80.0 -1.99 -63.4 -55.9 0.558 ...", "... .9/ 8281 + 5432=13713 117.1 -0.811 -39.1 -24.9 0.907 120 110.3-4.3/ 109.4-74.4/ 11969 + 5535=17504 132.3 -0.680 -34.1 -17.8 0.952 lead 61 = 60 kv. at step-up end of line. /o amp. Red. Factor, e 60 amp. kv. amp. Power-Factor. 0 0.918 0 65.5 76.4 0.024 20 0.940 21.3 63.8 77.5 0.332 40 0.965 41.4 62.1 82.9 0.558 60 0.990 60.6 60.6 91.4 0.728 80 1.015 78.8 59.1 101.5 0.837 100 1.045 95.7 57.5 112.3 0.907 120 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-25", "section_label": "Chapter 25: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 29375-32539", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-25/", "snippets": [ "... reactance; since a pulsation of reactance, when unsymmetrical with regard to the current wave, introduces a power component which can be represented by an \"effective resistance.\" Inversely, an unsymmetrical pulsation of the ohmic resistance introduces a wattless component, to be denoted by \"effective reactance.\" A typical case of a synchronously pulsating resistance is represented in the alternating arc. The apparent resistance of an arc depends upon the current through the arc; that is, the apparent resistance of the a ...", "... = j = ry^\\-. + ^- The instantaneous power consumed in the arc is ie = 2 rP j (l - ^) sin^ /3 + | sin /3 sin 3 iS } • Hence the effective power, p = .p(i-|). The apparent power, or volt-amperes consumed by the arc, IE = rP-^jl - e + ^'- Thus the power-factor of the arc, _ P^ _ 2 p-iE- I r ' Vl-^ + 2 that is, less than unity. 240. We find here a case of a circuit in which the power-factor — that is, the ratio of watts to volt-amperes — differs from unity without any displacement of phase; that is, while ...", "... power, p = .p(i-|). The apparent power, or volt-amperes consumed by the arc, IE = rP-^jl - e + ^'- Thus the power-factor of the arc, _ P^ _ 2 p-iE- I r ' Vl-^ + 2 that is, less than unity. 240. We find here a case of a circuit in which the power-factor — that is, the ratio of watts to volt-amperes — differs from unity without any displacement of phase; that is, while current and e.m.f. are in phase with each other, but are distorted, the alter- nating; wave cannot be replaced by an equivalent sine wave. ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "... by eddy currents is proportional to the square of the E.M.F. of self-induction, and therefore proportional to the square of the frequency and to the square of the magnetization. Only the energy component, g E, of eddy currents, is of interest, since the wattless component is identical with the wattless component of hysteresis, discussed in a preceding chapter. FOUCAULT OR EDDY CURRENTS. 131 88. To calculate the loss of power by eddy currents — Let V = volume of iron ; (B = maximum magnetic induction ; N= freque ...", "... quare of the E.M.F. of self-induction, and therefore proportional to the square of the frequency and to the square of the magnetization. Only the energy component, g E, of eddy currents, is of interest, since the wattless component is identical with the wattless component of hysteresis, discussed in a preceding chapter. FOUCAULT OR EDDY CURRENTS. 131 88. To calculate the loss of power by eddy currents — Let V = volume of iron ; (B = maximum magnetic induction ; N= frequency; y = electric conductivity of iron ; ...", "... uction of secondary E.M.Fs. in neighboring circuits ; that is, the interference of circuits running parallel with each other. In general, it is preferable to consider this phenomenon of mutual inductance as not merely producing an energy component and a wattless component of E.M.F. in the primary conductor, but to consider explicitly both the sec- ondary and the primary circuit, as will be done in the chapter on the alternating-current transformer. Only in cases where the energy transferred into the secondary circuit con ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-04", "section_label": "Chapter 5: Single-Phase Induction Motor", "section_title": "Single-Phase Induction Motor", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 8555-10582", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-04/", "snippets": [ "... 2 0.4 i, Zx = -0.2j, that is, both reactances are capacities. (34) : ex = e2 = 2.23 e0, * = 5, that is, the torque is five times as great as on true quarter-phase supply. 41 0.1 + o.i / i2 ai-o-ij' / = 10 e0 = i, that is, non-inductive, or unity power-factor. to = y = 3.166o, g = 1.58, v = 3.16, that is, the apparent starting-torque efficiency, or starting torque per volt-ampere input, of the single-phase induction motor with starting devices consisting of two capacities giving a true quarter- phase sys ...", "... or with starting devices consisting of two capacities giving a true quarter- phase system, is 3.16 as high as that of the same motor on a quarter-phase voltage supply, and the circuit is non-inductive in starting, while on quarter-phase supply, it has the power- factor 31.6 per cent, in starting. In a high-resistance motor: Z = 0.3 + 0.1 i, it is: k = 0.4, xx = 0.2, Z2 = -0.4j, Z2 = +0.2 j, that is, the one reactance is a capacity, the other an inductance. ei = e2 = 0.743 e0) t = 0.555, i = 3.33 6o, to =3. ...", "... v = 1.055, SINGLE-PHASE INDUCTION MOTOR 109 that is, the starting-torque efficiency is a little higher than with quarter-phase supply. In other words: This high-resistance motor gives 5.5 per cent, more torque per volt-ampere input, with unity power-factor, on single-phase supply, than it gives on quarter-phase supply with 95 per cent, power-factor. The value found for the low-resistance motor, t = 5, is how- ever not feasible, as it gives: ex = 62 = 2.23 e0, and in a quarter- phase motor designed for imp ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-20", "section_label": "Chapter 20: Single-Phase Induction Motors", "section_title": "Single-Phase Induction Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 21538-22301", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-20/", "snippets": [ "... is produced in quadrature ' with the main e.m.f. and impressed upon the motor, either directly or after com- bination with the single-phase main e.m.f. Such wattless quadrature e.m.f. can be produced by the common connection of two impedances of different power-factor, as an inductive reactance and a resistance, or an inductive and a condensive reactance connected in series across the mains. The investigation of these starting-devices offers a very instructive application of the symbolic method of investiga- tion of ...", "... e-half, in a three-phase motor running single- phase reduced to one-third. In consequence thereof the slip of speed in a single-phase induction motor is usually less than in a polyphase motor; but the exciting current is considerably greater, and thus the power-factor and the efficiency are lower. The preceding considerations obviously apply only when running so near synchronism that the magnetic field of the single-phase motor can be assumed as uniform, that is, the cross-magnetizing flux produced by the armature as ...", "... single-phase motor torque at slip s is: D = aieHl - {I - v) s]. 180. In the single-phase motor considerably more advan- tage is gained by compensating for the wattless magnetizing component of current by capacity than in the polyphase motor, where this wattless component of the current is relatively small. The use of shunted capacity, however, has the dis- advantage of requiring a wave of impressed e.m.f. very close to sine shape, since even with a moderate variation from sine shape the wattless charging current of the co ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... by eddy currents is proportional to the square of the E.M.F. of self-induction, and therefore proportional to the square of the frequency and to the square of the magnetization. Only the energy component, gEy of eddy currents, is of interest, since the wattless component is identical with the wattless component of hysteresis, discussed in a preceding chapter. 88, 89] FOUCAULT OR EDDY CURRENTS. 131 88. To calculate the loss of power by eddy currents Let V = volume of iron ; (B = maximum magnetic induction ; N = ...", "... square of the E.M.F. of self-induction, and therefore proportional to the square of the frequency and to the square of the magnetization. Only the energy component, gEy of eddy currents, is of interest, since the wattless component is identical with the wattless component of hysteresis, discussed in a preceding chapter. 88, 89] FOUCAULT OR EDDY CURRENTS. 131 88. To calculate the loss of power by eddy currents Let V = volume of iron ; (B = maximum magnetic induction ; N = frequency ; y = electric conductivity o ...", "... duction of secondary E.M.Fs. in neighboring circuits; that is, the interference of circuits running parallel with each other. In general, it is preferable to consider this phenomenon of mutual inductance as not merely producing an energy component and a wattless component of E.M.F. in the primary conductor, but to consider explicitly both the sec- ondary and the primary circuit, as will be done in the chapter on the alternating-current transformer. Only in cases where the energy transferred into the secondary circuit con ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-14", "section_label": "Chapter 16: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 14, "number": 16, "location": "lines 19374-20293", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-14/", "snippets": [ "... Fig. 124, with a polyphase (three-phase) current impressed on the rotating armature, A, and no winding on the field poles, starts, runs up to synchronous and does considerable work as synchronous motor, and underload may even give a fairly good (lagging) power- factor. With a single-phase current impressed upon the arma- ture, A, it does not start, but when brought up to synchronism, continues to run as synchronous motor. Driven by mechanical power, with a leading current load it is a generator. However, the operation ...", "... es electrical, and produces mechanical, power, as synchronous motor, if 6 > 0, that is, with lagging current ; positive, that is, the machine pro- duces electrical, and consumes mechanical power, as generator, if 6 > 0, that is, with leading current. The power-factor is: P y sin 2 $ V = Q „ L '. y2 2 Jl + -£- - 7 cos 2 6 hence, a maximum, if: dp or, expanded: de=0> 2 , 7 cos 2 0 = - and = {r 7 2 The power, P, is a maximum at given current, /, if: sin 2 6 = 1 ; that is: 6 = 45°; at giv ...", "... thus, at impressed e.m.f., E, and negligible resistance, if we denote the mean value of reactance: x - 2 *■//. Current: /- E x yjl +4*- y cos 20 Volt-amperes: «--...-.«■....-- xJl + j - 7 cos 2 0 Power: E*y sin 2^ 2x(l + ?- - 7 cos 2 0) Power-factor: /et r\\ 7 sin 2 0 V = cos {E, I) = ,-^ ■ — - 2 Jl + ^ - 7 cos 2 0 Maximum power at : cos 2 0 = y 72 1+4 Maximum power-factor at: 2 7 cos 2 0 = - and = '-• 7 2 0 > 0 : synchronous motor, with lagging current, 0 < 0: generator, with le ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-19", "section_label": "Chapter 21: Regulating Pole Converters", "section_title": "Regulating Pole Converters", "kind": "chapter", "sequence": 19, "number": 21, "location": "lines 30088-31715", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-19/", "snippets": [ "... s-motor armature reaction of the power component of the alternating current, and at unity power-faetor the converter thus has no resultant armature reaction, while with a lagging or leading current it has the magnetizing or demagnetizing re- action of the wattless component of the current. If by a sliift of the resultant flux from quadrature position with the brushes, by angle, t, the direct voltage is reduced by factor cos r, the direct current and therewith the direct-current armature reaction are increased, by factor, -. ...", "... h the alternating-current armature reac- tion, $0, or in phase with the resultant magnetic flux, that is, magnetizing or demagnetizing: $' = $ sin t = $0 tan r; that is, in the variable-ratio converter the alternating-current armature reaction at unity power-factor is neutralized by a component of the direct-current armature reaction, but a result- ant armature reaction, 5', remains, in the direction of the resultant magnetic field, that is, shifted by angle (90 — r) against the position of brushes. This armature re ...", "... , then is changed from the value which it would have at normal voltage ratio, by the factor — , as the product of direct volts and amperes must be the same as at normal voltage ratio, being equal to the alternating power input minus losses. With unity power-factor, the direct-current armature reac- tion, $, in a converter of normal voltage ratio is equal and opposite, and thus neutralized by the alternating-current armature reac- tion, $0, and at a change of voltage ratio from normal, by factor p, and thus change ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-49", "section_label": "Chapter 9: High-Frequency Conductors", "section_title": "High-Frequency Conductors", "kind": "chapter", "sequence": 49, "number": 9, "location": "lines 27003-27760", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "snippets": [ "... illatory high frequency discharges, as lightning. It is interesting to note the high power component of impe- dance existing at high frequencies and mainly due to the radia- tion resistance, which causes a rapid decay of the oscillation, due to the high power factor. The internal constants r1 and x1 are equal, and in the most important range of high frequencies, from 10,000 to 1,000,000 cycles, the external constants r2 and x2 are not very different from each other and their plotted curves intersect at some certain f ...", "... higher frequencies even the size and shape of the conductor become less important, and ultimately all con- ductors act practically alike. 85. From the data of the preceding table and Fig. 97 the* total effective resistance, reactance, impedance, and the power factor per meter length of conductor for high frequency dis- charge are given on p. 413. HIGH-FREQUENCY CONDUCTORS 413 Wire No. 4 B. and S. Gauge. Copper. Iron. Frequency 104 0.0212 0.0286 0.0356 0.59 3.6 105 0.202 0.221 0.299 0.67 30 ...", "... 2 0.0286 0.0356 0.59 3.6 105 0.202 0.221 0.299 0.67 30 10\" 1.986 1.626 2.57 0.77 257 104 0.185 0.168 0.250 0.74 25 105 0.717 0.736 1.028 0.70 103 10\" 3.62 3.26 4.87 0.75 487 Resistance r Reactance, x Impedance z Power factor Voltage drop at 100 amperes Copper Ribbon, 3 In. by J In. Wrought-iron Pipe, 2 In. by | In. Frequency 104 0.0199 0.0219 0.0296 105 0.198 0.162 0.256 0.77 26 106 1.972 1.072 2.24 0.88 224 104 0.0365 0.0385 0.0530 0.69 5.3 1 ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-14", "section_label": "Lecture 14: Alternating Current Railway Motor", "section_title": "Alternating Current Railway Motor", "kind": "lecture", "sequence": 14, "number": 14, "location": "lines 8649-9342", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-14/", "snippets": [ "... th the current. The voltage consumed by self-induction, due to the alternation of the magnetism, or \"e. m. f. of alternation\", is in quadrature with the current, or wattless ; that is, it consumes no power, but causes the current to lag, and so lowers the power factor of the motor; that is, causes the motor to take more volt-amperes than corresponds to its output, and so is objectionable. The useful voltage, or e. m. f. of rotation of the motor, is proportional to the speed ; or rather the \"frequency of rota- tion\", ...", "... sign requires a strong field and weak armature, to get little field distortion and therefore good commutation ; that is high n and low m. But such pro- portions, even at low supply frequency N and high frequency of rotation No, would give a hopelessly bad power factor, and ALTERNATING CURRENT MOTOR 179 thus a commercially impractical motor. In the alternating cur- rent commutator motor, it is therefore essential to use as strong an armature and as weak a field (that is, as large a number of armature turns m and as ...", "... quare of the armature turns. There is thus a best proportion between armature turns and field turns, which gives the lowest total self-induction. This is about in this propor- tion : armature turns m to field turns n = 2 -4- i ; and at this proportion the power factor of the motor, especially at low and moderate speeds, is still very poor. In alternating current commutator motors it is therefore essential to apply means to neutralize the armature self-induc- tion and armature reaction, so as to be able to increase the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-80", "section_label": "Apparatus Subsection 80: Direct-current Commutating Machines: C. Commutating Machines 221", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 221", "kind": "apparatus-subsection", "sequence": 80, "number": null, "location": "lines 13120-13188", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-80/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-80/", "snippets": [ "... m.f. induced in the induction motor secondary is of the frequency of slip, the speed controlling e.m.f. must either be supplied through the commutator or de- rived from a low frequency commutating machine as source. 4. For power-factor compensation. In an inductive circuit, the current lags behind the voltage or, what is the same, the voltage leads the current, and the power-factor thus can be raised by compensation either by introducing a leading cur ...", "... de- rived from a low frequency commutating machine as source. 4. For power-factor compensation. In an inductive circuit, the current lags behind the voltage or, what is the same, the voltage leads the current, and the power-factor thus can be raised by compensation either by introducing a leading current, as from condenser or overexcited synchronous motor, or by in- troducing a lagging voltage. In the commutating machines, the voltage induced in the ...", "... in phase with the field magnetism, and by lagging the field exciting current, 222 ELEMENTS OF ELECTRICAL ENGINEERING the commutating machines thus can be made to give a lagging voltage, that is, to compensate for low power-factor due to lagging current. Thus, by inserting such a commutating machine into the secondary of an induction machine, the latter can be made to give unity power-factor or even leading current. Such phase compensation is freque ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-83", "section_label": "Apparatus Section 4: Synchronous Converters: Armature Current and Heating", "section_title": "Synchronous Converters: Armature Current and Heating", "kind": "apparatus-section", "sequence": 83, "number": 4, "location": "lines 13889-15160", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-83/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-83/", "snippets": [ "... , the small power component of current supply- ing the losses in the converter has been neglected. These values apply only to the case where the alternating current is in phase with the supply voltage, that is, for unity power-factor of supply. If, however, the current lags, or leads, by the time angle 0, then the alternating current and direct current are not in opposition in the armature coil d midway between adjacent leads, Fig. 127, and the resul ...", "... 2 + g2) 16 (p COST + gsinr) n / 8 s2 16 s cos (T - 6) 2 11 + ~ rr^r • —^r n2 sin2 - TTH sin - n n 240 ELEMENTS OF ELECTRICAL ENGINEERING \\ FIG. 134. — Quarter-phase converter unity power-factor, armature current at collector lead. \\ \\ v_ FIG. 135. — Quarter-phase converter phase displacement 30 ture current at collector lead. 7 FIG. 136. — Quarter-phase converter phase displacement 30 degrees, arma- ture curre ...", "... s ordinates in Fig. 138. As seen, with increasing phase displacement, irrespectively whether lag or lead, the average as well as the maximum arma- ture heating very greatly increases. This shows the necessity of keeping the power-factor near unity at full load and overload, and when applied to phase control of the voltage by converter, means that the shunt field of the converter should be adjusted so as to give a considerable lagging current afho load, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-12", "section_label": "Chapter 12: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 10718-13483", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-12/", "snippets": [ "... e effect, or power, expended by the circuit. The power coeffi- cient of current, Power component of current ^ \" Total e.m.f. ' is called the effective conductance of the circuit. Ill 112 ALTERNATING-CURRENT PHENOMENA In the same way, the value, Wattless component of e.m.f. X = Total current is the effective reactance, and Wattless component of current Total e.m.f. is the effective suscepta7ice of the circuit. While the true ohmic resistance represents the expenditure of power as heat inside of the elec ...", "... component of current ^ \" Total e.m.f. ' is called the effective conductance of the circuit. Ill 112 ALTERNATING-CURRENT PHENOMENA In the same way, the value, Wattless component of e.m.f. X = Total current is the effective reactance, and Wattless component of current Total e.m.f. is the effective suscepta7ice of the circuit. While the true ohmic resistance represents the expenditure of power as heat inside of the electric conductor b}^ a current of uniform density, the effective resistance represents the ...", "... e time angle (90° — a), and the power is, therefore, P = IE cos (90° - a) ^- IE sin a. EFFECTIVE RESISTANCE AND REACTANCE 123 Thus the exciting current, /, consists of a power component, I sin a, called the hysteretic or magnetic power current, and a wattless component, I cos a, which is called the magnetizing current. Or, conversely, the e.m.f. consists of a power compo- nent, E sin a, the hysteretic power component, and a wattless component, E cos a, the e.m.f. consumed by self-induction. Denoting the absolute value ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-21", "section_label": "Chapter 21: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 22302-23970", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-21/", "snippets": [ "... r, in dotted lines, the kilovolt-amperes output, = IE, in dash-dotted lines, for the following conditions of external circuit: '0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 AMPS. Fig. 133. — Field characteristic of alternator at 60 per cent, power-factor on inductive load. In Fig. 132, non-inductive external circuit, x = 0. T In Fig. 133, inductive external circuit, of the condition, — = + 0.75, or a power-factor, O.G. In Fig. 134, inductive external circuit, of the condition, r = 0, or a power-f ...", "... 20 240 260 280 AMPS. Fig. 133. — Field characteristic of alternator at 60 per cent, power-factor on inductive load. In Fig. 132, non-inductive external circuit, x = 0. T In Fig. 133, inductive external circuit, of the condition, — = + 0.75, or a power-factor, O.G. In Fig. 134, inductive external circuit, of the condition, r = 0, or a power-factor, 0. In Fig. 135, external circuit with leading current, of the condi- tion, X = — 0.75, or a power-factor, 0.6. In Fig. 136, external circuit with leading curren ...", "... -factor on inductive load. In Fig. 132, non-inductive external circuit, x = 0. T In Fig. 133, inductive external circuit, of the condition, — = + 0.75, or a power-factor, O.G. In Fig. 134, inductive external circuit, of the condition, r = 0, or a power-factor, 0. In Fig. 135, external circuit with leading current, of the condi- tion, X = — 0.75, or a power-factor, 0.6. In Fig. 136, external circuit with leading current, of the condi- tion, r = 0, or a power-factor, 0. In Fig. 137, all the volt-ampere curve ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-20", "section_label": "Chapter 20: Beactiox Machines", "section_title": "Beactiox Machines", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 22388-23273", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "snippets": [ "... rnator by armature reaction can be explained by the fact that the counter E.M.F. of self-induction is not wattless or in quadrature with the cur- rent, but contains an energy component ; that is, that the reactance is of the form X = h —jx, where x is the wattless component of reactance and // the energy component of reactance, and // is positive if the reactance consumes power, — in which case the counter E.M.F. of self-induc- tion lags more than 90° behind the current, — while // is negative if the reactance produces power ...", "... es electrical, and produces mechanical, power, as synchronous motor, if w > ; that is, with lagging current. Positive ; that is, the machine produces electrical, and consumes mechanical, power, as generator, if w < ; that is, with leading current. The power factor is yr __ ;^ y sin 2 o) y cos 2 ta) ; hence, a maximum, if, . , ^ = 0; or, expanded, ^ ^ cos2a> = i + ^±iV8T7. y 4 4 ' The power, /*, is a maximum at given current, /, if sin 2 w = 1 ; that is, ci = 45° at given E.M.F., E^ the power is ...", "... , E, and negli- gible resistance, if we denote the mean value of reactance. Current „ / ^ xJl + lL — ycos2.S,. 318 AL TERN A TING-CURRENT PHENOMENA. [§211 Voltamperes, ^0 = y COS 2 (■> Power, p jg^ y sin 2 u» 2Arf 1 + y- - ycos2w Power factor, / = cos (^, /) = -^-^j: ?i?_ii O \" CD y cos 2 a) Maximum power at cos 2 u) = — ^ — . 4 Maximum power factor at cos25 = i + J±lv8T7 : synchronous motor, with lagging current, = 2 r/* ^ Z' 1 - ^A sin* <^ + i sin <^ sin 3 <^ Hence the effective power. §220] DISTORTION OF WAVESHAPE. 331 The apparent power, or volt amperes consumed by the arc, is, thus the power factor of the arc, 1-i ■' IE that is, less than unity. 220. We find here a case of a circuit in which the power factor — that is, the ratio of watts to volt amperes — differs from unity without any displacement of phase ; that is, while current and E.M.F ...", "... nce the effective power. §220] DISTORTION OF WAVESHAPE. 331 The apparent power, or volt amperes consumed by the arc, is, thus the power factor of the arc, 1-i ■' IE that is, less than unity. 220. We find here a case of a circuit in which the power factor — that is, the ratio of watts to volt amperes — differs from unity without any displacement of phase ; that is, while current and E.M.F. are in phase with each other, but are distorted, the alternating wave cannot be replaced by an equivalent sine wave ; ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-17", "section_label": "Chapter 17: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16362-17596", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "snippets": [ "... 304 AL TEKNA TING-CURRENT PHENOMENA. dotted lines, we have, for the following conditions of external circuit : In Fig. 129, non-inductive external circuit, x = 0. In Fig. 130, inductive external circuit, of the condition, r / x = -f .75, with a power factor, .6. In Fig. 131, inductive external circuit, of the condition, r= <>, with a power factor, 0. In Fig. 132, external circuit with leading current, of the condi- tion, r/x = — .75, with a power factor, .6. In Fig. 133, external circuit with leading cur ...", "... ns of external circuit : In Fig. 129, non-inductive external circuit, x = 0. In Fig. 130, inductive external circuit, of the condition, r / x = -f .75, with a power factor, .6. In Fig. 131, inductive external circuit, of the condition, r= <>, with a power factor, 0. In Fig. 132, external circuit with leading current, of the condi- tion, r/x = — .75, with a power factor, .6. In Fig. 133, external circuit with leading current, of the condi- tion, r = 0, with a power factor, 0. In Fig. 134, all the volt-ampere c ...", "... al circuit, of the condition, r / x = -f .75, with a power factor, .6. In Fig. 131, inductive external circuit, of the condition, r= <>, with a power factor, 0. In Fig. 132, external circuit with leading current, of the condi- tion, r/x = — .75, with a power factor, .6. In Fig. 133, external circuit with leading current, of the condi- tion, r = 0, with a power factor, 0. In Fig. 134, all the volt-ampere curves are shown together as complete ellipses, giving also the negative or synchronous motor part of the curve ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-21", "section_label": "Chapter 21: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 20502-21189", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-21/", "snippets": [ "... rnator by armature reaction can be explained by the fact that the counter E.M.F. of self-induction is not wattless or in quadrature with the cur- rent, but contains an energy component ; that is, that the reactance is of the form X = h —jx, where x is the wattless component of reactance and h the energy component of reactance, and h is positive if the reactance consumes power, — in which case the counter E.M.F. of self-induc- tion lags more than 90° behind the current, — while h is negative if the reactance produces power, — ...", "... electrical, and produces mechanical, power, as synchronous motor, if o> > 0 ; that is, with lagging current; positive, that is, the machine produces electrical, and consumes mechanical, power, as generator, if to > 0 ; that is, with leading current. The power factor is r j_ P_ _ y sin 2 ai hence, a maximum, if, d< or, expanded, 1 cos2£ = i The power, P, is a maximum at given current, /, if sin 2 w = 1 ; that is, to = 45° at given E.M.F., E, the power is p= __ hence, a maximum at or, expanded, ...", "... m at or, expanded, 1 + 1T 232. We have thus, at impressed E.M.F., E, and negli- gible resistance, if we denote the mean value of reactance, x=lTtNl. Current REACTION MACHINES. 381 Voltamperes, k- Power, ^g2 y sin 2 £ 2^fl+^--ycos2 Power factor, ,. / 77 T-N y sin 2 to f = cos (E, /) = ' 2 y/l + J^ _ y cos 2 A Maximum power at *+i Maximum power factor at to > 0 : synchronous motor, with lagging current, w < 0 : generator, with leading current. As an instance is shown in Fig. 168, wi ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-22", "section_label": "Chapter 22: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 21190-21982", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "snippets": [ "... tance ; since a pulsation of reactance, when unsymmetrical with regard to the current wave, introduces an energy component which can be represented by an \" effective resistance.\" Inversely, an unsymmetrical pulsation of the ohmic resistance introduces a wattless component, to be denoted by \"effective reactance.\" A typical case of a synchronously pulsating resistance is represented in the alternating arc. The apparent resistance of an arc depends upon the current passing through the arc ; that is, the apparent resistan ...", "... ference, and the apparent resistance of the arc, r.-f-ry/t-. + f The instantaneous power consumed in the arc is, Hence the effective power, DISTORTION OF WAVE-SHAPE. 395 The apparent power, or volt amperes consumed by the arc, is, thus the power factor of the arc, that is, less than unity. 241. We find here a case of a circuit in which the power factor — that is, the ratio of watts to volt amperes — differs from unity without any displacement of phase ; that is, while current and E.M.F. are in phase ...", "... the arc is, Hence the effective power, DISTORTION OF WAVE-SHAPE. 395 The apparent power, or volt amperes consumed by the arc, is, thus the power factor of the arc, that is, less than unity. 241. We find here a case of a circuit in which the power factor — that is, the ratio of watts to volt amperes — differs from unity without any displacement of phase ; that is, while current and E.M.F. are in phase with each other, but are distorted, the alternating wave cannot be replaced by an equivalent sine wave ; ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-16", "section_label": "Chapter 16: Load Balance Of Polyphase Systems", "section_title": "Load Balance Of Polyphase Systems", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 29302-30428", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-16/", "snippets": [ "... Unbalanced load on the generators causes a pulsating armature reaction: at single-phase load, the armature reaction pulsates between more than twice the average value, and a small reversed value, between f (cos a + 1) and F(cos a — 1), where cos a is the power-factor of the single-phase load. Especially in alternators of very high armature reaction, as modern steam-turbine alternators, a pulsation of the armatiu^ reaction is very objectionable. It causes a pulsation of the field flux, leading to excessive eddy-current ...", "... ent of power, and Q the amplitude of the double-frequency alternating component of power, and Q may be larger or smaller than P. It must be noted, that Q is not the total reactive power of the system — which would have to be considered, for instance, in power-factor compensation etc. — but Q is the vector resultant of the reactive powers of the individual circuits, while the total reactive power of the system is the algebraic sum of the individual reactive powers (see \"Theory and Calculation of Alternating- current P ...", "... where, from (20), P = Q sin a EI (20) Q = (21) 2 while in the general case (19) P and Q may have any values. Suppose now we select from the polyphase system a voltage, e' = E' cos (« - p) (22) and load it with an inductive load of zero power-factor, i'-rcos(«-i8-^) (23) E' . that is, we connect a reactor of a; = -y> into the phase e'. The power of (22) (23) then is p' = Q'cos(2<^-2<8-|) (24) where Q' = ^ (26) and the total power of the system, comprising (19) and (25), thus is Po = p + ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-40", "section_label": "Chapter 4: Arc Rectification", "section_title": "Arc Rectification", "kind": "chapter", "sequence": 40, "number": 4, "location": "lines 17755-19259", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "snippets": [ "... the rectified voltage, and therefrom the sum total of e.m.f. which has to be given by the d. c. reactive coil, and hereby the size of the d. c. reactive coil required to maintain the d. c. current fluctuation within certain given limits. The efficiency, power factor, regulation, etc., of such a mercury arc rectifier system are essentially those of the constant-current transformer feeding- the rectifier tube. Let / = frequency of the alternating-current supply system, i0 = mean value of the rectified direct current, ...", "... dary current of the transformer is 2 < the pulsation of the direct current is 7T2 cos sin x + 60 Ti + 6, the anode voltage of the rectifier is 2 #0 - sin 2 #c and herefrom follows the apparent efficiency of rectification, -V 61 the power factor, the efficiency, etc. 70° 80° Fig. 79. E.m.f. and current ratio and secondary power factor of constant- current mercury arc rectifier. From the equivalent sine waves, e and i, of the transformer secondary, and their phase angle, the primary impresse ...", "... sin x + 60 Ti + 6, the anode voltage of the rectifier is 2 #0 - sin 2 #c and herefrom follows the apparent efficiency of rectification, -V 61 the power factor, the efficiency, etc. 70° 80° Fig. 79. E.m.f. and current ratio and secondary power factor of constant- current mercury arc rectifier. From the equivalent sine waves, e and i, of the transformer secondary, and their phase angle, the primary impressed e.m.f. and the primary current of the transformer, and thereby the ARC RECTIFICATION 273 ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-25", "section_label": "Apparatus Section 4: Synchronous Machines: Self-inductance", "section_title": "Synchronous Machines: Self-inductance", "kind": "apparatus-section", "sequence": 25, "number": 4, "location": "lines 8907-9034", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-25/", "snippets": [ "... med by armature reaction is represented by OF'a = Fa in opposition to 01. Combining OF'a and OF gives OFQ = FQ, the field excitation. F, FIG. 53. — Diagram of generator, e.m.fs. and m.m.fs. for lagging reac- tive load. Power-factor 0 . 50. FIG. 54. — Diagram of generator e.m.fs. and m.m.fs. for leading reac- tive load. Power-factor 0.50. 136 ELEMENTS OF ELECTRICAL ENGINEERING In Figs. 52, 53, 54 are drawn the diagrams for 0 = zero or non-inducti ...", "... es OFQ = FQ, the field excitation. F, FIG. 53. — Diagram of generator, e.m.fs. and m.m.fs. for lagging reac- tive load. Power-factor 0 . 50. FIG. 54. — Diagram of generator e.m.fs. and m.m.fs. for leading reac- tive load. Power-factor 0.50. 136 ELEMENTS OF ELECTRICAL ENGINEERING In Figs. 52, 53, 54 are drawn the diagrams for 0 = zero or non-inductive load, 0 = 60 degrees, or 60 degrees lag (inductive load of power-factor 0.50), and 0 = — 60 de ...", "... leading reac- tive load. Power-factor 0.50. 136 ELEMENTS OF ELECTRICAL ENGINEERING In Figs. 52, 53, 54 are drawn the diagrams for 0 = zero or non-inductive load, 0 = 60 degrees, or 60 degrees lag (inductive load of power-factor 0.50), and 0 = — 60 deg., or 60 deg. lead (anti-inductive load of power-factor 0.50). Thus it is seen that with the same terminal voltage E a much higher field excitation, FQ, is required with inductive load than with ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-18", "section_label": "Chapter 18: Polyphase Induction Motors", "section_title": "Polyphase Induction Motors", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17717-20445", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-18/", "snippets": [ "... Ti < z, we have, qV,Eo\\ ^^' < T^' and since the starting current is, approximately J _ Eq ^ ~ 2 ' POLYPHASE INDUCTION MOTORS 225 we have, Do < I^M. Doo = 1 rEoI would be the theoretical torque developed at 100 per cent, efficiency and power-factor, by e.m.f. Eo, and current /, at synchronous speed. Thus, Do < Doo, and the ratio between the starting torque, Do, and the theo- retical maximum torque, Doo, gives a means to judge the per- fection of a motor regarding its starting torque. This rati ...", "... / 2000 40 1 i 1 1 1 ! / / ^ 30 //' / ^ 1000 30 1 ^ 10 i/ 10 w S( 00 SI 00 40 aWER BO OUTPl H T DO 60 JO 70 DO Fig. 123. hence, the efficiency is, Pi_ ^ ai (1 - s) Po' &lCl + 62C2' the power-factor, Po^ hiCi + &2C2 ^«0 V(6x2 + fe22)(Ci2 + C22)^ POLYPHASE INDUCTION MOTORS 235 the apparent efficiency, Pi tti (1 — s) the torque efficiency/ ai D Po^ biCi + 62C2 r- DUC ION- ) CI MOT JRVI s :s % ^' -.1- -.J ...", "... ^ Ox ^-0 ~ V(6i2 + 62^) (ci^ + ct^) 172. Most instructive in showing the behavior of an induction motor are the load curves and the speed curves. The load curves are curves giving, with the power output as abscissas, the current input, speed, torque, power-factor, effi- ciency, and apparent efficiency, as ordinates. The speed curves give, with the speed as abscissas, the torque, 1 That is the ratio of actual torque to torque which would be produced, if there were no losses of energy in the motor, at the same pow ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-35", "section_label": "Chapter 35: Balanced Symmetrical Polyphase Systems", "section_title": "Balanced Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 35, "number": 35, "location": "lines 37453-37957", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-35/", "snippets": [ "... ction, and use one of the F-cir- cuits as the equivalent single-phase circuit. 304. As an example may be considered the calculation of a long-distance transmission line, delivering 10,000 kw., three-phase power at 60 cycles, 80,000 volts and 90 per cent, power-factor at 100 miles from the generating station, with approximately 10 per cent, loss of power in the transmission line, and with the line conductors arranged in a triangle 6 ft. distant from each other. 29 450 ALTERNATING-CURRENT PHENOMENA 10,000 kw. tota ...", "... sion line, and with the line conductors arranged in a triangle 6 ft. distant from each other. 29 450 ALTERNATING-CURRENT PHENOMENA 10,000 kw. total power delivered gives 3,333 kw. per line or single-phase branch (F power). 3,333 kw. at 90 per cent, power-factor gives 3,700 kv.-amp. 80,000 volts between the lines gives 80,000 -^ \\^ = 46,100 volts from line to neutral, or per single-phase circuit. 3,700 kv.-amp. per circuit, at 46,100 volts, gives 80 amp. per line. 10 per cent, loss gives 333 kw. loss per line ...", "... ng, as approximation, the line capacity by a con- denser shunted across the middle of the line We have, impedance of half the line, Z = ^ +j| = 26 + 44johms. Choosing the voltage at the receiving end as zero vector, e = 46,100 volts, at 90 per cent, power-factor and therefore 43.6 per cent, induc- tance factor, the current is represented by 7 = 80 (0.9 - 0.436 j) =72-35 j. ^ Or. ii fi = permeability, k = dielectric constant of the medium sur- rounding the conductor, it is hence, V [^ I = \\W or. C = ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-16", "section_label": "Chapter 16: Aiitebnatingh-Current Osnebator", "section_title": "Aiitebnatingh-Current Osnebator", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 17025-18828", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "snippets": [ "... fiq. Its. Fitu m HoH-liKluctliv loaA dotted lines, we have, for the following conditions of external circuit : In Fig. 113, non-inductive external circuit, j: = 0. In Fig. 114, inductive external circuit, of the condition, r/.r = + .75, with a power factor, .6. In Fig. 115, inductive external circuit, of the condition, r = 0, with a power factor, 0, S1641 ALTERNATING-CURRENT GENERATOR. 241 In Fig. 116, external circuit with leading current, of the condi- tion, r jx = — .75, with a power factor, .6. ...", "... ons of external circuit : In Fig. 113, non-inductive external circuit, j: = 0. In Fig. 114, inductive external circuit, of the condition, r/.r = + .75, with a power factor, .6. In Fig. 115, inductive external circuit, of the condition, r = 0, with a power factor, 0, S1641 ALTERNATING-CURRENT GENERATOR. 241 In Fig. 116, external circuit with leading current, of the condi- tion, r jx = — .75, with a power factor, .6. In Fig. 117, external circuit with leading current, of the condi- tion, r = 0, with a powe ...", "... ith a power factor, .6. In Fig. 115, inductive external circuit, of the condition, r = 0, with a power factor, 0, S1641 ALTERNATING-CURRENT GENERATOR. 241 In Fig. 116, external circuit with leading current, of the condi- tion, r jx = — .75, with a power factor, .6. In Fig. 117, external circuit with leading current, of the condi- tion, r = 0, with a power factor, 0. 1 1 \\ 1 FIELD CHARA trasoo.^-MOj, 4 CTERI8T □ - 76lor eo< P. s \\ \\ \\ ^ / \\ N %% / '\\ \\ ss ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "section_label": "Chapter 10: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "... e effect, or power, expended by the circuit. The energy coefficient of current, a._ Energy component of current Total E.M.F. is called the effective conductance of the circuit. EFFECTIVE RESISTANCE AND REACTANCE. 105 In the same way, the value, _ Wattless component of E.M.F. Total current is the effective reactance, and , _ Wattless component of current TotafE.M.F. is the effective susceptance of the circuit. While the true ohmic resistance represents the expendi- ture of energy as heat inside of the electric ...", "... ._ Energy component of current Total E.M.F. is called the effective conductance of the circuit. EFFECTIVE RESISTANCE AND REACTANCE. 105 In the same way, the value, _ Wattless component of E.M.F. Total current is the effective reactance, and , _ Wattless component of current TotafE.M.F. is the effective susceptance of the circuit. While the true ohmic resistance represents the expendi- ture of energy as heat inside of the electric conductor by a current of uniform density, the effective resistance repre- sents ...", "... phase. Hence the cur- rent lags behind the E.M.F by ^ 90° — a, and the power is therefore, p=f£ cog (9QO _ a) = /E sin a Thus the exciting current, 7, consists of an energy compo- nent, / sin a, called the Jiysteretic or magnetic energy current, and a wattless component, / cos a, which is called the mag- netizing current. Or, conversely, the E.M.F. consists of an energy component, E sin a, the Jiysteretic energy E.M.F., and a wattless component, E cos a, the E.M.F. of self- induction. Denoting the absolute value of the ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-02", "section_label": "Chapter 2: Multiple Squirrel-Cage Induction Motor", "section_title": "Multiple Squirrel-Cage Induction Motor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3543-5554", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-02/", "snippets": [ "... and the power output: P = (1 - s) Z>. (22) (Herefrom subtracts the friction loss, to give the net power output.) The power input is: Po = /#o, Io/' = e22(cidi + c2d2), (23) and the volt-ampere input: Q = eoio. P Herefrom then follows the power-factor -gr * the torque effi- ciency y, , the apparent torque efficiency 7^-, the power efficiency P P jj- and the apparent power efficiency 7^ 23. As illustrations arc shown, in Figs. 14 and 15, the speed curves and the load curves of a double squirrel-cage ...", "... e of the triple squirrel-cage motor thus is: D = D, + D2 + D3, (31) and the power: P = (1 - s) Z>, (32) the power input is : PQ = /#o, /o/' = , that is, the lag of the current behind the voltage by angle w, the regulation 290 ELEMENTS OF ELECTRICAL ENGINEERING curve is derived from the vector diagram Fig. 158. The ir voltage is in phase with the ...", "... gives, by dropping out terms of higher order: v2 R — p (p cos co + £ sin co) + ~ (£ cos co — p sin co)2 In Figs. 159 and 160 are shown, for the angles of lag co = 20° (moderately inductive load, 94 per cent, power-factor), and co = 60° (highly inductive load, 50 per cent, power-factor), the regulation of the same three transformers as in Fig. 157, cal- culated respectively from the expression: REGULATION OF TRANSFORMERS Per cent, resistance ...", "... co + £ sin co) + ~ (£ cos co — p sin co)2 In Figs. 159 and 160 are shown, for the angles of lag co = 20° (moderately inductive load, 94 per cent, power-factor), and co = 60° (highly inductive load, 50 per cent, power-factor), the regulation of the same three transformers as in Fig. 157, cal- culated respectively from the expression: REGULATION OF TRANSFORMERS Per cent, resistance, p = 0.02 0.01 0.01 Per cent, reactance, £ = 0.02 0.04 ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-12", "section_label": "Theory Section 12: Impedance of Transmission Lines", "section_title": "Impedance of Transmission Lines", "kind": "theory-section", "sequence": 12, "number": 12, "location": "lines 3761-4464", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-12/", "snippets": [ "... oward the right, negative toward the left, and the vertical components positive upward, negative downward. Assuming the receiving voltage as zero line or positive hori- zontal line, the power current 7 is the horizontal, the wattless current I' the vertical component of the current. The e.m.f. con- sumed in resistance by the power current 7 is a horizontal com- ponent, and that consumed in resistance by the reactive current /' a vertical component, and the inv ...", "... formers, or any other apparatus containing resistance and reactance inserted in series into an alternating-current circuit. EXAMPLES 58. (1) An induction motor has 2000 volts impressed upon its terminals; the current and the power-factor, that is, the cosine of the angle of lag, are given as functions of the output in Fig. 31. The induction motor is supplied over a line of resistance r = 2.0 and reactance x = 4.0. (a) How must the generator voltage ...", "... age CQ = 2300, how will the voltage at the motor terminals vary? 64 ELEMENTS OF ELECTRICAL ENGINEERING We have / a* — ft —. e = 2000. 63.4°. «= -i l(e + iz)2 — 4 ezz sin2 tan 0i = ~ = 2. cos 0 = power-factor. Taking i from Fig. 31 and substituting, gives (a) the values of e0 for e = 2000, which are recorded in the table, and plotted in Fig. 31. JTPUT .10 20 30 40 50 60 70 80 90 100 110 .120 130 140 150 160 170 1 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-08", "section_label": "Chapter 8: Admittance, Conductance, Susceptance", "section_title": "Admittance, Conductance, Susceptance", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 4088-4673", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-08/", "snippets": [ "... tance, x, in the formula of Ohm's law, E = IZ. The resistance, r, gives the component of e.m.f. in phase with the current, or the power component of the e.m.f., Ir; the reactance, x, gives the component of the e.m.f. in quadrature with the current, or the wattless component of e.m.f., Ix; both combined give the total e.m.f., Iz = iVr^ + x^. Since e.m.fs. are combined by adding their complex expressions, we have: The joint impedance of a number of series-connected impedances is the sum of the individual impedances, when e ...", "... th the e.m.f., or wattless or reactive component, hE, of the current. g is called the conductance, and h the susceptance, of the cir- cuit. Hence the conductance, g, is the power component, and 56 ALTERNATING-CURRENT PHENOMENA the susceptance, h, the wattless component, of the admittance, Y = g ~ jb, while the numerical value of admittance is y = Vg' + h^; the resistance, r, is the power component, and the reactance, X, the wattless component, of the impedance, Z = r -^ jx, the numerical value of impedance being z ...", "... component, and 56 ALTERNATING-CURRENT PHENOMENA the susceptance, h, the wattless component, of the admittance, Y = g ~ jb, while the numerical value of admittance is y = Vg' + h^; the resistance, r, is the power component, and the reactance, X, the wattless component, of the impedance, Z = r -^ jx, the numerical value of impedance being z = Vr^ + x^. 50. As shown, the term admittance implies resolving the cur- rent into two components, in phase and in quadrature with the e.m.f., or the power or active component and ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-10", "section_label": "Chapter 10: Resistance And Reactance Of Transmission", "section_title": "Resistance And Reactance Of Transmission", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6993-9766", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-10/", "snippets": [ "... cuit — shunted by a susceptance, h, which can be varied without expenditure of energy. The two components of current can thus be considered separately, the energy component as deter- 78 TRANSMISSION LINES 79 mined by the load on the circuit, and the wattless component, which can be varied for the purpose of regulation. Obviously, in the same way, the voltage at the receiver circuit may be considered as consisting of two components, the power component, in phase with the current, and the wattless com- ponent, in quadr ...", "... ATTS Fig. 73. — Variation of voltage of transmission lines. Eo = 1000 volts, and a constant line impedance, Zq = 2.5 -f 6 j, or ro = 2.5 ohms, a^o = 6 ohms, z = 6.5 ohms, the following values: power component of current, gE, (Curve I) ; reactive, or wattless component of current, hE^ (Curve II) ; total current, yE^ (Curve III), and power factor at generator for the following conditions: a = 1.0 (Fig. 73); « = 0.7 (Fig. 74); a = 1.3 (Fig. 75). For the non-inductive receiver circuit (in dotted lines), the curve of e ...", "... onstant line impedance, Zq = 2.5 -f 6 j, or ro = 2.5 ohms, a^o = 6 ohms, z = 6.5 ohms, the following values: power component of current, gE, (Curve I) ; reactive, or wattless component of current, hE^ (Curve II) ; total current, yE^ (Curve III), and power factor at generator for the following conditions: a = 1.0 (Fig. 73); « = 0.7 (Fig. 74); a = 1.3 (Fig. 75). For the non-inductive receiver circuit (in dotted lines), the curve of e.m.f., E, and of the current, / = gE, are added in the three diagrams for compari ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-13", "section_label": "Chapter 13: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 13484-14333", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-13/", "snippets": [ "... r by eddy currents is proportional to the square of the e.m.f. of self-induction, and therefore proportional to the square of the frequency and to the square of the magnetization. Only the power component, gE, of eddy currents, is of interest, since the wattless component is identical with the wattless com- ponent of hysteresis, discussed in the preceding chapter. 106. To calculate the loss of power by eddy currents. Let V = volume of iron; B = maximum magnetic induction; / = frequency; X = electric conductivity of i ...", "... neration of secondary e.m.fs. in neighboring circuits; that is, the interference of circuits run- ning parallel with each other. In general, it is preferable to consider this phenomenon of mutual induction as not merely producing a power component and a wattless component of e.m.f. in the primary conductor, but to consider explicitly both the secondary and the primary circuit, as will be done in the chapter on the alternating-current transformer. Only in cases where the energy transferred into the secondary circuit const ...", "... scussion of the disturbance caused by one circuit upon a parallel circuit, may the effect on the primary circuit be con- sidered analogously as in the chapter on eddy currents by the introduction of a power component, representing the loss of power, and a wattless component, representing the decrease of self-induction. Let X = 2 7r/L = reactance of main circuit; that is, L = total num- ber of interlinkages with the main conductor, of the lines of magnetic force produced by unit current in that conductor; Xi — 2 tt/Li = ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-07", "section_label": "Chapter 7: Admittance, Conductance, Susceftance", "section_title": "Admittance, Conductance, Susceftance", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 3546-3871", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-07/", "snippets": [ "... nce^ x, in the formula of Ohm's law, E = IZ, The resistance, r, gives the component of E.M.F. in phase with the current, or the energy component of the E.M.F., Ir\\ the reactance, Xy gives the component of the E.M.F. in quadrature with the current, or the wattless component of E.M.F., Ix\\ both combined give the total E.M.F., — Iz = lWr' + x\\ Since E.M.Fs. are combined by adding their complex ex- pressions, we have : The joint impedance of a number of series-connected impe- dances is the sum of the individual impedances ...", "... ents the coefficient of current in quadrature with the K.M.F., or wattless com- ponent of current, bE, g may be called the conductance^ and b the susceptanccy of the circuit. Hence the conductance, g^ is the energy component, and the susceptance, by the wattless component, of the admittance, Y = g -\\-jby while the numerical value of admittance is — the resistance, r, is the energy component, and the reactance^ Xy the wattless component, of the impedance, Z = r — jx\\ the numerical value of impedance being — 40. As show ...", "... ircuit. Hence the conductance, g^ is the energy component, and the susceptance, by the wattless component, of the admittance, Y = g -\\-jby while the numerical value of admittance is — the resistance, r, is the energy component, and the reactance^ Xy the wattless component, of the impedance, Z = r — jx\\ the numerical value of impedance being — 40. As shown, the term admittance implies resolving the current into two components, in phase and in quadra- ture with the E.M.F., or the energy current and the watt- less current ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-09", "section_label": "Chapter 9: Kbsistanci: And Kbactance Of Transmission Iine8", "section_title": "Kbsistanci: And Kbactance Of Transmission Iine8", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 6371-8268", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "snippets": [ "... he non-inductive part of the circuit, — shunted by a susceptance, by which can be varied without expenditure of energy. The two components of current can thus be considered separately, the energy component as determined by the load on the circuit, and the wattless component, which can be varied for the purpose of regu- lation. Obviously, in the same way, the E.M.F. at the receiver circuit may be considered as consisting of two components, the energy component, in phase with the current, and the wattless component, in quadr ...", "... and the wattless component, which can be varied for the purpose of regu- lation. Obviously, in the same way, the E.M.F. at the receiver circuit may be considered as consisting of two components, the energy component, in phase with the current, and the wattless component, in quadrature with the current. This will correspond to the case of a reactance connected in series to the non-inductive part of the circuit. Since the effect of either resolution -into components is the same so far as the line is concerned, we need not ...", "... \"» ' \"\"^'^^s Z ^§^ I ^ „ - \"\"--^ J -: z ^J 1 IJM^i^lIU:: ' ---'^-'^ -\" \"= = --\"==^- — ^^■\"\"' ■:^j^4^:iijj nOl IT, Kll oJ^TTB FIj. 93. Yarlatlim of Vtltag* Energy component of current, gB, (Curve I.) ; Reactive, or wattless component of current, bE, (Curve II.) ; Total current, yE, (Curve III.) ; for the following conditions : a = 1.0 (Fig, r,8) i a= .7 (Fig. 59); a = 1.3 (Fig. 60). For the non-inductive receiver circuit (in dotted lines), the curve of E.M.F., /;, and of the curre ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-10", "section_label": "Chapter 10: F", "section_title": "F", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 8269-10499", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "snippets": [ "... t, or power, expended by the circuit. The energy coefficient of current, _ Energy component of current ^ Total E.M.F. is called the effective conductance of the circuit. § 733 EFFECTIVE RESISTANCE AND REACTANCE. 105 In the same way, the value, _ Wattless component of E.M.F. Total current is the effective reactance, and , _ Wattless compo nent of current ■\" Total E.M.F. is the effective susceptance of the circuit. While the true ohmic resistance represents the expendi- ture of energy as heat inside of the ele ...", "... phase. Hence the cur- rent lags behind the E.M.F by ^^ 90° — a, and the power is therefore, P= IE cos (90° ^a) = IE sin a. Thus the exciting current, /, consists of an energy com- ponent, / sin a, which is called the hysteretic energy current y and a wattless component, /cos a, which is called the mag- netizing current. Or, conversely, the E.M.F. consists of an energy component, E sin a, the hysteretic energy E.M.F., and a wattless component, E cos a, the E.M.F. of self induction. Denoting the absolute value of the im ...", "... gy com- ponent, / sin a, which is called the hysteretic energy current y and a wattless component, /cos a, which is called the mag- netizing current. Or, conversely, the E.M.F. consists of an energy component, E sin a, the hysteretic energy E.M.F., and a wattless component, E cos a, the E.M.F. of self induction. Denoting the absolute value of the impedance of the IIG AL TERNA TING-CURRENT PHENOMENA, [§ 80 circuit, -£\"//, by ir, — where z is determined by the mag- netic characteristic of the iron, and the shape of the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-07", "section_label": "Chapter 7: Admittance, Conductance, Susceptance", "section_title": "Admittance, Conductance, Susceptance", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 3132-3576", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-07/", "snippets": [ "... nce, x, in the formula of Ohm's law, E = IZ. The resistance, r, gives the component of E.M.F. in phase with the current, or the energy component of the E.M.F., Ir; the reactance, x, gives the component of the E.M.F. in quadrature with the current, or the wattless component of E.M.F., Ix ; both combined give the total E.M.F., — Since E.M.Fs. are combined by adding their complex ex- pressions, we have : The joint impedance of a number of series-connected impe- dances is the sum of the individual impedances, when expressed ...", "... esents the coefficient of current in quadrature with the E.M.F., or wattless com- ponent of current, bE. g is called the conductance, and b the susceptance, of the circuit. Hence the conductance, g, is the energy com- ponent, and the susceptance, b, the wattless component, of the admittance, Y = g -f jb, while the numerical value of admittance is — y = Vr1 + P ; the resistance, r, is the energy component, and the reactance, x, the wattless component, of the impedance, Z — r — jx, the numerical value of impedance being ...", "... onductance, g, is the energy com- ponent, and the susceptance, b, the wattless component, of the admittance, Y = g -f jb, while the numerical value of admittance is — y = Vr1 + P ; the resistance, r, is the energy component, and the reactance, x, the wattless component, of the impedance, Z — r — jx, the numerical value of impedance being — z = VV' + x\\ 40. As shown, the term admittance implies resolving the current into two components, in phase and in quadra- ture with the E.M.F., or the energy current and the watt- ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-09", "section_label": "Chapter 9: Resistance And Reactance Of Transmission Lines", "section_title": "Resistance And Reactance Of Transmission Lines", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 5334-6956", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "snippets": [ "... he non-inductive part of the circuit, — shunted by a susceptance, b, which can be varied without expenditure of energy. The two components of current can thus be considered separately, the energy component as determined by the load on the circuit, and the wattless component, which can be varied for the purpose of regu- lation. Obviously, in the same way, the E.M.F. at the receiver circuit may be considered as consisting of two components, the energy component, in phase with the current, and the wattless component, in quadr ...", "... and the wattless component, which can be varied for the purpose of regu- lation. Obviously, in the same way, the E.M.F. at the receiver circuit may be considered as consisting of two components, the energy component, in phase with the current, and the wattless component, in quadrature with the current. This will correspond to the case of a reactance connected in series to the non-inductive part of the circuit. Since the effect of either resolution into components is the same so far as the line is concerned, we need not m ...", "... CURRENT IV. POTENTIAL IN NON-INDUCTIVE RECEIVER CIRCUIT WITHOUT COMPENSATION OUTPUT N RECEIVER C RCUIT, KILOWATTS 30 10 80 60 70 80 90 Fig. 63. Variation of Voltage Transn\\jssion Lines. Energy component of current, gE, (Curve I.) ; Reactive, or wattless component of current, bE, (Curve II.) ; Total current, yE, (Curve III.) ; for the following conditions : a = 1.0 (Fig. 61) ; a = .7 (Fig. 62) ; a = 1.3 (Fig. 63). For the non-inductive receiver circuit (in dotted lines), the curve of E.M.F., E, and of the curre ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-12", "section_label": "Chapter 12: Power, And Double Frequency Quantities In General", "section_title": "Power, And Double Frequency Quantities In General", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 9381-9740", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "snippets": [ "... r of the circuit, = E I cos (E /) The component, PJ = is what may be called the \" wattless power,\" or the power- less or quadrature volt-amperes of the circuit, = E /sin (El}. The real component will be distinguished by the index 1, the imaginary or wattless component by the index/. By introducing this symbolism, the power of an alternat- ing circuit can be represented in the same way as in the direct current circuit, as the symbolic product of current and E.M.F. Just as the symbolic expression of current and E.M.F. ...", "... of vectors just as currents and E.M.F's in graphical or symbolic representation. The graphical methods of treatment of alternating cur- rent phenomena are here extended to include double fre- quency quantities as power, torque, etc. P1 — =p = cos w = power factor. PJ — = q = sin w = inductance factor of the circuit, and the general expression of power is, = Q (cos co -\\-j sin o>) 104. The introduction of the double frequency vector product P = \\E I~\\ brings us outside of the limits of alge- 154 ALTERNAT ...", "... since we have [EIJ = [IEJ [EI]J=-[IE]J that is, the imaginary component reverses its sign by the interchange of factors. The physical meaning is, that if the wattless power [E 7p is lagging with regard to E, it is leading with regard to/. The wattless component of power is absent, or the total apparent power is true power, if [EI]J = (W1 - A'11) = 0. that is, or, tan (E) = tan (/), that is, E and / are in phase or in opposition. The true power is absent, or the total apparent power wattless, if [El] ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "... into the primary circuit. Mutual inductance is neither in phase nor in quadrature with the current, and can therefore be resolved into an energy component of mutual inductance in phase with the current, which acts as an increase of resistance, and into a wattless component in quadrature with the current, which decreases the self-inductance. This mutual inductance is not always negligible, as, for instance, its disturbing influence in telephone circuits shows. The alternating potential of the line induces, by electro- st ...", "... outside of the circuit, which retain corresponding opposite charges on the line wires. This electrostatic influence re- quires the expenditure of a current proportional to the E.M.F., and consisting of an energy component, in phase with the E.M.F., and a wattless component, in quadrature thereto. The alternating electromagnetic field of force set up by the line current produces in some materials a loss of energy by magnetic hysteresis, or an expenditure of E.M'.F. in phase with the current, which acts as an increase of re ...", "... i Fig. 86. DISTRIBUTED CAPACITY. 173 ence of phase between both as function of the distance from receiver circuit ; under the conditions, E.M.F. at receiving end, 10,000 volts; hence, Ev =el = 10,000; current at receiving end, 65 amperes, with a power factor of .385. that is, / = t\\ + j // = 25 + 60 j ; line constants per unit length, r = 1, g = 2 X 10-5, hence, a = 4.95 x 10-3, ] 13 = 28.36 x 10 -3, j- length of line corresponding to one complete period of the wave x0 = L = — = 221.5 = (^ of ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-106", "section_label": "Apparatus Section 9: Alternating-current Transformer: Reactors", "section_title": "Alternating-current Transformer: Reactors", "kind": "apparatus-section", "sequence": 106, "number": 9, "location": "lines 18813-18948", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-106/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-106/", "snippets": [ "... generally understood, in the conventional definition : T^C • 1°SS Efficiency = 1 — -. — input and the input is given in total volt-amperes, the loss in energy volt-amperes, that is, watts. The efficiency then is 1 — power- factor. ALTERNATING-CURRENT TRANSFORMER 303 The transformer at open circuit is a reactor, but a very poor one, as its power-factor is high, that is, the efficiency low. In the transformer, the exciting ampere-turns are the ...", "... volt-amperes, the loss in energy volt-amperes, that is, watts. The efficiency then is 1 — power- factor. ALTERNATING-CURRENT TRANSFORMER 303 The transformer at open circuit is a reactor, but a very poor one, as its power-factor is high, that is, the efficiency low. In the transformer, the exciting ampere-turns are the (vector) difference between primary and secondary ampere-turns, are wasted, and therefore made as low as possible, by using a close ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-26", "section_label": "Apparatus Section 5: Synchronous Machines: Synchronous Reactance", "section_title": "Synchronous Machines: Synchronous Reactance", "kind": "apparatus-section", "sequence": 26, "number": 5, "location": "lines 9035-9169", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-26/", "snippets": [ "... sumed by synchronous reactance, E'0 = + jixQ, and the nominal generated e.m.f., E0 = E + E\\ + E'Q = (E cos 0 + ir) + j (E sin 19 + ix0) ; or, since . „ » , , , / power current \\ cos 6 = p = power-factor of the load ( = -. —. — ) \\ total current / and q = \\/l — p2 = sin 0 = inductance factor of the load (wattless current\\ total current' / ' it is Eo = (Ep +» + j (Eq + ix0), or, in absolute values, ...", "... sin 19 + ix0) ; or, since . „ » , , , / power current \\ cos 6 = p = power-factor of the load ( = -. —. — ) \\ total current / and q = \\/l — p2 = sin 0 = inductance factor of the load (wattless current\\ total current' / ' it is Eo = (Ep +» + j (Eq + ix0), or, in absolute values, Eo = V(Ep + ir)2 + (Eq + ^0)2; hence, E = VE02 - i2 (x0p - rq)2 - i (rp -f x^q). The power delivered by the alternator into ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-79", "section_label": "Apparatus Subsection 79: Direct-current Commutating Machines: C. Commutating Machines 219", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 219", "kind": "apparatus-subsection", "sequence": 79, "number": null, "location": "lines 13019-13119", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-79/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-79/", "snippets": [ "... with the field winding or excitation of the field from a quadrature phase of voltage. In the series motor the self-inductance of the field causes the main current to lag behind the impressed voltage and thereby lowers the power-factor of the motor. Thus, to get good power-factor, the field self-inductance must be made low, that is, the field as weak and the armature as strong as possible. With such a strong armature, and weak field, the commutating po ...", "... ield from a quadrature phase of voltage. In the series motor the self-inductance of the field causes the main current to lag behind the impressed voltage and thereby lowers the power-factor of the motor. Thus, to get good power-factor, the field self-inductance must be made low, that is, the field as weak and the armature as strong as possible. With such a strong armature, and weak field, the commutating pole is not sufficient to control magnetic disto ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-96", "section_label": "Apparatus Section 2: Alternating-current Transformer: Excitation", "section_title": "Alternating-current Transformer: Excitation", "kind": "apparatus-section", "sequence": 96, "number": 2, "location": "lines 16912-17026", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-96/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-96/", "snippets": [ "... volts as abscissae, and the total exciting current, and core loss as ordinates. The exciting current is usually not proportional to the voltage, due to the use of a closed magnetic circuit, and for the same reason, the power-factor of the exciting current is fairly high, from 40 to 60 per cent., except at high voltages, where magnetic saturation causes an abnormal increase of the magnetizing current. The power-factor is shown on Fig. 153. IE. Losse ...", "... it, and for the same reason, the power-factor of the exciting current is fairly high, from 40 to 60 per cent., except at high voltages, where magnetic saturation causes an abnormal increase of the magnetizing current. The power-factor is shown on Fig. 153. IE. Losses and Efficiency 113. The losses in the transformer are (a) The core loss, comprising the loss by hysteresis and eddy currents in the iron. This depends on the maximum magnetic flux, and ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "section_title": "Dibtbisnted Capacity, Inductance, Besistance, And", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "... into the primary circuit. Mutual inductance is neither in phase nor in quadrature with the current, and can therefore be resolved into an energy component of mutual inductance in phase with the current, which acts as an increase of resistance, and into a wattless component in quadrature with the current, which decreases the self-inductance. This mutual inductance is by no means negligible, as,, for instance, its disturbing influence in telephone circuits shows. The alternating potential of the line induces, by electro- ...", "... outside of the circuit, which retain corresponding opposite charges on the line wires. This electrostatic influence re- quires the expenditure of a current proportional to the E.M.F., and consisting of an energy component, in phase with the E.M.F., and a wattless component, in quadrature thereto. The alternating electromagnetic field of force set up by the line current produces in some materials a loss of energy by magnetic hysteresis, or an expenditure of E.M.F. in phase with the current, which acts as an increase of re- ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-19", "section_label": "Chapter 19: Commutatob Motobs", "section_title": "Commutatob Motobs", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 21339-22387", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "snippets": [ "... (.023 ^1 + .15y + 1.96 , . 1.4 . .023 A^, + .15 tan ID = , or, cos oi = *— ' .023 iV, + .15 ' ' V(\".023 A\\ + .15)\"'\"+TU0' Sa02] COMMUTATOR MOTORS. 305 In Fig. 147 are given, with the speed A^i as abscissae, the values of current /, power P, and power factor cos 2 of this motor. SER E3 MO OR IOf> '- r? ■^ -! H\" ao p 2 0, w -- ■ ^ / 1= A/1 ,y, ID\" / / p= Alfl nf Ml. / ( / C« M = -j-' — 1 Til' r™ i« ...", "... ous arrangements have been proposed, but have not found an application. §203] COMMUTATOR MOTORS. 307 203. Compared with the synchronous motor which has practically no lagging currents, and the induction motor which reaches very high power factors, the power factor of the series motor is low, as seen from Fig. 147, which repre- sents about the best possible design of such motors. In the alternating-series motor, as well as in the shunt motor, no position of an armature coil exists wherein the coil is dead; but in ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-20", "section_label": "Chapter 20: Commutator Motors", "section_title": "Commutator Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 19458-20501", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "snippets": [ "... r> A field ampere-turns It is in this case, 100 V(.023 vVi + ,15)2 + 1.96 230 ./v; (.023 A! + .15)2 + 1.96 368 AL TERNA TING-CURRENT PHENOMENA. In Fig. 163 are given, with the speed Nv as abscissae, the values of current /, power P, and power factor cos o> of this motor. SER ES MO FOP Er 00 ^ Vaf- 3 r = n= 03 .12 =(, x _.y = .5 >->w N = 60 P= 2 0,, hi TUMI _x ^ ^~~~ ^« < ^ 2Stt> s V( J23 ]( ~ QjF 1.9 gem / / 1Z'_. NI ...", "... rangements have been proposed, but have not found an application. 370 ALTERNATING-CURRENT PHENOMENA. 224. Compared with the synchronous motor which has practically no lagging currents, and the induction motor which reaches very high power factors, the power factor of the series motor is low, as seen from Fig. 163, which repre- sents about the best possible design of such motors. In the alternating-series motor, as well as in the shunt motor, no position of an armature coil exists wherein the coil is dead; but in ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-05", "section_label": "Chapter 6: Induction-Motor Regulation And Stability", "section_title": "Induction-Motor Regulation And Stability", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 10583-12397", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-05/", "snippets": [ "... ies between the motor terminals and the constant voltage supply, e., then can be calculated from the motor characteristics at constant termi- nal voltage, eBl as follows: At slip, I, and constant terminal voltage, ea, the current in the motor is i0, its power-factor p = cos 8. The effective or equiva- lent impedance of the motor at this slip then is z\" = .-, and, in complex quantities, Z* = .\" (cos 0 + i Bin 0), and the total irn- pedance, including that of transformers and line, thus is: Zx = Z° + Z = (?\" cos 6 + r ...", "... nge of torque produced by the momentary voltage change resulting from a current change di in the system; hence, is essentially a characteristic of the supply system and its regulation, but depends upon the motor de only in so far as .. depends tijmn the power-factor of the load. In Fig. 54 is shown the regulation coefficient, k,, of the supply- system of the motor, at 110 volts maintained constant at the motor terminals, and an impedance, Z = 0.16 + 0.8 j, between motor terminals and supply e.m.f. As seen, the regul ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-12", "section_label": "Chapter 14: Phase Conversion And Single-Phase Generation", "section_title": "Phase Conversion And Single-Phase Generation", "kind": "chapter", "sequence": 12, "number": 14, "location": "lines 17125-18412", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-12/", "snippets": [ "... a phase converter operating at con- stant supply voltage: of the constants: thus: and let #© * e© «= 100 volts; >'o - 0.01 -0.1;, Zv = Zi « 0.05 + 0.15;; I = 0.1 +0.3;; y , = u(j> -jq) = a (0.8 - 0.6;;, that is, a load of W) per cent, power-factor, winch m*>poudi- about to the average power-factor of au inductiou motoi . 224 ELECTRICAL APPARATUS It is, then, substituted into (11) to (13): . _ _ioo *■ (1.062 + 0.52 a) + j (0.36 a - 0.0 .r 80j)«L = 0, or no-load, this gives: es = 94.1 ...", "... ge: of the constants: thus: and let #© * e© «= 100 volts; >'o - 0.01 -0.1;, Zv = Zi « 0.05 + 0.15;; I = 0.1 +0.3;; y , = u(j> -jq) = a (0.8 - 0.6;;, that is, a load of W) per cent, power-factor, winch m*>poudi- about to the average power-factor of au inductiou motoi . 224 ELECTRICAL APPARATUS It is, then, substituted into (11) to (13): . _ _ioo *■ (1.062 + 0.52 a) + j (0.36 a - 0.0 .r 80j)«L = 0, or no-load, this gives: es = 94.1, li - 0, I, - 19.5; = ™, or short-circuit, this gi ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-appendix-01-synchronous-operation", "section_label": "Mathematical Appendix 5: Appendix: Synchronous Operation", "section_title": "Appendix: Synchronous Operation", "kind": "mathematical-appendix", "sequence": 5, "number": 5, "location": "PDF pages 27-68, lines 2165-5013", "status": "pdf-text-extracted-candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "snippets": [ "... nt always lags. Its lag is 90 degrees when the current is a maximum. With decrease of current, the lag decreases from 90 degrees in the one, and increases in the next beat, and approaches in phase respectively in opposition, when the current is a minimum. The power factor thus varies from zero at maximum current, to unity at zero current, and its average thus is low. Fig. 1 shows as Curve III the relation of ei to i for the exaggerated values s = .09. The power of one of the two alternators then is given by : 2F\" 2 = - sin s< ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-03-record", "section_label": "Report Record 4: Record of Four Troubles", "section_title": "Record of Four Troubles", "kind": "report-record", "sequence": 4, "number": 4, "location": "PDF pages 16-27, lines 1139-2164", "status": "pdf-text-extracted-candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-03-record/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-03-record/", "snippets": [ "... F of either machine. If then the circuit between the two machines should contain only resistance but no reactance, the interchange current between the two machines would be in phase with the resultant EMF, thus in quadrature to the EMF of either machine, or a wattless current with regards to the EMFs of the machines, that is, there would be no power transfer be- tween the machines, or no synchronizing power. If, however, in the circuit between the two machines the resistance is negligible compared with the reactance, the interchan ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-10", "section_label": "Lecture 10: Regulation And Control", "section_title": "Regulation And Control", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 4595-4930", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-10/", "snippets": [ "... onstant power factoi ; that is, if compounded for non-inductive load, the voltage drops on inductive load, since inductive load requires a greater field excitation than non-inductive load. 130 GENERAL LECTURES Brushes have to be shifted with change of power factor, that is, change from motor load to lighting load, etc. ; other- wise commutator sparks badly. These machines therefore were good in the early days when all the load was lighting load, but are unsuited at present for mixed load. 3rd. Form D alternator ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-13", "section_label": "Lecture 13: Electric Railway: Motor Characteristics", "section_title": "Electric Railway: Motor Characteristics", "kind": "lecture", "sequence": 13, "number": 13, "location": "lines 7124-8648", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-13/", "snippets": [ "... Si, is dropped still further by the inductive drop of voltage, to the curve Si, and then raised to the curve S by saturation. The eflFect of saturation in the alternating current motor usually is far less, since the magnetic field is alternating, and good power factor requires a low field excitation, and therefore high saturation cannot well be reached. The torque curves are the same as in the direct current motor, except that the effect of saturation is less marked. 1^2 GENERAL LECTURES In efficiency, the shun ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-08", "section_label": "Lecture 8: Arc Lamps And Arc Lighting", "section_title": "Arc Lamps And Arc Lighting", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 7141-8510", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-08/", "snippets": [ "... 1 constant-current effect, as discussed above. In alternating- current circuits, reactance may, and usually is, employed in- stead of the steadying resistance, and the waste of power thereby greatly decreased. Voltage, however, is still consumed and the power factor lowered. An additional waste of energy generally occurs in constant- potential arc-lamp circuits, due to the standard distribution voltages of low-potential circuits being higher than necessary for the operation of a single lamp, but too low for the oper ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-09", "section_label": "Theory Section 9: Vector Diagrams", "section_title": "Vector Diagrams", "kind": "theory-section", "sequence": 9, "number": 9, "location": "lines 2865-3233", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-09/", "snippets": [ "... ion Reactive component of £°d lotd lo^d ^ ^d current, 72 = -21.6 -16.2 -9.2 0 +9.7 hence, the total current, + /22 = 21.6 19.6 23.9 33.0 45.05 and the power factor, ^ = cos 0 = 0 56.0 92.0 100.0 97.7 the lag of the current, 0 = 90° 61° 23° 0° -11.5° the generator terminal voltage per line is E' = V(E + rj, = V(E + 7.6 A + 4.35 ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-11", "section_label": "Theory Section 11: Capacity and Condensers", "section_title": "Capacity and Condensers", "kind": "theory-section", "sequence": 11, "number": 11, "location": "lines 3586-3760", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-11/", "snippets": [ "... current and a dielectric hysteresis current, which latter, however, is generally so small as to be negligible, though in underground cables of poor quality, it may reach as high as 50 per cent, or more of the charging or wattless current of the condenser. 52. The capacity of one wire of a transmission line is i.nxio-6x/ . C = - — ~-i - , in mf., where Id = diameter of wire, cm.; 18 — distance of wire from return wire, cm.; I = length of wire, ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-112", "section_label": "Apparatus Section 6: Induction Machines: Phase Converter", "section_title": "Induction Machines: Phase Converter", "kind": "apparatus-section", "sequence": 112, "number": 6, "location": "lines 21647-21812", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-112/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-112/", "snippets": [ "... of suitable capacity, thereby generating the exciting current of the motor in the tertiary circuit. The primary circuit is thereby relieved of the exciting current of the motor, the efficiency essentially increased, and the power- factor of the single-phase motor with condenser in tertiary cir- cuit becomes practically unity over the whole range of load. At the same time, since the condenser current is derived by double 354 ELEMENTS OF ELECTRICAL ENGINE ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-15", "section_label": "Theory Section 15: Load Characteristic of Transmission Line", "section_title": "Load Characteristic of Transmission Line", "kind": "theory-section", "sequence": 15, "number": 15, "location": "lines 5832-6221", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-15/", "snippets": [ "... the square of the impressed e.m.f. divided by twice the sum of resistance and impedance of the line. At x = 0, this gives the common formula, Inductive Load 72. With an inductive receiving circuit of lag angle 6, or power-factor p = cos 8, and inductance factor q = sin 6, at e.m.f. E = e at receiving circuit, the current is denoted by I = I(p-jq); (15) thus the e.m.f. consumed by the line impedance Z = r -f jx is E! = ZI = I (p -jq)( ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-17", "section_label": "Theory Section 17: Impedance and Admittance", "section_title": "Impedance and Admittance", "kind": "theory-section", "sequence": 17, "number": 17, "location": "lines 6814-7380", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-17/", "snippets": [ "... troduced. e \" z ' which is called the admittance. The components of the admittance are called the conduc- tance and the susceptance. Resolving the current i into a power component i\\ in phase with the e.m.f. and a wattless component iz in quadrature with the e.m.f., the quantity i\\_ _ power current, or current in phase with e.m.f. e e.m.f. . = 9 is called the conductance. The quantity _*2_ _ reactive current, or current in quadrature with e.m. ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-21", "section_label": "Apparatus Introduction 21: Introduction", "section_title": "Introduction", "kind": "apparatus-introduction", "sequence": 21, "number": null, "location": "lines 8292-8517", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-21/", "snippets": [ "... us motors, which are usually preferred for large powers, especially where frequent starting and considerable starting torque are not needed. Synchronous machines may be used as compensators or synchronous condensers, to produce wattless current, leading by over-excitation, lagging by under-excitation, or may be used as phase converters by operat- ing a polyphase synchronous motor by one pair of terminals from a single-phase circuit. The most important class of conve ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-29", "section_label": "Apparatus Section 8: Synchronous Machines: Characteristic Curves of Synchronous Motor", "section_title": "Synchronous Machines: Characteristic Curves of Synchronous Motor", "kind": "apparatus-section", "sequence": 29, "number": 8, "location": "lines 9399-9553", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-29/", "snippets": [ "... compounding curves. r = 0.1, XQ = 5, E = 1000, and constant field excitation F0' that is, constant nominal counter-generated e.m.f. EQ = 1109 (corresponding to p = 1, # = 0 at 7 = 100), the values of current I and power-factor p. As iron loss is assumed 3000 watts, as friction 2000 watts. Such curves are called load characteristics of the synchronous motor. 18. In Fig. 68 are shown, with constant power output = PO, SYNCHRONOUS MACHINES 145 ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-81", "section_label": "Apparatus Section 1: Synchronous Converters: General", "section_title": "Synchronous Converters: General", "kind": "apparatus-section", "sequence": 81, "number": 1, "location": "lines 13189-13795", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-81/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-81/", "snippets": [ "... n These currents give only the power component of alternating current corresponding to the direct-current output. Added thereto is the current required to supply the losses in the machine, that is, to rotate it, and the wattless component if a phase dis- placement is produced in the converter. SYNCHRONOUS CONVERTERS 231" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-84", "section_label": "Apparatus Section 5: Synchronous Converters: Armature Reaction", "section_title": "Synchronous Converters: Armature Reaction", "kind": "apparatus-section", "sequence": 84, "number": 5, "location": "lines 15161-15475", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-84/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-84/", "snippets": [ "... of current required to rotate the machine, that is, to cover the internal losses of power, which is in quadrature with the field excitation or distorting, but of negligible magnitude. 2. The armature reaction due to the wattless component of alternating current where such exists. 3. An effect of oscillating nature, which may be called a higher harmonic of armature reaction. The direct current, as rectangular alternating current in the armature, changes in ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-87", "section_label": "Apparatus Section 9: Synchronous Converters: Inverted Converters", "section_title": "Synchronous Converters: Inverted Converters", "kind": "apparatus-section", "sequence": 87, "number": 9, "location": "lines 15735-15810", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-87/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-87/", "snippets": [ "... phase relation of the alternating current supplied by the converter; that is, the converter receives power from the direct-current system, and supplies power into the alter- nating-current system but at the same time receives wattless current from the alternating system, lagging at under-excitation, leading at over-excitation, and can in the same way as an ordinary converter or synchronous motor be used to compensate for watt- less currents in other parts of the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-95", "section_label": "Apparatus Section 1: Alternating-current Transformer: General", "section_title": "Alternating-current Transformer: General", "kind": "apparatus-section", "sequence": 95, "number": 1, "location": "lines 16804-16911", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-95/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-95/", "snippets": [ "... reactance x consume voltage in primary and secondary wind- ings. The voltage consumed by the resistance represents waste of power; the voltage consumed by reactance is wattless, but causes lag of current, that is, lowers the power factor; while the in- duced voltages give the power transfer from primary to sec- ondary. Efficiency therefore requires to make the former vol- tages as small as possible, and the induced voltages as near to the terminal voltages a ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-09", "section_label": "Chapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "section_title": "Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 4674-6992", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-09/", "snippets": [ "... ctice. It is interesting to note, from Fig. 60, that the largest part of the drop of potential due to inductive reactance, and rise to condensive reactance — or conversely — takes place between r = 1.0 and r = 0.9; or, in other words, a circuit having a power-factor cos 6 = 0.9 gives a drop several times larger than a non-inductive circuit, and hence must be considered as an inductive circuit. 3. Impedance in Series with a Circuit 58. By the use of reactance for controlling electric circuits, a certain amount of r ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-16", "section_label": "Chapter 16: Power, And Double-Frequency Quantities In", "section_title": "Power, And Double-Frequency Quantities In", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 16077-16520", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-16/", "snippets": [ "... tages in graphical or sijmbolic representation. 182 ALTERNATING-CURRENT PHENOMENA The graphical methods of treatment of alternating-current phenomena are here extended to include double-frequency quantities, as power, torque, etc. 2? = p- = cos 6 — power-factor. P' q = p- = sin 6 ^ induction factor ■* a of the circuit, and the general expression of power is P = Pa(p-\\- jq) = Pa (cos 9 -\\-j sin 6). 137. The introduction of the double-frequency vector product, P = [EI], brings us outside of the limits of a ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-22", "section_label": "Chapter 22: Armature Reactions Of Alternators", "section_title": "Armature Reactions Of Alternators", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 23971-25134", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-22/", "snippets": [ "... , i, as abscissas, at constant field-excitation, that is, constant nominal generated e.m.f., eo, for the constants Co = 2500 volts; x'o =10 ohms; r = 1 ohm; x'\\ = 4 ohms; for non-inductive load E = e, (Curve I.) and for inductive load of 60 per cent, power-factor, E = e (0.6 -\\- 0.8 j.) (Curve II.) For comparison are plotted in the same figure, in dotted lines, the regulation curves for constant synchronous reactance Xo = 10 ohms, that is, for the same open-circuit voltage and same short-circuit current. As ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... 60 of current, 21 by synchronous condenser, 339 in synchronous motor, demag- netizing, 261 Leakage, 112, 151 ' currents through dielectric, 152 in transformer, 189 of line, 174 reactance of transformer, 187 Line capacity, 169 phase control, 99 power factor control, 99 topographic characteristic, 43 Load curves of synchronous motor, 333 Magnetic cycle, 114 hysteresis, 112 Magnetizing current, 117 Maximum output of inductive line, 83 non-inductive circuit and in- ductive line, 81 478 INDEX Max ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1224-1727", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "snippets": [ "... quently, as in circuits containing iron, or in electrolytic conductors, upon the E.M.F. also. Hence, while the effective resist- ance, /', refers to the energy component of E.M.F., or the E.M.F. in phase with the current, the reactance, ;r, refers to the wattless component of E.M.F., or the E.M.F. in quadrature with the current. 3. The principal sources of reactance are electro-mag- netism and capacity. ELECTRO-MAGNETISM, An electric current, /, flowing through a circuit, produces a magnetic flux surrounding the conduc ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-13", "section_label": "Chapter 13: Ths Alternating^Cnrrent Traxsfobmer", "section_title": "Ths Alternating^Cnrrent Traxsfobmer", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 12673-14088", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "snippets": [ "... current c^ as abscis- sae, the values : secondary terminal voltage, in volts, secondary drop of voltage, in per cent, primary current, in amps, excess of primary current over proportionality with secondary, in per cent, primary angle of lag. The power-factor of the transformer, cos w^, is .45 at open secondary circuit, and is above .99 from 25 amperes, upwards, with a maximum of .995 at full load. ALTERNATING-CURRENT TRANSFORMER, 193" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-15", "section_label": "Chapter 15: Induction Motob", "section_title": "Induction Motob", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 14919-17024", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "snippets": [ "... essarily, it is T e shifted, as in a reversible motor. this necessitates the use of a strong field and weak armature to keep down the magnetic flux at the brushes. In the alternating- current motor the m ...", "... brushes, overcompensation in front of the field Fio. 158. — Distribution of m.m.f. in compensated motor. poles. The local undercompensated armature reaction at the brushes generates an e.m.f. in the coil short-circuited under the brush, and therewith a short-circuit current of commutation and sparking. In the conductively compensated motor, this can be avoided by overcompensation, that is, raising the flat top of the compensating m.m.f. to the maximum armature m.m.f., but this results in a lowering of the power-facto ...", "... or in the direction of the axis of the compensating winding, that is, at right angles (electrical) with the field flux. The field flux, *, depends upon and is in phase with the field current, except as far as it is modified by the magnetic action of the short-circuit current in the armature coil under the commu- tator brushes. In the conductively compensated series motor, 1, the quad- rature flux is zero at complete compensation, and in the direc- tion of the armature reaction with undercompensation, in oppo- sition ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2485-3386", "status": "candidate", "occurrence_count": 63, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-04/", "snippets": [ "... tray field (self-inductive reactance), etc., of the apparatus, resulting from the air gap in the magnetic circuit. 19. As instance of the use of the single-energy transient in engineering calculations may be considered the investigation of the momentary short-circuit phenomena of synchronous alter- nators. In alternators, especially high-speed high-power ma- chines as turboalternators, the momentary short-circuit current may be many times greater than the final or permanent short- circuit current, and this excess curr ...", "... e single-energy transient in engineering calculations may be considered the investigation of the momentary short-circuit phenomena of synchronous alter- nators. In alternators, especially high-speed high-power ma- chines as turboalternators, the momentary short-circuit current may be many times greater than the final or permanent short- circuit current, and this excess current usually decreases fairly slowly, lasting for many cycles. At the same time, a big cur- rent rush occurs in the field. This excess field current s ...", "... investigation of the momentary short-circuit phenomena of synchronous alter- nators. In alternators, especially high-speed high-power ma- chines as turboalternators, the momentary short-circuit current may be many times greater than the final or permanent short- circuit current, and this excess current usually decreases fairly slowly, lasting for many cycles. At the same time, a big cur- rent rush occurs in the field. This excess field current shows curious pulsations, of single and of double frequency, and in the beginn ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2162-2971", "status": "candidate", "occurrence_count": 58, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "snippets": [ "... tray field (self-inductive reactance), etc., of the apparatus, resulting from the air gap in the magnetic circuit. 19. As instance of the use of the single-energy transient in engineering calculations may be considered the investigation of the momentary short-circuit phenomena of synchronous alter- nators. In alternators, especially high-speed high-power mar chines as turboalternators, the momentary short-circuit current may be many times greater than the final or permanent short- circuit current, and this excess curr ...", "... e single-energy transient in engineering calculations may be considered the investigation of the momentary short-circuit phenomena of synchronous alter- nators. In alternators, especially high-speed high-power mar chines as turboalternators, the momentary short-circuit current may be many times greater than the final or permanent short- circuit current, and this excess current usually decreases very slowly, lasting for many cycles. At the same time, a big cur- rent rush occurs in the field. This excess field current sho ...", "... investigation of the momentary short-circuit phenomena of synchronous alter- nators. In alternators, especially high-speed high-power mar chines as turboalternators, the momentary short-circuit current may be many times greater than the final or permanent short- circuit current, and this excess current usually decreases very slowly, lasting for many cycles. At the same time, a big cur- rent rush occurs in the field. This excess field current shows curious pulsations, of single and of double frequency, and in the beginnin ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-36", "section_label": "Chapter 14: Short-Circuit Currents Of Alternators", "section_title": "Short-Circuit Currents Of Alternators", "kind": "chapter", "sequence": 36, "number": 14, "location": "lines 14549-15353", "status": "candidate", "occurrence_count": 48, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-36/", "snippets": [ "CHAPTER XIV. SHORT-CIRCUIT CURRENTS OF ALTERNATORS. 112. The short-circuit current of an alternator is limited by armature reaction and armature self-inductance; that is, the current in the armature represents a m.m.f. which with lagging current, as at short circuit, is demagnetiz ...", "CHAPTER XIV. SHORT-CIRCUIT CURRENTS OF ALTERNATORS. 112. The short-circuit current of an alternator is limited by armature reaction and armature self-inductance; that is, the current in the armature represents a m.m.f. which with lagging current, as at short circuit, is demagnetizing or opposing the impressed m.m.f. of field exc ...", "CHAPTER XIV. SHORT-CIRCUIT CURRENTS OF ALTERNATORS. 112. The short-circuit current of an alternator is limited by armature reaction and armature self-inductance; that is, the current in the armature represents a m.m.f. which with lagging current, as at short circuit, is demagnetizing or opposing the impressed m.m.f. of field excitation, and by combining therewith to a resultant m.m.f. reduces the magnetic flux from that corre- sponding to the field excitation to that corresponding to the resultant of field excitation ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-38", "section_label": "Apparatus Section 17: Synchronous Machines: Short-circuit Currents of Alternators", "section_title": "Synchronous Machines: Short-circuit Currents of Alternators", "kind": "apparatus-section", "sequence": 38, "number": 17, "location": "lines 10190-10429", "status": "candidate", "occurrence_count": 35, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-38/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-38/", "snippets": [ "XVII. Short-circuit Currents of Alternators 31. The short-circuit current of an alternator at full-load excitation usually is from two to five times full-load current, and even less in very large high-speed steam turbine alternators. It is w ...", "XVII. Short-circuit Currents of Alternators 31. The short-circuit current of an alternator at full-load excitation usually is from two to five times full-load current, and even less in very large high-speed steam turbine alternators. It is where EQ = nominal generated e.m.f., ZQ = sync ...", "... mpe- dance of alternator, representing the combined effect of arma- ture reaction and armature self-inductance. In the first moment after short circuiting, however, the current frequently is many times larger than the permanent short- circuit current, that is, where z = self-inductive impedance of the alternator. That is, in the first moment after short circuiting the poly- phase alternator the armature current is limited only by the arma- ture self-inductance, ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-13", "section_label": "Chapter 15: Synchronous Rectifier", "section_title": "Synchronous Rectifier", "kind": "chapter", "sequence": 13, "number": 15, "location": "lines 18413-19373", "status": "candidate", "occurrence_count": 31, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-13/", "snippets": [ "... cycle supply. Single-phase synchronous motors were started by such recti- fying commutators through which the field current passed, in series with the armature, and the first long-distance power trans- o Fio. 79. — Open-circuit rectifier. Fig. 80. — Short-circuit rectifier. mission in America (Telluride) was originally operated with single-phase machines started by rectifying commutator — the commutator, however, requiring frequent renewal. 139. The reversal of connection between the rectified circuit and the s ...", "... operated with single-phase machines started by rectifying commutator — the commutator, however, requiring frequent renewal. 139. The reversal of connection between the rectified circuit and the supply circuit may occur either over open-circuit, or over short-circuit. That is, either the rectified circuit is first disconnected from the supply circuit — which open-circuits both — and then connected in reverse direction, or the rectified circuit is connected to the supply circuit in reverse direction, before being disco ...", "... first disconnected from the supply circuit — which open-circuits both — and then connected in reverse direction, or the rectified circuit is connected to the supply circuit in reverse direction, before being disconnected in the previous direction — which short-circuits both circuits. The former, open-circuit rectification, results if the width of the gap between the commutator segments is greater than the width of the brushes, Fig. 79, the latter, short-circuit rectification, results if the width of the gap is less than ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 27, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... curve I — then any tendency of the current to increase — as by a momentary drop of the arc resistance — would lower the required arc voltage, and so increase the cur- rent, at constant supply voltage, hence still further lower the arc voltage, etc., and a short circuit would result. Vice versa, a momentary decrease of arc current, by requiring more volt- age than is available, would still further decrease the current, increase the required voltage, etc., and the arc would extin- guish. Therefore only such apparatus is ...", "... second ; and the effect of the oscillations in the system therefore varies accordingly: from the relatively harmless static displays; brush discharges, streamers, sparks, etc., of extremely high frequencies, down to the disastrous high power low frequency short circuit oscillations, in which even in 10,000 volt system*^, currents ^i many thousands of amperes may surge, which voltages approaching 100,000, and with which no protective device can cope, which does not have unlimited discharge capacity, that is, contains no ...", "... be as small as per- missible without causing a voltage rise due to the resistance of the discharge path. At the same time, the protective devices must be able to discharge practically unlimited currents, that is, currents of the magnitude of the momentary short circuit current of the system. This obviously requires that the pro- tective devices should have no appreciable resistance in the discharge path. Any lightning arrester containing series resistance obviously fails to protect as soon as the discharge current is s ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-06", "section_label": "Chapter 6: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 11051-12221", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-06/", "snippets": [ "... mechanical forces. In the large appara- tus, operating in the modern, huge, electric generating systems, these mechanical forces due to magnetic fields may, however, especially imder abnormal, though not infrequently occurring, conditions of operation (as short-circuits), assume such formi- dable values, so far beyond the normal mechanical strains, as to re- quire consideration. Thus generators and large transformers on big generating systems have been torn to pieces by the magnetic mechanical forces of short-circuits, c ...", "... as short-circuits), assume such formi- dable values, so far beyond the normal mechanical strains, as to re- quire consideration. Thus generators and large transformers on big generating systems have been torn to pieces by the magnetic mechanical forces of short-circuits, cables have been torn from ijieir supports, disconnecting switches blown open, etc. In the following, a general study of these forces will be given. This also gives a more rational and thereby more accurate de- 91 92 ELECTRIC CIRCUITS sign of the ...", "... ent. In this manner, it becomes possible, for instance, to express the mechanical work and thereby the pull of an alternating electromagnet, by simple expressions of voltage and current, or to give the mechanical strains occurring in a transformer under short-circuits, by an expression containing only the terminal voltage, the short-circuit current, and the distance between primary and secondary coils, without entering into the details of the construction of the apparatus. This general method, based on the law of cons ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-01-recommendations", "section_label": "Report Section 2: Recommendations", "section_title": "Recommendations", "kind": "report-section", "sequence": 2, "number": 2, "location": "PDF pages 7-12, lines 145-720", "status": "pdf-text-extracted-candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "snippets": [ "... the size of the system and especially due to the increasing interconnection of substations by tie cables. While such interconnection materially increases the economy in the use of the cables, it also increases the severity and extent of local troubles such as short circuits. Further- more, many of the controlling devices are not new any more. While it is economically not feasible to replace or remodel the con- trolling devices every few years with every advance of the art, it probably is economically feasible to do so with regar ...", "... rt, it probably is economically feasible to do so with regard to the con- trolling devices located in the generating stations proper. 2.) To study the possibility of intercepting many of the troubles in their beginning, before they have fully developed into a short circuit. Cable breakdowns apparently are not always instantaneous, but often [[END_PDF_PAGE:7]] [[PDF_PAGE:8]] Report of Charles P. Steinmetz develop gradually within a time from a few seconds to many days. A sufficiently sensitive differential relay thus may discov ...", "... stand that simple devices for getting high voltage direct current for testing purposes have been developed. 3.) To cut off the troubles from the generating stations by the in- stallation of feeder reactances. By far the largest majority of troubles leading to short circuit occur in the feeder cables and beyond them, in the substations, but very few only in the generators, and extremely few on the busbars. The gen- erators have power limiting reactors, but no power limiting reactors are used in the feeders, and as the result, an ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-22", "section_label": "Chapter 22: Armature Reactions Of Alternators", "section_title": "Armature Reactions Of Alternators", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 23971-25134", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-22/", "snippets": [ "... usts itself only gradually to the change of circuit conditions, at a rate of speed depending upon the constants of the field-exciting circuit, etc. The extreme case hereof takes place when suddenly short- circuiting an alternator; at the first moment the short-circuit current is limited only by the self-inductance, and the magnetic field still has full strength, the field-exciting current has greatly increased by the e.m.f. generated in the field circuit by the arma- ture reaction. Gradually the field-exciting current ...", "... s full strength, the field-exciting current has greatly increased by the e.m.f. generated in the field circuit by the arma- ture reaction. Gradually the field-exciting current and there- with the field magnetism die down to the values corresponding to the short-circuit condition. Thus the momentary short- circuit current of an alternator is far greater than the perma- nent short-circuit current; many times in a machine of low self-induction and high armature reaction, as a low-frequency, high-speed alternator of large c ...", "... has greatly increased by the e.m.f. generated in the field circuit by the arma- ture reaction. Gradually the field-exciting current and there- with the field magnetism die down to the values corresponding to the short-circuit condition. Thus the momentary short- circuit current of an alternator is far greater than the perma- nent short-circuit current; many times in a machine of low self-induction and high armature reaction, as a low-frequency, high-speed alternator of large capacity; relatively little in a machine of lo ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... circuit section of high inductance and small resistance and negligible capacity and conductance, as a generating station, with a circuit of distributed capacity and inductance, as a transmission line. The extreme case of such a discharge would occur if a short circuit at the busbars of a gen- erating station opens while the transmission line is connected to the generating station. Let r = the total resistance and L = the total inductance of the inductive section of the circuit; also let g = 0, C= 0, and L0 = inductan ...", "... m 131 machine 230 as rectifier 221 current control 220 properties 249 rectification 249 rectifiers 222 resistivities 9 starting 249 Arcing ground on lines and cables, as periodic transient phenomenon . . 23 Armature reactance, reaction and short-circuit current of alternator 199 Attenuation of alternating magnetic flux in iron 361 constants 434 of traveling wave, and loading 462 Booster, response to change of load 158 Brush arc machine 221, 230, 242, 248 Building up of direct-current generator 32 ...", "... Booster, response to change of load 158 Brush arc machine 221, 230, 242, 248 Building up of direct-current generator 32 of overcompounded direct-current machine 49 Cable, high-potential underground, standing waves 452 opening under load 112, 118 short-circuit oscillation 113, 118 starting 111,117 transient terms and oscillations 98, 102 561 562 INDEX PAGE Capacity, also see Condenser. and inductance, equations 48 and velocity of propagation 400, 401 distributed series 348 energy of complex cir ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-03-record", "section_label": "Report Record 4: Record of Four Troubles", "section_title": "Record of Four Troubles", "kind": "report-record", "sequence": 4, "number": 4, "location": "PDF pages 16-27, lines 1139-2164", "status": "pdf-text-extracted-candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-03-record/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-03-record/", "snippets": [ "... rs stated to be 1.75 ohms each, between Fisk A and Quarry Street, and between Quarry Street and Fisk B, and six tie cables of negligible reactance and about .3 ohms joint resistance between Fisk B and the Northwest Station. 1.) Sept. 18th, 19193:47 P. M. a) A short circuit close to the busbars of B section of Fisk Street held on for several seconds, before it was opened. As there are no power limiting reactors between Fisk B and North- west Station, and the six tie cables between these stations are of very low resistance, the N ...", "... ded as shut down. Of 26 machines on Fisk A, 12 dropped out and 14 stayed in; of 8 machines on Quarry Street, 4 dropped out and 4 stayed in. [[END_PDF_PAGE:16]] [[PDF_PAGE:17]] Report of Charles P. Steinmetz 11 c) Due to the voltage dropping to zero under the short circuit, the turbo-alternators in Fisk B and Northwest Station dropped out of syn- chronism with each other, and out of synchronism with Quarry Street and Fisk A; but Quarry Street and Fisk A remained in synchronism with each other. d) Due to the load being taken off ...", "... ch other, with practically zero voltage at the busbars, for six minutes longer. Then the voltage suddenly came back, the alternators in Fisk B pulling into synchronism with each other and with the one remaining (20,000 KW) machine in Northwest. Remarks : a) A short circuit at the busbars of a station section, pulling the voltage down to zero, necessarily must drop out all the synchronous machines on this section, unless the short circuit is opened so quickly, that the synchronous machines during the period of zero voltage did n ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-02-discussion-of-recommendations", "section_label": "Report Section 3: Discussion of Recommendations", "section_title": "Discussion of Recommendations", "kind": "report-section", "sequence": 3, "number": 3, "location": "PDF pages 12-16, lines 721-1138", "status": "pdf-text-extracted-candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-02-discussion-of-recommendations/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-02-discussion-of-recommendations/", "snippets": [ "... uld greatly reduce the frequency of troubles or keep them out of the generating system by isolating or localizing them by the feeder reactors, it obviously is not possible to absolutely guard against the occasional troubles in the generating sys- tem, such as short circuits. But as soon as the trouble is cleared as by the opening of the circuit breakers, in a second or a few seconds, the system should immediately return to normal, and to begin to pick up again the load which the short circuit dropped. The most serious feature of ...", "... in the generating sys- tem, such as short circuits. But as soon as the trouble is cleared as by the opening of the circuit breakers, in a second or a few seconds, the system should immediately return to normal, and to begin to pick up again the load which the short circuit dropped. The most serious feature of the troubles of September 18th, May 19th, and October 22nd, in my opinion, was that with the clearing of the short circuit, the sys- [[END_PDF_PAGE:12]] [[PDF_PAGE:13]] Report of Charles P. Steinmetz tern did not promptly ...", "... s, the system should immediately return to normal, and to begin to pick up again the load which the short circuit dropped. The most serious feature of the troubles of September 18th, May 19th, and October 22nd, in my opinion, was that with the clearing of the short circuit, the sys- [[END_PDF_PAGE:12]] [[PDF_PAGE:13]] Report of Charles P. Steinmetz tern did not promptly come back to normal voltage, but in a large part of the system (Fisk Street B and Northwest) the voltage remained practically zero for about a quarter of an ho ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-30", "section_label": "Chapter 8: Low Frequency Surges In High Potential Systems", "section_title": "Low Frequency Surges In High Potential Systems", "kind": "chapter", "sequence": 30, "number": 8, "location": "lines 7826-9227", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "snippets": [ "... ful in their weakening action on the insulation and the possibility of their starting a low frequency surge. The former ones only are considered in the present chapter. Their causes may be manifold, — changes of circuit conditions, as starting, opening a short circuit, existence of a flaring arc on the system, etc. In the circuit from the generating system to the capacity of the transmission line or the underground cables, we have always r2 < —j-; that is, the phenomenon is always oscillatory, and (_/ equations (2 ...", "... ting it to the impressed e.m.f., this term disappears. It is this component which may cause excessive potential differences. Two cases shall more fully be discussed, namely : (a) Opening the circuit of a transmission line under load, and (6) rupturing a short-circuit on the transmission line. 67. (a) If iQ is the instantaneous value of full-load current, e0 the instantaneous value of difference of potential at the condenser, n0 is small compared with e0, and \\/~xxc iQ is of the same magnitude as e0. Writing and ...", "... , while capacity exerts a cushioning effect. Low inductance and high capacity thus are of advantage when breaking full-load current in a circuit. 68. (6) If a transmission line containing resistance, induc- tance, and capacity is short-circuited, and the short-circuit suddenly opened at time t = 0, we have, for t < 0, and where and ET I =-COS (d - 0Q - y), tan y = -; (19) 114 TRANSIENT PHENOMENA thus, at time t = 0, _ E z (20) Substituting these values of e0 and i0 in equations (9) give ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-08", "section_label": "Lecture 8: Generation", "section_title": "Generation", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 3781-4217", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-08/", "snippets": [ "... armature reaction considered, but which is increased to allow for the self-induction. The last way (armature reaction), is used in designing machines; the second way (synchronous reactance) in calcula- tions with machines and systems. In the momentary short circuit current of alternators, however, the armature reaction and the self-induction must be considered separately, since they act differently. In the moment of short circuiting an alternator, the self- induction acts immediately in limiting the current, but no ...", "... he field poles, and retards the decrease of field magnetism resulting from the demagnetizing action of the armature current by inducing a current in the field winding, which tends to main- tain the field magetism. Therefore in the first moment after the short circuit the armature current is limited by self-induction only, and is therefore much larger than afterwards, when self-induction and armature reaction both act. In machines of low armature reaction and high self- induction, as high frequency alternators, the m ...", "... ature current is limited by self-induction only, and is therefore much larger than afterwards, when self-induction and armature reaction both act. In machines of low armature reaction and high self- induction, as high frequency alternators, the momentary short circuit current is not much larger than the permanent short circuit current. In machines of low self-induction, that is, of a well distributed armature winding, but high armature reac- tion, (that is, very large output per pole, as in steam turbine alternators,) ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-12", "section_label": "Chapter 14: Phase Conversion And Single-Phase Generation", "section_title": "Phase Conversion And Single-Phase Generation", "kind": "chapter", "sequence": 12, "number": 14, "location": "lines 17125-18412", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-12/", "snippets": [ "... ^ im. X Fia. 68. — Resist ance-inductance monocyclic square, regulation curve. For: q = 0, that is, non-inductive load, the voltage diagram is a curve shown by circles in Fig. 67, for 0, 2, 4, 6, 8 and 10 amp. load, the latter being the maximum or short-circuit value. For q = p, or a load of 45° load, the voltage diagram is the straight line shown by crosses in Fig. 67. That is, in this case, the monocyclic voltage, eB, is in quadrature with the supply voltage, 220 ELECTRICAL APPARATUS f,;it ;ill toads, ...", "... , which is in phase with e, and therefore could he neutralised by inserting into 6o a part of the voltage, e, by transformation. As seen in Fig. 68, the supply current is a maximum of 20 amp. at no-load, and decreases with increasing load, to 10 amp. at short-circuit load. The apparent efficiency of the device, that is, Ihe ratio of the volt-ampere output: Qa = eni„ to the volt-ampere input: Q = ei is given by the curve, y, in Fig. 68. As seen, the apparent efficiency is very low, reaching a maxi- mum of 14 pe ...", "... e average power-factor of au inductiou motoi . 224 ELECTRICAL APPARATUS It is, then, substituted into (11) to (13): . _ _ioo *■ (1.062 + 0.52 a) + j (0.36 a - 0.0 .r 80j)«L = 0, or no-load, this gives: es = 94.1, li - 0, I, - 19.5; = ™, or short-circuit, this gives: ei - 0, i, - 159, The voltage diagram is shown in Fig. 70, and the load char- acteristics or regulation curves in Fig. 71. As seen: the voltage, e-t, is already at no-load lower than the supply voltage, e«, due to the drop of voltage of ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-14", "section_label": "Lecture 14: Alternating Current Railway Motor", "section_title": "Alternating Current Railway Motor", "kind": "lecture", "sequence": 14, "number": 14, "location": "lines 8649-9342", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-14/", "snippets": [ "... the turn short circuited under the brush by its rotation through the magnetic field. As this field, however, is alternating, an e. m. f. is induced in the short circuited turn by the alternations of the lines of magnetic force enclosed by it, and causes a short circuit current and in that way, sparking. This e. m. f., being due to the alternation of the enclosed field flux, is independent of the speed of rotation ; it also exists with the motor at a standstill, and is a maximum in the armature turn under the brush, as t ...", "... n is very large; if not limited by the resistance or reactance of the coil, it is as many times greater than the full load current, as the field coil has turns. This causes serious sparking, if not taken care of. One way of mitigating the effect of this short circuit cur- rent is to reduce it by interposing resistance or reactance ; that is by making the leads between the armature turns and the commutator bars of high resistance or high reactance. Obvi- ously this arrangement can merely somewhat reduce the spark- 1 ...", "... e of the transformer field of the repul- sion motor, F*, with the required commutating field Fo, it is seen that at synchronism No = N, F* = F© ; that is, the trans- former field of the repulsion motor has the proper value as commutating field, so that no short circuit current is produced in ithe armature turn under the brush, but the commutation is as good as in a direct current motor with negligible armature reaction. At half synchronism, No = 2 ^' ^^^ transformer field of the repulsion motor : F^ = ^ F, is only one ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-102", "section_label": "Apparatus Section 5: Alternating-current Transformer: Short-circuit Current", "section_title": "Alternating-current Transformer: Short-circuit Current", "kind": "apparatus-section", "sequence": 102, "number": 5, "location": "lines 18398-18460", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-102/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-102/", "snippets": [ "V. Short-circuit Current 120. If a short circuit occurs at the secondary terminals of a transformer, and the power supply at the primary is sufficient to maintain the primary terminal voltage, the primary and second- ary currents of the t ...", "V. Short-circuit Current 120. If a short circuit occurs at the secondary terminals of a transformer, and the power supply at the primary is sufficient to maintain the primary terminal voltage, the primary and second- ary currents of the transformer are limited by its impe ...", "... nt to maintain the primary terminal voltage, the primary and second- ary currents of the transformer are limited by its impedance only. Thus, if r = P + j* is the impedance voltage, as fraction of full-load voltage, the short- circuit current of the transformer is 1 1 of the full-load current, thus usually is very large. In the three instances illustrated in Figs. 157, 159 and 160, with f = 0.02 + 0.02 j, hence f =0.028 0.01 + 0.04 j 0.04 ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-43", "section_label": "Chapter 3: The Natural Period Of The Transmission Line", "section_title": "The Natural Period Of The Transmission Line", "kind": "chapter", "sequence": 43, "number": 3, "location": "lines 21721-23178", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "snippets": [ "... os 0 sm r + - — + [-•••{» o 5 ) in volts. 33. As further example, assume now that this line is short- circuited at one end, I = 0, while supplied with 25-cycle alter- nating power at the other end, I = /0, and that the generator voltage drops, by the short circuit, to 30,000, and then the line cuts off from the generating system at about the maximum value of the short-circuit current, that is, at the moment of zero value of the impressed e.m.f. At a frequency of /0 = 25 cycles, the reactance per unit length of li ...", "... ed at one end, I = 0, while supplied with 25-cycle alter- nating power at the other end, I = /0, and that the generator voltage drops, by the short circuit, to 30,000, and then the line cuts off from the generating system at about the maximum value of the short-circuit current, that is, at the moment of zero value of the impressed e.m.f. At a frequency of /0 = 25 cycles, the reactance per unit length of line or per mile is x = 2 TT/OL = 0.188 ohm and the impedance is z = Vr2 + x* = 0.283 ohm, or, for the total lin ...", "... he impressed e.m.f. At a frequency of /0 = 25 cycles, the reactance per unit length of line or per mile is x = 2 TT/OL = 0.188 ohm and the impedance is z = Vr2 + x* = 0.283 ohm, or, for the total line, z0 = I0z = 56.6 ohms; hence, the approximate short-circuit current e 30,000 and its maximum value is i0 - 530 X \\/2 = 750 amp. Therefore, in equations (26), at time t = 0, or 0 = 0, e= 0 for all values of T except T = — ; hence, Zi sin (2 n - 1) yn = 0, or, yn - 0, 332 TRANSIENT PHENOMENA and thus ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-13", "section_label": "Chapter 13: Reactance Of Synchronous Machines", "section_title": "Reactance Of Synchronous Machines", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 23466-24022", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-13/", "snippets": [ "... energy stored in the machine, the magnetic energy of the result- ant field, Fig. 112, comes into consideration, and not the — ^much REACTANCE OF SYNCHRONOUS MACHINES 237 larger — energy, which the fields corresponding to e© and Xo would have. Thus the short-circuit transient of a heavily loaded ma- chine is essentially the same as that of the same machine at no- load, with the same terminal voltage, although in the former the field excitation and the nominal induced voltage may be very much larger. The use of the ...", "... . The reverse is the case at a sudden decrease of armature current. The extreme case hereof is fbund in the momentary short-cir- cuit currents of alternators,^ which with some types of machines may momentarily equal many times the value of the permanent short-circuit current. However, this phenomenon is not limited to short-circuit conditions only, but every change of ciurent in an alternator causes a momentary overshooting, the more so, the greater and more sudden the change is. 122. That part of the synchronous rea ...", "... . The extreme case hereof is fbund in the momentary short-cir- cuit currents of alternators,^ which with some types of machines may momentarily equal many times the value of the permanent short-circuit current. However, this phenomenon is not limited to short-circuit conditions only, but every change of ciurent in an alternator causes a momentary overshooting, the more so, the greater and more sudden the change is. 122. That part of the synchronous reactance, Xoj which is due to the magnetic lines, a, in Fig. Ill, is ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-07", "section_label": "Lecture 7: High Frequency Oscillations And Surges", "section_title": "High Frequency Oscillations And Surges", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3508-3780", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-07/", "snippets": [ "... ion, that is, its voltage and current, are the greater, the greater or more abrupt the change was in the circuit, which caused the oscillation by requiring a readjustment of the energy storage. The greatest change in a circuit, however, is the change from short circuit to open circuit, and the instantaneous opening of a short circuit on a transmission line — as it occasionally occurs by the sudden rupture of a short circuiting arc — ^therefore gives rise to the most powerful, and thereby most destructive oscillation. ...", "... r or more abrupt the change was in the circuit, which caused the oscillation by requiring a readjustment of the energy storage. The greatest change in a circuit, however, is the change from short circuit to open circuit, and the instantaneous opening of a short circuit on a transmission line — as it occasionally occurs by the sudden rupture of a short circuiting arc — ^therefore gives rise to the most powerful, and thereby most destructive oscillation. The wave length of oscillation thus depends on the length of the c ...", "... e of a short circuiting arc — ^therefore gives rise to the most powerful, and thereby most destructive oscillation. The wave length of oscillation thus depends on the length of the circuit in which the stored energy readjusts itself. For instance, in the short circuit oscillation of the system, the wave extends over the entire circuit, including generators and trans- formers ; and the entire circuit so represents one wave, or one- half wave, that is, the wave length is very considerable. If the readjustment of stored e ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-11", "section_label": "Lecture 11: Lightning Protection", "section_title": "Lightning Protection", "kind": "lecture", "sequence": 11, "number": 11, "location": "lines 4931-5294", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-11/", "snippets": [ "... the circuit conductors and the ground. When, however, electric light and power circuits made their appearance, this protection against lightning by a simple small spark gap to ground became insufficient, and this addi- tional problem arose : to open the short circuit of the machine current, which resulted from and followed the lightning dis- charge. This problem of opening the circuit after the discharge was solved by the magnetic blow-out, which is still used to a large extent on 500 volt railway circuits; by the h ...", "... half wave, but the arrester held an arc and burned up. Furthermore, the introduction of synchronous motors, and of parallel operation of generators, made it essential that the lightning arrester should open again instantly after dis- charge. For, if the short circuit current over the arrester lasted for any appreciable time: a few seconds, synchronous motors and converters dropped out of step, the generators broke their S3mchronism, and the system in this way would be shut down. The horn gap arrester, in which the arc ...", "... ke care of excessive currents, and such currents produce damage only in those instances where they occur at the moment of opening or closing a switch, by burning con- tacts, or where the mechanical forces exerted by them are dangerously large, as with the short circuit currents of the modern huge turbo-generators. 140 GENERAL LECTURES Excessive voltage, however, is practically instantaneous in its action, and the problem of lightning protection therefore is essentially that of protecting against excessive voltages. ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-101", "section_label": "Apparatus Section 4: Alternating-current Transformer: Regulation", "section_title": "Alternating-current Transformer: Regulation", "kind": "apparatus-section", "sequence": 101, "number": 4, "location": "lines 17538-18397", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-101/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-101/", "snippets": [ "... e sum of the primary and the secondary re- actance, the latter reduced to the primary by the ratio of trans- formation : Xi + a2x2. 116. The total reactance of primary and secondary, and also TRANSFORMER I mpedance and Short Circuit Losses 7 .1 .2 .3 .1 .5 .6 .7 .8 .9 1.0 1.1 1.2 1.3 l.i 1.5 FIG. 156. — Impedance and short circuit losses of transformer. the total (effective) resistance o ...", "... mary and secondary, and also TRANSFORMER I mpedance and Short Circuit Losses 7 .1 .2 .3 .1 .5 .6 .7 .8 .9 1.0 1.1 1.2 1.3 l.i 1.5 FIG. 156. — Impedance and short circuit losses of transformer. the total (effective) resistance of primary and secondary winding are measured by impressing voltage on the primary coil, with the secondary winding short-circuited, and measuring volts, amperes and watt ...", "... lts, amperes and watts. In this test the voltage usually is impressed upon the high voltage winding, as the impedance voltage is only a small part of the operating voltage of the transformer. Such \"impedance curves\" and \"short-circuit loss curves\" for the transformers in Figs. 154 and 155 are shown in Fig. 156. If the short-circuit loss is greater than the sum of primary and ALTERNA TING-CURRENT TRANSFORMER 287 secondary izr losses, the differenc ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-39", "section_label": "Chapter 3: Mechanical Rectification", "section_title": "Mechanical Rectification", "kind": "chapter", "sequence": 39, "number": 3, "location": "lines 15963-17754", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-39/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-39/", "snippets": [ "... respectively. The terminals are reversed. The shunt-resistance circuits are opened, leaving the circuits in series in opposite direction. Special cases hereof are: 1. If r = r0 = 0, that is, during rectification both circuits are short circuited. Such short-circuit rectification is feasible only in limited-current circuits, as on arc lighting machines, or in * If the circuit is reversed at the moment when the alternating current passes zero, due to self-inductance of the rectified circuit its current differs from z ...", "... ved from an e.m.f. very large compared with the voltage consumed in the recti- fied circuit, feeds, after rectification, a circuit of impedance Z = r — jx. This circuit is permanently shunted by a circuit of resistance rr Rectification takes place over short- circuit from the moment n — 02 to TT + 0jj that is, at n - 02the rectified and the alternating circuit are closed upon themselves at the rectifier, and this short-circuit opened, after rever- sal, at TT + 6lf as shown by the dia- grammatic representation of a t ...", "... uit is permanently shunted by a circuit of resistance rr Rectification takes place over short- circuit from the moment n — 02 to TT + 0jj that is, at n - 02the rectified and the alternating circuit are closed upon themselves at the rectifier, and this short-circuit opened, after rever- sal, at TT + 6lf as shown by the dia- grammatic representation of a two- pole model of such a rectifier in Fig. 54. In this case the space angles TT -f TJ and TT — r2 and the time angles TT -f Ol and TT - 02 are identical. This re ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1659-2484", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-03/", "snippets": [ "... function of the time, in Fig. 11 A, the flux is constant and denoted by $0 up to the moment of *o I 1 ^^\"^^-5 A K-L__ B io 1 1 C ^0 />:^^^ 0 ^ ■ ' Fig. 11. — Characteristics of Magnetic Single-energy Transient. time where the short circuit is applied, as indicated by the dotted line ^0. From ^0 on the magnetic flux decreases, as shown by curve . Since the magnetic flux is proportional to the current, the latter must follow a curve proportional to $, as shown in Fig. 115. The impressed vo ...", "... ist in the circuit, proportional to the current. e = ri. SINGLE-ENERGY TRANSIENTS. 21 This is the e.m.f. induced by the decrease of magnetic flux $, and is therefore proportional to the rate of decrease of $, that is, to -J-. In the first moment of short circuit, the magnetic flux still has full value $o, and the current i thus also full value U. Hence, at the first moment of short circuit, the induced e.m.f. e must be equal to eo, that is, the magnetic flux $ must begin to decrease at such rate as to induce ...", "... of magnetic flux $, and is therefore proportional to the rate of decrease of $, that is, to -J-. In the first moment of short circuit, the magnetic flux still has full value $o, and the current i thus also full value U. Hence, at the first moment of short circuit, the induced e.m.f. e must be equal to eo, that is, the magnetic flux $ must begin to decrease at such rate as to induce full voltage eo, as shown in Fig. IIC The three curves $, ^, and e are proportional to each other, and as e is proportional to the ra ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1531-2161", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "snippets": [ "... coil circuit as i~r. Plotting, there- fore, the magnetic flux of the coil as function of the time, in Fig. 11 A, the flux is constant and denoted by $0 up to the moment of Fig. 11. — Characteristics of Magnetic Single-energy Transient. time where the short circuit is applied, as indicated by the dotted line t0. From t0 on the magnetic flux decreases, as shown by curve <£. Since the magnetic flux is proportional to the current, the latter must follow a curve proportional to <£, as shown in Fig. IIB. The impressed vo ...", "... e circuit, proportional to the current. e = ri. SINGLE-ENERGY TRANSIENTS. 21 This is the e.m.f. induced by the decrease of magnetic flux <£, and is therefore proportional to the rate of decrease of <£, that is, to d<& -j- . In the first moment of short circuit, the magnetic flux $ still has full value 3>0, and the current i thus also full value iQ. Hence, at the first moment of short circuit, the induced e.m.f. e must be equal to eQ, that is, the magnetic flux $ must begin to decrease at such rate as to induce ...", "... ic flux <£, and is therefore proportional to the rate of decrease of <£, that is, to d<& -j- . In the first moment of short circuit, the magnetic flux $ still has full value 3>0, and the current i thus also full value iQ. Hence, at the first moment of short circuit, the induced e.m.f. e must be equal to eQ, that is, the magnetic flux $ must begin to decrease at such rate as to induce full voltage e0, as shown in Fig. 11C. The three curves <£, i, and e are proportional to each other, and as e is proportional to the ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-04", "section_label": "Chapter 5: Methods Of Approximation", "section_title": "Methods Of Approximation", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 15156-16482", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-04/", "snippets": [ "... ent lamp circuit, then, ._ _ _ _ef /xV] ~2 m i^' e r If the resistance is small compared with the reactance, as is the case in a reactive coil, then, e e £' r /r \\- 1 2 Vf^+x^ TrV ^ -,V^)-\"-'© <^-w, (28) Example 2. How does the short-circuit current of an alternator vary with the speed, at constant field excitation? When an alternator is short circuited, the total voltage generated in its armature is consumed by the resistance and the synchronous reactance of the armature. The voltage gene ...", "... where a is the ratio of the actual speed, to that speed at which the generated voltage is eo- If r is the resistance of the alternator armature, xq the synchronous reactance at speed So, the synchronous reactance at speed Sh x = axo, and the current at short circuit then is i=^^=^ , \"■\"> (29) Usually r and xo are of such magnitude that r consumes at full load about 1 per cent or less of the generated voltage, while the reactance voltage of xq is of the magnitude of from 20 to 50 per cent. Thus r is small compared ...", "... small, equation (29) can be approximated by aeo eo 1 = \\ \\axoJ \\ 2 xo\\ 2 \\axoj axo^ /I 4-1 — 1 '-.Ki)T ■ ■ ™ ^ )/ Then if a:o = 20r, the following relations exist: a= 0.2 0.5 1.0 2.0 i = -X0.9688 0.995 0.99875 0.99969 That is, the short-circuit current of an alternator is practi- cally constant independent of the speed, and begins to decrease only at very low speeds. 131. Exponential functions, logarithms, and trigonometric functions are the ones frequently met in electrical engineering. The ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-06", "section_label": "Lecture 6: Higher Harmonics Of The Generator Wave", "section_title": "Higher Harmonics Of The Generator Wave", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3133-3507", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-06/", "snippets": [ "... r cure and prevention there- fore must be different, and the method of elimination of one may be very harmful with the other type of harmonics. For instance, the voltage produced by a constant current harmonic as coming from a transformer is eliminated by short circuit Short circuiting a generator harmonic, however, gives large 8o GENERAL LECTURES short circuit currents, due to the constant potential character, and is therefore dangerous. HIGHER HARMONICS OF SYNCHRONOUS MACHINES In synchronous machines, as alter ...", "... ery harmful with the other type of harmonics. For instance, the voltage produced by a constant current harmonic as coming from a transformer is eliminated by short circuit Short circuiting a generator harmonic, however, gives large 8o GENERAL LECTURES short circuit currents, due to the constant potential character, and is therefore dangerous. HIGHER HARMONICS OF SYNCHRONOUS MACHINES In synchronous machines, as alternating current genera- tors, the higher harmonics are : At No Load I St. The distribution of ma ...", "... elta connection of generator windings there- fore is unsafe. As a result, generator windings are almost always connected in Y, Even with delta connection of gener- ator windings no triple frequency appears at the terminals, since its voltage disappears by short circuit. If the generator winding is connected in Y, the triple frequency voltages from terminal to neutral are in phase with each other; that is, in a three-phase Y connected generator, a single-phase voltage of triple frequency exists between the neutral and ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-104", "section_label": "Apparatus Section 7: Alternating-current Transformer: Types of Transformers", "section_title": "Alternating-current Transformer: Types of Transformers", "kind": "apparatus-section", "sequence": 104, "number": 7, "location": "lines 18521-18665", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-104/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-104/", "snippets": [ "... al characteristics there is no essential difference between the single-phase shell- type and the single-phase core-type transformer, there is a material difference in the three-phase transformer. In the shell type, Fig. 168, a short circuit of one of the three phases does not affect the magnetic and thus the electric circuit of the other two phases, in the core type Fig. 169, however, a short circuit of one of the three phases short circuits the magnetic ...", "... three-phase transformer. In the shell type, Fig. 168, a short circuit of one of the three phases does not affect the magnetic and thus the electric circuit of the other two phases, in the core type Fig. 169, however, a short circuit of one of the three phases short circuits the magnetic return of the other two phases, and so acts as a partial electrical short circuit of these two other phases. In shell-type transformers, Fig. 168, a triple harmonic ...", "... Fig. 168, a short circuit of one of the three phases does not affect the magnetic and thus the electric circuit of the other two phases, in the core type Fig. 169, however, a short circuit of one of the three phases short circuits the magnetic return of the other two phases, and so acts as a partial electrical short circuit of these two other phases. In shell-type transformers, Fig. 168, a triple harmonic of flux can exist, but not in the core t ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-106", "section_label": "Apparatus Section 9: Alternating-current Transformer: Reactors", "section_title": "Alternating-current Transformer: Reactors", "kind": "apparatus-section", "sequence": 106, "number": 9, "location": "lines 18813-18948", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-106/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-106/", "snippets": [ "... y these reactances is 15 per cent, of the circuit voltage. 131. With the increasing size and increasing voltage of modern central stations and the use of high-speed turbo-alternators ca- pable of momentarily giving very high short-circuit currents, the amount of power, which can be developed momentarily by a short circuit in the system near the generating station, has reached such ALTERNATING-CURRENT TRANSFORMER 305 destructive values, that a limitation ...", "... size and increasing voltage of modern central stations and the use of high-speed turbo-alternators ca- pable of momentarily giving very high short-circuit currents, the amount of power, which can be developed momentarily by a short circuit in the system near the generating station, has reached such ALTERNATING-CURRENT TRANSFORMER 305 destructive values, that a limitation of this power has become necessary, and as economy of operation forbids sectionalizing ...", "... r-limiting reactances, in the generator leads, in the bus bars, tie feeders and even the power feeders. Such re- actances are used of 2' to 8 per cent., and in bus bars even up to 25 per cent., and in case of a local short circuit, limit the current which can flow. Thus a 4 per cent, reactance would at a short circuit just beyond the reactance limit the current to -r - = 4 per cent. 25 times the normal, etc. But to do so, the reactance must ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "section_label": "Chapter 14: Dielectric Losses", "section_title": "Dielectric Losses", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "... ty, D, increases proportional thereto, until a finite limiting field intensity, Kq, or voltage gradient, gfo, is reached, beyond which the dielectric cannot be stressed, but breaks down and becomes dynamically conduct- ing, that is, punctures, and thereby short-circuits the dielectric field. The voltage gradient, go, at which disruption of the dielectric occurs is called the \"disruptive strength\" or \"dielectric strength\" of the dielectric. With air at atmospheric pressure and temperature, it is go = 30 kv. per centimet ...", "... ent e Q I To illustrate on a numerical instance: Let the distance between the metal plates A and Bhel = 1 cm. With nothing but air at atmospheric pressure and temperature between the plates, the gap would break down by a spark dis- charge, and short-circuit the circuit of Fig. 96; at e = 30 kv. maximum, and at e = 25 kv., no discharge would occur. Assuming now two glass plates, a and b, each of 0.3 cm. thick- ness and permittivity /co = 4, were inserted, leaving an air-gap of 0.4 cm. of permittivity ki = 1. ...", "... g'o = 0, and the gradient in the glass plates thus would become : g\\ = ^ = 41.7 kv. per cm. Thus the insertion of the glass plates would cause the air-gap to break down. The dynamic current which flows through the air-gap in this case would not be the short-circuit current of the 164 AL TERN A TING-C URREN T PHENOMENA electric circuit, as would be the case in the absence of the glass plates but it would merely be the capacity current of the glass plates; and it would not be followed by the arc, but passes as ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3721-4369", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-06/", "snippets": [ "... rsely, fc ^0 = eo y Y = eo2/o. (11) This relation is very important, as frequently in double-energy transients one of the quantities eo or io is given, and it is impor- tant to determine the other. For instance, if a line is short-circuited, and the short-circuit current io suddenly broken, the maximum voltage which can be induced by the dissipation of the stored magnetic energy of the short-circuit current is eo = IoZq. If one conductor of an ungrounded cable system is grounded, the maximum momentary current wh ...", "... or io is given, and it is impor- tant to determine the other. For instance, if a line is short-circuited, and the short-circuit current io suddenly broken, the maximum voltage which can be induced by the dissipation of the stored magnetic energy of the short-circuit current is eo = IoZq. If one conductor of an ungrounded cable system is grounded, the maximum momentary current which may flow to ground is iQ = e^yo, where eo = voltage between cable conductor and ground. If lightning strikes a line, and the maximum vo ...", "... e proximity of the conductors in the former. A cable, therefore, when receiving the moderate or small oscillating cur- rents which may originate in a transformer, gives only very low DOUBLE-ENERGY TRANSIENTS. 63 oscillating voltages, that is, acts as a short circuit for the trans- former oscillation, and therefore protects the latter. Inversely, if the large oscillating current of a cable enters a reactive device, as a current transformer, it produces enormous voltages therein. Thus, cable oscillations are more liabl ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3287-3955", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "snippets": [ "... ersely, /C io = eo y j = e02/o. (11) This relation is very important, as frequently in double-energy transients one of the quantities e$ or i0 is given, and it is impor- tant to determine the other. For instance, if a line is short-circuited, and the short-circuit current IQ suddenly broken, the maximum voltage which can be induced by the dissipation of the stored magnetic energy of the short-circuit current is e0 = igZo. If one conductor of an ungrounded cable system is grounded, the maximum momentary current wh ...", "... or i0 is given, and it is impor- tant to determine the other. For instance, if a line is short-circuited, and the short-circuit current IQ suddenly broken, the maximum voltage which can be induced by the dissipation of the stored magnetic energy of the short-circuit current is e0 = igZo. If one conductor of an ungrounded cable system is grounded, the maximum momentary current which may flow to ground is io = eo2/o, where e0 = voltage between cable conductor and ground. If lightning strikes a line, and the maximum v ...", "... e proximity of the conductors in the former. A cable, therefore, when receiving the moderate or small oscillating cur- rents which may originate in a transformer, gives only very low DOUBLE-ENERGY TRANSIENTS. 63 oscillating voltages, that is, acts as a short circuit for the trans- former oscillation, and therefore protects the latter. Inversely, if the large oscillating current of a cable enters a reactive device, as a current transformer, it produces enormous voltages therein. Thus, cable oscillations are more liabl ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-36", "section_label": "Apparatus Section 15: Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "section_title": "Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "kind": "apparatus-section", "sequence": 36, "number": 15, "location": "lines 9918-10123", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-36/", "snippets": [ "... short circuited through the synchronous impedance of the two alternators. . Since E' = OE\\ = 2 EI sin 9 deg. the maximum cross current is ffisin9deg. 0.156 ffi 1 = = = U.loo 1 o, 20 20 ET where IQ = -- = short-circuit current of the alternator at full- 20 load excitation. Thus, if the short-circuit current of the alter- nator is only twice full-load current, the cross current is 31.2 per cent, of full-load current. If the short-circuit ...", "... E' = OE\\ = 2 EI sin 9 deg. the maximum cross current is ffisin9deg. 0.156 ffi 1 = = = U.loo 1 o, 20 20 ET where IQ = -- = short-circuit current of the alternator at full- 20 load excitation. Thus, if the short-circuit current of the alter- nator is only twice full-load current, the cross current is 31.2 per cent, of full-load current. If the short-circuit current is 6 times full-load current, the cross current is 93.6 per cent, of full- ...", "... short-circuit current of the alternator at full- 20 load excitation. Thus, if the short-circuit current of the alter- nator is only twice full-load current, the cross current is 31.2 per cent, of full-load current. If the short-circuit current is 6 times full-load current, the cross current is 93.6 per cent, of full-load current or practically equal to full-load current. Thus SYNCHRONOUS MACHINES 157 the smaller the armature reaction, or the better the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-79", "section_label": "Apparatus Subsection 79: Direct-current Commutating Machines: C. Commutating Machines 219", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 219", "kind": "apparatus-subsection", "sequence": 79, "number": null, "location": "lines 13019-13119", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-79/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-79/", "snippets": [ "... m.f. induced by the rotation through the magnetic field is a maximum; in the position of commutation the e.m.f. induced by the alternation of the field flux is a maximum. To overcome the destructive sparking caused by the short circuit of the latter e.m.f. by the commutator brush is the problem of making a successful alternating-current commutator: 1. Inducing an opposite e.m.f. by a commutating field. As 220 ELEMENTS OF ELECTRICAL ENGINEERING the ...", "... etely sparkless commutation can be produced at speed. However, at standstill and low speeds this method fails, as the voltage induced by the rotation through the commutating field becomes zero at standstill. 2. Reducing the short-circuit current by high resistance leads between commutator and armature coil. This only mitigates the trouble, but due to the voltage drop in the lead resistance tends to increase sparking at speed. Also, the excessive con- ...", "... sparking at speed. Also, the excessive con- centration of heat in the commutating leads in the moment of starting tends to destroy them if the motor does not quickly start. 3. Narrow brushes, to reduce the duration of short circuit. 4. Low impressed frequency, so as to give low values to the induced e.m.f. This is the cause of the desire for abnormally low frequencies, as 15 and even 8 cycles, in alternating-current railway electrification. 5. ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-21", "section_label": "Chapter 21: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 22302-23970", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-21/", "snippets": [ "... NT PHENOMENA complete ellipses, giving also the negative or syn- chronous motor part of the curves. Such a curve is called a field characteristic. As shown, the e.m.f. curve at non-inductive load is nearly horizontal at open-circuit, nearly vertical at short-circuit, and is similar to an arc of an ellipse. With reactive load the curves are more nearly straight lines. The voltage drops on inductive load and rises on capacity load. 26 24 22 20 3^u :10 \\ \\ \\ FIELD CHARACTERISTIC Eo=2500, Zo= ...", "... S.' \\ \\ A 0 20 40 60 80 100 120 140 ICO 180 200 220 240 260 280 AMPS. Fig. 134. — Field characteristic of alternator on wattless inductive load. The output increases from zero at open-circuit to a maximum, and then decreases again to zero at short-circuit. 189. The dependence of the terminal voltage, £', upon the phase relation of the external circuit is shown in Fig. 138, which gives, at impressed e.m.f., £'0 = 2500 volts, and the currents, / = 50, 100, 150, 200, 250 amp., the terminal voltages, E, as o ...", "... very high synchronous reactance regulates for a terminal voltage proportional to the external resistance as a constant-current machine. Thus, every alternator acts as a constant-potential machine near open-circuit, and as a constant-current machine near short- circuit. Between these conditions, there is a range where the alternator regulates approximately as a constant-power machine, that is, current and e.m.f. vary in inverse proportion, as between 130 and 200 amp. in Fig. 132. The modern alternators are generally mo ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-16", "section_label": "Chapter 16: Aiitebnatingh-Current Osnebator", "section_title": "Aiitebnatingh-Current Osnebator", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 17025-18828", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "snippets": [ "... —5 a- m » tt:^ Fig. 114. FhU CHeneUtlstle of Antrnattt. at KX Poatr-facter on fntfoctAw looA Such a curve is called a ^e/tf c/iamcUristic. As shown, the E.M.F. curve at non-inductive load is nearly horizontal at open circuit, nearly vertical at .short circuit, and is similar to an arc of an ellipsis. With reactive load the curves are more nearly straight lines. The voltage drops rapidly on inductive, rises on capacity The output increases from zero at open circuit to a max- imum, and then decreases again ...", "... milar to an arc of an ellipsis. With reactive load the curves are more nearly straight lines. The voltage drops rapidly on inductive, rises on capacity The output increases from zero at open circuit to a max- imum, and then decreases again to zero at short circuit. 242 ALTERNATIXG-CURREKT PTIEKOMENA. [§164 1 ' i 1 1 1 s 0-2 ELD CMARACTERIS 50O. ZrMOj, r4o, B '^ N N s s \\ s. s V 1. ><• ■ ^., A N s^.. N ^^ S ^. \\ / s \\ / s \\ ...", "... high synchronous reac- tance regulates for a terminal voltage proportional to the external resistance, as a constant-current machine. Thus, every alternator acts as a constant-potential ma- chine near open circuit, and as a constant-current machine near short circuit. The modern alternators are generally more or less ma- § 167] ALTERNATING-CURRENT GENERATOR. 24T chines of the first class ; the old alternators, as built by Jablockkoff, Gramme, etc., were machines of the second class, used for arc lighting, where c ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "section_label": "Chapter 16: Induction Motor", "section_title": "Induction Motor", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "... — .085/. In Fig. 116 is shown, with the speed in per cent of •synchronism, as abscissae, the torque in kilogrammetres, as ordinates, in drawn lines, for the values of armature resistance : 116. Speed Characteristics of Induction Motor. rt = .02 : short circuit of armature, full speed. ^ = .045 : .025 ohms additional resistance. ^ = .18 : .16 ohms additional, maximum starting torque. ^ = .75 : .73 ohms additional, same starting torque as rt == .045. On the same Figure is shown the current per line, in dotte ...", "... per line as abscissae, the torque in kilogrammetres and the output in horse-power as ordinates in drawn lines, and the speed and the magnetism, in per cent of their synchronous values, as ordinates in dotted lines, for the armature resistance ^ = .02 or short circuit. 20 lase Induotio Motor. . 60Cyc 110V Jiagram =.03-.09j z£0=J&B \\ \\\\ \\\\ 12 -1 Amperes 150 1 200 2,50 300 Fig. 117. Current Characteristics of Induction Motor. In Fig. 118 is shown, with the speed, in per cent of ...", "... n the direction of the axis of the armature coil, but no secondary circuit at right angles therewith. That is, with the rotati .n 292 ALTERNATING-CURRENT PHENOMENA. of the armature the secondary circuit, corresponding to a primary circuit, varies from short circuit at coincidence of the axis of the armature coil with the axis of the primary coil, to open circuit in quadrature therewith, with the periodicity of the armature speed. That is, the apparent admittance of the primary circuit varies periodically from open- ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-17", "section_label": "Chapter 17: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16362-17596", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "snippets": [ "... glQ 20 0 Amp Fig. 130. Field Characteristic of Alternator, at 60% Power-factor on Inductive Load. Such a curve is called a field characteristic. As shown, the E.M.F. curve at non-inductive load is nearly horizontal at open circuit, nearly vertical at short circuit, and is similar to an arc of an ellipse. ALTERNATING-CURRENT GENERATOR. 305 \\ s, FIELD CHARACTt :0=25OO, Z?1-10j, r = RISTIC o, 90° Lag \\ \\ 1 R = 0. \\ \\ \\ \\ \\ \\ k o » >C\" -X A / S \\%< \\ o 2\" X X t s ...", "... nator, on Wattless Condenser Load. With reactive load the curves are more nearly straight lines. The voltage drops on inductive, rises on capacity load. The output increases from zero at open circuit to a maxi- mum, and then decreases again to zero at short circuit. AL TERN A TING-CURRENT GENERA TOR. 307 M VK 4^z W Fig. 134. Field Characteristic of Alternator. 186. The dependence of the terminal voltage, E, upon the phase relation of the external circuit is shown in Fig. 135, which gives, at imp ...", "... high synchronous reac- tance regulates for a terminal voltage proportional to the external resistance, as a constant-current machine. Thus, every alternator acts as a constant-potential ma- chine near open circuit, and as a constant-current machine near short circuit. Between these conditions, there is a range where the alternator regulates approximately as a constant power machine, that is current and E.M.F. vary in inverse proportion, as between 130 and 200 amperes in Fig. 129. The modern alternators are generally ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-14", "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "section_title": "Constant-Potential Constant-Current Trans Formation", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "... small values of r, the current, z, is approximately constant, and is 6o I = — Xo CONSTANT-CURRENT TRANSFORMATION 247 For small values of r, the power-factor cosfl — - is very low, however. Allowing a variation of current of 10 per cent, from short- circuit or no-load, r = 0, to full-load, or r = ri, it is, substituted in (2): No-load current: / -: / ^ y / ^ i < \\ s 1 / / \\ s ^ c JV N -^ \\ s / \\ \\ ^ y S 1 / ... .„. ...", "... = 792 ohms series reactance; the current: 8.33 2 = — -. — amp. yliW+V+^-'m) This current is shown by dotted line. In this case, in an inductive circuit, the current, i, has decreased 250 ELECTRIC CIRCUITS by 10 per cent, below the no-load or short-circuit value of 8.33 amp. that is, has fallen to 7.5 amp., at the resistance r = 187 ohms, or at the voltage of the receiving circuit, e = i V r« + x2 = n V 1 + fc« = 1.077 H = 1500 volts; while, in the case of a non-inductive load, the current has fallen off ...", "... is negligible. With inductive load, equation (11), the inductive reactance, rco, has still further to be decreased by the inductive reactance of the load, x. Substituting: __ eo Xoo — '^~~ as the value of the series inductive reactance at no-load or short- circuit, equations (11), (12), (13) assume the form: CONSTANT-CURRENT TRANSFORMATION 253 General inductive load: Xo = Vxoo^ - r2 - z, (14) Inductive load of — = fc: r Xo = Vxoo* - r2 - At (15) Non-inductive load : Xo = Vxoo^ - r2. (16) 131. As seen ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-08", "section_label": "Lecture 8: Arc Lamps And Arc Lighting", "section_title": "Arc Lamps And Arc Lighting", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 7141-8510", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-08/", "snippets": [ "... es with increase of current and, inversely, a momentary increase of current decreases the consumed voltage, and, on constant voltage supply, thereby increases the current, still further decreases the arc voltage and increases the current, and the arc thus short circuits; or a momentary decrease of current increases the required voltage and, at constant supply voltage, continues to decrease the cur- rent and thus increase still further the required voltage, that is, the arc goes out. On constant voltage supply only such ...", "... tion, and leaves no ampere-turns for producing the mag- netism; that is, the magnetic flux and thereby the machine voltage disappear. Thus, in such a machine, the current out- put at constant field excitation rises very little, from full volt- age down to short circuit, or, in other words, the machine regulates for approximately constant current. Perfect constant- current regulation is produced by a resistance shunted across the field, which is varied by an electromagnet in the machine circuit, and lowered — that is, mo ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-105", "section_label": "Apparatus Section 8: Alternating-current Transformer: Autotransformer", "section_title": "Alternating-current Transformer: Autotransformer", "kind": "apparatus-section", "sequence": 105, "number": 8, "location": "lines 18666-18812", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-105/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-105/", "snippets": [ "... \\ primary, and ez X (i* — ii) secondary circuit. The regulation of an autotransformer is better, and the effi- ciency higher, than that of the same structure as transformer, and the per cent, reactance lower, that is the short-circuit current higher in the autotransformer than in the same structure as transformer. Very often it is difficult to build autotransformers with sufficiently high internal reactance, to make them safe under momentary short circuit ...", "... e short-circuit current higher in the autotransformer than in the same structure as transformer. Very often it is difficult to build autotransformers with sufficiently high internal reactance, to make them safe under momentary short circuit as autotransformers, while they may be . perfectly safe as transformers, where the reactance is higher. This is a serious objection to the use of autotransformers in high-power systems." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-15", "section_label": "Theory Section 15: Load Characteristic of Transmission Line", "section_title": "Load Characteristic of Transmission Line", "kind": "theory-section", "sequence": 15, "number": 15, "location": "lines 5832-6221", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-15/", "snippets": [ "... e.m.f. (4) p = d = i V-Eo2 - x2i2 - ri2, (5) the power received at end of the line. The curve of e.m.f. e is an arc of an ellipse. With open circuit i = 0, e = E0 and P = 0, as is to be expected. At short circuit, e = 0, 0 = \\/#o2 — xzi2 — ri, and ° ; (6) X' that is, the maximum line current which can be established with a non-inductive receiver circuit and negligible line capacity. 71. The condition of maximum 'powe ...", "... is the e.m.f. times the power component of the current; thus P = elp __ = Ip \\/Eo*- P(rq-xp)* - Pp (rp + xq). (19) The curve of e.m.f., e, as function of the current I is again an arc of an ellipse. At short circuit e = 0; thus, substituted, /-£• (20) the same value as with non-inductive load, as is obvious. 73. The condition of maximum output delivered over the line is that is, differentiated, V#o2 -I2(rq-xp)2 = e + I (rp + ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-18", "section_label": "Chapter 18: Polyphase Induction Motors", "section_title": "Polyphase Induction Motors", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17717-20445", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-18/", "snippets": [ "... ce, Z = 0.03 + 0.09 j. Secondary impedance, Zi = 0.02 + 0.085 j. In Fig. 120 is shown, with the speed in per cent, of synchronism, as abscissas, the torque in kilogram-meters as ordinates in drawn Hnes, for the values of armature resistance: Ti = 0.02 : short-circuit of armature, full speed. ri = 0.045: 0.025 ohms additional resistance. Ti = 0.18 : 0.16 ohms additional, maximum starting torque. Ti = 0.75 : 0.73 ohms additional, same starting torque as n = 0.045. / / \\ s 28 20 H.P. THREE-PHASE / \\ 24 ...", "... e as abscissas, the torque in kilogram-meters and the output in horse- power as ordinates in drawn lines, and the speed and the mag- netism, in per cent, of their synchronous values, as ordinates in dotted lines, for the armature resistance, ri = 0.02, or short- circuit. 232 ALTERNATING-CURRENT PHENOMENA In Fig. 122 is shown, with the speed, in per cent, of synchro- nism, as abscissas, the torque in drawn hne, and the output in dotted hne, for the value of armature resistance ri = 0.045, for the whole range of speed ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-08", "section_label": "Chapter 8: Capacity", "section_title": "Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3872-6370", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "snippets": [ "... t. This combination of inductance and capacity acts as a transformer, and converts from constant potential to con- stant current and inversely, without introducing a displace- ment of phase between current and E.M.F. It is interesting to note here that a short circuit in the receiver circuit acts like a break in the supply circuit, and a break in the receiver circuit acts like a short circuit in the supply circuit. As an instance, in F^ig. 56 are plotted the numerical values of a transformation from constant potentia ...", "... t and inversely, without introducing a displace- ment of phase between current and E.M.F. It is interesting to note here that a short circuit in the receiver circuit acts like a break in the supply circuit, and a break in the receiver circuit acts like a short circuit in the supply circuit. As an instance, in F^ig. 56 are plotted the numerical values of a transformation from constant potential of 1,000 volts to constant current of 10 amperes. Since E^ = 1|000, / = 10, we have : x^ = 100 ; hence the constants of the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-15", "section_label": "Chapter 15: Induction Motob", "section_title": "Induction Motob", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 14919-17024", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "snippets": [ "... = .02 — .086/ 232 ALTERNATTNG-CURRENT PHENOMENA. [§158 In Fig. 107 is shown, with the speed in per cent of synchronism, as abscissae, the torque in kilogrammetres, as ordinates, in drawn lines, for the values of armature resistance : ri a .02 : short circuit of armature, full speed. /-J = ,045 : .025 ohms additional resistance. rx = .16 : .16 ohms additional resistance, maximum starting torque. ri => .75 : .73 ohms additional resistance, same starting torque as n — .045. ,2o'Kn.4-P'l-. f \\ a ...", "... rque in kilogrammetres and the output §168] INDUCTION MOTOR, 238 in kilowatts as ordinates in drawn lines, and the speed and the magnetism, in per cent of their synchronous values, as ordinates in dotted lines, for the armature resistance r^ = .02, or short circuit. In Fig. 109 is shown, with the speed, in per cent of synchronism, as abscissae, the torque in drawn line, and the output in dotted line, for the value of armature resis- tance r, = .045, for the whole range of speed from 120 per cent backwards speed to ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-19", "section_label": "Chapter 19: Commutatob Motobs", "section_title": "Commutatob Motobs", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 21339-22387", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "snippets": [ "... 194. In the repulsion motor the difficulty due to the equal and opposite rotary efforts, caused by the induced armature currents when acted upon by the inducing mag- netic field, is overcome by having the armature coils closed upon themselves, either on short circuit or through resist- ance, only in that position where the induced currents give a rotary effort in the desired direction, while, the armature coils are open-circuited in the position where the rotary effort of the induced currents would be in opposition ...", "... n diagram matically as ring wound A consists of a number of coils connected to a segmental commutator C, in general in the same way as in continuous-current ma- chines. Brushes standing under an angle of about 45° with the direction of the magnetic field, short-circuit either a part of the armature coils as shown in Fig. 142, or the whole armature by a connection from brush to brush as shown in Fig. 143. The former arrangement has the disadvantage of using a part of the armature coils only. The second arrangement h ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-08", "section_label": "Chapter 8: Circuits Containing Resistance, Inductance, And Capacity", "section_title": "Circuits Containing Resistance, Inductance, And Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3577-5333", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "snippets": [ "... t. This combination of inductance and capacity acts as a transformer, and converts from constant potential to con- stant current and inversely, without introducing a displace- ment of phase between current and E.M.F. It is interesting to note here that a short circuit in the receiver circuit acts like a break in the supply circuit, and a break in the receiver circuit acts like a short circuit in the supply circuit. As an instance, in Fig. 56 are plotted the numerical values of a transformation from constant potential ...", "... t and inversely, without introducing a displace- ment of phase between current and E.M.F. It is interesting to note here that a short circuit in the receiver circuit acts like a break in the supply circuit, and a break in the receiver circuit acts like a short circuit in the supply circuit. As an instance, in Fig. 56 are plotted the numerical values of a transformation from constant potential of 1,000 volts to constant current of 10 amperes. Since E^ = 1,000, 7=10, we have : x0 = 100 ; hence the constants of the ci ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-20", "section_label": "Chapter 20: Commutator Motors", "section_title": "Commutator Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 19458-20501", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "snippets": [ "... 215. In the repulsion motor the difficulty due to the equal and opposite rotary efforts, caused by the induced armature currents when acted upon by the inducing mag- netic field, is overcome by having the armature coils closed upon themselves, either on short circuit or through resist- ance, only in that position where the induced currents give Fig. 158. a rotary effort in the desired direction, while the armature coils are open-circuited in the position where the rotary effort of the induced currents would be in ...", "... wn diagrammatically as ring wound A consists of a number of coils connected to a segmental commutator C, in general in the same way as in continuous-current ma- chines. Brushes standing under an angle of about 45° with the direction of the magnetic field, short-circuit either a Fig. 159. part of the armature coils as shown in Fig. 158, or the whole armature by a connection from brush to brush as shown in Fig. 159. The former arrangement has the disadvantage of using a part of the armature coils only. The second ar ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-07", "section_label": "Chapter 8: Synchronizing Induction Motors", "section_title": "Synchronizing Induction Motors", "kind": "chapter", "sequence": 7, "number": 8, "location": "lines 13956-14465", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-07/", "snippets": [ "... rate in step with each other, within the limits of their synchronizing power. If the starting rheostat is short-circuited, or r = 0, it is, by (15), 61 = by and the synchronizing power vanishes, as is obvious, since in this case the motor secondaries are short-circuit (id and thus independent of each other in their frequency and speed. With parallel connection of induction-motor armatures a syn- chronizing power thus is exerted between the motors as long as any appreciable resistance exists in the external circuit, an ...", "... unstable positions of the motors, sc0*ri \"' (r, +«-,)*+ 8* (Xl +JV-' lue as the motor would give w i it il As the enters (19) short- SYNCHRONIZING INDUCTION MOTORS 165 circuited armature. This is to be expected, as the two motor armatures short-circuit each other. The synchronizing torque is a maximum for r = 45°, and is, by (14), (15), and (16): i), = ^6l~6. (20) As instances are shown, in Fig. 59, the motor torque, from equation (18), and the maximum synchronizing torque, from equation (20), for ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-16", "section_label": "Chapter 18: Surging Of Synchronous Motors", "section_title": "Surging Of Synchronous Motors", "kind": "chapter", "sequence": 16, "number": 18, "location": "lines 20975-21712", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-16/", "snippets": [ "... r due to the pulsation of e 298 ELECTRICAL APPARATUS caused by the pulsation of the armature reaction, as discussed in \"Theory and Calculation of Alternating-Current Phenomena.\" Any appliance increasing the area of the magnetic cycle of pulsation, as short-circuits around the field poles, therefore, increases the steadiness of a steady and increases the unsteadi- ness of an unsteady synchronous motor. In self-exciting synchronous converters, the pulsation of e is intensified by the pulsation of direct-current volta ...", "... e term, c2, or 3. A sufficiently large term, pP0. (1) refers to the design of the synchronous machine and the system on which it operates. (2) leads to the use of electro- magnetic anti-surging devices, as an induction motor winding in the field poles, short-circuits between the poles, or around the poles, and (3) leads to flexible connection to a load or a mo- mentum, as flexible connection with a flywheel, or belt drive of the load. The conditions of steadiness are : and if: 0>a, c2 + pP0 - h2 > 0, (c2 + p ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-17", "section_label": "Chapter 19: Alternating- Current Motors In General", "section_title": "Alternating- Current Motors In General", "kind": "chapter", "sequence": 17, "number": 19, "location": "lines 21713-23905", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-17/", "snippets": [ "... (108) gives: /\"o = ■-!- (^1 cos 02 — t\\ sin 02) 327 = -J m . EoC, Zl (HO) and: T Eo . EoC I'- T~' I,' - * (i - 1 c - f.) ) (111) 186. In the exact predetermination of the characteristics of such a motor, the effect of the short-circuit current under the brushes has to be taken into consideration, however. When a commutator is used, by the passage of the brushes from segment to segment coils are short-circuited. Therefore, in addition to the circuits considered above, a closed circuit on ...", "... rt-circuited. Therefore, in addition to the circuits considered above, a closed circuit on the rotor has to be introduced in the equations for every set of brushes. Re- duced to the stator circuit by the ratio of turns, the self-inductive impedance of the short-circuit under the brushes is very high, the current, therefore, small, but still sufficient to noticeably af- fect the motor characteristics, at least at certain speeds. Since, however, this phenomenon will be considered in the chapters on the single-phase motors ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-01", "section_label": "Chapter 1: Electric Conduction. Soled And Liquid", "section_title": "Electric Conduction. Soled And Liquid", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 959-3894", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-01/", "snippets": [ "... st across this rod in stationary conditions, is 25 volts at 1 amp. With increasing terminal voltage, the current thus gradually increases, until 25 volts is reached, and then with- out further increase of the impressed voltage the current rapidly rises to short-circuit values. Thus, such resistances can be used as excess-voltage cutout, or, when connected between circuit and ground, as excess-voltage grounding device: below 24 volts, it \\ RESISTIVITY TEMPERATURE 1 ^■ \\ CAST SILICON ROD !B CM. LENGTH 0. ...", "... ima voltage point. Thus so-called \"graphite resistances\" or \"carborundum resist- ances,' ' used in series to lightning arresters to limit the discharge, when exposed to a continual discharge for a sufficient time to reach high temperature, may practically short-circuit and there- by fail to limit the current. 12. From the dropping volt-ampere characteristic in some pyroelectric conductors, especially those of high resistance, of very high negative temperature coefficient and of considerable cross-section, results the ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-10", "section_label": "Chapter 10: Instability Of Circuits : The Arc", "section_title": "Instability Of Circuits : The Arc", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 17632-21381", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-10/", "snippets": [ "... stant impressed voltage of 80, the current could not re- main at 4 amp., but the current would either decrease with in- creasing rapidity, until the arc goes out, or the current would in- 164 ELECTRIC CIRCUITS crease with increasing rapidity, up to short-circuit, that is, until the supply source limits the current, 3. Instability leading again to iustability, and thus periodically repeating the phenomena. For instance, if an arc of the volt-ampere characteristic. A, in Fig. 79 is operated in a constant-current ...", "... - ampere characteristic, as discussed previously. Resistance in series to the condenser, C, also produces stability, if sufficiently large: with a sudden change of voltage in the arc INSTABILITY OF CIRCUITS 181 circuit, A, the condenser acts as a short-circuit in the first moment, passing the current without voltage drop, and the voltage thus has to be taken up by the shunt resistance, ri, giving the same con- dition of stability as with an arc in a constant-current circuit, shunted by a resistance, paragraph 8 ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... urrents, 347 self inductive and mutual in- ductive, of alternator arma- ture, 239 shunt in series circuit, 298 regulating series circuit by saturation, 302 of synchronous machines, 232 total, of transformer, 224 of transformer, measurement, 227 and short-circuit stress, 100 as wave screen, 153 Reactive power of system, total and resultant, 317 Recovery of induction motor after overload, 204 Rectification by arc, 32 by electronic conduction, 40 giving even harmonics, 159 Rectifying voltage range of alter- ...", "... s, 125 of reactance shunting series circuit, 302 value, magnetic, 46 Screen, wave-, 153 Secondary cell, 8 Self inductive armature flux of alternator, 234 Series operation, constant current, 297 constant voltage, 297 Shape of hysteresis curve, 68 Short circuit stress in transformer, 99 third harmonic in alternator, 244 Shunt protective device in series circuits, 298 Silicon as pyroelectric conductor, 13 steel, hysteresis, 62 magnetic properties, 79 Sine wave as standard, 111 Singing arc, 188 Singlepha ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-24", "section_label": "Chapter 2: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 24, "number": 2, "location": "lines 1993-2658", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "snippets": [ "... deration, however, - (a) In those cases where they reach excessive values. Thus in connecting a large transformer to an alternator the large initial value of current may do damage. In short-circuiting a large alternator, while the permanent or stationary short-circuit current is not excessive and represents little power, the very much larger momentary short-circuit current may be beyond the capacity of automatic circuit-opening devices and cause damage by its high power. In high-potential transmissions the potential d ...", "... rge transformer to an alternator the large initial value of current may do damage. In short-circuiting a large alternator, while the permanent or stationary short-circuit current is not excessive and represents little power, the very much larger momentary short-circuit current may be beyond the capacity of automatic circuit-opening devices and cause damage by its high power. In high-potential transmissions the potential differences produced by these transient terms may reach values so high above the normal voltage as to ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-32", "section_label": "Chapter 10: Mutual Inductance", "section_title": "Mutual Inductance", "kind": "chapter", "sequence": 32, "number": 10, "location": "lines 10475-12216", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "snippets": [ "... 0.1 that of the field copper, the effective resistance of the eddy current circuit, reduced to the field circuit, approximates five times that of the field circuit. Hence, if r2 — resistance of main field winding, rl = 5 r2 = resistance of the secondary short circuit which represents the eddy currents. Since the eddy currents extend beyond the space covered by the field poles, and considerably down into the iron, the self- inductance of the eddy current circuit is considerably greater than its mutual inductance with ...", "... is, giving a full load value of 1000 amperes at 200 volts. Making the assumptions set forth in the preceding paragraph, the following constants are taken: the armature resistance = 0.008 ohms and the series field 'winding resistance^ 0.004 ohm; hence, the short circuit — or eddy current resistance — rl = 0.02 ohm. Further- more let M = 900 X 10~6 henry = mutual inductance between main field and short-circuited secondary; hence, xm = 0.34 ohm = mutual reactance, and therefore, assuming a leakage flux of the secondary equ ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-38", "section_label": "Chapter 2: Circuit Control By Periodic Transient Phenomena", "section_title": "Circuit Control By Periodic Transient Phenomena", "kind": "chapter", "sequence": 38, "number": 2, "location": "lines 15626-15962", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-38/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-38/", "snippets": [ "... nd L = 400 henrys = inductance of the exciter field circuit. A resistor, having a resistance, rl = 24 ohms, is inserted in series to r0, L in the exciter field, and a potential magnet, con- trolled by the alternating current system, is arranged so as to short circuit resistance, rv if the alternating potential is below, to throw resistance rl into circuit again, if the potential is above normal. With a single resistance step, rv in the one position of the regulator, with rx short circuited, and only r0 as exciter fie ...", "... osition; while at light load, requiring low field excitation, the duration of the period of high resistance, 223 224 TRANSIENT PHENOMENA (TO _|_ rj} is greater, and that of the period of low resistance, r0, less. 7. Let, ^ = the duration of the short circuit of resistance rx; t2 = the time during which resistance rx is in circuit, and t0 = t, + tr During each period t0, the resistance of the exciter field, therefore, is r0 for the time tv and (r0 + rj for the time ty Furthermore, let, i1 = the current dur ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "... ery frequently. For instance, it may be caused if by a lightning stroke, etc., a quantity of dielectric energy is impressed Fig. 39. — Starting of Impulse, or Traveling Wave. upon a part of the circuit, as shown by curve A in Fig. 39, or if by a local short circuit a quantity of magnetic energy is impressed upon a part of the circuit. This energy then gradually distributes over the circuit, as indicated by the curves B, C, etc., of Fig. 39, that is, moves along the circuit, and the dissipation of the stored energy t ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 4745-5520", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "snippets": [ "... equently. For instance, it may be caused if by a lightning stroke, etc., a quantity of dielectric energy is impressed A • Fig. 39. — Starting of Impulse, or Traveling Wave. upon a part of the circuit, as shown by curve A in Fig. 39, or if by a local short circuit a quantity of magnetic energy is impressed upon a part of the circuit. This energy then gradually distributes over the circuit, as indicated by the curves B, C, etc., of Fig. 39, that is, moves along the circuit, and the dissipation of the stored energy t ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... efficiency is zero. If the problem is, to find the current at which the output of an alternator is a maximum, the solution i = 0 obviously is a minimum, and of the other two solutions, i\\ and io, the larger value, i2, again gives a minimum, zero output at short-circuit current, while the inter- mediate value i\\ gives the maximum. 10 1. The extremes of a function, therefore, are determined by equating its diiTerential quotient to zero, as is illustrated by the following examples : Example 4. In an impulse turbine, the ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... ^ -\"^ < / ^1 n^> / / J / / / / / / 2 3 4 3 6 b 8 3 1 X) 1^ a. e ■120 1001.00 80 0.-80 0.40 0.20 ^ 0 Fig. 86. Transmission Line Characteristics. For instance, when investigating the short-circuit current of an electric generating system, it is of importance to know whether this current is 3 or 4 times normal current, or whether it is 40 to 50 times normal current, but it is immaterial whether it is 45 to 46 or 50 times normal. In studying lightnin ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-04", "section_label": "Lecture 4: Load Factor And Cost Of Power", "section_title": "Load Factor And Cost Of Power", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 1527-2561", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-04/", "snippets": [ "... ircuit, in Fig. 17: 54.3%. In defining the load factor, it is necessary to state not only the time over which the load is to be averaged, as a day, or a year, but also the length of time which the maximum load must last, must be counted. For instance, a short circuit of a large motor during peak load, which is opened by the blowing of the fuses, may momentarily carry the load far beyond the station peak without being objectional. The minimum dura- tion of maximum load, which is chosen in determining the load factor, ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-05", "section_label": "Lecture 5: Long Distance Transmission", "section_title": "Long Distance Transmission", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2562-3132", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-05/", "snippets": [ "... o£ir/<~ Y r-0£lTA a) r-r ^J 0£l77l*r s) rmsf-WMsr tf.j o^e/vasiTA r) Ttro^^AAse frM££'^/fAS0 T Fife. 19. Transformer Connections. instance, the grounding of one line. It has the disadvantage that a ground on one circuit is a short circuit and so shuts down the circuit. LONG DISTANCE TRANSMISSION 71 In connections i, 4 and 6 no neutral is available for grounding and so three separate transformers have to be installed in Y connection for getting the neutral. In connections 2 and 3 ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-03", "section_label": "Lecture 3: Physiological Effects Of Radiation", "section_title": "Physiological Effects Of Radiation", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2366-3638", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-03/", "snippets": [ "... nd longer time before it begins to blur and ultimately becomes normal again. The inflammation of the eye produced by ultra-violet light appears to be different from that caused by exposure to high- power radiation of no specific effect, as the light of a short circuit of a high-power electric system, or an explosion, etc. The main differences are: 1. The effect of high-power radiation (power burn) appears immediately after exposure, while that of ultra-violet radiation (ultra-violet burn) appears from 6 to 18 hours ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-06", "section_label": "Theory Section 6: Self-inductance of Continuous-current Circuits", "section_title": "Self-inductance of Continuous-current Circuits", "kind": "theory-section", "sequence": 6, "number": 6, "location": "lines 1785-2249", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-06/", "snippets": [ "... tc. 33. (5) A coil of resistance r = 0.002 ohm and inductance L = 0.005 mh., carrying current / = 90 amp., is short circuited. 30 ELEMENTS OF ELECTRICAL ENGINEERING (a) What is the equation of the current after short circuit? (6) In what time has the current decreased to 0.1. its initial value? _ L* (a) i = /e L = 90 e-400'. (6) i = 0.1 7, c-400< = 0.1, after t = 0.00576 second. (6) When short circuiting the coil in Example 5, ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-23", "section_label": "Apparatus Section 2: Synchronous Machines: Electromotive Forces", "section_title": "Synchronous Machines: Electromotive Forces", "kind": "apparatus-section", "sequence": 23, "number": 2, "location": "lines 8658-8740", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-23/", "snippets": [ "... ight line. The synchronous reactance XQ is thus a quantity combining armature reaction and self-inductance of the alternator. It is the only quantity which can easily be determined by experiment by running the alternator on short circuit with excited field. If in this case IQ = current, PQ = loss of power in the armature coils, EQ = e.m.f. corresponding to the field excitation at open w p circuit, 7— = ZQ is the synchronous impedance, y^ = r0 is t ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-27", "section_label": "Apparatus Section 6: Synchronous Machines: Characteristic Curves of Alternating-current Generator", "section_title": "Synchronous Machines: Characteristic Curves of Alternating-current Generator", "kind": "apparatus-section", "sequence": 27, "number": 6, "location": "lines 9170-9291", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-27/", "snippets": [ "... nding to the same three conditions as Fig. 60. From the field characteristics of the alternator are derived the open-cir- cuit voltage of 1127 at full non-inductive load excitation, which is 1.127 times full-load voltage; the short-circuit current 225 at full non-inductive load excitation, which is 2.25 times full-load current; and the maximum output, 124 kw., at full non-induct- ive load excitation, which is 1.24 times rated output, at 775 volts and 160 amp. ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-42", "section_label": "Apparatus Subsection 42: Direct-current Commutating Machines: C. Commutating Machines", "section_title": "Direct-current Commutating Machines: C. Commutating Machines", "kind": "apparatus-subsection", "sequence": 42, "number": null, "location": "lines 10586-10645", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-42/", "snippets": [ "... All these windings are closed-circuit windings; that is, starting at any point, and following the armature conductor, the circuit returns into itself after passing all e.m.fs. twice in opposite direc- tion (thereby avoiding short circuit). An instance of an open- coil winding is shown in Fig. 84, a series-connected three-phase star winding similar to that used in the Thomson-Houston arc machine. Such open-coil windings, however, cannot be used in commutating ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-66", "section_label": "Apparatus Subsection 66: Direct-current Commutating Machines: C. Commutating Machines 201", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 201", "kind": "apparatus-subsection", "sequence": 66, "number": null, "location": "lines 11981-12083", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-66/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-66/", "snippets": [ "... per brushes, or it may be of the same or a higher magnitude than the internal resistance of the armature coil A. The latter is usually the case with carbon or graphite brushes. In the former case the resistance of the short-circuit of arma- ture coil A under commutation is approximately constant; in the latter case it varies from infinity in the moment of beginning commutation down to minimum, and then up again to infinity at the end of commutation. ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-73", "section_label": "Apparatus Subsection 73: Direct-current Commutating Machines: C. Commutating Machines", "section_title": "Direct-current Commutating Machines: C. Commutating Machines", "kind": "apparatus-subsection", "sequence": 73, "number": null, "location": "lines 12492-12659", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-73/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-73/", "snippets": [ "... ator. The terminal voltage is zero at no load or open circuit, increases with the load, reaches a maximum value at a certain current, and then decreases again and reaches zero at a certain maximum current, the current of short circuit. Curve B is plotted with constant coefficient of armature reac- tion q. Assuming the brushes to be shifted with the load and 212 ELEMENTS OF ELECTRICAL ENGINEERING 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 1.2 1.1 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-13", "section_label": "Chapter 13: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 13484-14333", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-13/", "snippets": [ "... certain circumstances eddy currents also exist in larger orbits from lamina to lamina through the whole magnetic structure. Obviously a calculation of these eddy currents is possible only in a particular structure. They are mostly surface currents, due to short circuits existing between the laminae at the surface of the magnetic structure. Furthermore, eddy currents are produced outside of the mag- netic iron circuit proper, by the magnetic stray field cutting electric conductors in the neighborhood, especially when dra ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-17", "section_label": "Chapter 17: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16521-17716", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-17/", "snippets": [ "... In the con- stant potential transformer, however, the primary and secondary coils are brought as near together as possible, or even inter- spersed, to reduce the cross-flux. There is, however, a limit, to which it is safe to reduce the cross-flux, as at short-circuit at the secondary terminals, it is the e.m.f. of self-induction of this cross-flux which limits the current, and with very low self-induction, these currents may become destructive by their mechanical forces. Therefore experience shows that in large power ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-23", "section_label": "Chapter 23: Synchronizing Alternators", "section_title": "Synchronizing Alternators", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 25135-25681", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-23/", "snippets": [ "... uch as is given by modern alter- nators— not too high to reduce the synchronizing power too much, nor too low to make the machine unsafe in case of accident, such as falling out of step, etc. If the armature reaction is very low, an accident — such as a short-circuit, falling out of step, opening of the field circuit, etc. — may destroy the machine. If the armature reaction is very high, the driving power has to be adjusted very carefully to constancy, since the synchronizing power of the alternators is too weak to ho ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-25", "section_label": "Chapter 25: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 29375-32539", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-25/", "snippets": [ "... cent. 250. Assuming now that in such transformers, connected with their primaries in Y into a three-phase circuit, the seconda- ries are connected in A. The third harmonics of e.m.f., generated in the three transformer secondaries, then are in series in short- circuit, thus produce a local current in the secondary transformer triangle. This current is of triple frequency, and hence supplies the third harmonic of exciting current, which was suppressed in the primary, and thereby eliminates the third harmonic of mag- net ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-32", "section_label": "Chapter 32: Transformation Of Polyphase Systems", "section_title": "Transformation Of Polyphase Systems", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 36062-36514", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-32/", "snippets": [ "... e primaries in Fig. 210. Since in this system each phase is transformed by a separate transformer, the voltages of the system remain balanced even at unbalanced load, within the limits of voltage variation due to the internal self-inductive impedance (or short-circuit impedance) of the transformers — which is small, while the exciting impedance (or open-circuit impedance) of the transformers, which causes the unbalancing in the Y-delta connection above discussed is enormous. 3. Y-Y connection of transformers between ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... tor, 261 of transformer, 187 voltage, 123 Series connection of impedances, 55, 59 of resistances and conduct- ances, 54 impedance in circuit, 69 operation of alternators, 294 reactance in circuit, 63 resistance in circuit, 60 Sharp zero wave, 370 Short circuit of alternator, 273, 288 Shunted condensance and lagging current, 72 Silent discharge from line, 174 Single-phase cable, topographical characteristic, 42 circuit equivalent to polyphase system, 448 efficiency, 466 induction motor, 245 system, 398 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... certain circumstances eddy currents also flow in larger orbits from lamina to lamina through the whole magnetic structure. Obviously a calculation of these eddy currents is possible only in a particular structure. They are mostly surface currents, due to short circuits existing between the laminae at the surface of the magnetic structure. Furthermore, eddy currents are induced outside of the magnetic iron circuit proper, by the magnetic stray field cutting electric conductors in the neighborhood, especially when draw ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-17", "section_label": "Chapter 17: Synchbonizino Aiitebkatobs", "section_title": "Synchbonizino Aiitebkatobs", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 18829-19345", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-17/", "snippets": [ "... ch as is given by modern alternators — not too high to reduce the synchronizing power too much, nor too low to make the machine unsafe in case of accident, such as falling out of step, etc. If the armature reaction is very low, an accident, — such as a short circuit, falling out of step, opening of the field circuit, etc., — may destroy the machine. If the armature reaction is very high, the driving-power has to be adjusted very carefully to constancy ; since the synchronizing power of the alternators is too weak to ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "... certain circumstances eddy currents also flow in larger orbits from lamina to lamina through the whole magnetic structure. Obviously a calculation of these eddy currents is possible only in a particular structure. They are mostly surface currents, due to short circuits existing between the laminae at the surface of the magnetic structure. Furthermore, eddy currents are induced outside of the magnetic iron circuit proper, by the magnetic stray field cutting electric conductors in the neighborhood, especially when draw ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "... iously, the more nearly sinusoidal the distribution of potential before the discharge, the more the low harmonics predominate, while a very un- equal distribution of potential, that is a very rapid change along the line, as caused for instance by a sudden short circuit rupturing itself instantly, causes the higher harmo- nics to predominate, which as a rule are more liable to cause excessive rises of voltage by resonance. 125. As has been shown, the electric distribution in a transmission line containing distributed ca ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-18", "section_label": "Chapter 18: Synchronizing Alternators", "section_title": "Synchronizing Alternators", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17597-18052", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-18/", "snippets": [ "... ch as is given by modern alternators — not too high to reduce the synchronizing power too much, nor too low to make the machine unsafe in case of accident, such as falling out of step, etc. If the armature reaction is very low, an accident, — such as a short circuit, falling out of step, opening of the field circuit, etc., — may destroy the machine. If the armature reaction is very high, the driving-power has to be adjusted very carefully to constancy ; since the synchronizing power of the alternators is too weak to ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "... In this case, for the last or synchronous-motor step, usually the direct-current supply will be connected between one phase and the other two phases, the latter remaining short-circuited to each other, as shown in Fig. 21, D. This arrangement retains a short-circuit in the rotor — now the field — in quadrature with the excitation, which acts as damper against hunting (Danielson motor). 58 ELECTRICAL APPARATUS In the synchronous motor, Fig. 21, D, produced from the induc- tion motor, Fig. 21, C, it is: Let: ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-05", "section_label": "Chapter 6: Induction-Motor Regulation And Stability", "section_title": "Induction-Motor Regulation And Stability", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 10583-12397", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-05/", "snippets": [ "... andstill, and thereby the starting torque of the motor, are lower than on a constant-poten- tial supply. Hereby then the margin of overload capacity of the motor is reduced, and the characteristic constant of the motor, or the ratio of exciting current to short-circuit current, is in- creased, that is, the motor characteristic made inferior to that given at constant voltage supply, the more so the higher the voltage drop in the supply circuit. Assuming then a three-phase motor having the following con- stants: primary ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-08", "section_label": "Chapter 9: Synchronous Induction Motor", "section_title": "Synchronous Induction Motor", "kind": "chapter", "sequence": 8, "number": 9, "location": "lines 14466-14550", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-08/", "snippets": [ "... rs a closed secondary circuit only in the direc- tion of the axis of the armature coil, but no secondary circuit at right angles therewith. That is, with the rotation of the arma- ture the secondary circuit, corresponding to a primary circuit, varies from short-circuit at coincidence of the axis of the arma- ture coil with the axis of the primary coil, to open-circuit in quadrature therewith, with the periodicity of the armature speed. That is, the apparent admittance of the primary circuit varies periodically from open ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-14", "section_label": "Chapter 16: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 14, "number": 16, "location": "lines 19374-20293", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-14/", "snippets": [ "... . of the reactive component of the armature current*. In the polyphase machine, this is constant in intensity and direc- tion, in the single-phase machine constant in direction, hut pul- sating in intensity, and the intensity pulsation can be reduced by a short-circuit winding around the field structure, as more fully discussed under \"Synchronous Machines.\" Thus a machine as shown diagram mat ically in Fig. 124, with a polyphase (three-phase) current impressed on the rotating armature, A, and no winding on the field po ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-19", "section_label": "Chapter 21: Regulating Pole Converters", "section_title": "Regulating Pole Converters", "kind": "chapter", "sequence": 19, "number": 21, "location": "lines 30088-31715", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-19/", "snippets": [ "... ter, as in Figs. 205 B and C, without affecting or appearing in the delta voltage, so can be used for varying the direct-current voltage, while the fifth harmonic can not be used in this way, but would reappear and 432 ELECTRICAL APPARATUS cause a short-circuit current in the supply voltage, hence should be made sufficiently small to be harmless. 235. The third harmonic thus can be used for varying the direct voltage in the three-phase converter diagrammatically shown in Fig. 206 A, and also in the six-phase co ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-22", "section_label": "Chapter 24: Conclusion", "section_title": "Conclusion", "kind": "chapter", "sequence": 22, "number": 24, "location": "lines 32820-33531", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-22/", "snippets": [ "... 1 Rotary terminal singlephase induc- tion motor, 172 S Secondary excitation of induction * motor, 52 Self induction of commutation, 420 Semi -inductor type of machine, 286 Series repulsion motor, 343, 374, 397 Shading coil starting device, 112 Short circuit rectifier, 237 Shunt resistance of rectifier, 235 and series motor starting of singlephase induction motor, 96 Singlephase commutator motor, 331 generation, 212, 229 induction motor, 93, 314 self starting by rotary ter- minals, 172 Six-phase rectifi ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-09", "section_label": "Chapter 9: Wave Screens. Even Harmonics", "section_title": "Wave Screens. Even Harmonics", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 16964-17631", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-09/", "snippets": [ "... f continuous voltage, such as a storage battery or direct-current WAVE SCREENS. EVEN HARMONICS 157 generator, at C, in the external circuit a pulsating voltage, e, and pulsating current, i, result. If the capacity, C, is so large as to practically short-circuit the alternating voltage, and the inductance, L, so high as to practically open-circuit the alternating voltage, the separation — of combi- nation — ^is practically complete, and independent of the frequency of the alternating wave. Wave screens based on ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-12", "section_label": "Chapter 12: Reactance Of Induction Apparatus", "section_title": "Reactance Of Induction Apparatus", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 22634-23465", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-12/", "snippets": [ "... the primary coil equals its resistance drop, eo = roi, then the Fig. 109. voltage across the secondary coil, s, gives the total reactance, x^, for s as primary, It would rarely be possible to vary the turns of the two coils, p and s. However, if we short-circuit s and pass an alternating current through p, then at the very low resultant magnetic flux and thus resultant m.m.f., primary and secondary current are practically in opposition and of the same m.m.f., and the mag- netic flux in the secondary coil is that ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-15", "section_label": "Chapter 15: Constant-Voltage Series Operation", "section_title": "Constant-Voltage Series Operation", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 27996-29301", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-15/", "snippets": [ "... tain circuit in case of one of the consuming devices open-circuiting On constant-current supply, a short-circuiting device, such as a film cutout, takes care of this. With series connection on con- stant-voltage supply, it is not permissible, however, to short- circuit a disabled consuming device, as this would increase the voltage on the other devices. Thus the shunt protective device in the constant-voltage series system must be such, that in case of one lamp burning out, the shunt consumes such a voltage as to mainta ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-16", "section_label": "Chapter 16: Load Balance Of Polyphase Systems", "section_title": "Load Balance Of Polyphase Systems", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 29302-30428", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-16/", "snippets": [ "... es and consequent re- duction of the output. The use of a squirrel-cage winding in the 314 LOAD BALANCE OF POLYPHASE SYSTEMS 315 field pole faces of the single-phase alternator reduces the pulsation of the field flux, but also increases the momentary short-circuit stresses. Thus, it is of interest to study the question of balancing unbal- anced polyphase circuits by stationary energy-storing devices, as reactor or condenser. 164. Let a voltage, e = E cos (1) be impressed upon a non-inductive load, giving ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-07", "section_label": "Chapter 3: The Natural Period Of The Transmission Line. 320", "section_title": "The Natural Period Of The Transmission Line. 320", "kind": "chapter", "sequence": 7, "number": 3, "location": "lines 836-874", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-07/", "snippets": [ "... ne end, grounded at other end. 322 30. Quarter-wave oscillation of transmission line. 323 31. Frequencies of line discharges, and complex discharge wave. 327 32. Example of discharge of line of constant voltage and zero current. 329 33. Example of short-circuit oscillation of line. 331 34. Circuit grounded at both ends : Half-wave oscillation. 333 35. The even harmonics of the half-wave oscillation. 334 36. Circuit open at both ends. 335 37. Circuit closed upon itself: Full-wave oscillation. 336 38. Wave s ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-25", "section_label": "Chapter 3: Inductance And Resistance In Continuous Current Circuits", "section_title": "Inductance And Resistance In Continuous Current Circuits", "kind": "chapter", "sequence": 25, "number": 3, "location": "lines 2659-3514", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-25/", "snippets": [ "... alue of ec at which self-excitation still takes place is given by equation (42) as ec = ^ = 20> that is, at one-third of full speed. If this series motor, with field and armature windings connected in generator position, — that is, reverse position, — short-circuits upon itself, r = 0.24 ohms, we have t = 0.0274 log e - 0.00073 log (876 - e) - 0.1075, (45) that is, self-excitation is practically instantaneous : e = 300 volts is reached after t = 0.044 seconds. Since for e = 300 volts, the current i = = 1250 a ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-29", "section_label": "Chapter 7: Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "section_title": "Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "kind": "chapter", "sequence": 29, "number": 7, "location": "lines 6798-7825", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "snippets": [ "... which the current should have at this moment. If, however, the circuit is closed at the moment where the current should be zero and the condenser e.m.f. maximum, the condenser being 104 TRANSIENT PHENOMENA without charge acts in the first moment like a short circuit, that is, the current begins at a value corresponding to the impressed e.m.f. divided by the line impedance. Thus if we neglect the resistance and if the condenser reactance equals n2 times line reactance, the current starts at n2 times its final rate; th ..." ] } ] }, { "id": "lightning-surges", "label": "Lightning and Surges", "aliases": [ "arrester", "arresters", "impulse", "impulses", "lightning", "surge", "surges" ], "total_occurrences": 648, "matching_section_count": 70, "matching_source_count": 12, "source_totals": [ { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 271, "section_count": 6 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 111, "section_count": 22 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 104, "section_count": 10 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 98, "section_count": 10 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 21, "section_count": 5 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 14, "section_count": 5 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 9, "section_count": 4 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 7, "section_count": 1 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 5, "section_count": 3 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 4, "section_count": 2 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 3, "section_count": 1 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 169, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... hing has yet been done in this direction systematically and intelligently, but all has been done by trial which at the best usually means producing more light than necessary, and throw- ing away the excess of diffused light by absorption. APPENDIX II LIGHTNING AND LIGHTNING PROTECTION Paper read before the Annual Convention of the National Electric Light Association, 1907. Revised to date. L LIGHTNING PHENOMENA IN THE CLOUDS. /n^ HE first man who attacked the problem of lightning and I lightning protectio ...", "... een done in this direction systematically and intelligently, but all has been done by trial which at the best usually means producing more light than necessary, and throw- ing away the excess of diffused light by absorption. APPENDIX II LIGHTNING AND LIGHTNING PROTECTION Paper read before the Annual Convention of the National Electric Light Association, 1907. Revised to date. L LIGHTNING PHENOMENA IN THE CLOUDS. /n^ HE first man who attacked the problem of lightning and I lightning protection, a century a ...", "... more light than necessary, and throw- ing away the excess of diffused light by absorption. APPENDIX II LIGHTNING AND LIGHTNING PROTECTION Paper read before the Annual Convention of the National Electric Light Association, 1907. Revised to date. L LIGHTNING PHENOMENA IN THE CLOUDS. /n^ HE first man who attacked the problem of lightning and I lightning protection, a century and half ago, was our -^ great citizen, Benjamin Franklin. He gave us the lightning rod, which is now universally recognized as the m ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-11", "section_label": "Lecture 11: Lightning Protection", "section_title": "Lightning Protection", "kind": "lecture", "sequence": 11, "number": 11, "location": "lines 4931-5294", "status": "candidate", "occurrence_count": 84, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-11/", "snippets": [ "ELEVENTH LECTURE LIGHTNING PROTECTION W\"~l HEN the first telegraph circuits were strung across the country, lightning protection became necessary, and ■^ was given to these circuits at the station by connecting spark gaps between the circuit conductors and the ground. When, how ...", "ELEVENTH LECTURE LIGHTNING PROTECTION W\"~l HEN the first telegraph circuits were strung across the country, lightning protection became necessary, and ■^ was given to these circuits at the station by connecting spark gaps between the circuit conductors and the ground. When, however, electric light and power circuits made their appearance, this protection against lightni ...", "... ghtning protection became necessary, and ■^ was given to these circuits at the station by connecting spark gaps between the circuit conductors and the ground. When, however, electric light and power circuits made their appearance, this protection against lightning by a simple small spark gap to ground became insufficient, and this addi- tional problem arose : to open the short circuit of the machine current, which resulted from and followed the lightning dis- charge. This problem of opening the circuit after the ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 32, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "... = ^6-^«'sin2(0Ta>-7), (2) and the average power flow is Po = avg p, (3) = 0. Hence, in a stationary oscillation, or standing wave of a uni- form circuit, the average flow of power, po, is zero, and no power flows along the circuit, but there is a surge of power, of double frequency. That is, power flows first one way, during one-quarter cycle, and then in the opposite direction, during the next quarter- cycle, etc. Such a transient wave thus is analogous to the permanent wave of reactive power. As i ...", "... (4) = eo^■oe-2\"' cos^ (0 T co - 7), 6o^o [1 + cos 2 ( =F CO -7)], (5) and the average flow of power is po = avg p, (6) Such a wave thus consists of a combination of a steady flow of power along the circuit, jpo, and a pulsation or surge, pi, of the same nature as that of the standing wave (2) : pi =^%-2\"*cos2((/)Tco-7). (7) Such a flow of power along the circuit is called a traveling wave. It occurs very frequently. For instance, it may be caused if by a lightning stroke, etc., a ...", "... and a pulsation or surge, pi, of the same nature as that of the standing wave (2) : pi =^%-2\"*cos2((/)Tco-7). (7) Such a flow of power along the circuit is called a traveling wave. It occurs very frequently. For instance, it may be caused if by a lightning stroke, etc., a quantity of dielectric energy is impressed Fig. 39. — Starting of Impulse, or Traveling Wave. upon a part of the circuit, as shown by curve A in Fig. 39, or if by a local short circuit a quantity of magnetic energy is impressed upon a ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 4745-5520", "status": "candidate", "occurrence_count": 32, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "snippets": [ "... = ^|V2«=Fco-7), (2) and the average power flow is Po = avg p, (3) = 0. Hence, in a stationary oscillation, or standing wave of a uni- form circuit, the average flow of power, p0, is zero, and no power flows along the circuit, but there is a surge of power, of double frequency. That is, power flows first one way, during one-quarter cycle, and then in the opposite direction, during the next quarter- cycle, etc. Such a transient wave thus is analogous to the permanent wave of reactive power. As i ...", "... In this case the flow of power is (4) P = = eQiQe-2ut cos2 co - 7), and the average flow of power is p0 = avg p, (5) (6) Such a wave thus consists of a combination of a steady flow of power along the circuit, p0) and a pulsation or surge, pi, of the same nature as that of the standing wave (2) : Such a flow of power along the circuit is called a traveling wave. It occurs very frequently. For instance, it may be caused if by a lightning stroke, etc., a quantity of dielectric energy is imp ...", "... flow of power along the circuit, p0) and a pulsation or surge, pi, of the same nature as that of the standing wave (2) : Such a flow of power along the circuit is called a traveling wave. It occurs very frequently. For instance, it may be caused if by a lightning stroke, etc., a quantity of dielectric energy is impressed A • Fig. 39. — Starting of Impulse, or Traveling Wave. upon a part of the circuit, as shown by curve A in Fig. 39, or if by a local short circuit a quantity of magnetic energy is impressed up ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-45", "section_label": "Chapter 5: Distributed Series Capacity", "section_title": "Distributed Series Capacity", "kind": "chapter", "sequence": 45, "number": 5, "location": "lines 23586-23947", "status": "candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "snippets": [ "... elements of the circuit are short enough so as to be represented, approximately, as conductor differentials, the circuit constitutes a circuit with distributed series capacity. An illustration of such a circuit' is afforded by the so-called \" multi-gap lightning arrester,\" as shown diagrammatically in Fig. 90, which consists of a large number of metal cylinders p, q . . . , with small spark gaps between the cylinders, connected between line L and ground G. This arrangement, Fig. 90, can be represented diagrammati ...", "... of the circuit are short enough so as to be represented, approximately, as conductor differentials, the circuit constitutes a circuit with distributed series capacity. An illustration of such a circuit' is afforded by the so-called \" multi-gap lightning arrester,\" as shown diagrammatically in Fig. 90, which consists of a large number of metal cylinders p, q . . . , with small spark gaps between the cylinders, connected between line L and ground G. This arrangement, Fig. 90, can be represented diagrammatically by ...", "... SERIES CAPACITY 349 the cylinders from q to the ground G, Figs. 90 and 91, must pass the gap between the adjacent cylinders p and g; that is, the charging current of the condenser represented by two adjacent -00000000000000-1 Fig. 90. Multi-gap lightning arrester. cylinders p and q is the sum of all the charging currents from qtoG', and as the potential difference between the two cylinders p and q is proportional to the charging current of the condenser 'filMI — i T Fig. 91. Equivalent circuit of ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "section_label": "Lecture 10: Continual And Cumulative Oscillations", "section_title": "Continual And Cumulative Oscillations", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... ulative oscillation thus involves an energy and frequency transformation, from the low-frequency or con- tinuous-current energy of the power supply of the system to the high-frequency energy of the oscillation. 119 120 ELECTRICAL DISCHARGES, WAVES AND IMPULSES This energy transformation may be brought about by the transient of energy readjustment, resulting from a change of circuit conditions, producing again a change of circuit conditions and thereby an energy readjustment by transient, etc. For instance, i ...", "... oscillation, that is, there must be such a phase displacement or lag within the oscil- lation, which gives a negative energy cycle, or reversed hysteresis loop. Thus, essential for such a continual oscillation is the 124 ELECTRICAL DISCHARGES, WAVES AND IMPULSES existence of a hysteresis loop, formed by the lag of the effect be- hind the cause. Such a hysteresis loop exists in the transient arc, as illustrated by Fig. 66: the transient volt-ampere charac- teristic of a short high-temperature metal arc, between t ...", "... tic of High Temperature Metal Arc Ti - C. 1 1 en \\\\ \\ ior> ■ \\ \\ \\ \\ ^ Vi A ■;^ 100 ' \\ \\ \\ K N :^ ^^ ZTtZn ^ ' nA c ] Ami 3 eres i V 0 Fig. 66. 126 ELECTRICAL DISCHARGES, WAVES AND IMPULSES 45. The frequency of the oscillations usually is the natural frequency of the oscillating circuit or section of circuit; but it may be some of the higher harmonics of the generator wave, where such harmonic is near the natural frequency of the system. T ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "CHAPTER II. LONG-DISTANCE TRANSMISSION LINE. 3. If an electric impulse is sent into a conductor, as a trans- mission line, this impulse travels along the line at the velocity of light (approximately), or 188,000 miles per second. If the line is open at the other end, the impulse there is reflected and returns at the same vel ...", "CHAPTER II. LONG-DISTANCE TRANSMISSION LINE. 3. If an electric impulse is sent into a conductor, as a trans- mission line, this impulse travels along the line at the velocity of light (approximately), or 188,000 miles per second. If the line is open at the other end, the impulse there is reflected and returns at the same velocity. If now at the moment when the impulse arrives at the start ...", "... DISTANCE TRANSMISSION LINE. 3. If an electric impulse is sent into a conductor, as a trans- mission line, this impulse travels along the line at the velocity of light (approximately), or 188,000 miles per second. If the line is open at the other end, the impulse there is reflected and returns at the same velocity. If now at the moment when the impulse arrives at the starting point a second impulse, of opposite direction, is sent into the line, the return of the first impulse adds itself, and so increases the seco ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "LECTURE VII. LINE OSCILLATIONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy surges between magnetic — and dielectric — , and a transient component, by which the total stored energy decreases. Considering only the periodic component, the maximum value of magnetic energy must equal the maximum value of dielectric '^'^e^gy- Li„^ Ce, ...", "... e of dielectric '^'^e^gy- Li„^ Ce, 0 \"^^0 (1) where Iq = maximum value of transient current, 60 = maximum value of transient voltage. This gives the relation between Bq and Iq, ^^ = Jl ,^ = 1, (2) where Zq is called the natural impedance or surge impedance, 2/0 the natural or surge admittance of the circuit. As the maximum of current must coincide with the zero of voltage, and inversely, if the one is represented by the cosine function, the other is the sine function; hence the periodic com- pon ...", "... 0 \"^^0 (1) where Iq = maximum value of transient current, 60 = maximum value of transient voltage. This gives the relation between Bq and Iq, ^^ = Jl ,^ = 1, (2) where Zq is called the natural impedance or surge impedance, 2/0 the natural or surge admittance of the circuit. As the maximum of current must coincide with the zero of voltage, and inversely, if the one is represented by the cosine function, the other is the sine function; hence the periodic com- ponents of the transient are ii = Iq c ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3956-4744", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "snippets": [ "LECTURE VII. LINE OSCILLATIONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy 7\" /j'2 f^ r/>2 surges between magnetic -^- and dielectric — , and a transient £i A component, by which the total stored energy decreases. Considering only the periodic component, the maximum mag- netic energy must equal the maximum dielectric energy, Lio2 _ Ceo2 \"2\" ~2~' ...", "... must equal the maximum dielectric energy, Lio2 _ Ceo2 \"2\" ~2~' where i0 = maximum transient current, e0 = maximum transient voltage. This gives the relation between eQ and io, e0 V/L_ 1 i-0 = \\C-ZQ-yQ' where ZQ is called the natural impedance or surge impedance, y0 the natural or surge admittance of the circuit. As the maximum of current must coincide with the zero of voltage, and inversely, if the one is represented by the cosine function, the other is the sine function; hence the periodic com- pone ...", "... nergy, Lio2 _ Ceo2 \"2\" ~2~' where i0 = maximum transient current, e0 = maximum transient voltage. This gives the relation between eQ and io, e0 V/L_ 1 i-0 = \\C-ZQ-yQ' where ZQ is called the natural impedance or surge impedance, y0 the natural or surge admittance of the circuit. As the maximum of current must coincide with the zero of voltage, and inversely, if the one is represented by the cosine function, the other is the sine function; hence the periodic com- ponents of the transient are ii = IQ c ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2485-3386", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-04/", "snippets": [ "... the change occurs at the moment when the two currents ii and 12 have the greatest difference, as shown in Fig. 15C, that is, at a point one-quarter period or 90 degrees distant from the intersec- tion of ii and 12. 32 ELECTRIC DISCHARGES, WAVES AND IMPULSES. If the current ii is zero, we get the starting of the alternating current in an inductive circuit, as shown in Figs. 16, A, B,C. The starting transient is zero, if the circuit is closed at the moment when the permanent current would be zero (Fig. 165), ...", "... sient currents also is zero. Since the three transient curves ii^, 12^, 4° are pro- portional to each other fas exponential curves of the same dura- tion T = —\\ and the sum of their initial values is zero, it follows 84 ELECTRIC DISCHARGES, WAVES AND IMPULSES. that the sum of their instantaneous values must be zero at any moment, and therefore the sum of the instantaneous values of the resultant currents (shown in drawn line) must be zero at any moment, not only during the permanent condition, but also dur- ...", "... tc., under the angles, that is, in the direction corresponding to the time 0, ^1, t2, etc. This is done in Fig. 19, and thereby the transient of the rotating field is constructed. Fig. 19, — Starting Transient of Rotating Field: Polar Form. WAVES AND IMPULSES. From this polar diagram of the rotating field, in Fig. 19, values OC can now be taken, corresponding to successive moments of time, and plotted in rectangular coordinates, as done in Fig. 20. As seen, the rotating field builds up from zero at the moment ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2162-2971", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "snippets": [ "... if the change occurs at the moment when the two currents i\\ and iz have the greatest difference, that is, at a point one-quarter period or 90 degrees distant from the intersection of i\\ and 12, as shown in Fig. 15C. 32 ELECTRIC DISCHARGES, WAVES AND IMPULSES. If the current ii is zero, we get the starting of the alternating current in an inductive circuit, as shown in Figs. 16, A, B, C. The starting transient is zero, if the circuit is closed at the moment when the permanent current would be zero (Fig. 16B) ...", "... ient currents also is zero. Since the three transient curves ii°, i'2°, iz° are pro- portional to each other fas exponential curves of the same dura- tion T = — ], and the sum of their initial values is zero, it follows 34 ELECTRIC DISCHARGES, WAVES AND IMPULSES. that the sum of their instantaneous values must be zero at any moment, and therefore the sum of the instantaneous values of the resultant currents (shown in drawn line) must be zero at any moment, not only during the permanent condition, but also dur- ...", "... that is, in the direction corresponding to the time 0, ^ t2, etc. This is done in Fig. 19, and thereby the transient of the rotating field is constructed. Fig. 19. — Starting Transient of Rotating Field: Polar Form. 36 ELECTRIC DISCHARGES, WAVES AND IMPULSES. _From this polar diagram of the rotating field, in Fig. 19, values OC can now be taken, corresponding to successive moments of time, and plotted in rectangular coordinates, as done in Fig. 20. As seen, the rotating field builds up from zero at the momen ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-47", "section_label": "Chapter 7: Distribution Of Alternating-Current Density In Conductor", "section_title": "Distribution Of Alternating-Current Density In Conductor", "kind": "chapter", "sequence": 47, "number": 7, "location": "lines 24981-26094", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "snippets": [ "... ductor, as for instance iron wires in high potential transmissions for branch lines of smaller power, or steel cables for long spans in transmission lines. (3) In the rail return of single-phase railways. (4) When carrying very high frequencies, such as lightning discharges, high frequency oscillations. In the last two cases, which probably are of the greatest impor- tance, the unequal current distribution usually is such that practically no current exists at the conductor center, and the effective resistance of ...", "... s at the conductor center, and the effective resistance of the track rail even for 25-cycle alternating current thus is several times greater than the ohmic resistance, and conductors of low ohmic resistance may offer a very high effective resistance to a lightning stroke. By subdividing the conductor into a number of smaller conductors, separated by some distance from each other, or by the use of a hollow -conductor, or a flat conductor, as a bar or ribbon, the effect is reduced, and for high-frequency discharges, ...", "... ke. By subdividing the conductor into a number of smaller conductors, separated by some distance from each other, or by the use of a hollow -conductor, or a flat conductor, as a bar or ribbon, the effect is reduced, and for high-frequency discharges, as lightning arrester connections, flat copper ribbon offers a very much smaller effective resistance than a round wire. Strand- ing the conductor, however, has no direct effect on this phenom- enon, since it is due to the magnetic action of the current, and the magne ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-10", "section_label": "Lecture 10: Inductance And Capacity Of Round Parallel Conductors", "section_title": "Inductance And Capacity Of Round Parallel Conductors", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6089-7274", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "snippets": [ "... foci) inside of the con- ductors, as shown in Fig. 9, page 11. With more than one return conductor, and with phase displacement between the return currents, as in a three-phase three-wire circuit, the path of the 119 'iJBLtiGTRIC DISCHARGES, WAVES AND IMPULSES. lines of force is still more complicated, and varies during the cyclic change of current. The calculation of such more complex magnetic and dielectric fields becomes simple, however, by the method of superposition of fields. As long as the magnetic a ...", "... from the conductor center, the length of the mag netic circuit is 2 irx, and if F = m.m.f. of the conductor, the mag- netizing force is and the field intensity hence the magnetic density (B 2F x (4) (5) 122 ELECTRIC DISCHARGES, WAVES AND IMPULSES. and the magnetic flux in the zone dx thus is d^=^fdx, I (6) and the magnetic flux interlinked with the conductor thus is X hence the total magnetic flux between the distances x\\ and z2 is rx*2 thus the inductance X 1. External magnetic fl ...", "... of conductors, and s = distance between conductor centers. Assuming uniform current density in the conductors, the flux distribution of conductor A then is as indicated diagrammatically in Fig. 61. * 0.4343 = log10*, 124 ELECTRIC DISCHARGES, WAVES AND IMPULSES. The flux then consists of three parts: 3>i, between the conductors, giving the inductance and shown shaded in Fig. 61. $2, inside of conductor A, giving the inductance $3, the flux external to A, which passes through conductor B and thereby inclo ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3721-4369", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-06/", "snippets": [ "... rgy storage by the cur- rent, r = resistance = coefficient of power dissipation by the current. If the energy is stored by the voltage e, as dielectric field, the duration of the transient would be TV - -, (3) g 59 60 ELECTRIC DISCHARGES, WAVES AND IMPULSES. where C = capacity = coefficient of energy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power consumption by the voltage, as leakage conductance by the voltage, corona, dielectric hysteresis, etc. Thus the tr ...", "... y, it obviously is This gives a relation between the maximum value of transient current and the maximum value of transient voltage: '\" \\l^- (9) v/ U V c -^ therefore is of the nature of an impedance z^^ and is called the natural impedance, or the surge im'pedance, of the circuit ; and Ic its reciprocal, \\ j = Vq, is the natural admittance, or the surge admittance, of the circuit. 62 ELECTRIC DISCHARGES, WAVES AND IMPULSES. The maximum transient voltage can thus be calculated from the maximum tran ...", "... value of transient voltage: '\" \\l^- (9) v/ U V c -^ therefore is of the nature of an impedance z^^ and is called the natural impedance, or the surge im'pedance, of the circuit ; and Ic its reciprocal, \\ j = Vq, is the natural admittance, or the surge admittance, of the circuit. 62 ELECTRIC DISCHARGES, WAVES AND IMPULSES. The maximum transient voltage can thus be calculated from the maximum transient current: eo = ^0 y g = ^'o^Jo, (10) and inversely, fc ^0 = eo y Y = eo2/o. (11) This relat ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3287-3955", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "snippets": [ "... gy storage by the cur- rent, r = resistance = coefficient of power dissipation by the current. If the energy is stored by the voltage e, as dielectric field, the duration of the transient would be TJ = -, (3) s/ 59 60 ELECTRIC DISCHARGES, WAVES AND IMPULSES. where C = capacity = coefficient of energy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power consumption by the voltage, as leakage conductance by the voltage, corona, dielectric hysteresis, etc. Thus the tr ...", "... s dielectric energy, it obviously is W _ Ceo2 ~2~ ~2\" This gives a relation between the maximum transient current and the maximum transient voltage: v/: -^ therefore is of the nature of an impedance z0, and is called the natural impedance, or the surge impedance, of the circuit ; and fc its reciprocal, V/y = yo, is the natural admittance, or the surge T J j admittance, of the circuit. 62 ELECTRIC DISCHARGES, WAVES AND IMPULSES. The maximum transient voltage can thus be calculated from the maxi ...", "... sient current and the maximum transient voltage: v/: -^ therefore is of the nature of an impedance z0, and is called the natural impedance, or the surge impedance, of the circuit ; and fc its reciprocal, V/y = yo, is the natural admittance, or the surge T J j admittance, of the circuit. 62 ELECTRIC DISCHARGES, WAVES AND IMPULSES. The maximum transient voltage can thus be calculated from the maximum transient current: #0 = 'Z'O V/ 7> = i&Qj (10) and inversely, /C io = eo y j = e02/o. (11) T ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-07", "section_label": "Lecture 7: High Frequency Oscillations And Surges", "section_title": "High Frequency Oscillations And Surges", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3508-3780", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-07/", "snippets": [ "SEVENTH LECTURE HIGH FREQUENCY OSCILLATIONS AND SURGES 1\"^ N an electric circuit, in addition to the power consump- tion by the resistance of the lines, an energy storage ■^ occurs as electrostatic energy, or electrostatic charge due to the voltage on the line (capacity) ; and as electromag- netic energy, ...", "... is, the wave length is very considerable. If the readjustment of stored energy takes place only over a section of the circuit, the wave length is shorter. For instance, if by a thunder cloud a static charge is induced on the trans- mission line, and by a lightning flash in the cloud, the cloud discharges, the electrostatic charge induced by it on the line HIGH FREQUENCY OSCILLATIONS 93 is set free and dissipates by an oscillation. In this case, the length of section on which an abnormal charge existed — one mil ...", "... ipates by an oscillation. In this case, the length of section on which an abnormal charge existed — one mile for instance — is a half wave of the oscillation, and the complete wave length would thus be two miles. Or, if a momentary discharge occurs over a lightning arrester to ground, the wave length may be only a few feet. The velocity with which the electric wave travels in an overhead line is practically the velocity of light, or about 188,000 miles per second: it would be exactly the velocity of light, except ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-49", "section_label": "Chapter 9: High-Frequency Conductors", "section_title": "High-Frequency Conductors", "kind": "chapter", "sequence": 49, "number": 9, "location": "lines 27003-27760", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "snippets": [ "CHAPTER IX. HIGH-FREQUENCY CONDUCTORS. 80. As the result of the phenomena discussed in the preceding chapters, conductors intended to convey currents of very high frequency, as lightning discharges, high frequency oscillations of transmission lines, the currents used in wireless telegraphy, etc., cannot be calculated by the use of the constants derived at low frequency, but effective resistance and inductance, and therewith the power cons ...", "... ed by the conductor, and the voltage drop, may be of an entirely different magnitude from the values which would be found by using the usual values of resistance and induc- tance. In conductors such as are used in the connections and the discharge path of lightning arresters and surge protectors, the unequal current distribution in the conductor (Chapter VII) and the power and voltage consumed by electric radiation, due to the finite velocity of the electric field (Chapter VIII), require con- sideration. The true ...", "... conductor, and the voltage drop, may be of an entirely different magnitude from the values which would be found by using the usual values of resistance and induc- tance. In conductors such as are used in the connections and the discharge path of lightning arresters and surge protectors, the unequal current distribution in the conductor (Chapter VII) and the power and voltage consumed by electric radiation, due to the finite velocity of the electric field (Chapter VIII), require con- sideration. The true ohmic resi ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-43", "section_label": "Chapter 3: The Natural Period Of The Transmission Line", "section_title": "The Natural Period Of The Transmission Line", "kind": "chapter", "sequence": 43, "number": 3, "location": "lines 21721-23178", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "snippets": [ "... of the long distance transmission line given in the preceding chapter can be made to the determination of the natural period of a transmis- sion line; that is, the frequency at which such a line discharges an accumulated charge of atmospheric electricity (lightning), or oscillates because of a sudden change of load, as a break of circuit, or in general a change of circuit conditions, as closing the circuit, etc. The discharge of a condenser through a circuit containing self- inductance and resistance is oscillatin ...", "... smission line open at one end. The discharge waves, n = 2, are shown in Fig. 86, those with n = 3, with two nodal points, in Fig. 87. \\ A / Fig. 87. Discharge of current and e.m.f. along a transmission line open at one end. 31. In case of a lightning discharge the capacity C0 is the capacity of the line against ground, and thus has no direct relation to the capacity of the line conductor against its return. The same applies to the inductance L0. If d = diameter of line conductor, lh= height of conduc ...", "... VS 2>cn sin (2 n - 1) (6 - rj sin (2 n - 1) r. (26) A simple harmonic oscillation as a line discharge would require a sinoidal distribution of potential on the transmission line at the instant of discharge, which is not probable, so that probably all lightning discharges of transmission lines or oscillations produced by sudden changes of circuit conditions are complex waves of many harmonics, which in their relative magnitude depend upon the initial charge and its distribution — that is, in the case of the ligh ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... ty of propagation < EN ERGY-SU PPLY- o — ^^ — o FIG. 13. has been measured by Herz by producing standing waves by combination of main wave and reflected wave. Still much higher frequencies are the oscillations between the cylinders of multi-gap lightning arresters, and the limit of fre- quency of electric waves would probably be given by the oscilla- ting discharge of two small spheres against each other when separated by a narrow gap. It probably is at about 5 X 1010 cycles, or 0.6 cm. wave length. The ...", "... agation < EN ERGY-SU PPLY- o — ^^ — o FIG. 13. has been measured by Herz by producing standing waves by combination of main wave and reflected wave. Still much higher frequencies are the oscillations between the cylinders of multi-gap lightning arresters, and the limit of fre- quency of electric waves would probably be given by the oscilla- ting discharge of two small spheres against each other when separated by a narrow gap. It probably is at about 5 X 1010 cycles, or 0.6 cm. wave length. The blank spa ...", "... ycles. Wave Length in Air (or Vacuum). Octave: Q^/ £. Alternating current 1> field: 15 20,000 km. = 12,500 mi. 25 12.000 km. = 7, 500 mi. 3.15 60 5, 000 km. = 3, 100 mi. 133 2,250 km. = 1,400 mi. High frequency cur- \\ rents, surges and oscillations, arcing V (9.57) 31.64 grounds, lightning phenomena, etc. J Wireless telegraph ( 105 3 km. = 10,000 ft. 9.63 ) A ~, waves : ( 107 30 m. = 100 ft. 16.25 \\ 6'62 Herzian waves: 107 109 30 m. = 100 ft. 30 cm. = 1 ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-10", "section_label": "Chapter 10: Instability Of Circuits : The Arc", "section_title": "Instability Of Circuits : The Arc", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 17632-21381", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-10/", "snippets": [ "... onary condition, and where phenomena of instability occurred, and made themselves felt as disturbances or troubles in electric circuits, they either remained imunderstood or the theo- retical study was limited to the specific phenomenon, as in the case of lightning, dropping out of step of induction motors, hunt- ing of synchronous machines, etc., or, as in the design of arc lamps and arc-lighting machinery, the opinion prevailed that theoretical calculations are impossible and only design by trying, based on practi ...", "... ly, on transients, and a great mass of information is thus available in the literature. These transients are more ex- tensively treated in \"Theory and Calculation of Transient Elec- tric Phenomena and Oscillations,\" and in \" Electric Discharges, Waves and Impulses, '' and therefore will be omitted in the fol- lowing. However, to some extent, the transients of our theoret- ical literature, still are those of the \"phantom circuit,\" that is, a circuit in which the constants r, L, C, g, are assumed as constant. The eff ...", "... re not in- cluded in the theoretical equations. Especially deficient is oiu* knowledge of the conditions under which the attenuation constant of the transient becomes zero or negative, and the transient thereby becomes permanent, or becomes a cumulative surge, and the phenomenon thereby one of unstable equilibrium. II. Unstable Electrical Equilibbixjm 83. If the effect brought about by a cause is such as to oppose or reduce the cause, the effect must limit itself and stability be finally reached. If, howeve ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... ation 483 Hertzian oscillators 388 High frequency alternators, momentary short-circuit current 201 conductor 370, 403 discharge 388 oscillating currents by periodic transient terms 220 oscillations of cables and transmission lines 103, 105 power surge of low-frequency 105 stray field and starting current of transformer 189 Impact angle at transition point of wave 527 Impedance of conductor at high frequency 407 effective high frequency 408, 413 of radiation 396 traveling wave 460 Inductance a ...", "... 408 Laminated iron, alternating magnetic flux 355 pole series booster, response to voltage change 158 Layer, effective, of alternating-current conductor 377 Leakage in telephone lines 455, 463 Length of wave 433 Lighting circuit, starting 27, 44 Lightning arrester, multigap 348 conductors 370 discharges 388 in thunder cloud 350 Limit condition of condenser equations 50 of frequency of condenser oscillations 73 Loading of telephone lines 455, 462 Local oscillations of cables and lines 103, 105 L ...", "... nated iron, alternating magnetic flux 355 pole series booster, response to voltage change 158 Layer, effective, of alternating-current conductor 377 Leakage in telephone lines 455, 463 Length of wave 433 Lighting circuit, starting 27, 44 Lightning arrester, multigap 348 conductors 370 discharges 388 in thunder cloud 350 Limit condition of condenser equations 50 of frequency of condenser oscillations 73 Loading of telephone lines 455, 462 Local oscillations of cables and lines 103, 105 Logarithmi ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1659-2484", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-03/", "snippets": [ "... GY TRANSIENTS IN CONTINUOUS- CURRENT CIRCUITS. 13. The simplest electrical transients are those in circuits in which energy can be stored in one form only, as in this case the change of stored energy can consist only of an increase or decrease ; but no surge or oscillation between several forms of energy can exist. Such circuits are most of the low- and medium-voltage circuits, — 220 volts, 600 volts, and 2200 volts. In them the capac- ity is small, due to the limited extent of the circuit, resulting from the ...", "... 1 Fig. 10. — Magnetic Single-energy Transient. negligible capacity), a magnetic field $0 10' Lio interlinks with the coil. Assuming now that the voltage eo is suddenly withdrawn, without changing 19 20 ELECTRIC DISCHARGES, WAVES AND IMPULSES. the constants of the coil circuit, as for instance by short- circuiting the terminals of the coil, as indicated at A. With no voltage impressed upon the coil, and thus no power supplied to it, current i and magnetic flux $ of the coil must finally be z ...", "... e caused, for instance, by a gradual increase of the resistance of the coil circuit), the induced voltage would retain its initial value eo up to the moment of time t = to -\\- T, where the current has fallen to zero, as 22 ELECTRIC DISCHARGES, WAVES AND IMPULSES. shown dotted in Fig. llC The area of this new voltage curve would be CqT, and since it is the same as that of the curve e, as seen above, it follows that the area of the voltage curve e is (3) Se^ = eoT, I = rioT, I and, combining (2) and (3), I ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 6125-6803", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-09/", "snippets": [ "... e circuit in velocity measure is Xi = aoh, where o-q = v LoCo. Thus, if L = inductance, C = capacity per transformer coil, n = number of transformer coils, for the transformer the unit of length is the coil; hence the 110 ELECTRIC DISCHARGES, WAVES AND IMPULSES. Ui = 900 = power- dissipation constant of the line, W2 = 100 = power-dissipation constant of transformer, and u^ = 1600 = power- dissipation constant of the load, and the respective lengths of the circuit sections are Xi = 1.5 X 10-3; X2 = 1 X 10-3; X ...", "... nodes, or points over which no power flows, one in the transformer and one in the load, and the power flows from the transformer over the line into the load; the transformer acts as generator of the power, and of this 112 ELECTRIC DISCHARGES, WAVES AND IMPULSES. power a fraction is consumed in the line, the rest suppUed to the load. 40. The diagram of this transient power transfer of the system thus is very similar to that of the permanent power transmis- sion by alternating currents: a source of power, a par ...", "... illustration may be considered a circuit comprising the high- potential coil of the step-up transformer, and the two lines, which are assumed as open at the step-down end, as illustrated diagram- matically in Fig. 56. 114 ELECTRIC DISCHARGES, WAVES AND IMPULSES. Choosing the same lengths and the same power-dissipation constants as in the previous illustrations, this gives: Line. 1.5X10-3 900 1.35 2 2/ A Transformer. 1X10-3 100 .1 iience, Wo = average u = —— = 700, and: S = —2^0 +60 ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1531-2161", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "snippets": [ "... RGY TRANSIENTS IN CONTINUOUS- CURRENT CIRCUITS. 13. The simplest electrical transients are those in circuits in which energy can be stored in one form only, as in this case the change of stored energy can consist only of an increase or decrease ; but no surge or oscillation between several forms of energy can exist. Such circuits are most of the low- and medium-voltage circuits, — 220 volts, 600 volts, and 2200 volts. In them the capac- ity is small, due to the limited extent of the circuit, resulting from the ...", "... ance L (but negligible capacity). A current iQ = — flows through the coil and a magnetic field $0 10~8 = - - interlinks with the coil. Assuming now that the voltage e0 is suddenly withdrawn, without changing 19 20 ELECTRIC DISCHARGES, WAVES AND IMPULSES. the constants of the coil circuit, as for instance by short- circuiting the terminals of the coil, as indicated at A, with no voltage impressed upon the coil, and thus no power supplied to it, current i and magnetic flux <£ of the coil must finally be z ...", "... be caused, for instance, by a gradual increase of the resistance of the coil circuit), the induced voltage would retain its initial value e0 up to the moment of time t = tQ + T, where the current has fallen to zero, as 22 ELECTRIC DISCHARGES, WAVES AND IMPULSES. shown dotted in Fig. 11C. The area of this new voltage curve would be e0T, and since it is the same as that of the curve e, as seen above, it follows that the area of the voltage curve e is = ri.r, and, combining (2) and (3), i0 cancels, and we get ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 5521-6088", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "snippets": [ "... circuit in velocity measure is Xi = o-oZi, where S2 = ...", "... by the following examples : Example 4. In an impulse turbine, the speed of the jet (steam jet or water jet) is Si. At what peripheral speed So is the output a maximum. The impulse force is proportional to the relative speed of the jet and the rotating impulse wheel; that is, to {S1-S2). The power is impulse force times speed S2\\ hence, P=^kS2{S^-S2), (3) and is an extreme for the value of S2, given by -j^ =^0; hence, Si-2>S2 = 0 and S2 = ^] (4) that is, when the peripheral speed of the impulse wheel equa ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-09", "section_label": "Lecture 9: Hunting Of Synchronous Machines", "section_title": "Hunting Of Synchronous Machines", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 4218-4594", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-09/", "snippets": [ "... t in motion, that is, the lower the frequency. Characteristic of this hunting therefore is that its fre- quency is changed by changing the field excitation. 2nd. If the speed of the engine varies during the rota- tion, rising and falling with the steam impulses, then the alternator speed and the frequency also pulsate with a speed equal to, or a multiple of the engine speed. If now two HUNTING OF SYNCHRONOUS MACHINES 117 such alternators happen to be thrown together so that the moment of maximum frequency of ...", "... st harmless, but increases the tendency to the hunting in No. I and No. 3, and therefore is not desirable; but steadiness of engine speed should be secured by the design of the engine, that is, by balancing the different forces in the engine, as the steam impulses and the momentum of the reciprocating masses, so as to give a uniform resultant. In such a case, when running from a single alternator, driven by a reciprocating engine with moderate speed pulsa- tion, (therefore receiving a slightly pulsating frequency) ...", "... ot hunting, but energy current required to make the motor speed follow the engine pulsation. If the frequency of oscillation of the machine (as deter- mined by its field excitation and the weight of its moving part) is the same as the frequency of engine impulses, that is, the same as the number of engine revolutions or a multiple thereof, then successive engine impulses will always come at the same moment of the machine beat and so continuously increase it: that is, the machine oscillation increases, or the mach ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... ing currents, and the means of producing such currents by disturbing the equi- 352 ELECTRIC CIRCUITS librium of the electric circuit; for instance, by the discharge of a condenser, by make-and-break of the circuit, by sudden electro- static charge, as lightning, etc. Obviously, the 'most important oscillating currents are those in a circuit of zero impedance, representing oscillating discharges of the circuit. Lightning strokes frequently belong to this class. Oscillating Discharges 193. The condition of an os ...", "... charge of a condenser, by make-and-break of the circuit, by sudden electro- static charge, as lightning, etc. Obviously, the 'most important oscillating currents are those in a circuit of zero impedance, representing oscillating discharges of the circuit. Lightning strokes frequently belong to this class. Oscillating Discharges 193. The condition of an oscillating discharge is Z = 0, that is, 1 o / ^ ^ 1^ T \\r^C 2aL 2L If r = 0, that is, in a circuit without resistance, we have a = 0, / = /=^j that is, ...", "... / = 0; that is, the current dies out without oscillation. From the foregoing we have seen that oscillating discharges — as for instance the phenomena taking place if a condenser charged to a given potential is discharged through a given circuit, or if lightning strikes the line circuit — are defined by the equation, Z = dec a. Since / = (h -- ji2) dec a, ^r = Jr dec a, ^z = - xj{a - j) dec a, ^r, = f\"^^ /(- « - J) dec a, we have r — ax — —-. — 5 Xc = 0, 1 + a hence, by substitution, f!x^ = xj {— a — j ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-30", "section_label": "Chapter 8: Low Frequency Surges In High Potential Systems", "section_title": "Low Frequency Surges In High Potential Systems", "kind": "chapter", "sequence": 30, "number": 8, "location": "lines 7826-9227", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "snippets": [ "CHAPTER VIII. LOW FREQUENCY SURGES IN HIGH POTENTIAL SYSTEMS. 64. In electric circuits of considerable capacity, that is, in extended high potential systems, as long distance transmission lines and underground cable systems, occasionally destructive high potential low frequency surges occ ...", "... NCY SURGES IN HIGH POTENTIAL SYSTEMS. 64. In electric circuits of considerable capacity, that is, in extended high potential systems, as long distance transmission lines and underground cable systems, occasionally destructive high potential low frequency surges occur; that is, oscillations of the whole system, of the same character as in the case of localized capacity and inductance discussed in the preceding chapter. While a system of distributed capacity has an infinite number of frequencies, which usually a ...", "... f the higher frequencies is negligible, the oscillation can be approxi- mated by the equations of oscillation given in Chapters V and VII, which are far simpler than the equations of an oscillation of a system of distributed capacity. Such low frequency surges comprise the total system, not only the transmission lines but also the step-up transformers, gen- erators, etc., and in an underground cable system in such an oscillation the capacity and inductance are indeed localized to a certain extent, the one in th ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1003-1658", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-02/", "snippets": [ "... magnetic field represents stored energy ly. To produce it, power, p, must therefore be supplied by the circuit. Since power is current times voltage : P = e'i, (2) * n^, if the flux interlinks the circuit n fold. 12 ELECTRIC DISCHARGES, WAVES AND IMPULSES. to produce the magnetic field $ of the current i, a voltage e' must be consumed in the circuit, which with the current i gives the power p, which supplies the stored energy w of the magnetic field $. This voltage e' is called the inductance voltage, or ...", "... with the dielectric fields the prehistoric conception of the electrostatic charge on the conductor still exists, and by its use destroys the analogy between the two components of the electric field, the magnetic and the 14 ELECTRIC DISCHARGES, WAVES AND IMPULSES. dielectric, and makes the consideration of dielectric fields un- necessarily complicated. There obviously is no more sense in thinking of the capacity current as current which charges the conductor with a quantity of electricitj^, than there is of spe ...", "... ctor 10-^ also appears undesirable, but when the electrical units were introduced the absolute unit appeared as too large a value of current as practical unit, and one-tenth of it was chosen as unit, and called \"ampere.\" 16 ELECTRIC DISCHARGES, WAVES AND IMPULSES. This gives the average voltage gradient, while the actual gradient in an ununiform field, as that between two conductors, varies, being higher at the denser, and lower at the less dense, portion of the field, and is 47r then is the dielectric-field i ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 883-1530", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "snippets": [ "... ed the inductance of the circuit. = Li. (1) The magnetic field represents stored energy w. To produce it, power, p, must therefore be supplied by the circuit. Since power is current times voltage, p = e'i. (2) 12 ELECTRIC DISCHARGES, WAVES AND IMPULSES. To produce the magnetic field $ of the current i, a voltage ef must be consumed in the circuit, which with the current i gives the power p, which supplies the stored energy w of the magnetic field . This voltage er is called the inductance voltage, o ...", "... with the dielectric fields the prehistoric conception of the electrostatic charge on the conductor still exists, and by its use destroys the analogy between the two components of the electric field, the magnetic and the 14 ELECTRIC DISCHARGES, WAVES AND IMPULSES. dielectric, and makes the consideration of dielectric fields un- necessarily complicated. There obviously is no more sense in thinking of the capacity current as current which charges the conductor with a quantity of electricity, than there is of spea ...", "... ctor 1Q-1 also appears undesirable, but when the electrical units were introduced the absolute unit appeared as too large a value of current as practical unit, and one-tenth of it was chosen as unit, and called \"ampere.\" 16 ELECTRIC DISCHARGES, WAVES AND IMPULSES. This gives the average voltage gradient, while the actual gradient in an ummiform field, as that between two conductors, varies, being higher at the denser, and lower at the less dense, portion of the field, and is then is the dielectric-field intens ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "... = .0111, 7j = 70.7, 70 = .00707 e. 122. An interesting application of this method is the determination of the natural period of a transmission line ; that is the frequency at which such a line discharges an accumulated charge of atmospheric electricity (lightning), or oscillates at a sudden change of load, as a break of cir- cuit. 182 ALTERNATING-CURRENT PHENOMENA. The discharge of a condenser through a circuit contain- ing self-induction and resistance is oscillating (provided that the resistance does not ex ...", "... 92, those with k = 2, with two nodal points, in Fig. 93. Thus k is the number of nodal points or zero points of current and of E.M.F. existing in the line (not counting zero points at the ends of the line, which of course are not nodes). In case of a lightning discharge the capacity C0 is the capacity of the line against ground, and thus has no direct relation to the capacity of the line conductor against its return. The same applies to the inductance L0. If d = diameter of line conductor, D = distance of co ...", "... . = 1.18/ 10+4 A simple harmonic oscillation as a line discharge would require a sinoidal distribution of potential on the trans- mission line at the instant of discharge, which is not proba- ble, so that probably all lightning discharges of transmission lines or oscillations produced by sudden changes of circuit conditions are complex waves of many harmonics, which in their relative magnitude depend upon the initial charge and its distribution — that is, in the case of the ligh ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-41", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 41, "number": 1, "location": "lines 19260-19338", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "snippets": [ "... e of importance in electrical engineering are : (a) Circuits containing distributed capacity and self-induc- tance, as long-distance energy transmission lines, long-distance telephone circuits, multiple spark-gaps, as used in some forms of high potential lightning arresters (multi-gap arrester), etc. (b) The distribution of alternating current in solid conductors and the increase of effective resistance and decrease of effective inductance resulting therefrom. (c) The distribution of alternating magnetic flux in ...", "... tance in electrical engineering are : (a) Circuits containing distributed capacity and self-induc- tance, as long-distance energy transmission lines, long-distance telephone circuits, multiple spark-gaps, as used in some forms of high potential lightning arresters (multi-gap arrester), etc. (b) The distribution of alternating current in solid conductors and the increase of effective resistance and decrease of effective inductance resulting therefrom. (c) The distribution of alternating magnetic flux in solid iron ...", "... ngineering are : (a) Circuits containing distributed capacity and self-induc- tance, as long-distance energy transmission lines, long-distance telephone circuits, multiple spark-gaps, as used in some forms of high potential lightning arresters (multi-gap arrester), etc. (b) The distribution of alternating current in solid conductors and the increase of effective resistance and decrease of effective inductance resulting therefrom. (c) The distribution of alternating magnetic flux in solid iron, or the screening ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-05", "section_label": "Lecture 5: Single-Energy Tra.Nsient Of Ironclad Circuit", "section_title": "Single-Energy Tra.Nsient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3387-3720", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-05/", "snippets": [ "... allic) permeability as proportional hereto, gives M = c((B^'-(BO, and, substituting gives M rrp/' ^, ^ CCEJOC' 1 + cOC'' * See \"On the Law of Hysteresis,\" Part II, A.I.E.E. Transactions, 1892, page 621. 54 ELECTRIC DISCHARGES, WAVES AND IMPULSES. or, substituting a, -:=r—i = (T, gives equation (1). /O 1 -j For X = 0 in equation (1), - = - ; for 5C = oo , (B = - ; that is, in equation (1), - = initial permeability, - = saturation value of (X (J magnetic density. If the magnetic circu ...", "... ^ 1 h h__ i{i^uy i l + 6^ ii + uy' and the integration of differential equation (7) then gives If then, for the time t = U, the current is i = Iq, these values substituted in (8) give the integration constant C: 56 ELECTRIC DISCHARGES, WAVES AND IMPULSES. and, subtracting (8) from (9), gives This equation is so complex in i that it is not possible to cal- culate from the different values of t the corresponding values of i; but inversely, for different values of i the corresponding values of t can be c ...", "... 5 Fig. 29. seconds Such is done in Fig. 29, for the values of the constants; r = .3, a = 4 X 10^ c = 4 X 104, h = .(), n = 300. SINGLE-ENERGY TRANSIENT OF IRONCLAD CIRCUIT. 57 O o s -1-3 M s 58 ELECTRIC DISCHARGES, WAVES AND IMPULSES. This gives T2 = A. Assuming io = 10 amperes for ^o = 0, gives from (10) the equa- tion: T = 2.92 - { 9.21 log'^ , ,\\ . + .921 log'^ i ' ^ ^ 1 + .6?; ' =\" ' i + .6?;^ Herein, the logarithms have been reduced to the base 10 by division with log^^ ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-05", "section_label": "Lecture 5: Single-Energy Transient Of Ironclad Circuit", "section_title": "Single-Energy Transient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2972-3286", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "snippets": [ "... en is (B^' — (B', and, assuming the (metallic) permeability as proportional hereto, gives and, substituting gives a, = cftco'rc^ * See \"On the Law of Hysteresis,\" Part II, A.I.E.E. Transactions, 1892, page 621. 54 ELECTRIC DISCHARGES, WAVES AND IMPULSES. or, substituting 1_ 1 *** / t*« ,—fc / (/ • gives equation (1). For OC = 0 in equation (1), ^ = - ; for 3C = oo » = - ; that is, uv a: cr in equation (1), - = initial permeability, - = saturation value of Oi (7 magnetic density. If the m ...", "... d the integration of differential equation (7) then gives If then, for the time t = tQ, the current is i = i0, these values substituted in (8) give the integration constant C: T1log- + !T2logio + T- + ^o + C = 0, (9) 56 ELECTRIC DISCHARGES, WAVES AND IMPULSES. and, subtracting (8) from (9), gives 1 + 6i 5 ' (10) This equation is so complex in i that it is not possible to cal- culate from the different values of t the corresponding values of i; but inversely, for different values of i the corresponding ...", "... otted: t = 1.0851g i— .50?) 2 3 4 5 Fig. 29. 6 seconds Such is done in Fig. 29, for the values of the constants a = 4 X 105, c = 4 X 104, b = .6, n = 300. SINGLE-ENERGY TRANSIENT OF IRONCLAD CIRCUIT. 57 58 ELECTRIC DISCHARGES, WAVES AND IMPULSES. This gives T = 4 Assuming i0 = 10 amperes for t0 = 0, gives from (10) the equa- tion : 4 T = 2.92 - 1 9.21 log10 ^ + . 921 .6 i Herein, the logarithms have been reduced to the base 10 by division with logwe = .4343. For comparison is s ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... -circuit current of an electric generating system, it is of importance to know whether this current is 3 or 4 times normal current, or whether it is 40 to 50 times normal current, but it is immaterial whether it is 45 to 46 or 50 times normal. In studying lightning phenomena, and, in general, abnormal voltages in electric systems, calculating the discharge capacity of lightning arres- ters, etc., the magnitude of the quantity is often sufficient. In 254 ^ ENGINEERING MATHEMATICS. calculating the critical speed o ...", "... normal current, or whether it is 40 to 50 times normal current, but it is immaterial whether it is 45 to 46 or 50 times normal. In studying lightning phenomena, and, in general, abnormal voltages in electric systems, calculating the discharge capacity of lightning arres- ters, etc., the magnitude of the quantity is often sufficient. In 254 ^ ENGINEERING MATHEMATICS. calculating the critical speed of turbine alternators, or the natural period of oscillation of synchronous machines, the same applies, since it is ...", "... nctions. In physics and in engineering, integration of special functions in this manner frequently leads to new special functions. For instance, in the study of the propagation through space, of the magnetic field of a conductor, in wireless telegraphy, lightning protection, etc., we get new functions. If ^=/(0 is the current in the conductor, as function of the time t, at a distance x from the conductor the magnetic field lags by the X time ti = -, where S is the speed of propagation (velocity of light). Sinc ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-08", "section_label": "Lecture 8: Generation", "section_title": "Generation", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 3781-4217", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-08/", "snippets": [ "... of less than 20 to 30 feet head there- fore are of little value and their development is economical only where electric power is valuable. Of the two types of turbines, the reaction turbine runs approximately at the speed of the water, and the action or impulse turbine at half the speed of the water. At the same head and thus the same speed of the water, the reaction turbine gives higher speed, and is therefore used in water powers of low and medium heads, where the speed of the water is low; while the impulse ( ...", "... impulse turbine at half the speed of the water. At the same head and thus the same speed of the water, the reaction turbine gives higher speed, and is therefore used in water powers of low and medium heads, where the speed of the water is low; while the impulse (turbine, as the Pelton wheel, is always used at very high heads, at which the reaction turbine would give too high speeds. Where water power is not available, the power has to be generated by the combustion of fuel. In this case, a greater freedom exis ...", "... aratus. The output depends upon the mean pressure in the cylinder, which is low; the strains on the maximum pressure, which is very high ; and the gas engine therefore must be very large, and its moving parts very strong and heavy, for its out- put. The impulse due to the rapid pressure change is very jerky — almost of the nature of an explosion — and the steadi- ness of the rate of rotation is therefore very low, requiring for electric driving very heavy flywheels and numerous cylinders. Compared with the stea ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-36", "section_label": "Apparatus Section 15: Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "section_title": "Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "kind": "apparatus-section", "sequence": 36, "number": 15, "location": "lines 9918-10123", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-36/", "snippets": [ "... r electric motors, this is usually the case; but with reciprocating machines, as steam engines, the torque and thus the speed of rotation rises and falls periodically during each revolution, with the frequency of the engine impulses. The alternator con- nected with the engine will thus not have uniform frequency, but a frequency which pulsates, that is, rises and falls. The amplitude of this pulsation depends upon the design of the engine, the momentum ...", "... will be a pulsating power cross current between the alternators, transferring power from the leading to the lagging machine, that is, alternately from the one to the other, and inversely, with the frequency of the engine impulses. These pulsating cross currents are the most undesirable, since they tend to make the voltage fluctuate and to tear the alternators out of synchro- nism with each other, especially when the conditions are favorable to a cum ...", "... e movers, especially steam A ^^ engines. With alternators driven by gas engines, the problem of parallel operation is made more difficult by the more jerky nature of the gas-engine ^ 73._Phase displacement between impulse. In such machines, alternators to be synchronized, therefore, squirrel-cage wind- ings in the field-pole faces are commonly used, to assist synchron- izing by the currents induced in this short-circuited winding, on the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-13", "section_label": "Chapter 13: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 13484-14333", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-13/", "snippets": [ "... n rails of the return circuit of alternating-current rail- ways, is given in Section III of \"Theory and Calculation of Tran- sient Electric Phenomena and Oscillations.\" In practice, this phenomenon is observed mainly with very high frequency currents, as lightning discharges, wireless tele- graph and lightning arrester circuits; in power-distribution cir- cuits it has to be avoided by either keeping the frequency suffi- ciently low or having a shape of conductor such that unequal current-distribution does not take ...", "... rent rail- ways, is given in Section III of \"Theory and Calculation of Tran- sient Electric Phenomena and Oscillations.\" In practice, this phenomenon is observed mainly with very high frequency currents, as lightning discharges, wireless tele- graph and lightning arrester circuits; in power-distribution cir- cuits it has to be avoided by either keeping the frequency suffi- ciently low or having a shape of conductor such that unequal current-distribution does not take place, as by using a tubular or a flat conducto ...", "... ways, is given in Section III of \"Theory and Calculation of Tran- sient Electric Phenomena and Oscillations.\" In practice, this phenomenon is observed mainly with very high frequency currents, as lightning discharges, wireless tele- graph and lightning arrester circuits; in power-distribution cir- cuits it has to be avoided by either keeping the frequency suffi- ciently low or having a shape of conductor such that unequal current-distribution does not take place, as by using a tubular or a flat conductor, or sev ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "section_label": "Chapter 30: Quartbr-Fhase System", "section_title": "Quartbr-Fhase System", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... hows the origin of the oscillating currents, and the means to produce such currents by disturbing the equilibrium of the electric circuit ; for instance, by the discharge of a condenser, by make and break of the circuit, by sudden electrostatic charge, as lightning, etc. Obviously, the most important oscillating currents are 420 APPENDIX II. [§292 those flowing in a circuit of zero impedance, representing oscillating discharges of the circuit. Lightning strokes usually belong to this class. Oscillating Dischar ...", "... nd break of the circuit, by sudden electrostatic charge, as lightning, etc. Obviously, the most important oscillating currents are 420 APPENDIX II. [§292 those flowing in a circuit of zero impedance, representing oscillating discharges of the circuit. Lightning strokes usually belong to this class. Oscillating Discharges. 292. The condition of an oscillating discharge is ^ = 0, that is, ' 2aL 2zVr«C a = c If r = 0, that is, in a circuit without resistance, we have a ^ Oj jV=1/2v VZ C ; that is, the ...", "... N = ; that is, the current dies out without oscillation. From the foregoing we have seen that oscillating dis- charges, — as for instance the phenomena taking place if a condenser charged to a given potential is discharged through a given circuit, or if lightning strikes the line circuit, — is defined by the equation : Z = dec a. Since • / = (/'i +jii) dec a, Er=^ Ir dec a, E, = ^xl{a +j) dec a, E,,= __^/(- ^ +/) deca, we have ^ ^ ^ a ^ _ a 1 -f <' hence, by substitution, Ej^= -v /(— (I -\\-j) dec a. ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-32", "section_label": "Chapter 32: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 25904-27405", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "snippets": [ "... hows the origin of the oscillating currents, and the means to produce such currents by disturbing the equilibrium of the electric circuit ; for instance, by the discharge of a condenser, by make and break of the circuit, by sudden electrostatic charge, as lightning, etc. Obviously, the most important oscillating currents are 508 APPENDIX II. those flowing in a circuit of zero impedance, representing oscillating discharges of the circuit. Lightning strokes usually belong to this class. Oscillating Discharges. ...", "... make and break of the circuit, by sudden electrostatic charge, as lightning, etc. Obviously, the most important oscillating currents are 508 APPENDIX II. those flowing in a circuit of zero impedance, representing oscillating discharges of the circuit. Lightning strokes usually belong to this class. Oscillating Discharges. 321. The condition of an oscillating discharge is Z = 0, that is, ~ ~ / .1 r 2aL 2Z~ ~1' If r = 0, that is, in a circuit without resistance, we have a = 0, Af = 1 / 2 TT VZT ; that i ...", "... = 0 ; that is, the current dies out without oscillation. From the foregoing we have seen that oscillating dis- charges, — as for instance the phenomena taking place if a condenser charged to a given potential is discharged through a given circuit, or if lightning strikes the line circuit, — are denned by the equation : Z = 0 dec a. Since / = (/V+y/a) dec a, Er = Ir dec a, Ex = -x I (a +/) dec a, Exc= _^L_/(- a +/) dec a, we have r-aX--^—Xc = ^ I + a? hence, by substitution, Exc= x /(— a +/) dec a. O ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-40", "section_label": "Chapter 4: Arc Rectification", "section_title": "Arc Rectification", "kind": "chapter", "sequence": 40, "number": 4, "location": "lines 17755-19259", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "snippets": [ "... NOMENA The effective value of the equivalent alternating secondary current of the transformer is derived by the subtraction of the two anode currents, or their superposition in reverse direction, as shown by curves VII, and is given by curve VIII. Each impulse of anode current covers an angle n + 00, or somewhat more than one half wave. Denoting, however, each anode wave by n, that is, considering each anode impulse as one half wave (which corresponds to a Ifower frequency— -), then, referred to the anode imp ...", "... superposition in reverse direction, as shown by curves VII, and is given by curve VIII. Each impulse of anode current covers an angle n + 00, or somewhat more than one half wave. Denoting, however, each anode wave by n, that is, considering each anode impulse as one half wave (which corresponds to a Ifower frequency— -), then, referred to the anode impulse x + V as half wave, the angle of overlap is TT 0, = 1 ^ , 71 -j- The direct current, i0, is the mean value of the anode current curves V, VI, ...", "... lse of anode current covers an angle n + 00, or somewhat more than one half wave. Denoting, however, each anode wave by n, that is, considering each anode impulse as one half wave (which corresponds to a Ifower frequency— -), then, referred to the anode impulse x + V as half wave, the angle of overlap is TT 0, = 1 ^ , 71 -j- The direct current, i0, is the mean value of the anode current curves V, VI, and, assuming the latter as equivalent sine waves of maximum value i2 = i0 + i' ', the direct curren ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-48", "section_label": "Chapter 8: Velocity Of Propagation Of Electric Field", "section_title": "Velocity Of Propagation Of Electric Field", "kind": "chapter", "sequence": 48, "number": 8, "location": "lines 26095-27002", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "snippets": [ "... eration only: 387 388 TRANSIENT PHENOMENA (a) At extremely high frequencies, hundreds of millions of cycles per second, as given by Hertzian resonators. (6) In high frequency discharges having no return circuit or no well defined return circuit, as lightning discharges. In this case the effective resistance of radiation may be so large com- pared with the ohmic resistance, even when considering the unequal current distribution in the conductor (Chapter VII), that the effect of the conductor material practical ...", "... may be so large com- pared with the ohmic resistance, even when considering the unequal current distribution in the conductor (Chapter VII), that the effect of the conductor material practically disappears. In the conductors forming the discharge path of lightning arresters this phenomenon therefore requires serious consideration. (c) With high frequencies, in the case where the field at a considerable distance from the conductor is of importance as in wireless telegraphy. In wireless telegraphy the electric fie ...", "... large com- pared with the ohmic resistance, even when considering the unequal current distribution in the conductor (Chapter VII), that the effect of the conductor material practically disappears. In the conductors forming the discharge path of lightning arresters this phenomenon therefore requires serious consideration. (c) With high frequencies, in the case where the field at a considerable distance from the conductor is of importance as in wireless telegraphy. In wireless telegraphy the electric field of the ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-01", "section_label": "Chapter 1: The General Number", "section_title": "The General Number", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 915-3491", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-01/", "snippets": [ "... GENERAL NUMBER. 33 may be called the linear numbers, as they represent the points of a line. Example: Steam Path in a Turbine. 23. As an example of a simple operation with general num- bers one may calculate the steam path in a two-wheel stage of an impulse steam turbine. +2^ 1 «)))»»)) « »)>M») > +a; Fig. 17. Path of Steam in a Two-wheel Stage of an Impulse Turbine. Let Fig. 17 represent diagrammatically a tangential section through the bucket rings of the turbine wheels. Wi and W2 are the ...", "... n a Turbine. 23. As an example of a simple operation with general num- bers one may calculate the steam path in a two-wheel stage of an impulse steam turbine. +2^ 1 «)))»»)) « »)>M») > +a; Fig. 17. Path of Steam in a Two-wheel Stage of an Impulse Turbine. Let Fig. 17 represent diagrammatically a tangential section through the bucket rings of the turbine wheels. Wi and W2 are the two revolving wheels, moving in the direction indicated by the arrows, with the velocity s = 400 feet per sec. / are t ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-04", "section_label": "Chapter 5: Methods Of Approximation", "section_title": "Methods Of Approximation", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 15156-16482", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-04/", "snippets": [ "... or instance. METHODS OF APPROXIMATION. 189 in astronomical calculations the mass of the earth (which absolutely can certainly not be considered a small quantity) is neglected as small quantity compared with the mass of the sun. Also in the effect of a lightning stroke on a primary distribution circuit, the normal line voltage of 2200 may be neglected as small compared with the voltage impressed by lightning, etc. 126. Example. In a direct-current shunt motor, the im- pressed voltage is eo = 125 volts; the arma ...", "... small quantity) is neglected as small quantity compared with the mass of the sun. Also in the effect of a lightning stroke on a primary distribution circuit, the normal line voltage of 2200 may be neglected as small compared with the voltage impressed by lightning, etc. 126. Example. In a direct-current shunt motor, the im- pressed voltage is eo = 125 volts; the armature resistance is ro = 0.02 ohm; the field resistance is ri = 50 ohms; the power consumed by friction is pf=^300 watts, and the power consumed by ir ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-05", "section_label": "Chapter 6: Empirical Curves", "section_title": "Empirical Curves", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 16483-21988", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-05/", "snippets": [ "... the frequency of hunting of synchronous machines, etc. In the phenomenon of hunting, frequently two periods are superimposed, forced frequency, resulting from the speed of generator, etc., and the natural frequency of the machine. Counting the number of impulses, /, per minute, and the number of nodes, n, gives the 71/ Tl two frequencies :/+- and/— -; and as one of these frequencies is the impressed engine frequency, this affords a check. Not infrequently wave-shape distortions are met, which are not due to ...", "... occurs in the secondary circuit of the single-phase induction motor; two sets of currents, of the frequencies /« and (2/—/^) exist (where / is the primary frequency and /s the frequency of slip). Of this nature, frequently, is the distortion produced by surges, oscillations, arcing grounds, etc., in electric circuits; it is a combination of the natural frequency of the circuit with the impressed frequency. Telephonic currents commonly show such multiple frequencies, which are not harmonics of each other." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-17", "section_label": "Chapter 17: Circuits With Distributed Leakage", "section_title": "Circuits With Distributed Leakage", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 30429-31656", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-17/", "snippets": [ "... neral, capacity and inductance require consideration as well as resistance and shunted conductance. This general case is fully discussed in \"Theory and Calculation of Transient Electric Phe- nomena and Oscillations,\" and in \"Electric Discharges, Waves and Impulses,\" more particularly in the fourth section of the former book. 173, Let, then, in a conductor having uniformly distributed leakage, or in that conductor section, in which the leakage can be considered as approximately uniformly distributed, r = resistan ...", "... Infinite resistance gives complete reflection of current and doubles the voltage, while zero resistance gives complete re- flection of voltage and doubles the current. The term,ro = -v/-, thus takes in direct-current circuits the same position as the ''surge impedance\" -v/t^ or -v/ y in alternating-cur- rent circuits. CIRCUITS WITH DISTRIBUTED LEAKAGE 335 176, Consider an instance: it has been proposed, for the pur- pose of effectively grounding the overhead ground wire used for protection of transmission ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-23", "section_label": "Chapter 1: The Constants Of The Electric Circuit", "section_title": "The Constants Of The Electric Circuit", "kind": "chapter", "sequence": 23, "number": 1, "location": "lines 1317-1992", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "snippets": [ "... equal magnitude is the electromagnetic energy —— and the electrostatic energy - ^ in the high-potential Zi iL long-distance transmission circuit, in the telephone circuit, and in the condenser discharge, and so in most of the phenomena resulting from lightning or other disturbances. In these cases all three circuit constants, r, L, and C, are of essential impor- tance. 10. In an electric circuit of negligible inductance L and negligible capacity C, no energy is stored, and a change in the circuit thus can be ...", "... e by the energy adjustment retarding the change, and only where energy is stored electrostatically and magnetically, the mechanical change of the circuit conditions, as the opening of the circuit, can be brought about instantly, and the stored energy then surges between electrostatic and magnetic energy. In the following, first the phenomena will be considered which result from the stored energy and its readjustment in circuits storing energy in one form only, which usually is as electro- magnetic energy, and th ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... a gap would have to be charged by induction, or the spheres charged separately and then brought near each other, or the spheres may be made a part of a series of spheres separated by gaps and connected across a high potential circuit, as in some forms of lightning arresters. Herefrom it appears that the highest frequency of oscillation of appreciable power which can be produced by a condenser discharge reaches billions of cycles per second, thus is enormously higher than the highest frequencies which can be produc ...", "... ld have to be charged by induction, or the spheres charged separately and then brought near each other, or the spheres may be made a part of a series of spheres separated by gaps and connected across a high potential circuit, as in some forms of lightning arresters. Herefrom it appears that the highest frequency of oscillation of appreciable power which can be produced by a condenser discharge reaches billions of cycles per second, thus is enormously higher than the highest frequencies which can be produced by ele ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-29", "section_label": "Chapter 7: Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "section_title": "Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "kind": "chapter", "sequence": 29, "number": 7, "location": "lines 6798-7825", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "snippets": [ "... consist of one definite frequency but an infinite series of frequencies, and the preceding discussion thus approximates only the fundamental frequency of the system. This, however, is the frequency which usually predominates in a high power low frequency surge of the system. In an underground cable system the preceding discussion applies more closely, since in such a system capacity and induc- tance are more nearly localized : the capacity is in the under- ground cables, which are of low inductance, and the in ...", "... n an underground cable system the tendency therefore is RESISTANCE, INDUCTANCE, AND CAPACITY 103 either towards a local, very high frequency oscillation, or travel- ing wave, of very limited power, in a part of the cables, or a low frequency high power surge, frequently of destructive magnitude, of the joint capacity of the cables, against the inductance of the generating system. 63. The physical meaning of the transient terms can best be understood by reviewing their origin. In a circuit containing resist ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-50", "section_label": "Chapter 1: General Equations", "section_title": "General Equations", "kind": "chapter", "sequence": 50, "number": 1, "location": "lines 27761-28694", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "snippets": [ "... d the effec- tive resistance, inductance, conductance, and capacity, respec- tively, per unit length of circuit. The unit of length of the circuit- may be chosen as is convenient, thus : the centimeters in the high- frequency oscillation over the multigap lightning arrester circuit, or a mile in a long-distance transmission circuit or high-potential cable, or the distance of the velocity of light, 300,000 km., etc. The permanent values of current and e.m.f. in such circuits of distributed constants have, for altern ...", "... c- tive resistance, inductance, conductance, and capacity, respec- tively, per unit length of circuit. The unit of length of the circuit- may be chosen as is convenient, thus : the centimeters in the high- frequency oscillation over the multigap lightning arrester circuit, or a mile in a long-distance transmission circuit or high-potential cable, or the distance of the velocity of light, 300,000 km., etc. The permanent values of current and e.m.f. in such circuits of distributed constants have, for alternating-cur ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-57", "section_label": "Chapter 8: Reflection And Refraction At Transition Point", "section_title": "Reflection And Refraction At Transition Point", "kind": "chapter", "sequence": 57, "number": 8, "location": "lines 34203-34896", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-57/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-57/", "snippets": [ "... tion of low inductance and high capacity, as from a transformer to a transmission line, the voltage of the wave is decreased. This explains the frequent increase to destructive voltages, when entering a station from the transmission line or cable, of an impulse or a wave which in the transmission line is of relatively harmless voltage. The ratio of the transmitted to the reflected wave is given by 2 VLjC, 2 and 2c2 L2C, (359) 530 TRANSIENT PHENOMENA 60. Example: Transmission line Lt = ...", "... s of the phase angle is constant, and the ratio of the tangent functions of the phase angle of the voltages is proportional, of the currents inversely proportional to the circuit constants c = y — • In other words, the transition of an electric wave or impulse from one section of a circuit to another takes place at a constant ratio of the tangent functions of the phase angle, which ratio is a constant of the circuit sections between which the transition occurs. This law is analogous to the law of refraction i ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-05", "section_label": "Lecture 5: Long Distance Transmission", "section_title": "Long Distance Transmission", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2562-3132", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-05/", "snippets": [ "... rostatic energy is : e*C 2 and the electromagnetic energy : i'L 2 In a high potential transmission line both energies are of about the same magnitude, and the energy can therefore see- saw between the two forms and thereby produce oscillations and surges resulting in the production of high voltages, which are not liable to occur in circuits in which one of the forms of stored energy is small compared with the other. In distribution systems up to 2200 volts and even some- what higher, the electrostatic en ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "section_label": "Chapter 14: Dielectric Losses", "section_title": "Dielectric Losses", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "... circuit, in which the power-factor decreases with increasing frequency, for instance, is that of the capacity of the transmission line; a dielectric circuit, in which the power-factor increases with the frequency, is that of the aluminum-cell light- ning arrester. 121. As seen, in the dielectric circuit, that is, in insulators in which the current is essentially a displacement current, the relations between voltage, current, power, phase angle and power- factor can be represented by the same symbolic equations ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-23", "section_label": "Chapter 23: Synchronizing Alternators", "section_title": "Synchronizing Alternators", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 25135-25681", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-23/", "snippets": [ "... the period of the engine revolution, due to the alternating transfer of the load from one engine to the other, which may even become so excessive as to throw the machines out of step, especially when by an ap- proximate coincidence of the period of engine impulses (or a multiple thereof), with the natural period of oscillation of the revolving structure, the effect is made cumulative. This diffi- culty as a rule does not exist with turbine or water-wheel driving, but is specially severe with gas-engine drive, and s ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... resistance due to unequal current distribution. The general solution of this problem for round conduc- tors leads to complicated equations, and can be found in Maxwell. In practice, this phenomenon is observed only with very high frequency currents, as lightning discharges ; in power distribution circuits it has to be avoided by either keeping the frequency sufficiently low, or having a shape of con- ductor such that unequal current distribution . does not take place, as by using a tubular or a stranded conductor ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "... esistance due to unequal current distribution. The general solution of this problem for round conduc- tors leads to complicated equations, and can be found else- where. In practice, this phenomenon is observed only with very high frequency currents, as lightning discharges ; in power distribution circuits it has to be avoided by either keeping the frequency sufficiently low, or having a shape of con- ductor such that unequal current distribution does not take place, as by using a tubular or a flat conductor, or ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-18", "section_label": "Chapter 18: Synchronizing Alternators", "section_title": "Synchronizing Alternators", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17597-18052", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-18/", "snippets": [ "... the period of the engine revo- lution, due to the alternating transfer of the load from one engine to the other, which may even become so excessive as to throw the machines out of step, especially when by an approximate coincidence of the period of engine impulses (or a multiple thereof), with the natural period of oscillation of the revolving structure, the effect is made cumulative. This difficulty as a rule does not exist with turbine or water- wheel driving. 192. In synchronizing alternators, we have to disti ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-13", "section_label": "Chapter 15: Synchronous Rectifier", "section_title": "Synchronous Rectifier", "kind": "chapter", "sequence": 13, "number": 15, "location": "lines 18413-19373", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-13/", "snippets": [ "... r. As seen, in Fig. 99, contact is made between the rectified cir- cuit and the alternating supply source, T, during one-half wave only, but the circuit is open during the reverse half wave, and the rectified circuit, Bt thus carries a series of separate impulses of cur- rent and voltage as shown in Fig. 100 as i\\. However, in this case the current in the alternating supply circuit is unidirectional also, is the same current, i\\. This current produces in the trans- former, T, a unidirectional magnetization, and, i ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-16", "section_label": "Chapter 16: Load Balance Of Polyphase Systems", "section_title": "Load Balance Of Polyphase Systems", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 29302-30428", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-16/", "snippets": [ "... = / cos (« - I) (8) and the instantaneous power thus, p = EI cos cos(<^ — ^j = -^ sm 2 = Qcos(20-^)i (9) Thus, the power comprises only an alternating component, but no continuous component; in other words, no power is consumed, but the power surges or alternates between +Q and — Q, that is, power is stored and then again returned to the circuit. If the circuit is closed by a capacity, C, the current leads the TT impressed voltage by ^, thus is i = / cos (« + I) (10) and the instantaneous powe ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-09", "section_label": "Chapter 5: Distributed Series Capacity. 348", "section_title": "Distributed Series Capacity. 348", "kind": "chapter", "sequence": 9, "number": 5, "location": "lines 888-903", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-09/", "snippets": [ "CHAPTER V. DISTRIBUTED SERIES CAPACITY. 348 43. Potential distribution in multigap circuit. 348 44. Probable relation of the multigap circuit to the lightning flash in the clouds. 349 45. The differential equations of the multigap circuit, and their integral equations. 350 46. Terminal conditions, and final equations. 351 47. Numerical example. 353" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-44", "section_label": "Chapter 4: Distributed Capacity Of High-Potential Transformers", "section_title": "Distributed Capacity Of High-Potential Transformers", "kind": "chapter", "sequence": 44, "number": 4, "location": "lines 23179-23585", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "snippets": [ "... rrent of the transformer or reactive coil. However, even in large transformers and at moderately high voltages, capacity effects occur in transformers, if the frequency is sufficiently high, as is the case with the currents produced in overhead lines by lightning discharges, or by arcing grounds resulting from spark discharges between conductor and ground, or in starting or disconnecting the transformer. With such frequencies, of many thousand cycles, the internal capacity of the transformer becomes very marked in ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-46", "section_label": "Chapter 6: Alternating Magnetic Flux Distribution", "section_title": "Alternating Magnetic Flux Distribution", "kind": "chapter", "sequence": 46, "number": 6, "location": "lines 23948-24980", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "snippets": [ "... ed frequency, practically uniform magnetic induction throughout its section, that is, negligible secondary currents. This, however, is no longer the case, even with the thinnest possible laminations, at extremely high frequencies, as oscillating currents, lightning discharges, etc., and under these conditions the magnetic flux distribution in the iron is not uniform, but the magnetic flux density, (B, decreases rapidly, and lags in phase, with increasing depth below the surface of the lamination, so that ultimately ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-51", "section_label": "Chapter 2: Discussion Of General Equations", "section_title": "Discussion Of General Equations", "kind": "chapter", "sequence": 51, "number": 2, "location": "lines 28695-29315", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "snippets": [ "... e time attenuation constants of the wave, 1 ) (64) U + S and h is the distance attenuation constant of the wave, L -I. (65) 9. If the frequency of the current and e.m.f. is very high, thousands of cycles and more, as with traveling waves, lightning disturbances, high-frequency oscillations, etc., q is a very large quantity compared with s, u, m, h, k, and k is a large quantity compared with h, then by dropping in equations (50) to (61) the terms of secondary order the equations can be simplified. ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-53", "section_label": "Chapter 4: Traveling Waves", "section_title": "Traveling Waves", "kind": "chapter", "sequence": 53, "number": 4, "location": "lines 30244-31450", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "snippets": [ "... l by again increasing the attenuation. For instance, if a long-distance telephone circuit has the following constants per mile: r = 1.31 ohms, L = 1.84 X 10~3 henry, g = 1.0 X 1Q-\" mho, and C = 0.0172 X 10~6 farad, the attenuation of a traveling wave or impulse is u0 = 0.00217; hence, for a distance or length of line of 1Q = 2000 miles, e-nA = £-4.34 = 0.0129; that is, the wave is reduced to 1.29 per cent of its original value. The best value of inductance, according to (157), is L = -C = 0.0225 henry, i ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-54", "section_label": "Chapter 5: Free Oscillations", "section_title": "Free Oscillations", "kind": "chapter", "sequence": 54, "number": 5, "location": "lines 31451-32708", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "snippets": [ "... c field of the circuit, or inversely, the accumulation of the energy of the electric field; and their appearance therefore presupposes the possibility of energy storage in more than one form so as to allow 478 FREE OSCILLATIONS 479 an interchange or surge of energy between its different forms, electromagnetic and electrostatic energy. Free oscillations occur only in circuits containing both capacity C and inductance, L. The absence of energy supply or abstraction defines the free oscillations by the condi ..." ] } ] }, { "id": "dielectric-field", "label": "Dielectric Field", "aliases": [ "dielectric", "dielectric field", "dielectrics" ], "total_occurrences": 561, "matching_section_count": 58, "matching_source_count": 11, "source_totals": [ { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 145, "section_count": 10 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 125, "section_count": 8 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 122, "section_count": 8 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 54, "section_count": 3 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 35, "section_count": 7 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 33, "section_count": 6 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 27, "section_count": 7 }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 11, "section_count": 3 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 5, "section_count": 4 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 2, "section_count": 1 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 2, "section_count": 1 } ], "section_hits": [ { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "section_label": "Chapter 14: Dielectric Losses", "section_title": "Dielectric Losses", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 106, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "CHAPTER XIV DIELECTRIC LOSSES Dielectric Hysteresis 116. Just as magnetic hysteresis and eddy currents give a power component in the inductive reactance, as \"effective resistance,\" so the energy losses in the dielectric lead to a power component in the condensive reactance, ...", "CHAPTER XIV DIELECTRIC LOSSES Dielectric Hysteresis 116. Just as magnetic hysteresis and eddy currents give a power component in the inductive reactance, as \"effective resistance,\" so the energy losses in the dielectric lead to a power component in the condensive reactance, which may be repre- ...", "CHAPTER XIV DIELECTRIC LOSSES Dielectric Hysteresis 116. Just as magnetic hysteresis and eddy currents give a power component in the inductive reactance, as \"effective resistance,\" so the energy losses in the dielectric lead to a power component in the condensive reactance, which may be repre- sented by an \"effective resistance of dielectric losses\" or an \"effective conductance of dielectric losses.\" In the alternating magnetic field, power is consumed by mag- netic hy ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1003-1658", "status": "candidate", "occurrence_count": 55, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-02/", "snippets": [ "... ircles 10 THE ELECTRIC FIELD. 11 are crowded together between the conductors, and the magnetic field consists of eccentric circles surrounding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from the conductors, that is, a dielectric flux passes between the conductors, which is measured by the number of lines of dielectric force ^. With a single conductor, the lines of dielectric force are radial straight lines, as shown dotted in Fig ...", "... gether between the conductors, and the magnetic field consists of eccentric circles surrounding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from the conductors, that is, a dielectric flux passes between the conductors, which is measured by the number of lines of dielectric force ^. With a single conductor, the lines of dielectric force are radial straight lines, as shown dotted in Fig. 8. By the return conductor, they are crowded toge ...", "... ding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from the conductors, that is, a dielectric flux passes between the conductors, which is measured by the number of lines of dielectric force ^. With a single conductor, the lines of dielectric force are radial straight lines, as shown dotted in Fig. 8. By the return conductor, they are crowded together between the conductors, and form arcs of circles, passing from conductor to return con ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 883-1530", "status": "candidate", "occurrence_count": 55, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "snippets": [ "... ircles 10 THE ELECTRIC FIELD. 11 are crowded together between the conductors, and the magnetic field consists of eccentric circles surrounding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from the conductors, that is, a dielectric flux passes between the conductors, which is measured by the number of lines of dielectric force ty. With a single conductor, the lines of dielectric force are radial straight lines, as shown dotted in Fi ...", "... gether between the conductors, and the magnetic field consists of eccentric circles surrounding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from the conductors, that is, a dielectric flux passes between the conductors, which is measured by the number of lines of dielectric force ty. With a single conductor, the lines of dielectric force are radial straight lines, as shown dotted in Fig. 8. By the return conductor, they are crowded tog ...", "... ding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from the conductors, that is, a dielectric flux passes between the conductors, which is measured by the number of lines of dielectric force ty. With a single conductor, the lines of dielectric force are radial straight lines, as shown dotted in Fig. 8. By the return conductor, they are crowded together between the conductors, and form arcs of circles, passing from conductor to return co ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-19", "section_label": "Theory Section 19: Fields of Force", "section_title": "Fields of Force", "kind": "theory-section", "sequence": 19, "number": 19, "location": "lines 7737-7990", "status": "candidate", "occurrence_count": 40, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-19/", "snippets": [ "... e earth, and water to run down hill — and this space thus is a field of gravitational force, the earth the gram- motive force. In the space surrounding conductors having a high potential difference, we observe a field of dielectric force, that is, electro- static or dielectric forces are exerted, and the potential difference between the conductors is the electromotive force of the dielectric field. The force exerted by the earth as gravimotive force, o ...", "... is space thus is a field of gravitational force, the earth the gram- motive force. In the space surrounding conductors having a high potential difference, we observe a field of dielectric force, that is, electro- static or dielectric forces are exerted, and the potential difference between the conductors is the electromotive force of the dielectric field. The force exerted by the earth as gravimotive force, on any mass in the gravitational field of the ...", "... tors having a high potential difference, we observe a field of dielectric force, that is, electro- static or dielectric forces are exerted, and the potential difference between the conductors is the electromotive force of the dielectric field. The force exerted by the earth as gravimotive force, on any mass in the gravitational field of the earth, causes the mass to move with increasing rapidity. The direction of motion then shows the direction in which the ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "section_label": "Lecture 10: Continual And Cumulative Oscillations", "section_title": "Continual And Cumulative Oscillations", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 28, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... enon by which the stored energy readjusts itself to a change of circuit conditions. In an oscilla- tory transient, the difference of stored energy of the previous and the after condition of the circuit, at a circuit change, oscillates between magnetic and dielectric energy. As there always must be some energy dissipation in the circuit, the oscillating energy of the transient must steadily decline, that is, the transient must die out, at a rate depending on the energy dissipation in the cir- cuit. Thus, the oscilla ...", "... echanism, by which the hysteresis cycle supplies the energy of continual oscillations, has been investigated in the case of the hunting of synchronous machines,* but is still practically un- known in the case of continual oscillations between magnetic and dielectric energy in electric circuits. Recurrent oscillations, as in Fig. 59, must be or very soon be- come continual, that is, the successive wave trains are of approx- imately constant amplitude, since each starts with the same energy, the stored energy of the s ...", "... 2. A continual oscillation involves an energy transformation from the power supply of the system to the oscillation frequency. The energy of the oscillation which gives its destructiveness thus is not limited to the small amount of the stored magnetic and dielectric energy of the system, but is supplied continuously from the engine or turbine power. 3. The continual oscillation is not a resonance phenomenon which depends on the frequency of the exciting disturbance just coinciding with one of the natural frequencies ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3721-4369", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-06/", "snippets": [ "... energy is stored by the current i, as magnetic field. To = -, (2) r where L = inductance = coefficient of energy storage by the cur- rent, r = resistance = coefficient of power dissipation by the current. If the energy is stored by the voltage e, as dielectric field, the duration of the transient would be TV - -, (3) g 59 60 ELECTRIC DISCHARGES, WAVES AND IMPULSES. where C = capacity = coefficient of energy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power consumpt ...", "... urrent. If the energy is stored by the voltage e, as dielectric field, the duration of the transient would be TV - -, (3) g 59 60 ELECTRIC DISCHARGES, WAVES AND IMPULSES. where C = capacity = coefficient of energy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power consumption by the voltage, as leakage conductance by the voltage, corona, dielectric hysteresis, etc. Thus the transient of the spontaneous discharge of a condenser would be represented by e = eoe~'^\\ (4) ...", "... 0 ELECTRIC DISCHARGES, WAVES AND IMPULSES. where C = capacity = coefficient of energy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power consumption by the voltage, as leakage conductance by the voltage, corona, dielectric hysteresis, etc. Thus the transient of the spontaneous discharge of a condenser would be represented by e = eoe~'^\\ (4) Similar single-energy transients may occur in other systems. For instance, the transient by which a water jet approaches con- stan ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3287-3955", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "snippets": [ "... , if energy is stored by the current i, as magnetic field, T0 = £, (2) where L = inductance = coefficient of energy storage by the cur- rent, r = resistance = coefficient of power dissipation by the current. If the energy is stored by the voltage e, as dielectric field, the duration of the transient would be TJ = -, (3) s/ 59 60 ELECTRIC DISCHARGES, WAVES AND IMPULSES. where C = capacity = coefficient of energy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power consump ...", "... rrent. If the energy is stored by the voltage e, as dielectric field, the duration of the transient would be TJ = -, (3) s/ 59 60 ELECTRIC DISCHARGES, WAVES AND IMPULSES. where C = capacity = coefficient of energy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power consumption by the voltage, as leakage conductance by the voltage, corona, dielectric hysteresis, etc. Thus the transient of the spontaneous discharge of a condenser would be represented by e = e0e~£ct. (4) ...", "... 0 ELECTRIC DISCHARGES, WAVES AND IMPULSES. where C = capacity = coefficient of energy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power consumption by the voltage, as leakage conductance by the voltage, corona, dielectric hysteresis, etc. Thus the transient of the spontaneous discharge of a condenser would be represented by e = e0e~£ct. (4) Similar single-energy transients may occur in other systems. For instance, the transient by which a water jet approaches con- sta ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-10", "section_label": "Lecture 10: Inductance And Capacity Of Round Parallel Conductors", "section_title": "Inductance And Capacity Of Round Parallel Conductors", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6089-7274", "status": "candidate", "occurrence_count": 25, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "snippets": [ "... inkages of the mag- netic flux to the current, £ = ?- (i) i/ where = magnetic flux or number of lines of magnetic force, and n the number of times which each line of magnetic force interlinks with the current i. The capacity is the ratio of the dielectric flux to the voltage, where \\f/ is the dielectric flux, or number of lines of dielectric force, and e the voltage which produces it. With a single round conductor without return conductor (as wireless antennae) or with the return conductor at infinite d ...", "... = ?- (i) i/ where = magnetic flux or number of lines of magnetic force, and n the number of times which each line of magnetic force interlinks with the current i. The capacity is the ratio of the dielectric flux to the voltage, where \\f/ is the dielectric flux, or number of lines of dielectric force, and e the voltage which produces it. With a single round conductor without return conductor (as wireless antennae) or with the return conductor at infinite dis- tance, the lines of magnetic force are concentr ...", "... ux or number of lines of magnetic force, and n the number of times which each line of magnetic force interlinks with the current i. The capacity is the ratio of the dielectric flux to the voltage, where \\f/ is the dielectric flux, or number of lines of dielectric force, and e the voltage which produces it. With a single round conductor without return conductor (as wireless antennae) or with the return conductor at infinite dis- tance, the lines of magnetic force are concentric circles, shown by drawn lines in Fi ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "... mutual inductance ; ^ = effective reactance of mutual inductance. The susceptance of mutual inductance is negative, or of opposite sign from the reactance of self-inductance. Or, Mutual inductance consumes energy and decreases the self- inductance. Dielectric and Electrostatic Phenomena. 98. While magnetic hysteresis and eddy currents can be considered as the energy component of inductance, con- densance has an energy component also, namely, dielectric hysteresis. In an alternating magnetic field, energy is co ...", "... ance consumes energy and decreases the self- inductance. Dielectric and Electrostatic Phenomena. 98. While magnetic hysteresis and eddy currents can be considered as the energy component of inductance, con- densance has an energy component also, namely, dielectric hysteresis. In an alternating magnetic field, energy is con- sumed in hysteresis due to molecular friction, and similarly, energy is also consumed in an alternating electrostatic field in the dielectric medium, in what is called electrostatic or dielectr ...", "... con- densance has an energy component also, namely, dielectric hysteresis. In an alternating magnetic field, energy is con- sumed in hysteresis due to molecular friction, and similarly, energy is also consumed in an alternating electrostatic field in the dielectric medium, in what is called electrostatic or dielectric hysteresis. FOUCAULT OR EDDY CURRENTS. 145 While the laws of the loss of energy by magnetic hys- teresis are fairly well understood, and the magnitude of the effect known, the phenomenon of dielect ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... b = — ^-^^^ — ■* = effective susceptance of mutual inductance. The susceptance of mutual inductance is negative, or of opposite sign from the susceptance of self-inductance. Or, Mutual itidtutance consumes energy and decreases the self- inductatice. Dielectric and Electrostatic Phenomena, 98. While magnetic hysteresis and eddy currents can be considered as the energy component of inductance, cori- densance has an energy component also, called dielectric hysteresis. In an alternating magnetic field, energy is c ...", "... ce consumes energy and decreases the self- inductatice. Dielectric and Electrostatic Phenomena, 98. While magnetic hysteresis and eddy currents can be considered as the energy component of inductance, cori- densance has an energy component also, called dielectric hysteresis. In an alternating magnetic field, energy is con- sumed in hysteresis due to molecular friction, and similarly, energy is also consumed in an alternating electrostatic field in the dielectric medium, in what is called dielectric hys- teresis. ...", "... cori- densance has an energy component also, called dielectric hysteresis. In an alternating magnetic field, energy is con- sumed in hysteresis due to molecular friction, and similarly, energy is also consumed in an alternating electrostatic field in the dielectric medium, in what is called dielectric hys- teresis. i 99] FOUCAULT OR EDDY CURRENTS. 145 While the laws of the loss of energy by magnetic hys- teresis are fairly well understood, and the magnitude of the effect known, the phenomenon of dielectric hyste ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... ts of half-axis OB' downward; the complex imaginary or general numbers are represented by the points outside of the coordinate axes. INDEX Absolute values of complex quanti- ties, 37 Actual generated e.m.f., alternator, 272 Admittance, 55 of dielectric, 154 due to eddy currents, 137 to hysteresis, 129 Admittivity of dielectric circuit, 160 Air-gap in magnetic circuit, 119, 132 Ambiguity of vectors, 39 Amplitude, 6, 20 Apparent capacity of distorted wave, 386 efficiency of induction motor, 234 i ...", "... epresented by the points outside of the coordinate axes. INDEX Absolute values of complex quanti- ties, 37 Actual generated e.m.f., alternator, 272 Admittance, 55 of dielectric, 154 due to eddy currents, 137 to hysteresis, 129 Admittivity of dielectric circuit, 160 Air-gap in magnetic circuit, 119, 132 Ambiguity of vectors, 39 Amplitude, 6, 20 Apparent capacity of distorted wave, 386 efficiency of induction motor, 234 impedance of transformer, 201 torque efficiency of induction motor, 234 Arc c ...", "... value of wave, 11 Balanced polyphase system, 397 Balance factor of polyphase system, 406 Brush discharge, 112 Cable, topographical characteristic, 42 Capacity, 4, 9 of line, 174 Choking coil, 96 Circuit characteristic of line and cable, 44 dielectric and dynamic, 159 factor of general wave, 383 Coefficient of eddy currents, 138 of hysteresis, 123 Combination of sine waves, 31 Compensation for lagging currents by condensance, 72 Condensance in symbolic expression, 36 Condenser as reactance a ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-20", "section_label": "Theory Section 20: Nomenclature", "section_title": "Nomenclature", "kind": "theory-section", "sequence": 20, "number": 20, "location": "lines 7991-8291", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-20/", "snippets": [ "... I. E. E., but as far as possible standard letters have been used, and script letters avoided as impracticable or at least inconvenient in writing and still more in typewriting. Therefore F has been chosen for m.m.f., and dielectric field intensity changed to K. Also, a few symbols not contained in the Standardization Rules had to be added. NOMENCLATURE TABLE OP SYMBOLS 119 Symbol Name Unit Character E, e. Voltage Volt Electrical I, i. . Pote ...", "... R Reluctance (magnetic Electrical L M S .. . resistance) Inductance Mutual inductance Self-inductance Henry; milhenry Henry; milhenry Henry; milhenry Magnetic Magnetic Magnetic *,Q D K Leakage inductance Dielectric flux Electric quantity or charge Dielectric density Dielectric field inten- Lines of dielectric force Coulombs Dielectric lines per cm.2 Coulombs per cm.2 Dielectric Dielectric Dielectric k sity Permittivity Diele ...", "... .. . resistance) Inductance Mutual inductance Self-inductance Henry; milhenry Henry; milhenry Henry; milhenry Magnetic Magnetic Magnetic *,Q D K Leakage inductance Dielectric flux Electric quantity or charge Dielectric density Dielectric field inten- Lines of dielectric force Coulombs Dielectric lines per cm.2 Coulombs per cm.2 Dielectric Dielectric Dielectric k sity Permittivity Dielectric Specific capacity 120 ELEMENTS OF ELECTR ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-23", "section_label": "Chapter 1: The Constants Of The Electric Circuit", "section_title": "The Constants Of The Electric Circuit", "kind": "chapter", "sequence": 23, "number": 1, "location": "lines 1317-1992", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "snippets": [ "... as that factor of the electric power P which is proportional to the electrostatic field. Current i and voltage e, therefore, are mathematical fictions, factors of the power P, introduced to represent respectively the magnetic and the electrostatic or \" dielectric \" phenomena. The current i is measured by the magnetic action of a circuit, as in the ammeter; the voltage e, by the electrostatic action of a circuit, as in the electrostatic voltmeter, or by producing a current i by the voltage e and measuring this cur ...", "... cuit, as in the electrostatic voltmeter, or by producing a current i by the voltage e and measuring this current i by its magnetic action, in the usual voltmeter. The coefficients L and (7, which are the proportionality factors of the magnetic and of the dielectric component of the electric field, are called the inductance and the capacity of the circuit, respectively. As electric power P is resolved into the product of current i and voltage e, the power loss in the conductor, Ph therefore can also be resolved int ...", "... di i r>/ T • di - = L-,and: P' = Lt-, (7) and the total energy absorbed by the magnetic field during the rise of current from zero to i is WM --P'dt (8) = LJidi, that is, ,, WM - (9) THE CONSTANTS OF THE ELECTRIC CIRCUIT 1 A change of the dielectric field of the conductor, ^, absorbs a current proportional to the change of the dielectric field : and absorbs the power or, by equation (3), P»=ei'=e—, (11) (12) and the total energy absorbed by the dielectric field during a rise of voltage from 0 to ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "... r, x, g, b, will always be consid- ered as the coefficients of the power and reactive components of current and e.m.f. — ^that is, as the effective quantities — so that the results are directly appHcable to the general electric circuit containing iron and dielectric losses. Introducing now, in Chapters VIII, to XI, instead of \"ohmic resistance,\" the term \"effective resistance,\" etc., as discussed in the preceding chapter, the results apply also — within the range discussed in the preceding chapter — to circuits cont ...", "... line conductors are of 1 cm. diameter, and at a distance from each other of 50 cm,, and that the length of transmission is 50 km., we get the capacity of the transmission line from the formula — C = 1.11 X 10-« kl H- 4 loge 2- microfarads, where k = dielectric constant of the surrounding medium = 1 in air; I = length of conductor = 5 X 10\" cm.; ■ d = distance of conductors from each other = 50 cm.; 5 = diameter of conductor = 1 cm. Hence C = 0.3 microfarad, the condensive reactance is x = ^ — 7f< ohms, wh ...", "... ious at high frequencies, such as those of telephone currents. The effect of eddy currents has already been referred to under \"mutual inductive reactance,\" of which it is a power component. The alternating electrostatic field of force expends energy in dielectrics by corona and dielectric hysteresis. In concentric cables, where the electrostatic gradient in the dielectric is com- paratively large, the dielectric losses may at high potentials consume appreciable amounts of energy. The dielectric loss appears in the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "section_title": "Dibtbisnted Capacity, Inductance, Besistance, And", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "... nstance, that the line conductors are of 1 cm diameter, and at a distance from each other of 50 cm, and that the length of transmission is 50 km, we get the capacity of the transmission line from the formula — c = microfarads, 4 log nat -^ where K = dielectric constant of the surrounding medium = 1 in air ;. / = length of conductor = 5 X 10* cm. ; d = distance of conductors from each other = 50 cm. ; 8 = diameter of conductor = 1 cm. Since C = .3 microfarads, the capacity reactance is 10« . 152 AL ...", "... ry serious at high frequencies, such as those of telephone currents. The effect of eddy currents has already been referred to under \"mutual inductance,\" of which it is an energy component. The alternating electrostatic field of force expends energy in dielectrics by what is called dielectric hysteresis. In concentric cables, where the electrostatic gradient in the dielectric is comparatively large, the dielectric hysteresis may at high potentials consume far greater amounts of energy than the resistance does. The ...", "... , such as those of telephone currents. The effect of eddy currents has already been referred to under \"mutual inductance,\" of which it is an energy component. The alternating electrostatic field of force expends energy in dielectrics by what is called dielectric hysteresis. In concentric cables, where the electrostatic gradient in the dielectric is comparatively large, the dielectric hysteresis may at high potentials consume far greater amounts of energy than the resistance does. The dielectric hysteresis § 10 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "... e conductors are of 1 cm. diameter, and at a distance from each other of 50 cm., and that the length of transmission is 50 km., we get the capacity of the transmission line from the formula — C = 1.11 X 10 -«K/ -=- 4 loge 2 d/ 8 microfarads, where K = dielectric constant of the surrounding medium = 1 in air ; / = length of conductor = 5 x 106 cm. ; d = distance of conductors from each other = 50 cm. ; 8 = diameter of conductor = 1 cm. Since C = .3 microfarads, the capacity reactance is x — 106 / 2 TT NC ohm ...", "... ry serious at high frequencies, such as those of telephone currents. The effect of eddy currents has already been referred to under \"mutual inductance,\" of which it is an energy component. The alternating electrostatic field of force expends energy in dielectrics by what is called dielectric hysteresis. In concentric cables, where the electrostatic gradient in the dielectric is comparatively large, the dielectric hysteresis may at high potentials consume considerable amounts of energy. The dielectric hysteresis ap ...", "... , such as those of telephone currents. The effect of eddy currents has already been referred to under \"mutual inductance,\" of which it is an energy component. The alternating electrostatic field of force expends energy in dielectrics by what is called dielectric hysteresis. In concentric cables, where the electrostatic gradient in the dielectric is comparatively large, the dielectric hysteresis may at high potentials consume considerable amounts of energy. The dielectric hysteresis appears in the circuit DISTR ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... very serious at high fre- quencies such as those of telephone currents. The effect of eddy currents has already been referred to under \" mutual inductance,\" of which if is a power component. The alternating electrostatic field of force expends power in dielectrics by what is called dielectric hysteresis. In concentric cables, where the electrostatic gradient in the dielectric is com- paratively large, the dielectric hysteresis may at high potentials consume considerable amounts of power. The dielectric hystere- sis ...", "... ncies such as those of telephone currents. The effect of eddy currents has already been referred to under \" mutual inductance,\" of which if is a power component. The alternating electrostatic field of force expends power in dielectrics by what is called dielectric hysteresis. In concentric cables, where the electrostatic gradient in the dielectric is com- paratively large, the dielectric hysteresis may at high potentials consume considerable amounts of power. The dielectric hystere- sis appears in the circuit as co ...", "... een referred to under \" mutual inductance,\" of which if is a power component. The alternating electrostatic field of force expends power in dielectrics by what is called dielectric hysteresis. In concentric cables, where the electrostatic gradient in the dielectric is com- paratively large, the dielectric hysteresis may at high potentials consume considerable amounts of power. The dielectric hystere- sis appears in the circuit as consumption of a current whose component in phase with the e.m.f. is the dielectric pow ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 557-1002", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-01/", "snippets": [ "... d does not represent the entire phenome- non. While electric power flows over the line A, there is a magnetic field surrounding the line conductors, and an electrostatic field issuing from the line conductors. The magnetic field and the electrostatic or \" dielectric \" field represent stored energy. Thus, during the permanent conditions of the flow of power through the circuit Fig. 3, there is electric energy stored in the space surround- ing the line conductors. There is energy stored also in the genera- tor and in t ...", "... successive oscillations or changes between potential gravitational and kinetic mechanical Double-energy Transient of Pendulum. NATURE AND ORIGIN OF TRANSIENTS. 9 energy. Thus in electric circuits containing energy stored in the magnetic and in the dielectric field, the change of the amount of stored energy — decrease or increase — frequently occurs by a series of successive changes from magnetic to dielectric and back again from dielectric to magnetic stored energy. This for instance is the case in the charge or di ...", "... TRANSIENTS. 9 energy. Thus in electric circuits containing energy stored in the magnetic and in the dielectric field, the change of the amount of stored energy — decrease or increase — frequently occurs by a series of successive changes from magnetic to dielectric and back again from dielectric to magnetic stored energy. This for instance is the case in the charge or discharge of a condenser through an inductive circuit. If energy can be stored in more than two different forms, still more complex phenomena may oc ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 460-882", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "snippets": [ "... d does not represent the entire phenome- non. While electric power flows over the line A , there is a magnetic field surrounding the line conductors, and an electrostatic field issuing from the line conductors. The magnetic field and the electrostatic or \"dielectric \" field represent stored energy. Thus, during the permanent conditions of the flow of power through the circuit Fig. 3, there is electric energy stored in the space surround- ing the line conductors. There is energy stored also in the genera- tor and in t ...", "... ve oscillations or changes between potential gravitational and kinetic mechanical Fig. 6. Double-energy Transient of Pendulum. NATURE AND ORIGIN OF TRANSIENTS. energy. Thus in electric circuits containing energy stored in the magnetic and in the dielectric field, the change of the amount of stored energy — decrease or increase — frequently occurs by a series of successive changes from magnetic to dielectric and back again from dielectric to magnetic stored energy. This for instance is the case in the charge or di ...", "... OF TRANSIENTS. energy. Thus in electric circuits containing energy stored in the magnetic and in the dielectric field, the change of the amount of stored energy — decrease or increase — frequently occurs by a series of successive changes from magnetic to dielectric and back again from dielectric to magnetic stored energy. This for instance is the case in the charge or discharge of a condenser through an inductive circuit. If energy can be stored in more than two different forms, still more complex phenomena may oc ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-02", "section_label": "Lecture 2: Conclusions From The Relativity Theory", "section_title": "Conclusions From The Relativity Theory", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 736-2388", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... and define the field as ''a condition of energy storage in space exerting a force on a body susceptible to this energy.'' The space surrounding a magnet is a magnetic field. If we electrify a piece of sealing wax by rubbing it, it surrounds itself by a dielectric or electrostatic field, and bodies susceptible to electrostatic forces- — such as light pieces of paper — are attracted. The earth is surrounded by a gravitational field, the lines of gravitational force CONCLUSIONS FROM RELATIVITY THEORY 19 issuing r ...", "... ent through the coil, the magnetic field alternates — that is, is a periodic phenomenon or a wave, an alternating magnetic field wave. Similarly, by connecting an insulated conductor to a source of voltage we produce surrounding it an electro- static or dielectric field — a constant field if the voltage is constant, an alternating dielectric field — that is, a periodic or wave phenomenon^ — ^if we use an alternating voltage. CONCLUSIONS FROM RELATIVITY THEORY 21 Magnetic and dielectric fields are usually combined, sin ...", "... enomenon or a wave, an alternating magnetic field wave. Similarly, by connecting an insulated conductor to a source of voltage we produce surrounding it an electro- static or dielectric field — a constant field if the voltage is constant, an alternating dielectric field — that is, a periodic or wave phenomenon^ — ^if we use an alternating voltage. CONCLUSIONS FROM RELATIVITY THEORY 21 Magnetic and dielectric fields are usually combined, since where there is a current producing a magnetic field there is a voltage prod ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-33", "section_label": "Chapter 33: Efficiency Of Systems", "section_title": "Efficiency Of Systems", "kind": "chapter", "sequence": 33, "number": 33, "location": "lines 36515-37127", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-33/", "snippets": [ "... um potential only, but where the limitation of potential depends upon the problem of insulating the conductors against disruptive discharge, the proper com- parison is on the basis of equality of the maximum difference of potential; that is, equal maximum dielectric strain on the insulation. In this case, the comparison voltage may be either the poten- tial difference between any two conductors of the system, or it may be the potential difference between any conductor of the system and the ground, depending on the ...", "... this case, the comparison voltage may be either the poten- tial difference between any two conductors of the system, or it may be the potential difference between any conductor of the system and the ground, depending on the character of the circuit. The dielectric stress is from conductor to conductor, or be- tween any two conductors, in a system which is insulated from the ground, as is mostly the case in medium voltage overhead transmissions, and frequently in underground cables. In an ungrounded cable system, i ...", "... f the copper of the alternating system. This comparison of the alternating with the continuous-cur- rent system is not proper, however, since the continuous-current voltage may introduce, besides the electrostatic strain, an elec- trolytic strain on the dielectric which does not exist in the alter- nating system, and thus may make the action of the continuous- current voltage on the insulation more severe than that of an equal alternating voltage. Besides, self-induction having no effect on a steady current, contin ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-05", "section_label": "Lecture 5: Single-Energy Tra.Nsient Of Ironclad Circuit", "section_title": "Single-Energy Tra.Nsient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3387-3720", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-05/", "snippets": [ "LECTURE V. SINGLE-ENERGY TRA.NSIENT OF IRONCLAD CIRCUIT. 22. Usually in electric circuits; current, voltage, the magnetic field and the dielectric field are proportional to each other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnet ...", "... h other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnetic materials, or if the dielectric field reaches densities beyond the dielectric strength of the carrier of the field, etc.; and the proportionality between current or voltage and their respective fields, the magnetic and the dielectric, thus ceases, or, as it may be expressed, the inductance L ...", "... ponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnetic materials, or if the dielectric field reaches densities beyond the dielectric strength of the carrier of the field, etc.; and the proportionality between current or voltage and their respective fields, the magnetic and the dielectric, thus ceases, or, as it may be expressed, the inductance L is not constant, but varies w^ith the cu ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-05", "section_label": "Lecture 5: Single-Energy Transient Of Ironclad Circuit", "section_title": "Single-Energy Transient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2972-3286", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "snippets": [ "LECTURE V. SINGLE-ENERGY TRANSIENT OF IRONCLAD CIRCUIT. 22. Usually in electric circuits, current, voltage, the magnetic field and the dielectric field are proportional to each other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnet ...", "... h other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnetic materials, or if the dielectric field reaches densities beyond the dielectric strength of the carrier of the field, etc. ; and the proportionality between current or voltage and their respective fields, the magnetic and the dielectric, thus ceases, or, as it may be expressed, the inductance L ...", "... ponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnetic materials, or if the dielectric field reaches densities beyond the dielectric strength of the carrier of the field, etc. ; and the proportionality between current or voltage and their respective fields, the magnetic and the dielectric, thus ceases, or, as it may be expressed, the inductance L is not constant, but varies with the cu ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-04", "section_label": "Lecture 4: The Characteristics Of Space A. The Geometry Of The Gravitational Field", "section_title": "The Characteristics Of Space A. The Geometry Of The Gravitational Field", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3595-6820", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-04/", "snippets": [ "... c energy and the electromagnetic field do not yet satisfactorily fit into it. INDEX Aberration of light, 15 Absolute number, meaning, 38 Accelerated motion, and gravitation, 52 Acceleration, 9, 47 Action at distance, 19 Alternating current, 14 dielectric field, 20 Analogue, 2 dimensional, of uni- verse, 119 Axioms of mathematics, 70 metric, of space, 95, 110 B Beltrami's pseudosphere, 91 Bending of space, 88 Betel geuse, 67 Bolyai, 71 Bullet velocity, 13 C Capacity and wave velocity, 23 Centri ...", "... ements, 92 Corpuscular theory of light, 13 Curvature of bundle as 2-space, 102 of curve, 82 of space, 80, 81, 83 Cylinder, as Euclidean 2-space, 90 D Deflection of light in gravitational field, 55 angle and equation, 59 Detonation velocity, 13 Dielectric field, 18 intensity, 47 Differential metric space, 115 Dimensions of physical space, 97 Direction of curve, 82 Distance between two events, 32 measure of time, 33 E Earth as elliptic 2-space, 75 Einstein, law of gravitation, 11 Electric field, 47 qu ...", "... ing system, 25, 27 Ether, 12, 14 as solid, 14 drift, 14 fallacy of conception, 16 illogical, 18 unnecessary, 17 waves, 18 Euclid, 71 Euclidean geometry, 64, 72, 74 F Fallacy of ether conception, 16 Faraday, 12, 17 Field, centrifugal, 47 dielectric, 18 electromagnetic, 21 electrostatic, 18 gravitational, 18, 46, 47 magnetic, 18 of energy, 22 of force, 12, 18 Finite volume of universe, 63 Force, magnetic, 46 Four-dimensional space with sphere as element, 99 Fraction, meaning of, 38 Fre ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... r oscillation 66, 72 Decay of continuous current in inductive circuit 17 of wave of condenser oscillation 72 Decrement of condenser oscillation 65, 72 resultant time, of complex circuit 504 Destructive voltages in cables and transmission lines 120 Dielectric constant, numerical values 11 strength, numerical values 11 Dielectric also see Electrostatic. Direct-current generator, self-excitation 32 railway, transient effective resistance 379 Disappearance of transient term in alternating-current circuit 43 ...", "... of wave of condenser oscillation 72 Decrement of condenser oscillation 65, 72 resultant time, of complex circuit 504 Destructive voltages in cables and transmission lines 120 Dielectric constant, numerical values 11 strength, numerical values 11 Dielectric also see Electrostatic. Direct-current generator, self-excitation 32 railway, transient effective resistance 379 Disappearance of transient term in alternating-current circuit 43 Discharge of condenser , . 51 Geissler tube 9 inductive, as wave 535 ...", "... of condenser oscillation 72 Electric circuit, general equations 428 field, velocity of propagation 387 Electrolytes, resistivities 8 Electrolytic rectifiers 222 Electromagnetic, also see Magnetic. axis of electric field 4 Electrostatic, also see Dielectric. axis of electric field 4 energy of complex circuit 517 field, energy of 7 Elimination of pulsations in direct-current circuit by capacity 134 Energy of complex circuit 513 condenser discharge 70 electric field 4, 7 transfer in complex circuit ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1659-2484", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-03/", "snippets": [ "... energy can exist. Such circuits are most of the low- and medium-voltage circuits, — 220 volts, 600 volts, and 2200 volts. In them the capac- ity is small, due to the limited extent of the circuit, resulting from the low voltage, and at the low voltage the dielectric energy thus is negligible, that is, the circuit stores appreciable energy only by the magnetic field. A circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectri ...", "... ielectric energy thus is negligible, that is, the circuit stores appreciable energy only by the magnetic field. A circuit of considerable capacity, but negligible inductance, if of high resistance, would also give one form of energy storage only, in the dielectric field. The usual high-voltage capacity circuit, as that of an electrostatic machine, while of very small inductance, also is of very small resistance, and the momentary discharge currents may be very consider- able, so that in spite of the very small inductanc ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "LECTURE VII. LINE OSCILLATIONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy surges between magnetic — and dielectric — , and a transient component, by which the total stored energy decreases. Considering only the periodic component, the maximum value of magnetic energy must equal the maximum value of dielectric '^'^e^gy- Li„^ Ce, 0 \"^^0 (1) where Iq = maxim ...", "... by which the stored energy surges between magnetic — and dielectric — , and a transient component, by which the total stored energy decreases. Considering only the periodic component, the maximum value of magnetic energy must equal the maximum value of dielectric '^'^e^gy- Li„^ Ce, 0 \"^^0 (1) where Iq = maximum value of transient current, 60 = maximum value of transient voltage. This gives the relation between Bq and Iq, ^^ = Jl ,^ = 1, (2) where Zq is called the natural impedance or surge impedance ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "LECTURE VIII. TRAVELING WAVES. 33. In a stationary oscillation of a circuit having uniformly distributed capacity and inductance, that is, the transient of a circuit storing energy in the dielectric and magnetic field, current and voltage are given by the expression i = ioe-\"^ cos ((/> T CO — 7), ^ . . e = eoe~\"' sin ((^ =F co — 7), where 2 surges between magnetic -^- and dielectric — , and a transient £i A component, by which the total stored energy decreases. Considering only the periodic component, the maximum mag- netic energy must equal the maximum dielectric energy, Lio2 _ Ceo2 \"2\" ~2~' where i0 = maximum transient curr ...", "... e stored energy 7\" /j'2 f^ r/>2 surges between magnetic -^- and dielectric — , and a transient £i A component, by which the total stored energy decreases. Considering only the periodic component, the maximum mag- netic energy must equal the maximum dielectric energy, Lio2 _ Ceo2 \"2\" ~2~' where i0 = maximum transient current, e0 = maximum transient voltage. This gives the relation between eQ and io, e0 V/L_ 1 i-0 = \\C-ZQ-yQ' where ZQ is called the natural impedance or surge impedance, y0 the natural o ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 4745-5520", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "snippets": [ "LECTURE VIII. TRAVELING WAVES. 33. In a stationary oscillation of a circuit having uniformly distributed capacity and inductance, that is, the transient of a circuit storing energy in the dielectric and magnetic field, current and voltage are given ^by the expression i = iQe~ut cos (0 T co - 7), ) e = e0e~ut sin ( T co — 7), ) where 0 is the time angle, co the distance angle, u the exponential decrement, or the \"power-dissipation constant,\" and ...", "... and a pulsation or surge, pi, of the same nature as that of the standing wave (2) : Such a flow of power along the circuit is called a traveling wave. It occurs very frequently. For instance, it may be caused if by a lightning stroke, etc., a quantity of dielectric energy is impressed A • Fig. 39. — Starting of Impulse, or Traveling Wave. upon a part of the circuit, as shown by curve A in Fig. 39, or if by a local short circuit a quantity of magnetic energy is impressed upon a part of the circuit. This energy ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... : S = -L= , (5) VLC where L is the inductance, C the capacity of the conductor per unit length (the length measured in the same measure as the speed S). The inductance L is proportional to the permeability /*, and the capacity C proportional to the dielectric constant, or specific capacity K of the medium surrounding the conductor, that is, the medium through which the electric wave propagates; that is, A V p* where A is a proportionality constant. The ratio of the speed of propagation of an electric wave ...", "... and « = 1; hence, (8) where Sl is the speed of propagation in the medium of constants /^ and jcr Comparing equation (8) with (4) it follows : Vl = d*-, (9) that is, the square of the refractive index d equals the product of permeability JJL and dielectric constant K. Since for most media the permeability /JL = 1, for all except e maneti mri the magnetic materials RELATION OF BODIES TO RADIATION. 25 This relation between the constant of the electric circuit K and the constant of optics d was on ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-11", "section_label": "Theory Section 11: Capacity and Condensers", "section_title": "Capacity and Condensers", "kind": "theory-section", "sequence": 11, "number": 11, "location": "lines 3586-3760", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-11/", "snippets": [ "... ing, the e.m.f. of the condenser is 106/ 106 The value z0 = fn is called the condensive reactance of the ^ 7T/C condenser. 56 ELEMENTS OF ELECTRICAL ENGINEERING Due to the energy loss in the condenser by dielectric hysteresis, the current leads the e.m.f. by somewhat less than 90 time de- grees, and can be resolved into a wattless charging current and a dielectric hysteresis current, which latter, however, is generally so small as to ...", "... OF ELECTRICAL ENGINEERING Due to the energy loss in the condenser by dielectric hysteresis, the current leads the e.m.f. by somewhat less than 90 time de- grees, and can be resolved into a wattless charging current and a dielectric hysteresis current, which latter, however, is generally so small as to be negligible, though in underground cables of poor quality, it may reach as high as 50 per cent, or more of the charging or wattless current of the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1120-1683", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-01/", "snippets": [ "... in circuits where energy is expended only in heating the conductor, is the same as the ohmic resistance of continuous-current circuits. In circuits, however, where energy is also expended outside of the conductor by magnetic hysteresis, mutual inductance, dielectric hysteresis, etc., r is larger than the true ohmic resistance of the conductor, since it refers to the total expenditure of energy. It may be called then the effective re- sistance. It may no longer be a constant of the circuit. The reactance, x, does not ...", "... f e.m.f. to the current. Since in alternating-cur- rent circuits, in addition to the energy expended iii the ohmic re- sistance of the conductor, energy is expended, partly outside, partly inside of the conductor, by magnetic hysteresis, mutual induction, dielectric hysteresis, etc., the effective resistance, r, is in general larger than the true resistance of the conductor, sometimes many time larger, as in transformers at open sec- ondary circuit, and is no longer a constant of the circuit. It is more fully discuss ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1224-1727", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "snippets": [ "... ircuits where energy is expended only in heating the conductor, is the same as the ohmic resistance of continuous-current circuits. In circuits, how- ever, where energy is also expended outside of the con- ductor by magnetic hysteresis, mutual inductance, dielectric hysteresis, etc., r is larger than the true ohmic resistance of the conductor, since it refers to the total expenditure of energy. It may be called then the effective resistance. It is no longer a constant of the circuit. The reactance, ;r, does not rep ...", "... the energy component of E.M.F. to the cur- rent. Since in alternating-current circuits, besides by the ohmic resistance of the conductor, energy is expended, partly outside, partly even inside, of the conductor, by magnetic hysteresis, mutual inductance, dielectric hystere- sis, etc., the effective resistance, r, is in general larger than the true resistance of the conductor, sometimes many times larger, as in transformers at open secondary circuit, and is not a constant of the circuit any more. It is more fully di ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-28", "section_label": "Chapter 28: Copper Efficiency Of Systems", "section_title": "Copper Efficiency Of Systems", "kind": "chapter", "sequence": 28, "number": 28, "location": "lines 26584-27052", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-28/", "snippets": [ "... nly, but where the limitation of potential depends upon the problem of insulating the conductors against disruptive discharge, the proper comparison is on the basis of equality of the maximum difference of potential in the system ; that is, equal maximum dielectric strain on the insulation. The same consideration holds in moderate potential power circuits, in considering the danger to life from wires or high differences of potential. Thus the comparison of different systems of long-dis- tance transmission at high ...", "... half the copper of the alternating system. This comparison of the alternating with the continuous*- current system is not proper however, since the continuous- current potential introduces, besides the electrostatic strain, an electrolytic strain on the dielectric which does not exist in the alternating system, and thus makes the action of the continuous-current potential on the insulation more severe than that of an equal alternating potential. Besides, at the voltages which came under consideration, the continuou ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 963-1366", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "snippets": [ "... ircuits where energy is expended only in heating the conductor, is the same as the ohmic resistance of continuous-current circuits. In circuits, how- ever, where energy is also expended outside of the con- ductor by magnetic hysteresis, mutual inductance, dielectric hysteresis, etc., r is larger than the true ohmic resistance of the conductor, since it refers to the total expenditure of energy. It may be called then the effective resistance. It is no longer a constant of the circuit. The reactance, x, does not repr ...", "... the energy component of E.M.F. to the cur- rent. Since in alternating-current circuits, besides by the ohmic resistance of the conductor, energy is expended, partly outside, partly even inside, of the conductor, by magnetic hysteresis, mutual inductance, dielectric hystere- sis, etc., the effective resistance, r, is in general larger than the true resistance of the conductor, sometimes many times larger, as in transformers at open secondary circuit, and is not a constant of the circuit any more. It is more fully di ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-30", "section_label": "Chapter 30: Efficiency Of Systems", "section_title": "Efficiency Of Systems", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 25136-25597", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-30/", "snippets": [ "... ly, but where the limitation of potential depends upon the problem of insulating the conductors against disruptive discharge, the proper comparison is on the basis of equality of the maximum difference of potential in the system ; that is, •equal maximum dielectric strain on the insulation. The same consideration holds in moderate potential power circuits, in considering the danger to life from live wires entering human habitations. Thus the comparison of different systems of long-dis- tance transmission at high ...", "... half the copper of the alternating system. This comparison of the alternating with the continuous- current system is not proper however, since the continuous- current potential introduces, besides the electrostatic strain, an electrolytic strain on the dielectric which does not exist in the alternating system, and thus makes the action of the continuous-current potential on the insulation more severe than that of an equal alternating potential. Besides, self- induction having no effect on a steady current, continu ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-12", "section_label": "Chapter 14: Phase Conversion And Single-Phase Generation", "section_title": "Phase Conversion And Single-Phase Generation", "kind": "chapter", "sequence": 12, "number": 14, "location": "lines 17125-18412", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-12/", "snippets": [ "... e factor of the single-phase system is zero or negative, while that of the balanced polyphase system is unity. For such energy storage may be used capacity, or inductance, or momentum or a combination thereof: Energy storage by capacity, that is, in the dielectric fu Id, required per kilovolt-ampere at 60 cycles about 200O <-.•■. ol space, at a cost of about $10. Inductance, that is. energy storage by the magnetic field, requires about 1000 c.e. per kilo- volt-ampere at 60 cycles, at a cost of $1, while energy stor ...", "... a quarter of the mass of the mechanical structure (motor, etc.) is revolving, and that the energy storage takes place by a pulsation of speed of per cent., then 1 kva. at 60 cycles would require 600 c.e. of terial, at 40c, Obviously, at the limits of dielectric or magnetic field strength, or at the limits of mechanical speeds, very much larger amounts of energy per bulk could be stored. Thus for instance, at the limits of steam-turbine rotor speeds, about 400 meter-seconds, in a very heavy material as tungsten, ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-01", "section_label": "Chapter 1: Electric Conduction. Soled And Liquid", "section_title": "Electric Conduction. Soled And Liquid", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 959-3894", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-01/", "snippets": [ "... , not an electrolytic condenser, and the counter e.m.f., which gives the capacity effect, is not electrolytic polarization. The aluminum cell is a true electro- static condenser, in which the film of alumina, formed on the positive aluminum plates, is the dielectric. Its characteristic is, that the condenser is self-healing; that is, a puncture of the alum- ina film causes a current to flow, which electroljrtically produces alumina at the puncture hole, and so closes it. The capacity is very high, due to the great th ...", "... s a current to flow, which electroljrtically produces alumina at the puncture hole, and so closes it. The capacity is very high, due to the great thinness of the film, but the energy losses are considerable, due to the continual puncture and repair of the dielectric film. P3nroelectric Conductors 8. A third class of conductors are the pyroelectric conductors or pyroelectrolytes. In some features they are intermediate between the metallic conductors and the electrolytes, but in their essen- tial characteristics the ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-03", "section_label": "Lecture 3: Gravitation And The Gravitational Fleld", "section_title": "Gravitation And The Gravitational Fleld", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2389-3594", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-03/", "snippets": [ "... ss, the same quantity which in the days of action at a distance was called the magnetic pole strength, and which is related to the magnetic flux $ by: $ = AtP. The force exerted by an electric field on an electrified body is: F=KQ, (2) where K is the dielectric field intensity and Q the electric mass or electric quantity, also called electrostatic charge, measured in coulombs. The force exerted by a gravitational field is : F = gN, (3) where g is the gravitational field intensity and N the sus- ceptibility of the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 3267-3618", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-06/", "snippets": [ "... ement, 90° ahead of the current, Oh, and proportional thereto. In the same Hne element we have a current, hh^, in phase with the voltage, OEi, and proportional thereto, representing 44 ALTERNATING-CURRENT PHENOMENA the loss of current by leakage, dielectric hysteresis, etc., and a current, /i^ /i^\\ 90° ahead of the voltage, 0E-[, and proportional thereto, the charging current of the line element as condenser; and in this manner passing along the line, element by element, we ultimately reach the generator ter ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-12", "section_label": "Chapter 12: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 10718-13483", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-12/", "snippets": [ "... nalytically with alternating-current circuits containing iron. 90. The foremost sources of energy loss in alternating-current circuits, outside of the true ohmic resistance loss, are as follows : 1. Molecular friction, as, (a) Magnetic hysteresis; (6) Dielectric hysteresis. 2. Primary electric currents, as, (a) Leakage or escape of current through the insulation, brush discharge, corona. (6) Eddy currents in the conductor or unequal current distribution. EFFECTIVE RESISTANCE AND REACTANCE 113 -» 3. Se ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-25", "section_label": "Chapter 25: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 29375-32539", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-25/", "snippets": [ "... ed out under the assumption of sine waves, as done in the preceding chapters. Similar phenomena take place in circuits containing polari- zation cells, leaky condensers, or other apparatus representing a synchronously varying negative reactance. Possibly dielectric hysteresis in condensers causes a distortion similar to that due to magnetic hysteresis. Inversely, at very high voltages, where corona appears on the conductors, with a sine wave of impressed voltage, a distor- tion of the capacity current wave occurs, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-26", "section_label": "Chapter 26: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 32540-33010", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-26/", "snippets": [ "... lation. The striking-distance of an alternating voltage depends upon the maximum value, except at extremely high frequencies, such as oscillating discharges. In the latter, the very short duration of the voltage peak may reduce the disruptive strength, as dielectric disruption requires energy, that is, not only voltage, but time also." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-35", "section_label": "Chapter 35: Balanced Symmetrical Polyphase Systems", "section_title": "Balanced Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 35, "number": 35, "location": "lines 37453-37957", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-35/", "snippets": [ "... Choosing the voltage at the receiving end as zero vector, e = 46,100 volts, at 90 per cent, power-factor and therefore 43.6 per cent, induc- tance factor, the current is represented by 7 = 80 (0.9 - 0.436 j) =72-35 j. ^ Or. ii fi = permeability, k = dielectric constant of the medium sur- rounding the conductor, it is hence, V [^ I = \\W or. C = (4) 452 ALTERNATING-CURRENT PHENOMENA This gives: Voltage at receiver circuit, e = 46,100 volts; current in receiver circuit, Z = 72 — 35 j amp. ; im ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-10", "section_label": "Chapter 10: F", "section_title": "F", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 8269-10499", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "snippets": [ "... ytically with alternating-current circuits containing iron. 73. The foremost sources of energy loss in alternating- current circuits, outside of the true ohmic resistance loss, are as follows : 1.) Molecular friction, as, a.) Magnetic hysteresis; b) Dielectric hysteresis. 106 ALTERNATING-CURRENT PHENOMENA. [§ 74 2.) Primary electric currents, as, a.) Leakage or escape of current through the in- sulation, brush discharge ; b.) Eddy currents in the conductor or unequal current distribution. 3.) Secondary ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-21", "section_label": "Chapter 21: Dibtobtiox Of Wavs-Shafe And Its Causes", "section_title": "Dibtobtiox Of Wavs-Shafe And Its Causes", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 23274-24559", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "snippets": [ "... ied out under the assumption of sine waves, as done in the preceding chapters. Similar phenomena take place in circuits containing polarization cells, leaky condensers, or other apparatus representing a synchronously varying negative reactance. Possibly dielectric hysteresis in condensers causes a dis- tortion similar to that due to magnetic hysteresis. Pulsation of Resistance, 219. To'a certain extent the investigation of the effect of synchronous pulsation of the resistance coincides with that of reactance ; s ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 2774-3131", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-06/", "snippets": [ "... sumed by the reactance of the line element, 90° ahead of the current OIV and proportional thereto. In the same line element we have a current IJ^ in phase with the E.M.F. OEV and proportional thereto, representing the loss of energy current by leakage, dielectric hysteresis, etc., and a current ^V/', 90° ahead of the E.M.F. OEV and proportional thereto, the charging current of the line ele- ment as condenser, and in this manner passing along the line, element by element, we ultimately reach the generator terminal ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "section_label": "Chapter 10: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "... ically with alternating-current circuits containing iron. 73. The foremost sources of energy loss in alternating- current circuits, outside of the true ohmic resistance loss, are as follows : 1.) Molecular friction, as, a.) Magnetic hysteresis ; b.) Dielectric hysteresis. 106 .ALTERNATING-CURRENT PHENOMENA. 2.) Primary electric currents, as, a.} Leakage or escape of current through the insu- lation, brush discharge ; b.) Eddy currents in the conductor or unequal current distribution. 3.) Secondary or indu ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-22", "section_label": "Chapter 22: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 21190-21982", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "snippets": [ "... ied out under the assumption of sine waves, as done in the preceding chapters. Similar phenomena take place in circuits containing polarization cells, leaky condensers, or other apparatus representing a synchronously varying negative reactance. Possibly dielectric hysteresis in condensers causes a dis- tortion similar to that due to magnetic hysteresis. Pulsation of Resistance. 240. To a certain extent the investigation of the effect of synchronous pulsation of the resistance coincides with that of reactance ; s ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-05", "section_label": "Chapter 5: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 9062-11050", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-05/", "snippets": [ "CHAPTER V MAGNETISM Magnetic Constants 47. With the exception of a few ferromagnetic substances, the magnetic permeability of all materials, conductors and dielectrics, gases, liquids and solids, is practically unity for all industrial purposes. Even liquid oxygen, which has the highest permea- bility, differs only by a fraction of a per cent, from non-magnetic materials. Thus the permeability of neodymium, which is o ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-09", "section_label": "Chapter 9: Wave Screens. Even Harmonics", "section_title": "Wave Screens. Even Harmonics", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 16964-17631", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-09/", "snippets": [ "... ay illustrate some of the numerous wave- shape distortions which are met in electrical engineering, their characteristics, origin, effects, use and danger. Numerous other wave distortions, such as those produced by arcs, by unidirec- tional conductors, by dielectric effects such as corona, by Y con- nection of transformers for reactors, by electrolytic polarization, by pulsating resistance or reactance, etc., are discussed in other chapters or may be studied in a similar manner. v/" ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... tance have a negative term added, which depends on the decrement a. Such a negative resistance repre- sents energy production, and its meaning in the present case is, that with the decrease of the oscillating current and voltage, their stored magnetic and dielectric energy become available. Circuits of Zero Impedance 190. In an oscillating-current circuit of decrement, a, of resistance, r, inductive reactance, x, and condensive reactance, Xc, the impedance was represented in symbolic expression by or numerically ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-24", "section_label": "Chapter 2: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 24, "number": 2, "location": "lines 1993-2658", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "snippets": [ "... seconds of time. 13. If an electrostatic condenser of capacity C is connected to a continuous e.m.f. e0, no current exists, in stationary con- dition, in this direct-current circuit (except that a very small current may leak through the insulation or the dielectric of the condenser), but the condenser is charged to the potential dif- ference eo; or contains the electrostatic charge Q = to0. In the moment of closing the circuit of e.m.f. e0 upon the capacity C, the condenser contains no charge, that is, zero pote ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-45", "section_label": "Chapter 5: Distributed Series Capacity", "section_title": "Distributed Series Capacity", "kind": "chapter", "sequence": 45, "number": 5, "location": "lines 23586-23947", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "snippets": [ "... uctor, as from turn to turn or layer to layer of a transformer coil. In some circuits, in addition to this shunted capacity, dis- tributed series capacity also exists, that is, the circuit is broken at frequent and regular intervals by gaps filled with a dielectric or insulator, as air, and the two faces of the conductor ends thus constitute a condenser in series with the circuit. Where the elements of the circuit are short enough so as to be represented, approximately, as conductor differentials, the circuit consti ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-50", "section_label": "Chapter 1: General Equations", "section_title": "General Equations", "kind": "chapter", "sequence": 50, "number": 1, "location": "lines 27761-28694", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "snippets": [ "... tion moves along the circuit with the speed — *., or, in other words, (15) is the speed of propagation of the electric phenomenon in the cir- cuit. (If no energy losses occur, r = 0, g = 0, in a straight con- ductor in a medium of unit magnetic and dielectric constant, that is, unit permeability and unit inductive capacity, S is the velocity of light.) 4. Since (11) is a quadratic equation, several pairs or corre- sponding values of a and b exist, which, in the most general case, are complex imaginary. The t ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-52", "section_label": "Chapter 3: Standing Waves", "section_title": "Standing Waves", "kind": "chapter", "sequence": 52, "number": 3, "location": "lines 29316-30243", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "snippets": [ "... se three- conductor 12,000-volt cable. Assume the conductor as stranded and of a section equiva- lent to No. 00 B. and S. G. Calculating the constants in the same manner, except that the expression for the capacity, equation (119), multiplies with the dielectric constant or specific capacity of the cable insula- tion, and that f ig verv small, about three or less; or taking the ^r values of the circuit constants from tests of the cable, we get values of the magnitude, per mile of single conductor, r = 0.41 ohm ..." ] } ] }, { "id": "hysteresis", "label": "Hysteresis", "aliases": [ "hysteresis", "magnetic lag", "molecular friction" ], "total_occurrences": 560, "matching_section_count": 88, "matching_source_count": 11, "source_totals": [ { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 109, "section_count": 11 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 107, "section_count": 13 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 100, "section_count": 11 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 83, "section_count": 10 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 74, "section_count": 14 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 38, "section_count": 13 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 23, "section_count": 6 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 14, "section_count": 3 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 5, "section_count": 2 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 4, "section_count": 2 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 3, "section_count": 3 } ], "section_hits": [ { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-04", "section_label": "Chapter 4: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 6942-9061", "status": "candidate", "occurrence_count": 53, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-04/", "snippets": [ "CHAPTER IV MAGNETISM Hysteresis 36. Unlike the electric current, which requires power for its maintenance, the maintenance of a magnetic flux does not require energy expenditure (the energy consumed by the magnetizing current in the ohmic resistance of the magnetizing winding being an ...", "... on, at least in those materials, which have permeabilities materially higher than unity. Thus, if a magnetic flux is periodically changed, between + B and — B, or between Bi and Bz, as by an alternating or pul- sating current, a dissipation of energy by molecular friction occurs during each magnetic cycle. Experiment shows that the energy consumed per cycle and cm.^ of magnetic material depends only on the limits of the cycle, Bi and B2, but not on the speed or wave shape of the change. If the energy which is consumed by ...", "... occurs during each magnetic cycle. Experiment shows that the energy consumed per cycle and cm.^ of magnetic material depends only on the limits of the cycle, Bi and B2, but not on the speed or wave shape of the change. If the energy which is consumed by molecular friction is sup- plied by an electric current as magnetizing force, it has the effect that the relations between the magnetizing current, i, or magnetic field intensity, H, and the magnetic flux density, B, is not revers- ible, but for rising, H, the density, B, i ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-12", "section_label": "Chapter 12: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 10718-13483", "status": "candidate", "occurrence_count": 37, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-12/", "snippets": [ "... the electric conductor b}^ a current of uniform density, the effective resistance represents the total expenditure of power. Since in an alternating-current circuit, in general power is expended not only in the conductor, but also outside of it, through hysteresis, secondary currents, etc., the effective resist- ance frequently differs from the true ohmic resistance in such way as to represent a larger expenditure of power. In dealing with alternating-current circuits, it is necessarj-, therefore, to substitute ev ...", "... the cause of most of the difficulties met in dealing analytically with alternating-current circuits containing iron. 90. The foremost sources of energy loss in alternating-current circuits, outside of the true ohmic resistance loss, are as follows : 1. Molecular friction, as, (a) Magnetic hysteresis; (6) Dielectric hysteresis. 2. Primary electric currents, as, (a) Leakage or escape of current through the insulation, brush discharge, corona. (6) Eddy currents in the conductor or unequal current distribution. EFFE ...", "... met in dealing analytically with alternating-current circuits containing iron. 90. The foremost sources of energy loss in alternating-current circuits, outside of the true ohmic resistance loss, are as follows : 1. Molecular friction, as, (a) Magnetic hysteresis; (6) Dielectric hysteresis. 2. Primary electric currents, as, (a) Leakage or escape of current through the insulation, brush discharge, corona. (6) Eddy currents in the conductor or unequal current distribution. EFFECTIVE RESISTANCE AND REACTANCE ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "section_label": "Chapter 10: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 36, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "... electric conductor by a current of uniform density, the effective resistance repre- sents the total expenditure of energy. Since, in an alternating-current circuit in general, energy is expended not only in the conductor, but also outside of it, through hysteresis, secondary currents, etc., the effective resistance frequently differs from the true ohmic resistance in such way as to represent a larger expenditure of energy. In dealing with alternating-current circuits, it is necessary, therefore, to substitute ever ...", "... cause of most of the difficulties met in dealing analytically with alternating-current circuits containing iron. 73. The foremost sources of energy loss in alternating- current circuits, outside of the true ohmic resistance loss, are as follows : 1.) Molecular friction, as, a.) Magnetic hysteresis ; b.) Dielectric hysteresis. 106 .ALTERNATING-CURRENT PHENOMENA. 2.) Primary electric currents, as, a.} Leakage or escape of current through the insu- lation, brush discharge ; b.) Eddy currents in the conductor or une ...", "... in dealing analytically with alternating-current circuits containing iron. 73. The foremost sources of energy loss in alternating- current circuits, outside of the true ohmic resistance loss, are as follows : 1.) Molecular friction, as, a.) Magnetic hysteresis ; b.) Dielectric hysteresis. 106 .ALTERNATING-CURRENT PHENOMENA. 2.) Primary electric currents, as, a.} Leakage or escape of current through the insu- lation, brush discharge ; b.) Eddy currents in the conductor or unequal current distribution. 3.) ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-09", "section_label": "Chapter 10: Hysteresis Motor", "section_title": "Hysteresis Motor", "kind": "chapter", "sequence": 9, "number": 10, "location": "lines 14551-14761", "status": "candidate", "occurrence_count": 28, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-09/", "snippets": [ "CHAPTER X HYSTERESIS MOTOR 98. In it revolving magnetic field, a circular iron disk, or iron cylinder of uniform magnetic reluctance in the direction of the revolving field, is set in rotation, even if subdivided so as to preclude the production of eddy currents. Thin rotati ...", "... magnetic field, a circular iron disk, or iron cylinder of uniform magnetic reluctance in the direction of the revolving field, is set in rotation, even if subdivided so as to preclude the production of eddy currents. Thin rotation is due to the effect of hysteresis of the revolving disk or cylinder, and such a motor may thus be called a hysteresis motor. Let / be the iron disk exposed to a rotating magnetic field or resultant m.m.f. The axis of resultant magnetization in the disk, /, does not coincide with the axis ...", "... ce in the direction of the revolving field, is set in rotation, even if subdivided so as to preclude the production of eddy currents. Thin rotation is due to the effect of hysteresis of the revolving disk or cylinder, and such a motor may thus be called a hysteresis motor. Let / be the iron disk exposed to a rotating magnetic field or resultant m.m.f. The axis of resultant magnetization in the disk, /, does not coincide with the axis of the rotating field, but lags behind the latter, thus producing a couple. That is ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-10", "section_label": "Chapter 10: F", "section_title": "F", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 8269-10499", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "snippets": [ "... electric conductor by a current of uniform density, the effective resistance repre- sents the total expenditure of energy. Since, in an alternating-current circuit in general, energy is expended not only in the conductor, but also outside of it, through hysteresis, secondary currents, etc., the effective resistance frequently differs from the true ohmic resistance in such way as to represent a larger expenditure of energy. In dealing with alternating-current circuits, it is necessary, therefore, to substitute ever ...", "... cause of most of the difficulties met in dealing analytically with alternating-current circuits containing iron. 73. The foremost sources of energy loss in alternating- current circuits, outside of the true ohmic resistance loss, are as follows : 1.) Molecular friction, as, a.) Magnetic hysteresis; b) Dielectric hysteresis. 106 ALTERNATING-CURRENT PHENOMENA. [§ 74 2.) Primary electric currents, as, a.) Leakage or escape of current through the in- sulation, brush discharge ; b.) Eddy currents in the conductor or ...", "... in dealing analytically with alternating-current circuits containing iron. 73. The foremost sources of energy loss in alternating- current circuits, outside of the true ohmic resistance loss, are as follows : 1.) Molecular friction, as, a.) Magnetic hysteresis; b) Dielectric hysteresis. 106 ALTERNATING-CURRENT PHENOMENA. [§ 74 2.) Primary electric currents, as, a.) Leakage or escape of current through the in- sulation, brush discharge ; b.) Eddy currents in the conductor or unequal current distribution. ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 25, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "CHAPTER XI. FOUCAULT OR EDDY CURRENTS. 86. While magnetic hysteresis or molecular friction is a magnetic phenomenon, eddy currents are rather an elec- trical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When ...", "CHAPTER XI. FOUCAULT OR EDDY CURRENTS. 86. While magnetic hysteresis or molecular friction is a magnetic phenomenon, eddy currents are rather an elec- trical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric ...", "CHAPTER XI. FOUCAULT OR EDDY CURRENTS. 86. While magnetic hysteresis or molecular friction is a magnetic phenomenon, eddy currents are rather an elec- trical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric conductor, the magnetic field induces a current therein. The M.M.F. of this current reacts upon and affects the magnetic field, more or less ; consequently, an alt ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 23, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "CHAPTER XI. FOUOAULT OR EDDY 0UBBENT8. • 86. While magnetic hysteresis or molecular friction is a magnetic phenomenon, eddy currents are rather an elec- trical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When ...", "CHAPTER XI. FOUOAULT OR EDDY 0UBBENT8. • 86. While magnetic hysteresis or molecular friction is a magnetic phenomenon, eddy currents are rather an elec- trical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric ...", "CHAPTER XI. FOUOAULT OR EDDY 0UBBENT8. • 86. While magnetic hysteresis or molecular friction is a magnetic phenomenon, eddy currents are rather an elec- trical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric conductor, the magnetic field induces a current therein. The M.M.F. of this current reacts upon and affects the magnetic field, more or less ; consequently, an alt ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-25", "section_label": "Chapter 25: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 29375-32539", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-25/", "snippets": [ "... itch arma- ture windings, such pronounced wave shape distortions as shown by the unitooth alternators shown as illustrations, have become infrequent. Pulsation of Reactance 236. The main causes of a pulsation of reactance are mag- netic saturation and hysteresis, and synchronous motion. Since in an iron-clad magnetic circuit the magnetism is not propor- tional to the m.m.f., the wave of magnetism and thus the wave of e.m.f. will differ from the wave of current. As far as this distortion is due to the variation of ...", "... of magnetism and thus the wave of e.m.f. will differ from the wave of current. As far as this distortion is due to the variation of permeability, the distortion is symmetrical and the wave of generated e.m.f. represents no power. The distortion caused by hysteresis, or the lag of the magnetism behind the m.m.f., causes an unsymmetrical distor- tion of the wave which makes the wave of generated e.m.f. differ by more than 90° from the current wave and thereby represents power — the power consumed by hysteresis. In p ...", "... used by hysteresis, or the lag of the magnetism behind the m.m.f., causes an unsymmetrical distor- tion of the wave which makes the wave of generated e.m.f. differ by more than 90° from the current wave and thereby represents power — the power consumed by hysteresis. In practice both effects are always superimposed; that is, in a ferric inductive reactance, a distortion of wave-shape takes place due to the lack of proportionality between magnetism and m.m.f. as expressed by the variation in the hysteretic cycle. T ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-10", "section_label": "Theory Section 10: Hysteresis and Effective Resistance", "section_title": "Hysteresis and Effective Resistance", "kind": "theory-section", "sequence": 10, "number": 10, "location": "lines 3234-3585", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-10/", "snippets": [ "10. HYSTERESIS AND EFFECTIVE RESISTANCE 46. If an alternating current 01 = I, in Fig. 21, exists in a circuit of reactance x = 2 irfL and of negligible resistance, the HYSTERESIS AND EFFECTIVE RESISTANCE 49 magnetic flux produce ...", "10. HYSTERESIS AND EFFECTIVE RESISTANCE 46. If an alternating current 01 = I, in Fig. 21, exists in a circuit of reactance x = 2 irfL and of negligible resistance, the HYSTERESIS AND EFFECTIVE RESISTANCE 49 magnetic flux produced by the current, 0$ = $, is in phase with the current, and the e.m.f. generated by this flux, or counter e.m.f. of self-inductance, OE'\" = E'\" = xl, lags 90 degrees ...", "... ly avail- able source of energy in the magnetic cir- cuit, the expenditure of energy by molec- ular magnetic friction appears as a lag of the magnetism behind the m.m.f. of the Q| r >i current, that is, as magnetic hysteresis, and can be measured thereby. Magnetic hysteresis is, however, a dis- tinctly different phenomenon from molec- ular magnetic friction, and can be more or less eliminated, as for instance by me- chanical vibration, or can be ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "section_label": "Chapter 16: Induction Motor", "section_title": "Induction Motor", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "... Let I0 = exciting current, or current passing through the motor, per primary circuit, when doing no work (at synchronism), and K= g -j- j 'b = orimary admittance per circuit = — . We thus have, ge = magnetic energy current, ge* = loss of power oy hysteresis (and eddy currents) per primary coil. Hence = total loss of energy by hysteresis and eddys, as calculated according to Chapter X. be = magnetizing current, and n0be = effective M.M.F. per primary circuit; hence ^n0be = total effective M.M.F. ; z ...", "... it, when doing no work (at synchronism), and K= g -j- j 'b = orimary admittance per circuit = — . We thus have, ge = magnetic energy current, ge* = loss of power oy hysteresis (and eddy currents) per primary coil. Hence = total loss of energy by hysteresis and eddys, as calculated according to Chapter X. be = magnetizing current, and n0be = effective M.M.F. per primary circuit; hence ^n0be = total effective M.M.F. ; z and l^-n^be = total maximum M.M.F., as resultant of the M.M.Fs. of the /0-phases, ...", "... Power of the Induction Motor. 158. We can arrive at the same results in a different way : By the counter E.M.F. e of the primary circuit with current / ' = f0 + 7X the power is consumed, e I = e I0 + e 7r The power e I0 is that consumed by the primary hysteresis and eddys. The power e 1^ disappears in the primary circuit by being transmitted to the secondary system. Thus the total power impressed upon the .secondary system, per circuit, is Pi-tf, Of this power a part, £1fl, is consumed in the secondary circ ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-01", "section_label": "Chapter 1: Speed Control Of Induction Motors", "section_title": "Speed Control Of Induction Motors", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1368-3542", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-01/", "snippets": [ "... be permissible only in the end connections, or the squirrel-cage end ring, but then, iron could be used as resistance material, which has a materially higher temperature coefficient, and the required temperature rise thus would probably be no higher. B. Hysteresis Starting Device 4. Instead of increasing the secondary resistance with increas- ing slip, to get high torque at low speeds, the same result can be produced by the use of an effective resistance, such as the effect- ive or equivalent resistance of hystere ...", "... teresis Starting Device 4. Instead of increasing the secondary resistance with increas- ing slip, to get high torque at low speeds, the same result can be produced by the use of an effective resistance, such as the effect- ive or equivalent resistance of hysteresis, or of eddy currents. As the frequency of the secondary current varies, a magnetic circuit energized by the secondary current operates at the varying frequency of the slip, s. At a given current, i\\, the voltage required to send the current through the ...", "... Y' = g' - jb' = V (tan a - j) = - J = (tan a - j) (7) 8 8 8 1 \"Theoiy and Calculation of Al format iri^-rurr^nt Phfjiornwia,\" Chapter XII. 6 ELECTRICAL APPARATUS Assuming tan a = 0.6, which is a fair value for a closed mag- netic circuit of high hysteresis loss, it is: Y' = bg (0.6 - j), the exciting admittance at slip, s. Assume then, that such an admittance, F', is connected in series into the secondary circuit of the induction motor,* for the pur- pose of using the effective resistance of hysteresis, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... aginary or general numbers are represented by the points outside of the coordinate axes. INDEX Absolute values of complex quanti- ties, 37 Actual generated e.m.f., alternator, 272 Admittance, 55 of dielectric, 154 due to eddy currents, 137 to hysteresis, 129 Admittivity of dielectric circuit, 160 Air-gap in magnetic circuit, 119, 132 Ambiguity of vectors, 39 Amplitude, 6, 20 Apparent capacity of distorted wave, 386 efficiency of induction motor, 234 impedance of transformer, 201 torque efficiency ...", "... ush discharge, 112 Cable, topographical characteristic, 42 Capacity, 4, 9 of line, 174 Choking coil, 96 Circuit characteristic of line and cable, 44 dielectric and dynamic, 159 factor of general wave, 383 Coefficient of eddy currents, 138 of hysteresis, 123 Combination of sine waves, 31 Compensation for lagging currents by condensance, 72 Condensance in symbolic expression, 36 Condenser as reactance and suscep- tance, 96 with distorted wave, 384 motor on distorted wave, 392 motor, single-phase ...", "... suscep- tance, 96 with distorted wave, 384 motor on distorted wave, 392 motor, single-phase induction, 249, 257 synchronous, 339 Conductance of circuit with induc- tive line, 84 direct current, 55 due to eddy currents, 137 effective, 111 due to hysteresis, 126 parallel and series connection, 54 Conductivity, dielectric, 153 of dielectric circuit, 160 Constant current from constant po- tential, 76 synchronous motor, 337 potential constant current trans- formation, 76 Consumed voltage, by resistance, r ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-34", "section_label": "Chapter 12: Magnetic Saturation And Hysteresis In Alternat Ing-Current Circuits", "section_title": "Magnetic Saturation And Hysteresis In Alternat Ing-Current Circuits", "kind": "chapter", "sequence": 34, "number": 12, "location": "lines 12885-13935", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-34/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-34/", "snippets": [ "CHAPTER XII. MAGNETIC SATURATION AND HYSTERESIS IN ALTERNAT- ING-CURRENT CIRCUITS. 99. If an alternating e.m.f. is impressed upon a circuit con- taining resistance and inductance, the current and thereby the magnetic flux produced by the current immediately assume their final or permanent values only ...", "... normal value, in the iron-clad circuit, if the magnetic flux density reaches into the range of magnetic saturation, very much higher values of transient current are found. Due to the far greater effect of the resistance with such MAGNETIC SATURATION AND HYSTERESIS 181 excessive values of current, the transient term of current during the first half waves decreases at a more rapid rate ; due to the lack of proportionality between current and magnetic flux density, the transient term does not follow the exponential l ...", "... rcuit, the current is not only not proportional to the magnetic flux density, but the same magnetic flux density can be produced by different currents, or with the same current the flux density can have very different values, depending on the point of the hysteresis cycle. Therefore the magnetic flux density for zero current may equal zero, or, on the decreasing branch of the hysteresis cycle, Fig. 43, may be + 7600, or, on the increasing branch, — 7600. Thus, when closing the electric circuit energizing an iron-clad ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "section_label": "Lecture 10: Continual And Cumulative Oscillations", "section_title": "Continual And Cumulative Oscillations", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... y, which oscillates during the next wave train, is supplied to the line, this energy must be supplied during the oscillation, that is, there must be such a phase displacement or lag within the oscil- lation, which gives a negative energy cycle, or reversed hysteresis loop. Thus, essential for such a continual oscillation is the 124 ELECTRICAL DISCHARGES, WAVES AND IMPULSES existence of a hysteresis loop, formed by the lag of the effect be- hind the cause. Such a hysteresis loop exists in the transient arc, as illu ...", "... re must be such a phase displacement or lag within the oscil- lation, which gives a negative energy cycle, or reversed hysteresis loop. Thus, essential for such a continual oscillation is the 124 ELECTRICAL DISCHARGES, WAVES AND IMPULSES existence of a hysteresis loop, formed by the lag of the effect be- hind the cause. Such a hysteresis loop exists in the transient arc, as illustrated by Fig. 66: the transient volt-ampere charac- teristic of a short high-temperature metal arc, between titanium and carbon. In this ...", "... gives a negative energy cycle, or reversed hysteresis loop. Thus, essential for such a continual oscillation is the 124 ELECTRICAL DISCHARGES, WAVES AND IMPULSES existence of a hysteresis loop, formed by the lag of the effect be- hind the cause. Such a hysteresis loop exists in the transient arc, as illustrated by Fig. 66: the transient volt-ampere charac- teristic of a short high-temperature metal arc, between titanium and carbon. In this figure, the stationary arc characteristic, that is, the relation between ar ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-21", "section_label": "Chapter 21: Dibtobtiox Of Wavs-Shafe And Its Causes", "section_title": "Dibtobtiox Of Wavs-Shafe And Its Causes", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 23274-24559", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "snippets": [ "... + -^ cos (0 - i,) + 51 [f cos {{2 y + 1) hence, the E.M.F. [,,sin((2y + l)^-a,) + .,^,siii((2y+l)^-V)]! §§216,217] DISTORTIOiV OF WAVE-SHAPE. 327 Pulsation of Reactance. 216. The main causes of a pulsation of reactance are : magnetic saturation and hysteresis, and synchronous motion. Since in an ironclad magnetic circuit the magnetism is not proportional to the M.M.F., the wave of magnetism and thus the wave of E.M.F. will differ from the wave of cur- rent. As far as this distortion is due to the variation of ...", "... of magnetism and thus the wave of E.M.F. will differ from the wave of cur- rent. As far as this distortion is due to the variation of permeability, the distortion is symmetrical and the wave of induced E.M.F. represents no power. The distortion caused by hysteresis, or the lag of the magnetism behind the M.M.F., causes an unsymmetrical distortion of the wave which makes the wave of induced E.M.F. differ by more than 90° from the current wave and thereby represents power, — the power consumed by hysteresis. In prac ...", "... caused by hysteresis, or the lag of the magnetism behind the M.M.F., causes an unsymmetrical distortion of the wave which makes the wave of induced E.M.F. differ by more than 90° from the current wave and thereby represents power, — the power consumed by hysteresis. In practice both effects are always superimposed ; that is, in a ferric inductance, a distortion of wave-shape takes place due to the lack of proportionality between magnetism and M.M.F. as expressed by the variation of the permea- bility in the hyster ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-22", "section_label": "Chapter 22: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 21190-21982", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "snippets": [ "... stantaneous magnetic flux is : 00 = $ cos 13 ey cos (2 y ff - cos((2y+l) hence, the E.M.F. 2 ; sm(P — DISTORTION OF WAVE-SHAPE. 391 Pulsation of Reactance. 237. The main causes of a pulsation of reactance are : magnetic saturation and hysteresis, and synchronous motion. Since in an ironclad magnetic circuit the magnetism is not proportional to the M.M.F., the wave of magnetism and thus the wave of E.M.F. will differ from the wave of cur- rent. As far as this distortion is due to the variation of ...", "... f magnetism and thus the wave of E.M.F. will differ from the wave of cur- rent. As far as this distortion is due to the variation of permeability, the distortion is symmetrical and the wave of induced E.M.F. 'represents no power. The distortion caused by hysteresis, or the lag of the magnetism behind the M.M.F., causes an unsymmetrical distortion of the wave which makes the wave of induced E.M.F. differ by more than 90° from the current wave and thereby represents power, — the power consumed by hysteresis. In prac ...", "... caused by hysteresis, or the lag of the magnetism behind the M.M.F., causes an unsymmetrical distortion of the wave which makes the wave of induced E.M.F. differ by more than 90° from the current wave and thereby represents power, — the power consumed by hysteresis. In practice both effects are always superimposed ; that is, in a ferric inductance, a distortion of wave-shape takes place due to the lack of proportionality between magnetism and M.M.F. as expressed by the variation in the hysteretic cycle. This pul ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... ical action in electrolytic con- duction, 6 Chromium, magnetic properties, 83 Circuit with distributed leakage, 330 magnetic, 43 Closed magnetic circuit, wave dis- tortion, 139 C/obalt iron alloy, magnetic, 78 magnetic properties, 80 Coefficient of hysteresis, 61 Coherer action of pyroelectric con- ductor, 19 Compensating voltage balancing un- balanced power, 320 Condenser, electrostatic, 9 power equation, 319 tending to instability, 164. See Capacity, Conductance with oscillating cur- rents, 349 Conduc ...", "... 8 Electrodes, 6 Electrolytic cell, 8 condenser, 9 conductor, 442 INDEX 357 Electromagnet, 91 constant current, 93 potential, 98 efficiency, 99 Electronic conduction, 28, 40 Elimination of harmonics by alter- nator design, 116 Energy of hysteresis, 57 storage in constant potential constant current transfor- mation, 280 Even harmonics, 114, 153, 157 Excessive very high harmonics in distortion by magnetic sat- uration, 140 Exciting current of transformer de- pending on wave shape, 137 Exponent ...", "... storage in constant potential constant current transfor- mation, 280 Even harmonics, 114, 153, 157 Excessive very high harmonics in distortion by magnetic sat- uration, 140 Exciting current of transformer de- pending on wave shape, 137 Exponent of hysteresis, 66 Face conductor in alternator, 114 Faraday's law of electrolytic con- duction, 6 Ferrites, magnetic, 80 Ferromagnetic density, 45 Field flux of alternator, 232 Film cutout in series circuits, 298 Flat top wave, 111 Flicker of lamps and wave shap ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "section_label": "Chapter 14: Dielectric Losses", "section_title": "Dielectric Losses", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "CHAPTER XIV DIELECTRIC LOSSES Dielectric Hysteresis 116. Just as magnetic hysteresis and eddy currents give a power component in the inductive reactance, as \"effective resistance,\" so the energy losses in the dielectric lead to a power component in the condensive reactance, which may be repre- sented by ...", "CHAPTER XIV DIELECTRIC LOSSES Dielectric Hysteresis 116. Just as magnetic hysteresis and eddy currents give a power component in the inductive reactance, as \"effective resistance,\" so the energy losses in the dielectric lead to a power component in the condensive reactance, which may be repre- sented by an \"effective resistance of dielect ...", "... ic lead to a power component in the condensive reactance, which may be repre- sented by an \"effective resistance of dielectric losses\" or an \"effective conductance of dielectric losses.\" In the alternating magnetic field, power is consumed by mag- netic hysteresis. This is proportional to the frequency, and to the 1.6*'' power of the magnetic density, and is considerable, amounting in a closed magnetic circuit to 40 to 60 per cent, of the total volt-amperes. In the dielectric field, the energy losses usually are v ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-03", "section_label": "Chapter 3: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 5445-6941", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-03/", "snippets": [ "... asses through the zero point H = Oj B = 0, and thereby runs into the curve, J5i. The rising magnetization curve, or standard magnetic charac- teristic determined by the step-by-step method, J5i, thus is noth- ing but the rising branch of an unsymmetrical hysteresis cycle, traversed between such limits +Bo and — Ao, that the rising branch of the hysteresis cycle passes through the zero point. 33. The characteristic shape of a hysteresis cycle is that it is a loop, pointed at either end and thereby having an inflexio ...", "... magnetization curve, or standard magnetic charac- teristic determined by the step-by-step method, J5i, thus is noth- ing but the rising branch of an unsymmetrical hysteresis cycle, traversed between such limits +Bo and — Ao, that the rising branch of the hysteresis cycle passes through the zero point. 33. The characteristic shape of a hysteresis cycle is that it is a loop, pointed at either end and thereby having an inflexion point about the middle of either branch. In the unsymmetrical loop +Bif —Aq of Fig. 25, th ...", "... by-step method, J5i, thus is noth- ing but the rising branch of an unsymmetrical hysteresis cycle, traversed between such limits +Bo and — Ao, that the rising branch of the hysteresis cycle passes through the zero point. 33. The characteristic shape of a hysteresis cycle is that it is a loop, pointed at either end and thereby having an inflexion point about the middle of either branch. In the unsymmetrical loop +Bif —Aq of Fig. 25, the zero point is fairly close to one extreme, Aoj and the inflexion point, character ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-05", "section_label": "Chapter 5: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 9062-11050", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-05/", "snippets": [ "... own exception herefrom seems to be an iron-cobalt alloy, which is alleged to have a saturation value about 10 per cent, higher than that of iron, though cobalt is lower than iron. The coefficient of magnetic hardness, a, however, and the co- efficient of hysteresis, 77, vary with the chemical, and more still with the physical characteristic of the magnetic material, over an enormous range. Thus, a special high-silicon steel, and the chilled glass hard tool steel in the following tables, have about the same percenta ...", "... ge of non-magnetic constituents, 4 per cent., and about the same saturation value, S = 19.2 X 10^, but the coefficient of hardness of chilled tool steel, a = 8 X 10~^, is 200 times that of the special silicon steel, a = 0.04 X 10\"^, and the coefficient of hysteresis of the chilled tool steel, 17 = 75 X 10\"', is 125 times that of the sili- con steel, 77 = 0.6 X 10\"'. Hardness and hysteresis loss seem to depend in general on the physical characteristics of the material, and on the chemical constitution only as far as i ...", "... ness of chilled tool steel, a = 8 X 10~^, is 200 times that of the special silicon steel, a = 0.04 X 10\"^, and the coefficient of hysteresis of the chilled tool steel, 17 = 75 X 10\"', is 125 times that of the sili- con steel, 77 = 0.6 X 10\"'. Hardness and hysteresis loss seem to depend in general on the physical characteristics of the material, and on the chemical constitution only as far as it affects the phys- ical characteristics. Chemical compounds of magnetic metals are in general not ferromagnetic, except a f ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-14", "section_label": "Chapter 16: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 14, "number": 16, "location": "lines 19374-20293", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-14/", "snippets": [ "... he armature reactance does oof vary with the posi- tion of the armature in the field, us shown in Fig. 125, such ■ H excitation hy reactive armature currents does not occur, and direct-current field excitation is always necessary (except in the so-called \"hysteresis motor\"). Vectorially this is shown in Figs. 124 and 125 by the relalivc position of the magnetic flux, *, the voltage, E, in quadrature to *, and the m.m.f. of the current, /. In Fig. 125, where / and 4> coincide, I and E are in quadrature, that is, the ...", "... . of self-induction lags more than 90° behind the current — while h is negative if the reactance produces power — in which case the counter e.m.f. of self-induction lags less than 90° behind the current. 149. A case of this nature occurs in the effect of hysteresis, from a different point of view. In \"Theory and Calcuation of Al- ternating Current\" it was shown, thai -magnetic hysteresis distorts the current wave in such a way that the equivalent sine wave, REACTION MACHINES 263 that is, the sine wave of equal e ...", "... se the counter e.m.f. of self-induction lags less than 90° behind the current. 149. A case of this nature occurs in the effect of hysteresis, from a different point of view. In \"Theory and Calcuation of Al- ternating Current\" it was shown, thai -magnetic hysteresis distorts the current wave in such a way that the equivalent sine wave, REACTION MACHINES 263 that is, the sine wave of equal effective strength and equal power with the distorted wave, is in advance of the wave of magnetism by what is called the angle ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-13", "section_label": "Chapter 13: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 13484-14333", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-13/", "snippets": [ "CHAPTER XIII FOUCAULT OR EDDY CURRENTS 105. While magnetic hysteresis due to molecular friction is a magnetic phenomenon, eddy currents are rather an electrical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. Wh ...", "CHAPTER XIII FOUCAULT OR EDDY CURRENTS 105. While magnetic hysteresis due to molecular friction is a magnetic phenomenon, eddy currents are rather an electrical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric co ...", "CHAPTER XIII FOUCAULT OR EDDY CURRENTS 105. While magnetic hysteresis due to molecular friction is a magnetic phenomenon, eddy currents are rather an electrical phenomenon. When iron passes through a magnetic field, a loss of energy is caused by hysteresis, which loss, however, does not react magnetically upon the field. When cutting an electric conductor, the magnetic field produces a current therein. The m.m.f. of this current reacts upon and affects the magnetic field, more or less; consequently, an alte ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "section_title": "Dibtbisnted Capacity, Inductance, Besistance, And", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "... E.M.F., and consisting of an energy component, in phase with the E.M.F., and a wattless component, in quadrature thereto. The alternating electromagnetic field of force set up by the line current produces in some materials a loss of energy by magnetic hysteresis, or an expenditure of E.M.F. in phase with the current, which acts as an increase of re- sistance. This electromagnetic hysteretic loss may take place in the conductor proper if iron wires are used, and will then be very serious at high frequencies, such ...", "... hose of telephone currents. The effect of eddy currents has already been referred to under \"mutual inductance,\" of which it is an energy component. The alternating electrostatic field of force expends energy in dielectrics by what is called dielectric hysteresis. In concentric cables, where the electrostatic gradient in the dielectric is comparatively large, the dielectric hysteresis may at high potentials consume far greater amounts of energy than the resistance does. The dielectric hysteresis § 107] DISTRIBU ...", "... t is an energy component. The alternating electrostatic field of force expends energy in dielectrics by what is called dielectric hysteresis. In concentric cables, where the electrostatic gradient in the dielectric is comparatively large, the dielectric hysteresis may at high potentials consume far greater amounts of energy than the resistance does. The dielectric hysteresis § 107] DISTRIBUTED CAPACITY. 157 appears in the circuit as consumption of a current, whose component in phase with the E.M.F. is the diele ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "... E.M.F., and consisting of an energy component, in phase with the E.M.F., and a wattless component, in quadrature thereto. The alternating electromagnetic field of force set up by the line current produces in some materials a loss of energy by magnetic hysteresis, or an expenditure of E.M'.F. in phase with the current, which acts as an increase of re- sistance. This electromagnetic hysteretic loss may take place in the conductor proper if iron wires are used, and will then be very serious at high frequencies, such ...", "... hose of telephone currents. The effect of eddy currents has already been referred to under \"mutual inductance,\" of which it is an energy component. The alternating electrostatic field of force expends energy in dielectrics by what is called dielectric hysteresis. In concentric cables, where the electrostatic gradient in the dielectric is comparatively large, the dielectric hysteresis may at high potentials consume considerable amounts of energy. The dielectric hysteresis appears in the circuit DISTRIBUTED CAPA ...", "... t is an energy component. The alternating electrostatic field of force expends energy in dielectrics by what is called dielectric hysteresis. In concentric cables, where the electrostatic gradient in the dielectric is comparatively large, the dielectric hysteresis may at high potentials consume considerable amounts of energy. The dielectric hysteresis appears in the circuit DISTRIBUTED CAPACITY. 165 as consumption of a current, whose component in phase with the E.M.F. is the dielectric energy current, which ma ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "... e reaction, is the reciprocal of the exciting acceptance of the induction machine. The total or synchronous reactance of the induction machine as synchronous motor thus is: * - x« + x' .1 = x. + r The exciting conductance, g, represents the loss by hysteresis, etc., in the iron of the machine. As synchronous machine, this loss is supplied by the mechanical power, and not electrically, and the hysteresis loss in the induction machine as synchronous motor thus is: e*g. We thus have: The induction motor of th ...", "... synchronous motor thus is: * - x« + x' .1 = x. + r The exciting conductance, g, represents the loss by hysteresis, etc., in the iron of the machine. As synchronous machine, this loss is supplied by the mechanical power, and not electrically, and the hysteresis loss in the induction machine as synchronous motor thus is: e*g. We thus have: The induction motor of the constants, per phase: Exciting admittance: 70 = g — jb, Primary self-inductive impedance: Z0 ■= r0 + jx<>, Secondary self-inductive impedance: Z ...", "... ary or rotor, be- comes a synchronous motor of the constants, per phase: Armature resistance: r0, Synchronous impedance: x = Xo + r* (1) Total power consumed in field excitation : P = 2 t»r„ (2) where i = field exciting current. Power consumed by hysteresis: P - e*g. (3) it is then: or: 60 ELECTRICAL APPARATUS 42. Let, in a synchronous motor: E0 = impressed voltage, E = counter e.m.f., or nominal induced voltage, Z — r + jx = synchronous impedance, / = i\\ — 3H = current, #o = $ + ZJ = # ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-07", "section_label": "Chapter 7: Shaping Of Waves : General", "section_title": "Shaping Of Waves : General", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 12222-12961", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-07/", "snippets": [ "... its more energy than the sine wave. Fig. 46. Inversely, a peaked wave of voltage, such as Fig. 48, and such as the common saw-tooth wave of the uni tooth alternator, is superior in transformers and similar devices, as it transform s tho energy with less hysteresis loss. The peaked voltage wave. Fig. 4:8, gives a flat-topped wave of magnetism. Fig. 47, and therciby transforms the voltage with a lesser maximum magnetic flux, than ^ sine wave of the same effective value, that is, the same powc^r. the hysteresis loss d ...", "... h less hysteresis loss. The peaked voltage wave. Fig. 4:8, gives a flat-topped wave of magnetism. Fig. 47, and therciby transforms the voltage with a lesser maximum magnetic flux, than ^ sine wave of the same effective value, that is, the same powc^r. the hysteresis loss depends on the maximum value of t\\u) mag- 5tic flux, the reduction of the maximum value of tho magncitic; fl^Jx, due to a peaked voltage wave, results in a lower hyHtorvMiH ioes, and thus higher efficiency of transformation. This reduc- ^i^on of loss ...", "... he reduction of the maximum value of tho magncitic; fl^Jx, due to a peaked voltage wave, results in a lower hyHtorvMiH ioes, and thus higher efficiency of transformation. This reduc- ^i^on of loss may amount to as much as 15 to 25 p(;r cent, of the ^^otal hysteresis loss, in extreme cases. Inversely, a peaked voltage wave like Fig. 48 would be obj(i(j- t-xonable in high- voltage transmission apparatus, by giving an un- necessary high insulation strain, and a flat-top wave of voltage ^vke Fig. 47, when impressed upon ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-12", "section_label": "Chapter 12: Reactance Of Induction Apparatus", "section_title": "Reactance Of Induction Apparatus", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 22634-23465", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-12/", "snippets": [ "... such cases, the magnetic fields of the reactance of the electric circuit may be merely a more or less fictitious component of the resultant mag- netic field. The industrial importance hereof is that many phenomena, such as the loss of power by magnetic hysteresis, the m.m.f. required for field excitation, etc., are related to the resultant magnetic field, thus not equal to the sum of the corresponding effects of the components. 216 REACTANCE OF INDUCTION APPARATUS 217 As the transformer is the simplest alter ...", "... actance is not entirely arbitrary. Assuming we assign all the reactance to the primary, and consider the secondary as having no reactance. Then the mutual mag- netic flux and mutual induced voltage would be cf = jP = jPo - [ro + i (xo + xi)] /o and the hysteresis loss in the transformer would correspond hereto, by the usual assumption in transformer calculations. 224 ELECTRIC CIRCUITS Assigning, however, all the reactance to the secondary circuit, and assuming the primary as non-inductive, the mutual flux and ...", "... in transformer calculations. 224 ELECTRIC CIRCUITS Assigning, however, all the reactance to the secondary circuit, and assuming the primary as non-inductive, the mutual flux and mutual induced voltage would be c^ = ^ = ^o — ^o/o, hence larger, and the hysteresis loss calculated therefrom larger than under the previous assumption. The first assumption would give too low, and the last too high a calculated hysteresis loss, in most cases. By the usual transformer theory, the hysteresis loss under load is calculate ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... the e.m.f. and consisting of a power component in phase with the e.m.f. and a reactive com- ponent in quadrature thereto. The alternating electromagnetic field of force set up by the line current produces in some materials a loss of power by mag- netic hysteresis, or an expenditure of e.m.f. in phase with the cur- rent, which acts as an increase of resistance. This electro- magnetic hysteresis loss may take place in the conductor proper if iron wires are used, and may then be very serious at high fre- quencies suc ...", "... rnating electromagnetic field of force set up by the line current produces in some materials a loss of power by mag- netic hysteresis, or an expenditure of e.m.f. in phase with the cur- rent, which acts as an increase of resistance. This electro- magnetic hysteresis loss may take place in the conductor proper if iron wires are used, and may then be very serious at high fre- quencies such as those of telephone currents. The effect of eddy currents has already been referred to under \" mutual inductance,\" of which if i ...", "... as those of telephone currents. The effect of eddy currents has already been referred to under \" mutual inductance,\" of which if is a power component. The alternating electrostatic field of force expends power in dielectrics by what is called dielectric hysteresis. In concentric cables, where the electrostatic gradient in the dielectric is com- paratively large, the dielectric hysteresis may at high potentials consume considerable amounts of power. The dielectric hystere- sis appears in the circuit as consumption o ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-17", "section_label": "Chapter 17: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16521-17716", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-17/", "snippets": [ "... agnetic circuit, such as the \"hedgehog\" transformer, the m.m.f., F, is the sum of the m.m.f. consumed in the iron and in the air part of the magnetic circuit (see Chapter XII). The power component of the exciting current represents the power consumed by hysteresis and eddy currents and the small ohmic loss. The exciting current is not a sine wave, but is, at least in the closed magnetic circuit transformer, greatly distorted by hysteresis, though less so in the open magnetic circuit trans- former. It can, however ...", "... he power component of the exciting current represents the power consumed by hysteresis and eddy currents and the small ohmic loss. The exciting current is not a sine wave, but is, at least in the closed magnetic circuit transformer, greatly distorted by hysteresis, though less so in the open magnetic circuit trans- former. It can, however, be represented by an equivalent sine wave, /oo, of equal intensity and equal power with the distorted wave, and a wattless higher harmonic, mainly of triple frequency. Since the ...", "... ctive resistances of the two circuits, r'o and r'l, by: r'o -^ r'l = ro -^ ri; or, if from the construction of the transformer as the use of large solid conductors, it can be seen that the one circuit is entirely or mainly the seat of the power loss by hysteresis, eddies, etc., which is represented by the additional effective resistance, r\" , this resistance, r\", is entirely or mainly assigned to this circuit. In general, it therefore may be assumed: r 0 = ro X a^o x' Xi — 2a2 ro + « ri r 1 = r ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-08", "section_label": "Chapter 8: Shaping Of Waves By Magnetic Saturation", "section_title": "Shaping Of Waves By Magnetic Saturation", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 12962-16963", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-08/", "snippets": [ "... . 66. It is interesting to note that in, the peak reactance, ia approxi- mately constant, that is, does not decrease with increasing mag- netic saturation. (The higher value at beginning saturation, for / — 20, may possibly be due to an inaccuracy in the hysteresis cycle of Fig. 55, a too great steepness near the zero value, rather than being actual.) It is interesting to realize, that when measuring the reactance of a closed magnetic circuit reactor by voltmeter and ammeter readings, it is not permissible to vary ...", "... ransformer increases approximately ^/26 = 4.47 times, and the maximum voltage peak 20 times above the full-load voltage of the transformer. As the shape of the magnetic flux density and voltage waves are determined by the current and flux relation of the hysteresis cy- cles, and the latter are entirely empirical and can not be expressed mathematically, therefore it is not possible to derive an exact mathematical equation for these distorted and peaked voltage waves from their origin. Nevertheless, especially at high ...", "... column of Table III, the form factors, p, calculated in this manner, and in the last column are given the actual form factors, po, derived from the curves 60 to 63. As seen, the agreement is well within the un- certainty of observation of the shape of the hysteresis cycles, except perhaps at 7 = 20, and there probably the calculated value is more nearly correct. 69. The peaked voltage wave induced by the saturated closed magnetic circuit can, by assuming it as symmetrical and counting the time from the center of th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1120-1683", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-01/", "snippets": [ "... \\/r\" + X\". The resistance, r, in circuits where energy is expended only in heating the conductor, is the same as the ohmic resistance of continuous-current circuits. In circuits, however, where energy is also expended outside of the conductor by magnetic hysteresis, mutual inductance, dielectric hysteresis, etc., r is larger than the true ohmic resistance of the conductor, since it refers to the total expenditure of energy. It may be called then the effective re- sistance. It may no longer be a constant of the circu ...", "... where energy is expended only in heating the conductor, is the same as the ohmic resistance of continuous-current circuits. In circuits, however, where energy is also expended outside of the conductor by magnetic hysteresis, mutual inductance, dielectric hysteresis, etc., r is larger than the true ohmic resistance of the conductor, since it refers to the total expenditure of energy. It may be called then the effective re- sistance. It may no longer be a constant of the circuit. The reactance, x, does not represent ...", "... ratio of the power component of e.m.f. to the current. Since in alternating-cur- rent circuits, in addition to the energy expended iii the ohmic re- sistance of the conductor, energy is expended, partly outside, partly inside of the conductor, by magnetic hysteresis, mutual induction, dielectric hysteresis, etc., the effective resistance, r, is in general larger than the true resistance of the conductor, sometimes many time larger, as in transformers at open sec- ondary circuit, and is no longer a constant of the cir ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-04", "section_label": "Chapter 4: Vector Representation", "section_title": "Vector Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2149-2759", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-04/", "snippets": [ "... s motor circuit under the circumstances stated above. 23. As a further example, we may consider the diagram of an alternating-current transformer, feeding through its secondary circuit an inductive load. For simplicity, we may neglect here the magnetic hysteresis, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the magnetic flux is zero and rising. The magnetic flux then passes its maxi- mum at the time ?? = 90°, and the phase of the m ...", "... ch is de- termined by the magnetic characteristic of the iron and the section and length of the magnetic circuit of the transformer; this m.m.f. is in phase with the flux, $, and is represented by the vector, OF, in effective ampere-turns. The effect of hysteresis, neglected at present, is to shift OF ahead of 0, by an angle, a, the angle of hysteretic lead. (See Chapter on Hysteresis.) This m.m.f., F, is the resultant of the secondary m.m.f., Fi, 28 ALTERNATING-CURRENT PHENOMENA and the primary m.m.f., ...", "... ormer; this m.m.f. is in phase with the flux, $, and is represented by the vector, OF, in effective ampere-turns. The effect of hysteresis, neglected at present, is to shift OF ahead of 0, by an angle, a, the angle of hysteretic lead. (See Chapter on Hysteresis.) This m.m.f., F, is the resultant of the secondary m.m.f., Fi, 28 ALTERNATING-CURRENT PHENOMENA and the primary m.m.f., Fp; or graphically, OF is the diagonal of a parallelogram with OFi and OFq as sides, OFi and OF being known, we find OFq, the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "... the e.m.f. and consisting of a power component, in phase with the e.m.f., and a reactive component, in quadrature thereto. The alternating electromagnetic field of force set up by the line current produces in some materials a loss of energy by magnetic hysteresis, or an expenditure of e.m.f. in phase with the current, which acts as an increase of resistance. This electromagnetic hysteretic loss may take place in the con- ductor proper if iron wires are used, and will then be very serious at high frequencies, such ...", "... ose of telephone currents. The effect of eddy currents has already been referred to under \"mutual inductive reactance,\" of which it is a power component. The alternating electrostatic field of force expends energy in dielectrics by corona and dielectric hysteresis. In concentric cables, where the electrostatic gradient in the dielectric is com- paratively large, the dielectric losses may at high potentials consume appreciable amounts of energy. The dielectric loss appears in the circuit as consumption of a current, ...", "... senting consumption of power, and due to: Resistance, and its increase by unequal current distri- bution; to the power component of mutual inductive reactance or to induced currents; to the power component of self-inductive reactance or to electromagnetic hysteresis, and to radiation. e.m.fs. consumed in quadrature with the current, I, and = xl, wattless, and due to: Self -inductance, and mutual inductance. Currents consumed in phase with the e.mf., E, and = g E, representing consumption of power, and due to: Leak ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-04", "section_label": "Chapter 4: Graphic Befrisxintation", "section_title": "Graphic Befrisxintation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2122-2743", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "snippets": [ "... otor circuit under the circumstances stated above. 21. As a further example, we may consider the dia- gram of an alternating-current transformer, feeding through its secondary circuit an inductive load. For simplicity, we may neglect here the magnetic hysteresis, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the magnetic flux is zero. The phase of the flux, that is, the amplitude of its maximum value, is 90° in this case, and, conse ...", "... quired, which is determined by the magnetic characteristic of the iron, and the section and length of the magnetic circuit of the transformer ; it is in phase with the flux 4>, and repre- sented by the vector OFy in effective ampere-turns. The effect of hysteresis, neglected at present, is to shift OF ahead of OMy by an angle a, the angle of hysteretic lead. (See Chapter on Hysteresis.) This M.M.F., $F, is the resultant of the secondary M.M.F., IFj, and the primary M.M.F., IF^; or graphically, OF is the diagonal ...", "... of the transformer ; it is in phase with the flux 4>, and repre- sented by the vector OFy in effective ampere-turns. The effect of hysteresis, neglected at present, is to shift OF ahead of OMy by an angle a, the angle of hysteretic lead. (See Chapter on Hysteresis.) This M.M.F., $F, is the resultant of the secondary M.M.F., IFj, and the primary M.M.F., IF^; or graphically, OF is the diagonal of a parallelogram with OF^ and OF^ as sides. OF^ and OF being known, we find OF^^ the primary ampere- turns, n^ , and ther ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-13", "section_label": "Chapter 13: Ths Alternating^Cnrrent Traxsfobmer", "section_title": "Ths Alternating^Cnrrent Traxsfobmer", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 12673-14088", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "snippets": [ "... er with open magnetic circuit, such as the \"hedgehog\" transformer, the M.M.F., iF, is the sum of the M.M.F. consumed in the iron and in the air part of the magnetic circuit (see Chapter X.). The energy of the exciting current is the energy con- sumed by hysteresis and eddy currents and the small ohmic loss. The exciting current is not a sine wave, but is, at least in the closed magnetic circuit transformer, greatly distorted by hysteresis, though less so in the open magnetic circuit transformer. It can, however, ...", "... apter X.). The energy of the exciting current is the energy con- sumed by hysteresis and eddy currents and the small ohmic loss. The exciting current is not a sine wave, but is, at least in the closed magnetic circuit transformer, greatly distorted by hysteresis, though less so in the open magnetic circuit transformer. It can, however, be represented by an equiv- alent sine wave, /^o, of equal intensity and equal power with the distorted wave, and a wattless higher harmonic, mainly of triple frequency. Since th ...", "... '~rI \"\" P \"\" Extemaf^istance of secondiry'cir^t ~ ^al resistance, ** Xq _. q __ x^\\AC\\ I\"* ^\"*'* ^ reactance of tr ansformer ___ percentage mtcr- J^ * Kxtemai resistance of secondary circuit ||^| reaCtance R..,.= h = ratio ^.!^\"j::^::^™r:' = percentage hysteresis, R b = a = ratio — -*'^*ii\"*l*-*=\"'^l^- = Percentage magnetizing cur- ** ** ^ Toul secondary current rent and if d represents the load of the transformer, as fraction of full load, we have JO Ra § 1 29 ] AL TERN A TING-CURRENT TRANSFORMER, 189 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-20", "section_label": "Chapter 20: Beactiox Machines", "section_title": "Beactiox Machines", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 22388-23273", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "snippets": [ "... more than 90° behind the current, — while // is negative if the reactance produces power, — in which case the counter E.M.F. of self-induction lags less than 90° behind the current. 206. A case of this nature has been discussed already in the chapter on Hysteresis, from a different point of view. 310 ALTERNATING-CUKREXT PHKNOMENA. [§ 207 There the effect of magnetic hysteresis was found to distort the current wave in such a way that the equivalent sine wave, that is, the sine wave of equal effective strength and ...", "... E.M.F. of self-induction lags less than 90° behind the current. 206. A case of this nature has been discussed already in the chapter on Hysteresis, from a different point of view. 310 ALTERNATING-CUKREXT PHKNOMENA. [§ 207 There the effect of magnetic hysteresis was found to distort the current wave in such a way that the equivalent sine wave, that is, the sine wave of equal effective strength and equal power with the distorted wave, is in advance of the wave of magnetism by what is called tlie angle of hystereti ...", "... epresenting not only the electrical energy consumed by molecular magnetic friction, but also the me- chanical output. Hence, ruch a synchronous motor can be called \" hyste- resis motor,\" since the mechanical work is done by an ex- tension of the loop of hysteresis. 208. It is evident that the variation of reluctance must bo symmetrical with regard to the field poles ; that is, that the two extreme values of reluctance, maximum and mini- 5 208] REACTION MACHINES. mum, will take place at the moment where th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-04", "section_label": "Chapter 4: Graphic Representation", "section_title": "Graphic Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 1743-2321", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "snippets": [ "... motor circuit under the circumstances stated above. 21. As a further example, we may consider the dia- gram of an alternating-current transformer, feeding through its secondary circuit an inductive load. For simplicity, we may neglect here the magnetic hysteresis, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the magnetic flux is zero. The phase of the flux, that is, the amplitude of its maximum value, is 90° in this case, and, conse ...", "... NOMENA. which is determined by the magnetic characteristic of the iron, and the section and length of the magnetic circuit of the transformer ; it is in phase with the flux $, and repre- sented by the vector OF, in effective ampere-turns. The effect of hysteresis, neglected at present, is to shift OF ahead of O®, by an angle a, the angle of hysteretic lead. (See Chapter on Hysteresis.) This M.M.F., O7, is the resultant of the secondary M.M.F., JFlf and the primary M.M.F., SF0; or graphically, OF is the diagonal ...", "... of the transformer ; it is in phase with the flux $, and repre- sented by the vector OF, in effective ampere-turns. The effect of hysteresis, neglected at present, is to shift OF ahead of O®, by an angle a, the angle of hysteretic lead. (See Chapter on Hysteresis.) This M.M.F., O7, is the resultant of the secondary M.M.F., JFlf and the primary M.M.F., SF0; or graphically, OF is the diagonal of a parallelogram with OFl and OF0 as sides. OF1 and OF being known, we find OF0, the primary ampere- turns, and therefrom ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-14", "section_label": "Chapter 14: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 11605-12682", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "snippets": [ "... mer with open magnetic circuit, such as the \"hedgehog\" transformer, the M.M.F., &, is the sum of the M.M.F. consumed in the iron and in the air part of the magnetic circuit (see Chapter X.). The energy of the exciting current is the energy con- sumed by hysteresis and eddy currents and the small ohmic loss. The exciting current is not a sine wave, but is, at least in the closed magnetic circuit transformer, greatly distorted by hysteresis, though less so in the open magnetic circuit transformer. It can, however, ...", "... apter X.). The energy of the exciting current is the energy con- sumed by hysteresis and eddy currents and the small ohmic loss. The exciting current is not a sine wave, but is, at least in the closed magnetic circuit transformer, greatly distorted by hysteresis, though less so in the open magnetic circuit transformer. It can, however, be represented by an equiv- alent sine wave, f00, of equal intensity and equal power with the distorted wave, and a wattless higher harmonic, mainly of triple frequency. Since th ...", "... esistance of transformer _ percentage R0 ~ External resistance of secondary circuit ~ na^ resistance, 2 X0 _ __ ratjQ Internal reactance of transformer _ percentage J£ ' External resistance of secondary circuit nal reactance X*.- h - ratio - percentage hysteresis, ,, , , . Magnetizing current percentage magnetizing cur- •KO °o= g = -10 Totalsecondarycurrent = rent^ and if d represents the load of the transformer, as fraction of full load, we have ALTERNATING-CURRENT TRANSFORMER. 215 and, **.-«. a S ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-05", "section_label": "Lecture 5: Single-Energy Tra.Nsient Of Ironclad Circuit", "section_title": "Single-Energy Tra.Nsient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3387-3720", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-05/", "snippets": [ "... ility curve of the iron. Furthermore, the transient due to a decrease of the stored magnetic energy differs in shape and in value from that due to an increase of magnetic energy, since the rising and decreasing magnetization curves differ, as shown by the hysteresis cycle. Since no satisfactory mathematical expression has yet been found for the cyclic curve of hysteresis, a mathematical calcula- tion is not feasible, but the transient has to be calculated by an 52 SINGLE-ENERGY TRANSIENT OF IRONCLAD CIRCUIT. 53 ...", "... n shape and in value from that due to an increase of magnetic energy, since the rising and decreasing magnetization curves differ, as shown by the hysteresis cycle. Since no satisfactory mathematical expression has yet been found for the cyclic curve of hysteresis, a mathematical calcula- tion is not feasible, but the transient has to be calculated by an 52 SINGLE-ENERGY TRANSIENT OF IRONCLAD CIRCUIT. 53 approximate step-by-step method, as illustrated for the starting transient of an alternating-current transf ...", "... . * At any density (B', the remaining magnetizability then is (B^' — (B', and, assuming the (metallic) permeability as proportional hereto, gives M = c((B^'-(BO, and, substituting gives M rrp/' ^, ^ CCEJOC' 1 + cOC'' * See \"On the Law of Hysteresis,\" Part II, A.I.E.E. Transactions, 1892, page 621. 54 ELECTRIC DISCHARGES, WAVES AND IMPULSES. or, substituting a, -:=r—i = (T, gives equation (1). /O 1 -j For X = 0 in equation (1), - = - ; for 5C = oo , (B = - ; that is, in equation (1), - = ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-05", "section_label": "Lecture 5: Single-Energy Transient Of Ironclad Circuit", "section_title": "Single-Energy Transient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2972-3286", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "snippets": [ "... ility curve of the iron. Furthermore, the transient due to a decrease of the stored magnetic energy differs in shape and in value from that due to an increase of magnetic energy, since the rising and decreasing magnetization curves differ, as shown by the hysteresis cycle. Since no satisfactory mathematical expression has yet been found for the cyclic curve of hysteresis, a mathematical calcula- tion is not feasible,, but the transient has to be calculated by an '^''\"r '*_/ ? :,\": \\ : 52 SINGLE-ENERGY TRANSIENT O ...", "... n shape and in value from that due to an increase of magnetic energy, since the rising and decreasing magnetization curves differ, as shown by the hysteresis cycle. Since no satisfactory mathematical expression has yet been found for the cyclic curve of hysteresis, a mathematical calcula- tion is not feasible,, but the transient has to be calculated by an '^''\"r '*_/ ? :,\": \\ : 52 SINGLE-ENERGY TRANSIENT OF IRONCLAD CIRCUIT. 53 approximate step-by-step method, as illustrated for the starting transient of an alt ...", "... ron is about &x' = 20,000 lines per cm2. * At any density (B', the remaining magnetizability then is (B^' — (B', and, assuming the (metallic) permeability as proportional hereto, gives and, substituting gives a, = cftco'rc^ * See \"On the Law of Hysteresis,\" Part II, A.I.E.E. Transactions, 1892, page 621. 54 ELECTRIC DISCHARGES, WAVES AND IMPULSES. or, substituting 1_ 1 *** / t*« ,—fc / (/ • gives equation (1). For OC = 0 in equation (1), ^ = - ; for 3C = oo » = - ; that is, uv a: cr in equat ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... 240 270 300 -1.5 + 1.7 + 3.7 + 0.2 + 0.3 -0.2 In table X A, are given, in columns 1, 3, 5, the angles 6, from 10 deg. to 10 deg., and in columns 2, 4, 6, the correspond- ing values of the exciting current i, as derived by calculation from the hysteresis cycle of the iron, or by measuring from the TRIGONOMETRIC SERIES. 137 photographic film of the oscillograph. Column 7 then gives one-third the sum of columns 2, 4, and 6, that is, the third har- monic with its overtones, is. To find the 9th harmo ...", "... t from a limited number of observations the highest accuracy of the constants. 123. As instance, the method of least squares may be applied in separating from the observations of an induction motor, when running light, the component losses, as friction, hysteresis, etc. MAXIMA AND MINIMA. 183 In a 440-volt 50-h.p. induction motor, when running light, that is, without load, at various voltages, let the terminal voltage e, the current input i, and the power input p be observed as given in the first three col ...", "... 0 640 700 43 56 75 3700 5000 8000 370 627 1125 3330 4370 6875 3080 3600 4150 + 250 + 770 ■■ + 2725 The power consumed by the motor while running light consists of: The friction loss, which can be assumed as con- stant, a; the hysteresis loss, which is proportional to the 1.6th power of the magnetic flux, and therefore of the voltage, he^-^\\ the eddy current losses, which are proportional to the square of the magnetic flux, and therefore of the voltage, ce^; and the i^r loss in the windin ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-31", "section_label": "Apparatus Section 10: Synchronous Machines: Efficiency and Losses", "section_title": "Synchronous Machines: Efficiency and Losses", "kind": "apparatus-section", "sequence": 31, "number": 10, "location": "lines 9651-9718", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-31/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-31/", "snippets": [ "... efficiency and losses. the method of adding the losses, and the latter is therefore com- monly used. The losses consist of the following: the resistance loss in the armature; the resistance loss in the field circuit; the hysteresis and eddy current losses in the magnetic circuit; the friction and windage losses, and eventually load losses, that is, losses due to eddy currents and hysteresis produced by the load current in the armature. The resistance ...", "... the armature; the resistance loss in the field circuit; the hysteresis and eddy current losses in the magnetic circuit; the friction and windage losses, and eventually load losses, that is, losses due to eddy currents and hysteresis produced by the load current in the armature. The resistance loss in the armature is proportional to the square of the current, I. The resistance loss in the field circuit is proportional to the square of the field exc ...", "... ance loss in the field circuit is proportional to the square of the field excitation current, that is, the square of the nominal generated or counter-generated e.m.f., EQ. 10 150 ELEMENTS OF ELECTRICAL ENGINEERING The hysteresis loss is proportional to the 1.6th power of the real generated e.m.f., El = E ± Ir. The eddy current loss is usually proportional to the square of the generated e.m.f., E\\. The friction and windage loss is assumed as ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-64", "section_label": "Apparatus Section 12: Direct-current Commutating Machines: Efficiency and Losses", "section_title": "Direct-current Commutating Machines: Efficiency and Losses", "kind": "apparatus-section", "sequence": 64, "number": 12, "location": "lines 11864-11904", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-64/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-64/", "snippets": [ "... n deriving the efficiency by adding the individual losses are: 1. Loss in the resistance of the armature, the commutator leads, brush contacts and brushes, in the shunt field and the series field with their rheostats. 2. Hysteresis and eddy currents in the iron at a voltage equal to the terminal voltage, plus resistance drop in a generator, or minus resistance drop in a motor. 3. Eddy currents in the armature conductors when large and not protecte ...", "... n the armature conductors when large and not protected, and in pole faces when solid and the air gap is small. 4. Friction of bearings, of brushes on the commutator, and windage. 5. Load losses, due to the increase of hysteresis and of eddy currents under load, caused by the change of the magnetic dis- tribution, as local increase of magnetic density and of stray field. The friction of the brushes and the loss in the contact resist- ance of the ...", "... oss in the contact resist- ance of the brushes are frequently quite considerable, especially with low-voltage machines. Constant or approximately constant losses are: friction of bearings and of commutator brushes, and windage; hysteresis and eddy current losses; and shunt field excitation. Losses D.'C. COMMUTATING MACHINES 199 increasing with the load, and proportional or approximately proportional to the square of the current: armature resistance losses; se ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-18", "section_label": "Chapter 18: Polyphase Induction Motors", "section_title": "Polyphase Induction Motors", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17717-20445", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-18/", "snippets": [ "... 211 Let 7o = exciting current, or current through the motor, per primary circuit, when doing no work (at synchronism), and F = g — j6 = primary exciting admittance per circuit = — • We thus have, ge = magnetic power current, ge~ = loss of power by hysteresis (and eddy currents) per primary coil. Hence Poge^ = total loss of power by hysteresis and eddies, as calculated according to Chapter XII. he = magnetizing current, and nobe = effective m.m.f. per primary circuit; hence -wnohe = total effective m.m. ...", "... en doing no work (at synchronism), and F = g — j6 = primary exciting admittance per circuit = — • We thus have, ge = magnetic power current, ge~ = loss of power by hysteresis (and eddy currents) per primary coil. Hence Poge^ = total loss of power by hysteresis and eddies, as calculated according to Chapter XII. he = magnetizing current, and nobe = effective m.m.f. per primary circuit; hence -wnohe = total effective m.m.f., and — ^nobe = total maximum m.m.f., as resultant of the m.m.fs. V2 of the po-ph ...", "... 7. Siimli'v iti'iiirdir iiltt'Tiinlrtr. alternator, and thereby ia at a disadvantage where the limit of magnetic density in the armature is set only by magnetic saturation. As regards to the hysteresis loss in the armature of the in- ductor alternator, the magnetic cycle is an unsyrametrieal cycle, between two values of the same direction, Bx and B%, and the loss therefore is materially greater than it would be with a symmetrical cycle of the same ampli ...", "... it, the amplitude of the magnetic pulsation in the inductor machine may have to be kept very much lower than in the standard type, the core loss of the machine may be no larger, or may even be smaller than that of the standard type, in spite of the higher hysteresis coefficient, 170. 169. The inductor-machine type, Fig. 136, must have an £—21 \\f\\j\\j\\/\\r\\/\\j\\r ^ :f-A J fttfMtai«4**Aft« ! I >U Fig. 138. — Alexanderson high frequency inductor alternator. auxiliary air gap in the magnetic circuit, sep ...", "... cycles per revolution, thus as syn- chronous motor would run at half the speed of a standard syn- chronous machine of p poles. As the result hereof, in starting polyphase synchronous machines by impressing polyphase voltage on the armature and using the hysteresis and the induced currents in the field poles, for producing the torque of starting and acceleration, there frequently appears at half synchronism a tendency to drop into step with the field structure as inductor. This results in an increased torque when ap ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-17", "section_label": "Chapter 19: Alternating- Current Motors In General", "section_title": "Alternating- Current Motors In General", "kind": "chapter", "sequence": 17, "number": 19, "location": "lines 21713-23905", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-17/", "snippets": [ "... onsumes an e.m.f. 90° ahead of ♦, or 90—ci degrees ahead of /. This may be resolved in a reactive component: E = 2x/ft* eos a = 2 t/LI = xl, the o.m.f, con- sumed by self-induction, and power component: E\" = 2r/n* sin a = 2irfHI = r\"I = e.m.f. consumed by hysteresis (eddj currents, etc.), and is, therefore, in vector representation denoted by: E' = jxf and E\" = f>% where: x = 2 irfL — reactance, and L = inductance, r\" = effective hysteretic resistance. The ohmic resistance of the circuit, r', consumes an e.n ...", "... machine. In those, the mutual inductive reactance has been represented, not by the mutual inductive impedance, Z, but by its reciprocal value, the exciting admittance: Y = ■=• It is then: r0 is the coefficient of power consumption by ohmic resistance, hysteresis and eddy currents of the self-inductive flux — effective resistance. x0 is the coefficient of e.m.f. consumed by the self-inductive or leakage flux — self-inductive reactance. r is the coefficient of powfer consumption by hysteresis and eddy currents d ...", "... y ohmic resistance, hysteresis and eddy currents of the self-inductive flux — effective resistance. x0 is the coefficient of e.m.f. consumed by the self-inductive or leakage flux — self-inductive reactance. r is the coefficient of powfer consumption by hysteresis and eddy currents due to the mutual magnetic flux (hence contains no ohmic resistance component). x is the coefficient of e.m.f. consumed by the mutual magnetic flux. The e.m.f. consumed by the circuit is then: # = Zol + Zh l (1) If one of the circ ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-18", "section_label": "Chapter 20: Single-Phase Commutator Motors", "section_title": "Single-Phase Commutator Motors", "kind": "chapter", "sequence": 18, "number": 20, "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "... e an = e. l this diagram, and in the preceding approximate calculat magnetic flux, *, has been assumed in phase with the curren l reality, however, the equivalent sine wave of magn $, lags behind the equivalent sine wave of exciting curren he angle of hysteresis lag, and still further by the po ase tx, on- the file, on, ,/- etic ,/. wcr SINGLE-PHASE COMMUTATOR MOTORS 365 consumed by eddy currents, and, especially in the commutator motor, by the power consumed in the short-circuit current under ...", "... e.m.f. of rotation is not entirely a power e.m.f., but contains a wattless lagging component. The e.m.f. of alternation, OE0, is 90° ahead of O*, hence less than 90° ahead of OI, and therefore contains a power component representing the power consumed by hysteresis, eddy currents, and the short-circuit current under the brushes. Completing now the diagram, it is seen that Hie phase angle, 9, is reduced, that is, the power-factor of the motor increased by 366 ELECTRICAL APPARATUS the increased loss of power, ...", "... in single-phase commutator motors ate BOB ' tially the same as in other types of machines: (a) Friction losses— air friction or windage, lwaring friction and commutator brush friction, and also ■ :■ . mechanical transmission losses. (6) Core losses, as hysteresis and eddy currents. These an1 of two classes — the alternating core hiss, due to the alternation of the magnetic flux in the main field, quadrature field, and arma- ture and the rotating core loss, due to the rotation of the arma- ture; through the magneti ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-46", "section_label": "Chapter 6: Alternating Magnetic Flux Distribution", "section_title": "Alternating Magnetic Flux Distribution", "kind": "chapter", "sequence": 46, "number": 6, "location": "lines 23948-24980", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "snippets": [ "... yer carries magnetic flux. The apparent permeability of the iron thus decreases at very high frequency, and this has led to the opinion that at very high fre- quencies iron cannot follow a magnetic cycle. There is, however, no evidence of such a \" viscous hysteresis,\" but it is probable that iron follows magnetically even at the highest frequencies, traversing practically the same hysteresis cycle irrespective of 355 356 TRANSIENT PHENOMENA the frequency, if the true m.m.f., that is, the resultant of the im ...", "... opinion that at very high fre- quencies iron cannot follow a magnetic cycle. There is, however, no evidence of such a \" viscous hysteresis,\" but it is probable that iron follows magnetically even at the highest frequencies, traversing practically the same hysteresis cycle irrespective of 355 356 TRANSIENT PHENOMENA the frequency, if the true m.m.f., that is, the resultant of the impressed m.m.f. and the m.m.f. of the secondary currents in the iron, is considered. Since with increasing frequency, at constant ...", "... m.m.f. of the secondary currents in the iron, is considered. Since with increasing frequency, at constant impressed m.m.f., the resultant m.m.f. decreases, due to the increase of the demagnetizing secondary currents, this simulates the effect of a viscous hysteresis. Frequently also, for mechanical reasons, iron sheets of greater thickness than would give uniform flux density have to be used in an alternating field. Since rapidly varying magnetic fields usually are alternating, and the subdivision of the iron is u ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3721-4369", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-06/", "snippets": [ "... DISCHARGES, WAVES AND IMPULSES. where C = capacity = coefficient of energy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power consumption by the voltage, as leakage conductance by the voltage, corona, dielectric hysteresis, etc. Thus the transient of the spontaneous discharge of a condenser would be represented by e = eoe~'^\\ (4) Similar single-energy transients may occur in other systems. For instance, the transient by which a water jet approaches con- stant velocity ...", "... pation exponent of the double-energy transient -K2+8 IS given as r 2L* This is correct only if g = 0, that is, the conductance, which rep- resents the power dissipation resultant from the voltage (by leak- age, dielectric induction and dielectric hysteresis, corona, etc.), is negligible. Such is the case in most power circuits and trans- mission lines, except at the highest voltages, where corona appears. It is not always the case in underground cables, high-potential DOUBLE-ENERGY TRANSIENTS. 69 transfo ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3287-3955", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "snippets": [ "... DISCHARGES, WAVES AND IMPULSES. where C = capacity = coefficient of energy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power consumption by the voltage, as leakage conductance by the voltage, corona, dielectric hysteresis, etc. Thus the transient of the spontaneous discharge of a condenser would be represented by e = e0e~£ct. (4) Similar single-energy transients may occur in other systems. For instance, the transient by which a water jet approaches con- stant velocity ...", "... the dissipation exponent of the double-energy transient is given as r 2L' This is correct only if g = 0, that is, the conductance, which rep- resents the power dissipation resultant from the voltage (by leak- age, dielectric induction and dielectric hysteresis, corona, etc.), is negligible. Such is the case in most power circuits and trans- mission lines, except at the highest voltages, where corona appears. It is not always the case in underground cables, high-potential DOUBLE-ENERGY TRANSIENTS. 69 tra ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-11", "section_label": "Theory Section 11: Capacity and Condensers", "section_title": "Capacity and Condensers", "kind": "theory-section", "sequence": 11, "number": 11, "location": "lines 3586-3760", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-11/", "snippets": [ "... .m.f. of the condenser is 106/ 106 The value z0 = fn is called the condensive reactance of the ^ 7T/C condenser. 56 ELEMENTS OF ELECTRICAL ENGINEERING Due to the energy loss in the condenser by dielectric hysteresis, the current leads the e.m.f. by somewhat less than 90 time de- grees, and can be resolved into a wattless charging current and a dielectric hysteresis current, which latter, however, is generally so small as to be negligi ...", "... CAL ENGINEERING Due to the energy loss in the condenser by dielectric hysteresis, the current leads the e.m.f. by somewhat less than 90 time de- grees, and can be resolved into a wattless charging current and a dielectric hysteresis current, which latter, however, is generally so small as to be negligible, though in underground cables of poor quality, it may reach as high as 50 per cent, or more of the charging or wattless current of the condenser. ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-18", "section_label": "Theory Section 18: Equivalent Sine Waves", "section_title": "Equivalent Sine Waves", "kind": "theory-section", "sequence": 18, "number": 18, "location": "lines 7381-7736", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-18/", "snippets": [ "... (6) are found as the relative instantaneous values of magnetic flux density. Since the maximum magnetic flux density is 15,000 the in- 15 000 stantaneous values are B = B' ' . , plotted in column (7). From the hysteresis cycle in Fig. 42 are taken the values of magnetizing force /, corresponding to magnetic flux density B. They are recorded in column (8), and in column (9) the instan- taneous values of m.m.f. F = If, where I = 50 = le ...", "... values of p', er, and i', we have 264.8 = 1000 X 1.198 cos 6. hence, cos 0 = 0.221, 6 = 77.2°, 112 ELEMENTS OF ELECTRICAL ENGINEERING and the angle of hysteretic advance of phase, a = 90° - 0 = 12.8°. The hysteresis current is then i' cos e = 0.265, and the magnetizing current, i' sin 0 = 1.165. Adding the instantaneous values of e.m.f. eQ in column (4) 14 648 gives 14,648; thus the mean value, — f-r— = 813.8. Since the J ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-33", "section_label": "Apparatus Section 12: Synchronous Machines: Starting of Synchronous Motors", "section_title": "Synchronous Machines: Starting of Synchronous Motors", "kind": "apparatus-section", "sequence": 33, "number": 12, "location": "lines 9749-9820", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-33/", "snippets": [ "... e the current is leading, with higher impressed voltage lagging, in a synchronous motor. 152 ELEMENTS OF ELECTRICAL ENGINEERING face of the field pole opposite to the armature projections lags behind the m.m.f., due to hysteresis and eddy currents, and thus is still remanent, while the m.m.f. of the projection 1 decreases, and is attracted by the rising m.m.f. of projection 2, etc., or, in other words, while the maximum m.m.f. in the armature has ...", "... ion- ary field, the armature to revolve in the opposite direction B). Lamination of the field poles reduces the starting torque caused by eddy currents in the field poles, but increases that caused by remanent magnetism or hysteresis, due to the higher permeability of the field poles. Thus the torque per volt-ampere input is approximately the same in either case, but with laminated i FIG. 72. — Magnetic circuit of a polyphase synchronous motor. poles ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-96", "section_label": "Apparatus Section 2: Alternating-current Transformer: Excitation", "section_title": "Alternating-current Transformer: Excitation", "kind": "apparatus-section", "sequence": 96, "number": 2, "location": "lines 16912-17026", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-96/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-96/", "snippets": [ "... - ponent, imj is called the magnetizing current, and is usually greatly distorted in wave shape, while the energy component, 280 ELEMENTS OF ELECTRICAL ENGINEERING ih, does not much differ from a sine wave, and is the hysteresis energy current: /o = ih - Jim- Under load, the primary current then consists of two com- ponents: the load current 7'2 which is the transformed second- ary current 7'2 = — > and the exciting, current IQ. The total ...", "... gnetic saturation causes an abnormal increase of the magnetizing current. The power-factor is shown on Fig. 153. IE. Losses and Efficiency 113. The losses in the transformer are (a) The core loss, comprising the loss by hysteresis and eddy currents in the iron. This depends on the maximum magnetic flux, and thus on the induced voltage: and as the induced voltage is practically equal to the impressed voltage 61, at constant impressed voltage, the ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-21", "section_label": "Chapter 23: Review", "section_title": "Review", "kind": "chapter", "sequence": 21, "number": 23, "location": "lines 32138-32819", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-21/", "snippets": [ "... or generator, but the disadvantage of not being standard yet. Heyland Motor. — 59, 210. Squirrel-cage induction motor with commutator for power-factor compensation. Hunt Motor. — 30. Internally concatenated induction motor. (See \"Concatenation (l).\") Hysteresis Motor. — X, 98. Motor with polyphase stain ud laminated rotor of uniform reluctance in all directions, without winding. Gives constant torque at all speeds, by the hystereBM of the rotor, as motor below and as generatoi above HynchroDBSB, while at synchro ...", "... chine.,,) 470 ELECTRICAL APPARATUS Starting Devices. — Polyphase induction motor: Remittance of high temperature coefficient, 2. Gives good torque curve at low speed and good regulation at speed, but requires high temperature in the resistance. Hysteresis device, 4. Gives good speed regulation and good torque at low speed and in starting, but somewhat impairs the power-factor. Eddy-current device, 5; double and triple squirrel-cage, 18. 20, 24; and deep-bar rotor, 7. Give good speed regulation combined w ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-09", "section_label": "Chapter 9: Wave Screens. Even Harmonics", "section_title": "Wave Screens. Even Harmonics", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 16964-17631", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-09/", "snippets": [ "... by superimposed. The magnetic flux then oscillates sinusoidally, not between equal and opposite values, but between two unequal values, which may be of the same, or of opposite signs. That is, it performs an unsymmetrical magnetic cycle. Neglecting again hysteresis, that is, assuming the rising WAVE SCREENS. EVEN HARMONICS 159 and the decreasing magnetization curve as coincident — which is permissible as approximation, since the hysteresis contributes little to distortion — ^and choosing the same magnetization cu ...", "... ns. That is, it performs an unsymmetrical magnetic cycle. Neglecting again hysteresis, that is, assuming the rising WAVE SCREENS. EVEN HARMONICS 159 and the decreasing magnetization curve as coincident — which is permissible as approximation, since the hysteresis contributes little to distortion — ^and choosing the same magnetization curve as in the preceding, curve I in Fig. 64, we may as an instance con- sider a sinusoidal magnetic pulsation between the limits +15.4 and +19.7, corresponding to a variation of the ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-40", "section_label": "Chapter 4: Arc Rectification", "section_title": "Arc Rectification", "kind": "chapter", "sequence": 40, "number": 4, "location": "lines 17755-19259", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "snippets": [ "... ermissible in an arc circuit. The total variation of the rectified current then is 2 aiOJ i.e., the alternating component of the direct current has the maximum value ai0, hence the effective value — i_ i0 (or for a = 0.2, 0.141 10) and the frequency 2/. Hysteresis and eddy losses in the direct-current reactive coil, therefore, correspond to an alternating current of frequency 2f and effective value a -—— i0, or about 0.141 -iQ, i.e., are small even at relatively high densities. 256 TRANSIENT PHENOMENA I ...", "... ernating-current reactive coils the current varies, unidirectionally, between 0 and i0 (1 + a), i. e., its alternating i0 and the effec- component has the maximum value tive value-— = iQ (or, for a = + 0.2, 0.425 i0) and the fre- JU quency/. The hysteresis loss, therefore, corresponds to an alternating current of frequency / and effective value %> or about 0.425 i0. With decreasing load, at constant alternating-current supply, the rectified direct current slightly increases, due to the increas- ing overl ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-05", "section_label": "Chapter 6: Empirical Curves", "section_title": "Empirical Curves", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 16483-21988", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-05/", "snippets": [ "... tial function has the characteristic of being proportional to its differential quotient, the exponential function thus rationally represents the dying out of the current in an inductive circuit. On the other hand, the relation between the loss by magnetic hysteresis and the magnetic density: W=-q(^^'^, is an empirical equation since no reason can be seen for this law of the 1.6th power, except that it agrees with the observa- tions. A rational equation, as a deduction from a general law of nature, applies universal ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-06", "section_label": "Lecture 6: Higher Harmonics Of The Generator Wave", "section_title": "Higher Harmonics Of The Generator Wave", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3133-3507", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-06/", "snippets": [ "... sine wave, and if the magnetism is not a sine wave, but contains higher harmonics, the e. m. f. is not a sine wave, but contains the harmonics induced by the harmonics of magnetism. The exciting current of the transformer depends on tht magnetism by the hysteresis cycle; if the magnetism is a sine wave, the exciting current therefore cannot be a sine wave, but 82 GENERAL LECTURES must contain higher harmonics- — mainly the third harmonic, which reaches 20 to 30% of the fundamental, or even more at saturatio ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-09", "section_label": "Lecture 9: Hunting Of Synchronous Machines", "section_title": "Hunting Of Synchronous Machines", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 4218-4594", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-09/", "snippets": [ "... nting. If the oscillation is small it may do no harm ; if it is greater, it may cause fluctuation of voltage, resulting in flick- ering of lights, etc. ; if it gets very large, it may throw the ma- chines out of step. Some causes of hunting are: 1st. Magnetic lag. 2nd. Pulsation of engine speed. 3rd. Hunting of engine governors. 4th. Wrong speed characteristic of engine. ii6 GENERAL LECTURES I St. When the machines move apart from each other, magnetic attraction opposes their separation. When they pull to ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-13", "section_label": "Lecture 13: Electric Railway: Motor Characteristics", "section_title": "Electric Railway: Motor Characteristics", "kind": "lecture", "sequence": 13, "number": 13, "location": "lines 7124-8648", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-13/", "snippets": [ "... rtion, Mo to M, and is given by the curve S ; and in the same proportion the torque is decreased to the curve Ti. From this torque curve the lost torque is now subtracted ; that is, the torque represent- ing the power consumed in friction and gear losses, hysteresis and eddy currents, etc. Some of the losses of power are MOTOR CHARACTERISTICS 171 approximately constant ; others are approximately proportional to the square of the current; and the lost torque, being equal to the power loss divided by the speed, can ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-110", "section_label": "Apparatus Section 4: Induction Machines: Induction Generator", "section_title": "Induction Machines: Induction Generator", "kind": "apparatus-section", "sequence": 110, "number": 4, "location": "lines 21158-21588", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-110/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-110/", "snippets": [ "... excitation and thus drops its load as soon as the voltage falls below saturation. Since, however, the field of the induction generator is alter- nating, it is usually not feasible to run at saturation, due to ex- cessive hysteresis losses, except for very low frequencies. 346 ELEMENTS OF ELECTRICAL ENGINEERING 2d. The power-factor of the external circuit depends upon the voltage impressed upon it. This, for instance, is the case if the circuit c ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-14", "section_label": "Theory Section 14: Rectangular Coordinates", "section_title": "Rectangular Coordinates", "kind": "theory-section", "sequence": 14, "number": 14, "location": "lines 5264-5831", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-14/", "snippets": [ "... s where ii = Ii cos 0i, iz = Ii sin 0i, (6) and the primary load current corresponding thereto is I' = - aii = aii - jaiz. (7) The primary exciting current, Joo = h - jg, (8) where h = J0o sin a is the hysteresis current, g = I0o cos a the reactive magnetizing current. Thus the total primary current is J0 = I' + J00 = (aii + h) -j (aiz + g). (9) The e.m.f. consumed by primary resistance rQ is r0Jo = TQ (aii + h) - jr0 ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-28", "section_label": "Apparatus Section 7: Synchronous Machines: Synchronous Motor", "section_title": "Synchronous Machines: Synchronous Motor", "kind": "apparatus-section", "sequence": 28, "number": 7, "location": "lines 9292-9398", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-28/", "snippets": [ "... Ep-ir); that is, the current times the power component of the nominal counter-generated e.m.f. Obviously to get the available mechan- ical power, the power consumed by mechanical friction and by molecular magnetic friction or hysteresis, and the power of field excitation, have to be subtracted from this value P0." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-60", "section_label": "Apparatus Section 9: Direct-current Commutating Machines: Saturation Curves", "section_title": "Direct-current Commutating Machines: Saturation Curves", "kind": "apparatus-section", "sequence": 60, "number": 9, "location": "lines 11695-11710", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-60/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-60/", "snippets": [ "... generated voltage, or terminal voltage at open circuit and normal speed, as function of the ampere-turns per pole field excitation. Such curves are of the shape shown in Fig. 105 as A. Owing to the remanent magnetism or hysteresis of the iron part of the magnetic circuit, the saturation curve taken with decreasing field excitation usually does not coincide with that taken with increasing field excitation, but is higher, and by gradually first increasi ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-86", "section_label": "Apparatus Section 7: Synchronous Converters: Variable Ratio Converters (\"split Pole\" Converters)", "section_title": "Synchronous Converters: Variable Ratio Converters (\"split Pole\" Converters)", "kind": "apparatus-section", "sequence": 86, "number": 7, "location": "lines 15586-15734", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-86/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-86/", "snippets": [ "... s indicate by their beats the approach of the converter to synchronism. When starting, the field circuit of the converter has to be opened or at least greatly weakened. The starting of the polyphase converter is largely a hysteresis effect and entirely so in machines with laminated field poles, while in ma- chines with solid magnet poles or with a short-circuited winding (squirrel-cage) in the field poles, secondary currents in the latter contribute to ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-98", "section_label": "Apparatus Section 2: Alternating-current Transformer: Low T*r Loss Type,", "section_title": "Alternating-current Transformer: Low T*r Loss Type,", "kind": "apparatus-section", "sequence": 98, "number": 2, "location": "lines 17030-17323", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-98/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-98/", "snippets": [ "... . 5 per cent. 2 per cent. For convenience, exciting current and losses are frequently given in per cent, of the full-load output of the transformer. The curves correspond to non-inductive load. The core loss comprises hysteresis, which varies with the 1.6 power of the induced voltage and eddies proportional to the square of induced voltage. Hence, within the narrow range of variation of the induced voltage between no load and full load of a cons ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 3267-3618", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-06/", "snippets": [ "... ahead of the current, Oh, and proportional thereto. In the same Hne element we have a current, hh^, in phase with the voltage, OEi, and proportional thereto, representing 44 ALTERNATING-CURRENT PHENOMENA the loss of current by leakage, dielectric hysteresis, etc., and a current, /i^ /i^\\ 90° ahead of the voltage, 0E-[, and proportional thereto, the charging current of the line element as condenser; and in this manner passing along the line, element by element, we ultimately reach the generator terminal volta ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-09", "section_label": "Chapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "section_title": "Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 4674-6992", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-09/", "snippets": [ "... a constant potential alternating-current system, the voltage at the terminals of a receiver circuit can be varied by the use of a variable reactance in series with the circuit, without loss of energy except the unavoidable loss due to the resistance and hysteresis of the reactance; and that, if the series reactance is very large compared with the resistance of the receiver circuit, the current in the receiver circuit becomes more or less inde- pendent of the resistance — that is, of the power consumed in the receiv ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-33", "section_label": "Chapter 33: Efficiency Of Systems", "section_title": "Efficiency Of Systems", "kind": "chapter", "sequence": 33, "number": 33, "location": "lines 36515-37127", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-33/", "snippets": [ "... During changes of current, as make and break, and changes of load, especially rapid changes, there may consequently be gen- erated in these circuits e.m.fs. far exceeding their normal poten- tials. Inversely, however, with alternating voltages, dielectric hysteresis, etc., may cause heating and thereby lower the disruptive strength. At the voltages which came under con- sideration, the continuous current is usually excluded to begin with. EFFICIENCY OF SYSTEMS 439 Thus we get: If a given power is to be transmit ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-08", "section_label": "Chapter 8: Capacity", "section_title": "Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3872-6370", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "snippets": [ "... in a constant potential alternating-current system, the voltage at the terminals of a receiver circuit can be varied by the use of a variable reactance in series to the circuit, without loss of energy except the unavoidable loss due to the resistance and hysteresis of the reactance ; and that, if the series reactance is very large compared with the resis- tance of the receiver circuit, the current in the receiver circuit becomes more or less independent of the resis- tance, — that is, of the power consumed in the re ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 2774-3131", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-06/", "snippets": [ "... the reactance of the line element, 90° ahead of the current OIV and proportional thereto. In the same line element we have a current IJ^ in phase with the E.M.F. OEV and proportional thereto, representing the loss of energy current by leakage, dielectric hysteresis, etc., and a current ^V/', 90° ahead of the E.M.F. OEV and proportional thereto, the charging current of the line ele- ment as condenser, and in this manner passing along the line, element by element, we ultimately reach the generator terminal voltages E ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-08", "section_label": "Chapter 8: Circuits Containing Resistance, Inductance, And Capacity", "section_title": "Circuits Containing Resistance, Inductance, And Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3577-5333", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "snippets": [ "... in a constant potential alternating-current system, the voltage at the terminals of a receiver circuit can be varied by the use of a variable reactance in series to the circuit, without loss of energy except the unavoidable loss due to the resistance and hysteresis of the reactance; and that, if the series reactance is very large compared with the resis- tance of the receiver circuit, the current in the receiver circuit becomes more or less independent of the resis- tance,— that is, of the power consumed in the rece ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-02", "section_label": "Chapter 2: Multiple Squirrel-Cage Induction Motor", "section_title": "Multiple Squirrel-Cage Induction Motor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3543-5554", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-02/", "snippets": [ "... at no-load, in the same manner as a single induction motor approaches synchronism. With increasing load, the slip below half syn- chronism increases. In reality, at half synchronism, s = 0.5, there is a slight torque produced by the first motor, as the hysteresis energy current of the second motor comes from the secondary of the first motor, and therein, as energy current, produces a small torque. More generally, any pair of induction motors connected in concatenation divides the speed so that the sum of their tw ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-04", "section_label": "Chapter 5: Single-Phase Induction Motor", "section_title": "Single-Phase Induction Motor", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 8555-10582", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-04/", "snippets": [ "... xter- nal circuit, where such exists. Z0, Yi and Y2 thus refer to the self-inductive impedances, in which the energy component is due to effective resistance, and Y and Y' refer to the mutual inductive impedances, in which the energy component is due to hysteresis and eddy currents. a = shaded portion of pqje, as fraction of total pole; thus (1 — a) = unshaded portion of pole. If: eo = impressed single-phase voltage, $i = voltage induced by flux in unshaded portion of pole, $2 = voltage induced by flux in sha ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-11", "section_label": "Chapter 12: Frequency Converter Or General Alternating Current Transformer", "section_title": "Frequency Converter Or General Alternating Current Transformer", "kind": "chapter", "sequence": 11, "number": 12, "location": "lines 14897-17124", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-11/", "snippets": [ "... d since the total effect must be the exciting current: i o — to tj 0, it follows that : i'x — i't = i'o and i\"\\ + i#/t = t 99 Hence, the stator power current and rotor power current, i'x and i\\y are equal to each other (when neglecting the small hysteresis power current). The synchronous exciter of the machine must supply in addition to the magnetizing current, the total reactive current of the load. Or in other words, such a machine requires a synchronous exciter of a volt-ampere capacity equal to the volt ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-13", "section_label": "Chapter 15: Synchronous Rectifier", "section_title": "Synchronous Rectifier", "kind": "chapter", "sequence": 13, "number": 15, "location": "lines 18413-19373", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-13/", "snippets": [ "... ELECTRICAL APPARATUS magnitude, that is, larger than the exciting current of the trans- former, it .saturates the transformer iron. Running at or beyond magnetic saturation, the primary exciting current of the trans- former then becomes excessive, the hysteresis heating due to the unsymmetrical magnetic cycle is greatly increased, and the transformer endangered or destroyed. Half-wave rectifiers thus are impracticable except for extremely small power. The full-wave contact-making rectifier, Fig. 97 or 98, doe ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-20", "section_label": "Chapter 22: Unipolar Machines", "section_title": "Unipolar Machines", "kind": "chapter", "sequence": 20, "number": 22, "location": "lines 31716-32137", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-20/", "snippets": [ "... n the high-speed steam turbttM arrived, the study of the design of high-powered steam-turbine- driven unipolars was undertaken, and a number of such machines built and installed. In the huge turbo-alternators of today, the largest lo— i- the core loss: hysteresis and eddies in the iron, which often is K than all the other losses together. Theoretically, the Uni point machine has no core loss, as the magnetic flux does not change anywhere, and solid steel thus is used throughout — and has to be used, due to the sh ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-22", "section_label": "Chapter 24: Conclusion", "section_title": "Conclusion", "kind": "chapter", "sequence": 22, "number": 24, "location": "lines 32820-33531", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-22/", "snippets": [ "... ecting induc- tion motor stability, 137 H Half wave rectifier, 245 Harmonic torque of induction motor, 144 Heyland motor, 92 Higher harmonic torques in induc- tion motor, 144 Homopolar, see Unipolar. Hunt motor, 49 Hunting, see Surging. Hysteresis generator, 169 motor, 168 starting device of induction motor, 5 I Independent phase rectifier, 251 Inductance storing energy in phase conversion, 212 Inductive compensation of single- phase commutator motor, 343 devices starting singlephase i ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-01", "section_label": "Chapter 1: Electric Conduction. Soled And Liquid", "section_title": "Electric Conduction. Soled And Liquid", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 959-3894", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-01/", "snippets": [ "... but can stand low voltage only — 1 volt or less — and therefore is of limited industrial value. As chemical action requires appreciable time, such electrolytic condensers show at commercial frequencies high losses of power by what may be called \" chemical hysteresis,\" and therefore low efficiences, but they are alleged to become efficient at very low frequencies. For this reason, they have 10 ELECTRIC CIRCUITS been proposed in the secondaries of induction motors, for power- factor compensation. Iron plates in alk ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-06", "section_label": "Chapter 6: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 11051-12221", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-06/", "snippets": [ "... se of a cyclic change, the variation from position 110 ELECTRIC CIRCUITS 1 to 2 is different from that from position 2 back to 1, such a cyclic change produces or consumes energy. w = I id(iL) + I id(iL) = f id(iL) Jl J2 Jl Such a case is the hysteresis cycle. The reaction machine (see Theory and Calculation of Electrical Apparatus) is based on such cycle. SECTION II" ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-11", "section_label": "Chapter 11: Instability Of Circuits: Induction And Syn Chronous Motors", "section_title": "Instability Of Circuits: Induction And Syn Chronous Motors", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 21382-22633", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-11/", "snippets": [ "... load to p2 the position further forward corresponding to the decreased load. V then shows the oscillation of speed corresponding to the oscillation of position. The dotted curve, Wi, then shows the energy losses resulting from the oscillation of speed (hysteresis and eddies in the pole faces, currents in damper windings), that is, the damping power, assumed as proportional to the square of the speed. If there is no lag of the synchronizing force behind the position displacement, the synchronizing force, that is, ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-26", "section_label": "Chapter 4: Inductance And Resistance In Alternating Current Circuits", "section_title": "Inductance And Resistance In Alternating Current Circuits", "kind": "chapter", "sequence": 26, "number": 4, "location": "lines 3515-4071", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-26/", "snippets": [ "... in this case 7 cos (0 — 00) is the circle, -r-e h x cos 00 the exponential or loxodromic spiral. As a rule, the transient term in alternating-current circuits containing resistance and inductance is of importance only in circuits containing iron, where hysteresis and magnetic saturation complicate the phenomenon, or in circuits where unidirectional or periodically recurring changes take place, as in rectifiers, and some such cases are considered in the following chapters." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... produced, from low commercial frequencies up to hundred thousands of cycles. At frequencies between 500 and 2000 cycles, the use of iron in the reactive coil has to be restricted to an inner core, and at frequencies above this iron cannot be used, since hysteresis and eddy currents would cause excessive damping of the oscil- lation. The reactive coil then becomes larger in size. 47. Assuming 96 per cent efficiency of the reactive coil and 99 per cent of the condenser, gives since r = 0.05 x, r - 0.05 V ..." ] } ] }, { "id": "admittance", "label": "Admittance", "aliases": [ "admittance", "admittances" ], "total_occurrences": 481, "matching_section_count": 79, "matching_source_count": 10, "source_totals": [ { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 136, "section_count": 17 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 109, "section_count": 15 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 73, "section_count": 13 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 68, "section_count": 9 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 55, "section_count": 9 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 16, "section_count": 5 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 9, "section_count": 4 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 7, "section_count": 3 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 4, "section_count": 2 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 4, "section_count": 2 } ], "section_hits": [ { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "section_label": "Chapter 16: Induction Motor", "section_title": "Induction Motor", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 28, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "... econdary frequency is s N, the secondary in- duced E.M.F. (reduced to primary system) is El = — se. Let I0 = exciting current, or current passing through the motor, per primary circuit, when doing no work (at synchronism), and K= g -j- j 'b = orimary admittance per circuit = — . We thus have, ge = magnetic energy current, ge* = loss of power oy hysteresis (and eddy currents) per primary coil. Hence = total loss of energy by hysteresis and eddys, as calculated according to Chapter X. be = magnetizing cur ...", "... f (R = reluctance of magnetic circuit per pole, as dis- cussed in Chapter X., it is A^^ft*. * Complete discussion hereof, see Chapter XXV. INDUCTION MOTOR. 241 Thus, from the hysteretic loss, and the reluctance, the constants, g and b, and thus the admittance, Fare derived. Let rQ = resistance per primary circuit ; XQ = reactance per primary circuit ; thus, •^o = ro — j XQ = impedance per primary circuit; rv = resistance per secondary circuit reduced to pri- mary system ; xv = reactance per secondary ci ...", "... ncy of 60 cycles. The impressed E.M.F. is 110 volts between lines, and the motor star connected, hence the E.M.F. impressed per circuit : ~ = 63.5 ; or EQ = 63.5. 260 AL TERN A TING-CURRENT PHENOMENA. The constants of the motor are : Primary admittance, Y = .1 + .4 j. Primary impedance, Z = .03 — .09 j. Secondary impedance, Zx = .02 — .085/. In Fig. 116 is shown, with the speed in per cent of •synchronism, as abscissae, the torque in kilogrammetres, as ordinates, in drawn lines, for the values of ar ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-20", "section_label": "Chapter 20: Single-Phase Induction Motors", "section_title": "Single-Phase Induction Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 21538-22301", "status": "candidate", "occurrence_count": 23, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-20/", "snippets": [ "... sity — the total volt-amperes excitation of the single-phase induction motor must be the same as of the same motor on polyphase circuit, it follows that by operating a quarter-phase motor from single-phase circuit on one primary coil, its primary exciting admittance is doubled. Operating a three-phase motor single-phase on one circuit its primary exciting admittance is trebled. The self-inductive primary impedance is the same single-phase as polyphase, but the secondary impedance reduced to the primary is lowered, s ...", "... e same motor on polyphase circuit, it follows that by operating a quarter-phase motor from single-phase circuit on one primary coil, its primary exciting admittance is doubled. Operating a three-phase motor single-phase on one circuit its primary exciting admittance is trebled. The self-inductive primary impedance is the same single-phase as polyphase, but the secondary impedance reduced to the primary is lowered, since in single-phase operation all secondary circuits corre- spond to the one primary circuit used. Thu ...", "... d the effect of the magnetic field produced by the starting device, have to be considered. The exciting current of the single-phase motor consists of the primary exciting current or current producing the main magnetic flux, and represented by ^ constant admittance, 7oS the primary exciting admittance of the motor, and the secondary exciting current, that is, that component of primary current corresponding to the secondary current which gives the excita- 248 ALTERNATING-CURRENT PHENOMENA tion for the quadrature ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-109", "section_label": "Apparatus Section 3: Induction Machines: Single -phase Induction Motor", "section_title": "Induction Machines: Single -phase Induction Motor", "kind": "apparatus-section", "sequence": 109, "number": 3, "location": "lines 20428-21157", "status": "candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-109/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-109/", "snippets": [ "... admit- tance per circuit Y = g — jb and self-inductive impedances ZQ = rQ + jxQ and Zi = TI + jxi per circuit with the same motor operating as single-phase motor from one pair of termi- nals, the single-phase exciting admittance is Y' = 3 Y (so as to give, the same volt-amperes excitation 3 eF), the primary 330 ELEMENTS OF ELECTRICAL ENGINEERING self-inductive impedance is the same, ZQ = r0 + jxo', the sec- ondary self-inductive impedance si ...", "... by the armature magnetization equal to the main magnetic flux produced by the impressed e.m.f. If an accurate calculation of the motor at intermediate speed and at standstill is required, the changes of effective exciting admittance and of secondary impedance, due to the decrease of the quadrature flux, have to be considered. At synchronism the total exciting admittance gives the m.m.f. of main flux and auxiliary flux, while at standstill the quad- r ...", "... intermediate speed and at standstill is required, the changes of effective exciting admittance and of secondary impedance, due to the decrease of the quadrature flux, have to be considered. At synchronism the total exciting admittance gives the m.m.f. of main flux and auxiliary flux, while at standstill the quad- rature flux has disappeared or decreased to that given by the starting device, and thus the total exciting admittance has de- 1.0 0.9 0.8 0 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-17", "section_label": "Chapter 17: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16521-17716", "status": "candidate", "occurrence_count": 21, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-17/", "snippets": [ "... y much smaller. Symbolic Method 149. In symbolic representation by complex quantities the transformer problem appears as follows: The exciting current, /oo, of the transformer depends upon the primary e.m.f., which dependence can be represented by an admittance, the \"primary admittance,\" Fo = g^i — jbo, of the transformer. The resistance and reactance of the primary and the secondary circuit are represented in the impedance by Zo = To + jxo, and Zi = ri + jxi. Within the limited range of variation of the mag ...", "... c Method 149. In symbolic representation by complex quantities the transformer problem appears as follows: The exciting current, /oo, of the transformer depends upon the primary e.m.f., which dependence can be represented by an admittance, the \"primary admittance,\" Fo = g^i — jbo, of the transformer. The resistance and reactance of the primary and the secondary circuit are represented in the impedance by Zo = To + jxo, and Zi = ri + jxi. Within the limited range of variation of the magnetic density in a const ...", "... transformer. The resistance and reactance of the primary and the secondary circuit are represented in the impedance by Zo = To + jxo, and Zi = ri + jxi. Within the limited range of variation of the magnetic density in a constant-potential transformer, admittance and impedance can usually, and with sufficient exactness, be considered as constant. Let no = number of primary turns in series; Hi = number of secondary turns in series; a = — = ratio of turns; ni ' Fo = ^0 — jho = primary admittance Exciting c ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-12", "section_label": "Chapter 12: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 10718-13483", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-12/", "snippets": [ "... z — where z is determined by the magnetic characteristic of the iron and the shape of the magnetic and electric circuits — the impedance is represented, in phase and intensity, by the symbolic expression, Z — r -{- jx =^ z '&\\n a -\\- jz cos a; and the admittance by, 1 ^ g — JO = - Bin a — J- cos a = y sm a — jy cos a. The quantities z, r, x, and y, g, h are, however, not constants as in the case of the circuit without iron, but depend upon the intensity of magnetization, B — that is, upon the e.m.f. This depen ...", "... REACTANCE 129 m.m.f., / — effective current, since I\\/2 = maximum current, the magnetic flux, (R (R Substituting this in the equation of the counter e.m.f. of self- induction, E = V2 irfn^ 10\"', we have „ 2 wnJI 10-« ^= ^ 5 hence, the absolute admittance of the circuit is y = ^^ -^^^E = 2^f^T where 10« , , a = ^ — 5, a constant. 2 Trrr Therefore, the absolute admittance, y, of a circuit of negligible resistance is proportional to the magnetic reluctance, (R, and in- versely proportional to the fr ...", "... he equation of the counter e.m.f. of self- induction, E = V2 irfn^ 10\"', we have „ 2 wnJI 10-« ^= ^ 5 hence, the absolute admittance of the circuit is y = ^^ -^^^E = 2^f^T where 10« , , a = ^ — 5, a constant. 2 Trrr Therefore, the absolute admittance, y, of a circuit of negligible resistance is proportional to the magnetic reluctance, (R, and in- versely proportional to the frequency, f, and to the square of the number of turns, n. 100. In a circuit containing iron, the reluctance, (R, varies with t ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "section_label": "Chapter 10: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "... s, — where s is determined by the mag- netic characteristic of the iron, and the shape of the magnetic and electric circuits, — the impedance is repre- sented, in phase and intensity, by the symbolic expression, Z = r — jx = z sin a — jz cos a ; and the admittance by, Y = g + j b = - sin a -j- j - cos a = y sin a -f- jy cos a. z z The quantities, z, r, x, and y, g, b, are, however, not constants as in the case of the circuit without iron, but depend upon the intensity of magnetization, (B, — that is, upon the ...", "... (R = magnetic reluctance of a circuit, £FA = maximum M.M.F., I — effective current, since /V2 = maximum cur- rent, the magnetic flux, (R (R Substituting this in the equation of the counter E.M.F. of self-induction we have (R hence, the absolute admittance of the circuit is (RIO8 = a& E ~ 2 TT n*N ~ N ' 108 where a = , a constant. 2 TT n Therefore, the absolute admittance, y, of a circuit of neg- ligible resistance is proportional to the magnetic reluctance, (R, and inversely proportional to the f ...", "... flux, (R (R Substituting this in the equation of the counter E.M.F. of self-induction we have (R hence, the absolute admittance of the circuit is (RIO8 = a& E ~ 2 TT n*N ~ N ' 108 where a = , a constant. 2 TT n Therefore, the absolute admittance, y, of a circuit of neg- ligible resistance is proportional to the magnetic reluctance, (R, and inversely proportional to the frequency, N, and to the square of the number of turns, n. 82. In a circuit containing iron, the reluctance, (R, varies with th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-08", "section_label": "Chapter 8: Admittance, Conductance, Susceptance", "section_title": "Admittance, Conductance, Susceptance", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 4088-4673", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-08/", "snippets": [ "CHAPTER VIII ADMITTANCE, CONDUCTANCE, SUSCEPTANCE 48. If in a continuous-current circuit, a number of resistances, Ti, r2, ?'3, . . ., are connected in series, their joint resistance, R, is the sum of the individual resistances, K = ri + r2 + ra + . . . If, however, a number o ...", "... refore. The joint resistance of a number of series-connected resistances is equal to the sum of the individual resistances; the joint conduct- ance of a number of parallel-connected conductances is equal to the sum of the individual conductances. 64 ADMITTANCE, CONDUCTANCE, SUSCEPTANCE 55 49. In alternating-current circuits, instead of the term resist- ance we have the term impedance, Z = r -\\- jx, with its two components, the resistance, r, and the reactance, x, in the formula of Ohm's law, E = IZ. The resist ...", "... ected circuits; or, in other words, when several currents are produced by the same e.m.f., such as in cases where Ohm's law is expressed in the form, / = I . Z It is preferable, then, to introduce the reciprocal of impe- dance, which may be called the admittance of the circuit, or Z As the reciprocal of the complex quantity, Z = r -{- jx, the admittance is a complex quantity also, or Y = g — jh; it con- sists of the component, g, which respresents the coefficient of current in phase with the e.m.f., or the pow ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-14", "section_label": "Chapter 14: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 11605-12682", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "snippets": [ "... PHENOMENA. Symbolic Method. 134. In symbolic representation by complex quantities the transformer problem appears as follows : The exciting current, 700, of the transformer depends upon the primary E.M.F., which dependance can be rep- resented by an admittance, the \" primary admittance,\" °f tne transformer. Fig. 105. The resistance and reactance of the primary and the secondary circuit are represented in the impedance by Z0=r0- jx0, and Zl=rl- j xl . Within the limited range of variation of the magnetic ...", "... hod. 134. In symbolic representation by complex quantities the transformer problem appears as follows : The exciting current, 700, of the transformer depends upon the primary E.M.F., which dependance can be rep- resented by an admittance, the \" primary admittance,\" °f tne transformer. Fig. 105. The resistance and reactance of the primary and the secondary circuit are represented in the impedance by Z0=r0- jx0, and Zl=rl- j xl . Within the limited range of variation of the magnetic density in a constant pot ...", "... er. Fig. 105. The resistance and reactance of the primary and the secondary circuit are represented in the impedance by Z0=r0- jx0, and Zl=rl- j xl . Within the limited range of variation of the magnetic density in a constant potential transformer, admittance and impedance can usually, and with sufficient .exactness, be considered as constant. Let n0 = number of primary turns in series ; #1 = number of secondary turns in series ; a = — = ratio of turns ; Y0 = g0 4- jb0 = primary admittance Exciting cur ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-17", "section_label": "Theory Section 17: Impedance and Admittance", "section_title": "Impedance and Admittance", "kind": "theory-section", "sequence": 17, "number": 17, "location": "lines 6814-7380", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-17/", "snippets": [ "17. IMPEDANCE AND ADMITTANCE 82. In direct-current circuits the most important law is Ohm's law, e -i or e r ir, or r = -.> where e is the e.m.f. impressed upon resistance r to produce current i therein. Since in alternating ...", "... t i therein. Since in alternating-current circuits a current i through a resistance r may produce additional e.m.fs. therein, when apply- a ing Ohm's law, i — - to alternating-current circuits, e is the IMPEDANCE AND ADMITTANCE ' 99 total e.m.f. resulting from the impressed e.m.f. and all e.m.fs. produced by the current i in the circuit. Such counter e.m.fs. may be due to inductance, as self-induc- tance, or mutual inductance, to capacity, chemi ...", "... of e.m.f., ez = ix\\ = reactive component of e.m.f. p 83. Instead of the term impedance z — - with its components, I? the resistance and reactance, its reciprocal can be introduced. e \" z ' which is called the admittance. The components of the admittance are called the conduc- tance and the susceptance. Resolving the current i into a power component i\\ in phase with the e.m.f. and a wattless component iz in quadrature with the e.m.f., th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-10", "section_label": "Chapter 10: F", "section_title": "F", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 8269-10499", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "snippets": [ "... — where z is determined by the mag- netic characteristic of the iron, and the shape of the magnetic and electric circuits, — the impedance is repre- sented, in phase and intensity, by the symbolic expression, Z =^ r ^ jx = ;? sin a — jz cos a ; and the admittance by, K = ^ + y ^ = - sin a + y - cos a = >» sin a + jy cos a. z z The quantities, xr, r, ;r, and y^ gy 6, are, however, not constants as in the case of the circuit without iron, but depend upon the intensity of magnetization, (B, — that is, upon the E ...", "... .M.F., / = effective current, since / V2 = maximum cur- rent, the magnetic flux, ^ IF^ «/V2 (R CR • Substituting this in the equation of the counter E.M.F. of self-induction, ^=V2 7r^«*10-», , J, 27r«^^Z10-» we have E = ; (R hence, the absolute admittance of the circuit is ^= VJM^ = -^ = (R10« a^ E 2irn^N N' , 10» where a = - — - , a constant. Therefore^ the absolute admittance^ y$ of a circuit of neg- ligible resistance is proportional to the magnetic reluctance^ (R, and inversely proportiona ...", "... of the counter E.M.F. of self-induction, ^=V2 7r^«*10-», , J, 27r«^^Z10-» we have E = ; (R hence, the absolute admittance of the circuit is ^= VJM^ = -^ = (R10« a^ E 2irn^N N' , 10» where a = - — - , a constant. Therefore^ the absolute admittance^ y$ of a circuit of neg- ligible resistance is proportional to the magnetic reluctance^ (R, and inversely proportional to the frequency f N, and to the square of the number of tums^ n. 82. In a circuit containing iron, the reluctance, (R, varies with th ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-04", "section_label": "Chapter 5: Single-Phase Induction Motor", "section_title": "Single-Phase Induction Motor", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 8555-10582", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-04/", "snippets": [ "... ll only their component parallel with the primary circuit corres ponds. 61. Hereby the single-phase motor constants are derived from the constants of the same motor structure as polyphase motor. Let, in a polyphase motor: Y = g — jb = primary exciting admittance; 2o = To + Jin = primary self-inductive im- pedance; Z\\ = fi + jxi = secondary self-inductive im- pedance (reduced to the pri- mary by the ratio of turns, in the usual manner}; the characteristic constant of the motor then is: & - y (z„ + zx). (i) ...", "... self-inductive im- pedance; Z\\ = fi + jxi = secondary self-inductive im- pedance (reduced to the pri- mary by the ratio of turns, in the usual manner}; the characteristic constant of the motor then is: & - y (z„ + zx). (i) The total, or resultant admittance respectively impedance of SINGLE-PHASE INDUCTION MOTOR 95 the motor, that is, the joint admittance respectively impedance of all the phases, then is: In a three-phase motor: 7a = 3 Y, Zo° = H Z,, , (2) Zi° = H Zv In a quarter-phase motor: ...", "... mary by the ratio of turns, in the usual manner}; the characteristic constant of the motor then is: & - y (z„ + zx). (i) The total, or resultant admittance respectively impedance of SINGLE-PHASE INDUCTION MOTOR 95 the motor, that is, the joint admittance respectively impedance of all the phases, then is: In a three-phase motor: 7a = 3 Y, Zo° = H Z,, , (2) Zi° = H Zv In a quarter-phase motor: Y° - 2 Y, ] Zo° - H Zo, (3) Z,° = M Z,. 1 In the same motor, as single-phase motor, it is then: at s ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-07", "section_label": "Chapter 7: Admittance, Conductance, Susceftance", "section_title": "Admittance, Conductance, Susceftance", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 3546-3871", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-07/", "snippets": [ "CHAPTER VII. ADMITTANCE, CONDUCTANCE, SUSCEFTANCE. 38. If in a continuous-current circuit, a number of resistances, rj, rj, rg, . . . are connected in series, their joint resistance, Ry is the sum of the individual resistances ^ = ^1 + ^2 + 'a + • • • If, however, a number ...", "... ferable in case of series connection, and the use of the reciprocal term conductance in parallel connections ; therefore, The joint resistance of a number of series -connected resis- tances is equal to the sum of the individual resistances ; the § 30] ADMITTANCE, CONDUCTANCE, SUSCEPTANCE. 53 joint conductance of a number of parallel-connected conduc- tances is equal to the sum of the individual conductances, 39. In alternating-current circuits, instead of the term resistance we have the term impedance , Z = r — ...", "... -connected circuits ; or, in other words, when several currents are pro- duced by the same E.M.F., such as in cases where Ohm's law is expressed in the form, -?• It is preferable, then, to introduce the reciprocal of impedance, which may be called the admittance of the circuit, or Z As the reciprocal of the complex quantity, Z =^ r — jxy the admittance is a complex quantity also, or 64 AL TERN A TING-CURRENT PHENOMENA . [ § 40 it consists of the component g^ which represents the co- efficient of current i ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-13", "section_label": "Chapter 13: Ths Alternating^Cnrrent Traxsfobmer", "section_title": "Ths Alternating^Cnrrent Traxsfobmer", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 12673-14088", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "snippets": [ "... T PHENOMKAA Symbolic Method. 124- In symbolic representation by complex quantities the transformer problem appears as follows : The exciting current, /„, of the transformer depends upon the primary K.M.K., which dcpendance can be rc|> resented by an admittance, the \" primary admittance,\" Y^=^ g^ ■\\- j b^, of the transformer. rig. 9B. The resistance and reactance of the primary and the secondary circuit are represented in the impedance by ^u = r^ —j^ut and Z| = r, —Jx\\- Within the limited range of variatio ...", "... thod. 124- In symbolic representation by complex quantities the transformer problem appears as follows : The exciting current, /„, of the transformer depends upon the primary K.M.K., which dcpendance can be rc|> resented by an admittance, the \" primary admittance,\" Y^=^ g^ ■\\- j b^, of the transformer. rig. 9B. The resistance and reactance of the primary and the secondary circuit are represented in the impedance by ^u = r^ —j^ut and Z| = r, —Jx\\- Within the limited range of variation of the magnetic density ...", "... r. rig. 9B. The resistance and reactance of the primary and the secondary circuit are represented in the impedance by ^u = r^ —j^ut and Z| = r, —Jx\\- Within the limited range of variation of the magnetic density in a constant [iotential transformer, admittance and impedance can usually, and with sufficient exactness, be considered as constant. Let «„ = number of primary turns in series; t, = number of secondary turns in series; a ^ -^ = ratio of turns; ^« =K\" — /''.. = primary admittance ~ i'riiMIJ cuunlt ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-07", "section_label": "Chapter 7: Admittance, Conductance, Susceptance", "section_title": "Admittance, Conductance, Susceptance", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 3132-3576", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-07/", "snippets": [ "CHAPTER VII. ADMITTANCE, CONDUCTANCE, SUSCEPTANCE. 38. If in a continuous-current circuit, a number of resistances, ?\\, r%, r3, . . . are connected in series, their joint resistance, R, is the sum of the individual resistances If, however, a number of resistances are connected ...", "... is preferable in case of series connection, and the use of the reciprocal term conductance in parallel connections ; therefore, The joint resistance of a number of series-connected resis- tances is equal to the sum of the individual resistances ; the ADMITTANCE, CONDUCTANCE, SUSCEPTANCE. 53 joint conductance of a number of parallel-connected conduc~ tances is equal to the sum of the individual conductances. 39. In alternating-current circuits, instead of the term resistance we have the term impedance, Z = r —J ...", "... el-connected circuits ; or, in other words, when several currents are produced by the same E.M.F., such as in cases where Ohm's law is expressed in the form, -I- It is preferable, then, to introduce the reciprocal of impedance, which may be called the admittance of the circuit, or >-*• As the reciprocal of the complex quantity, Z = r —jx, the admittance is a complex quantity also, or Y = g+jb; 54 ALTERNATING-CURRENT PHENOMENA. it consists of the component g, which represents the co- efficient of current i ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "... or and apparent efficiency necessarily are very low. As illustration is shown in Fig. 20 the load curve of a typical 100-hp. 60-cycle 80-polar induction motor (90 revolutions per minute) of the constants: Impressed voltage: ea = 500. Primary exciting admittance: Ya = 0.02 — 0.6 j. Primary self-inductive impedance: Zu = 0.1 + 0.3j. Secondary self-inductive impedance: Zi = 0.1 + 0.3 j. INDUCTION MOTOR 53 As seen, at full-load of 75 kw. output, the efficiency is 80 per cent., which is fair for a slow-spee ...", "... slow-speed motor. But the power-factor is 55 per cent., the apparent efficiency only 44 per cent., and the exciting current is 75 per cent, of full- load current. This motor-load curve may be compared with that of a typical induction motor, of exciting admittance: Y0 = 0.01 -O.lj, given on page 234 of \"Theory and Calculation of Alternating- current Phenomena\" 5th edition, and page 319 of \"Theoretical - LOW 8PEE0 1 1DUCTI0N MOTOR l\\ '-i*i Y.-.02-.SJ Z,-.l+.3j -'I-. 1 — i- m v. / :> -350 ...", "... quadrature with the excitation, which acts as damper against hunting (Danielson motor). 58 ELECTRICAL APPARATUS In the synchronous motor, Fig. 21, D, produced from the induc- tion motor, Fig. 21, C, it is: Let: l'\"» = 8 — jk = primiiry exciting admittance of the induction machine, Z0 = r« -f jxn = primary self-inductive impe- dance, Z\\ = t\\ + jxt = secondary self-inductive im- pedance. Fio. 21. — Sturtiiig of induction motor and synchronous. The secondary resistance, r,, is that of t lie field e ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-35", "section_label": "Chapter 35: Balanced Symmetrical Polyphase Systems", "section_title": "Balanced Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 35, "number": 35, "location": "lines 37453-37957", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-35/", "snippets": [ "... tages are usually called in a three-phase systeni, delta voltage c = Y voltage 448 BALANCED SYMMETRICAL POLYPHASE SYSTEMS 449 That is, all ring voltages are divided, all ring currents multiplied with c; all ring impedances are divided, all ring admittances multiplied with the square of the ratio, c^. For instance, if in a three-phase induction motor with delta- connected circuits, the impedance of each circuit is Z = r -{- jx, and the voltage impressed upon the circuit terminals E, and the motor is sup ...", "... it may not be the same which this circuit would have as independent single- phase circuit. If the branches of the polyphase circuit, which constitute the equivalent single-phase circuits, are electrically or magnetic- ally interlinked, the constants, as admittance, impedance, etc., of the equivalent single-phase circuit often are different from those of the same circuit on single-phase supply, and the poly- phase values then must be used in the equivalent single-phase circuits which replace the polyphase system. ...", "... olyphase system. This is the case in induction machines, in the armatures of synchronous machines, etc., where the phases are in mutual in- duction with each other. Let, in a star or Y-connected three-phase induction motor: Y = g -jb be the exciting admittance and e the impressed voltage per three- phase Y circuit or constituent single-phase circuit. BALANCED SYMMETRICAL POLYPHASE SYSTEMS 455 The exciting current per circuit then is: I = eY or, absolute: i = ey if n = number of turns per circuit, f = ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-01", "section_label": "Chapter 1: Speed Control Of Induction Motors", "section_title": "Speed Control Of Induction Motors", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1368-3542", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-01/", "snippets": [ "... vary relatively little with the magnetic density and thus the current, over a wide range,1 thus may approxi- mately be assumed as constant. That is, the hysteretic con- ductance is proportional to the susceptance : g' = V tan a. ((>) Thus, the exciting admittance, of a closed magnetic circuit of negligible resistance and negligible eddy-current losses, at the frequency of slip, «, is given by: Y' = g' - jb' = V (tan a - j) = - J = (tan a - j) (7) 8 8 8 1 \"Theoiy and Calculation of Al format iri^-rurr^nt Phfj ...", "... 8 8 1 \"Theoiy and Calculation of Al format iri^-rurr^nt Phfjiornwia,\" Chapter XII. 6 ELECTRICAL APPARATUS Assuming tan a = 0.6, which is a fair value for a closed mag- netic circuit of high hysteresis loss, it is: Y' = bg (0.6 - j), the exciting admittance at slip, s. Assume then, that such an admittance, F', is connected in series into the secondary circuit of the induction motor,* for the pur- pose of using the effective resistance of hysteresis, which in- creases with the frequency, to control the motor ...", "... rurr^nt Phfjiornwia,\" Chapter XII. 6 ELECTRICAL APPARATUS Assuming tan a = 0.6, which is a fair value for a closed mag- netic circuit of high hysteresis loss, it is: Y' = bg (0.6 - j), the exciting admittance at slip, s. Assume then, that such an admittance, F', is connected in series into the secondary circuit of the induction motor,* for the pur- pose of using the effective resistance of hysteresis, which in- creases with the frequency, to control the motor torque curve. The total secondary impedance then ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-108", "section_label": "Apparatus Section 2: Induction Machines: Polyphase Induction Motor", "section_title": "Induction Machines: Polyphase Induction Motor", "kind": "apparatus-section", "sequence": 108, "number": 2, "location": "lines 19166-20427", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-108/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-108/", "snippets": [ "... ion machine shall be treated, and the single-phase type discussed only in so far as it differs from the typical polyphase machine. 2. CALCULATION 136. In the polyphase induction motor, Let Y = g — jb = primary exciting admittance, or admit- tance of the primary circuit with open secondary circuit; that is, ge = magnetic power current, be = wattless magnetizing current, where e = counter-generated e.m.f. of the motor; ZQ = r0 + jxQ = primary se ...", "... equently met in poor motors. 141. The shape of the characteristic motor curves depends entirely on the three complex constants, Y, Zi, and ZQ, but is essentially independent of the impressed voltage. Thus a change of the admittance Y has no effect on the char- acteristic curves, provided that the impedances Z\\ and Z0 are 320 ELEMENTS OF ELECTRICAL ENGINEERING changed inversely proportional thereto, such a change merely representing the effect of a ...", "... which characterize the stationary alternating-current transformer on non-inductive load. Instead of conductance g, susceptance 6, resistance r, and react- ance x, as characteristic constants may be chosen: the absolute exciting admittance y = \\/g2 -f- &2; the absolute self-inductive impedance z — \\/r2-}-x2', the power-factor of admittance 0 = g/y, and the power-factor of impedance a = r/z. 142. If the admittance y is reduced rz-fold and the impedance z ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "section_label": "Chapter 14: Dielectric Losses", "section_title": "Dielectric Losses", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "... r. It is then : yA g = -y- = electric conductance kA C = -J- = electrostatic capacity of the layer of dielectric, hence: 2 irfk A b = 2irfC = — J — = capacity susceptance, and (1) 154 AL TERN A TING-C URREN T PHENOMENA Y = g -\\- jh = admittance, thus : Z =y = r — jx = impedance, where: 9 r = ^ = vector resistance (not ohmic resistance, but energy component of impedance, T see paragraph 89.) X = r = vector reactance, and (2) y = y/g^ + &^ = absolute admittance, (z = -y/r^ -\\- x ...", "... Y = g -\\- jh = admittance, thus : Z =y = r — jx = impedance, where: 9 r = ^ = vector resistance (not ohmic resistance, but energy component of impedance, T see paragraph 89.) X = r = vector reactance, and (2) y = y/g^ + &^ = absolute admittance, (z = -y/r^ -\\- x^ = absohite impedance.) If then. El = potential drop across the first, E^ = potential drop across the second layer of dielectric, E = El -\\- Eo = voltage impressed upon the dielectric. (3) The current i, which traverses the dielectric ...", "... i and r^ are negligible compared with Xi and x^, and it is: e P = V = Xi + Xo {xi + 0:2)- ri + Ti (11) Xi + X2 Substituting now for the impedance quantities Z= r — jx, which have no direct physical meaning in the dielectric field, the admittance quantities Y = g -{- jh, which have the physical meaning that g is the effective ohmic conductance, b the capacity susceptance, it is: g negligible compared with h and y, and b = y. Thus, by (2) : . ebM _ 2x/CiC2e ' ~ 61 + 62 ~ C1 + C2 ^ ^ hence p ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... then, El = E = e.m.f. between 0 and 1 in the generator. Ei = jE = e.m.f. between 0 and 2 in the generator. Let 1 1 and 1 2 = currents in 1 and in 2, 7o = current in 0, Z] and Z2 = impedances of lines 1 and 2, Zo = impedance of line 0, Yi and F2 = admittances of circuits 0 to 1, and 0 to 2, /'i and /'2 = currents in circuits 0 to 1, and 0 to 2, E\\ and E'2 = potential differences at circuit 0 to 1, and 0 to 2. it is then, Ii -\\- h -\\- h = 0, or, lo = — {Ii + ^2); that is, 7o is common return of Ii and /j. ...", "... resented by the points of half-axis OB' downward; the complex imaginary or general numbers are represented by the points outside of the coordinate axes. INDEX Absolute values of complex quanti- ties, 37 Actual generated e.m.f., alternator, 272 Admittance, 55 of dielectric, 154 due to eddy currents, 137 to hysteresis, 129 Admittivity of dielectric circuit, 160 Air-gap in magnetic circuit, 119, 132 Ambiguity of vectors, 39 Amplitude, 6, 20 Apparent capacity of distorted wave, 386 efficiency of induc ...", "... requency power and torque with distorted wave, 381 quantities, 180 peak wave. 370 T connections of transformers to six -phase, 430 ^ connection of transformers to six-phase, 429 Drop of voltage in line, 25 Dynamic circuit, 159 Eddy currents, 112 admittance, 137 coefficient, 138 conductance, 137 in conductor, 144 loss with distorted wave, 377 of power, 136 Effective circuit constants. 168 .2, f». &. HI valiK? at wav*-. It in i^olar dia|tmm. «^ Kffi«i««MO^ iff drruit wiith indutrtive induction ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "section_label": "Chapter 30: Quartbr-Fhase System", "section_title": "Quartbr-Fhase System", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... en : £^ = E = E.M.F. between and 1 in the generator. E2 =^ J E = E.M.F. between and 2 in the generator. • Let : Ii and I2 = currents in 1 and in 2, Iq = current in 0, Z, and Za == impedances of lines 1 and 2, Zq = impedance of line 0. K, and Y^ = admittances of circuits to 1, and to 2, // and 73'= currents in circuits to 1, and to 2, ^/and ^2'= potential differences at circuit to 1, and to 2. it is then, 7, + /a + /« = ) ^ or, /o = - (A + ^2) i ^ ^ that is, lo is common return of /i and /]. Further, le ...", "... xponential decrement of the oscillating wave, a the angular decrement of the oscillating wave. The oscillating wave can be represented by the equation In the instance represented by Figs. 181 and 182, we have A = .4, a = .1435, a = 8.2°. Impcdarice and Admittance, 283. In complex imaginary quantities, the alternating wave /* '»\\ s = £\" cos (<^ — cu) is represented by the symbol E — e (cos ci +y sin w) = c^ -\\- je^ . By an extension of the meaning of this symbolic ex- pression, the oscillating wave E=^et~^ ...", "... ance x^ , with an expo- nential decrement a, the apparent impedance, in symbolic expression, is : Z=\\r-x (a +j) +T-^ (- \" +/) } dec a, i. 1 + a- ) + I X =r {'■-\"hTTT^A'-if^)}''''\"' 416 APPENDIX II. [§ 287 and, absolute, «a= Vr«» + x^ Admittance, /= !€\"\"*♦ cos (<^ — w) = current. Then from the preceding discussion, the electromotive force consumed by resistance r, inductive reactance ;r, and capa- city reactance x^y is E = />-«* I cos ( L 1 + a'^ i ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-32", "section_label": "Chapter 32: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 25904-27405", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "snippets": [ "... then : EI = E = E.M.F. between 0 and 1 in the generator. Ez=jE = E.M.F. between 0 and 2 in the generator. Let: ./i and 72 = currents in 1 and in 2, 70 = current in 0, Z-L and Zz = impedances of lines 1 and 2, Z0 = impedance of line 0. Yl and Y2 = admittances of circuits 0 to 1, and 0 to 2, // and //= currents in circuits 0 to 1, and 0 to 2, Eia.-ndE2'= potential differences at circuit 0 to 1, and 0 to 2. it is then, 7, -f 78 + 70 = 0 ) «v or, I0 =-(/; + 72) j that is, 70 is common return of 7: and 72. ...", "... oscillating wave, a the angular decrement of the oscillating wave. The oscillating wave can be represented by the equation £ = ec-**™\" cos ($ — 5). In the instance represented by Figs. 181 and 182> we have A = .4, a = .1435, a = 8.2°. Impedance and Admittance. 312. In complex imaginary quantities, the alternating wave * = e cos (* - ffl) is represented by the symbol E = e (cos w -\\-j sin w) = cos ( ...", "... ting current circuit of resistance r, induc- tive reactance x, and capacity reactance xc , with an expo- nential decrement a, the apparent impedance, in symbolic expression, is : *' 1 +a2/ V 1 +** = ra — jxa; 504 APPENDIX 77. and, absolute, Admittance. 316. Let /=/e-a*cos^_£)==current< Then from the preceding discussion, the electromotive force consumed by resistance r, inductive reactance x, and capa- city reactance xc , is cos $ — r — ax — a*e — sin (<£ — = iza(.~a^ cos (<£ — w + 8), where ta ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-08", "section_label": "Chapter 9: Synchronous Induction Motor", "section_title": "Synchronous Induction Motor", "kind": "chapter", "sequence": 8, "number": 9, "location": "lines 14466-14550", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-08/", "snippets": [ "... , corresponding to a primary circuit, varies from short-circuit at coincidence of the axis of the arma- ture coil with the axis of the primary coil, to open-circuit in quadrature therewith, with the periodicity of the armature speed. That is, the apparent admittance of the primary circuit varies periodically from open-circuit admittance to the short- circuited transformer admittance. At synchronism such a motor represents an electric circuit of an admittance varying with twice the periodicity of the primary frequen ...", "... idence of the axis of the arma- ture coil with the axis of the primary coil, to open-circuit in quadrature therewith, with the periodicity of the armature speed. That is, the apparent admittance of the primary circuit varies periodically from open-circuit admittance to the short- circuited transformer admittance. At synchronism such a motor represents an electric circuit of an admittance varying with twice the periodicity of the primary frequency, since twice per period the axis of the armature coil and that of the ...", "... the axis of the primary coil, to open-circuit in quadrature therewith, with the periodicity of the armature speed. That is, the apparent admittance of the primary circuit varies periodically from open-circuit admittance to the short- circuited transformer admittance. At synchronism such a motor represents an electric circuit of an admittance varying with twice the periodicity of the primary frequency, since twice per period the axis of the armature coil and that of the primary coil coincide. A varying admittance is ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-11", "section_label": "Chapter 12: Frequency Converter Or General Alternating Current Transformer", "section_title": "Frequency Converter Or General Alternating Current Transformer", "kind": "chapter", "sequence": 11, "number": 12, "location": "lines 14897-17124", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-11/", "snippets": [ "... agnetizing current than the closed magnetic circuit stationary transformer, and this again results in general in a higher self- inductive impedance. Thus, the frequency converter and in- duction motor magnetically represent transformers of high ex- citing admittance and high self-inductive impedance. 104. The mutual magnetic flux of the transformer is pro- duced by the resultant m.m.f. of both electric circuits. It is determined by the counter e.m.f., the number of turns, and the frequency of the electric circuit, b ...", "... primary and secondary (thus representing driving by external mechanical power). Let: n0 = number of primary turns in series per circuit; nx = number of secondary turns in series per circuit; a = = ratio of turns; Til Y = g — jb = primary exciting admittance per circuit; where: g = effective conductance; b = susceptance; Zq = r0 + jxo = internal primary self-inductive impedance per circuit, where: r0 = effective resistance of primary circuit; Xq = self-inductive reactance of primary circuit; Zn = n + ...", "... that is, against its torque, by mechanical power. Mostly a synchronous motor is em- ployed, connected to the primary mains, which by overexcitation compensates also for the lagging current of the frequency converter. Let: Y = g — jb = primary exciting admittance per circuit of the frequency converter. Z\\ = fi + j%\\ = internal self-inductive impedance per sec- ondary circuit, at the secondary frequency. Zo = r0 + jxo = internal self-inductive impedance per primary circuit at the primary frequency. a = ratio o ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-02", "section_label": "Chapter 2: Multiple Squirrel-Cage Induction Motor", "section_title": "Multiple Squirrel-Cage Induction Motor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3543-5554", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-02/", "snippets": [ "... as it is most convenient, with the mutual inductive voltage, c, as starting point, to pass to the secondary current by the self-inductive impedance, to the primary current and primary impressed voltage by the primary self-inductive impedance and exciting admittance. In the calculation of multiple squirrel-cage induction motors, it is preferable to introduce the true induced voltage, that is, the voltage induced by the resultant magnetic flux interlinked with the various circuits, which is the resultant of the mutua ...", "... duced to primary circuit. jj? = voltage induced in secondary and primary circuits by mutual magnetic flux, #o = voltage impressed upon primary, /o = primary current, Z0 = r0 + jx0 = primary self -inductive impedance, and Yo = g — jb = primary exciting admittance. *8ee \"Electric Circuits\", Chapter XII. Reactance of Induction Apparatus. 30 ELECTRICAL APPARATUS The leakage reactance, Xj, of the inner squirrel cage is Hint due to the flux produced by the current in the inner squirrel cage, which passes betw ...", "... tities of the innermost squirrel cage be denoted by index 3, those of the middle squirrel cage by 2, of the outer squirrel cage by 1, of the primary circuit by 0, and the mutual inductive quantities without index. Also let: Yo = g — jb = primary exciting admittance. It is then, at slip s: current in the innermost squirrel cage: INDUCTION MOTOR 35 current in the middle squirrel cage: /* — zr> current in the outer squirrel cage: *l — 7~> (2) (3) primary current: /o = U + I* + U + Fo#. (4) The ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-15", "section_label": "Chapter 15: Constant-Voltage Series Operation", "section_title": "Constant-Voltage Series Operation", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 27996-29301", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-15/", "snippets": [ "... ge, ei, and current, ii, thus conductance ff = j^ (1) ei be connected in series into a circuit of supply voltage, eo = nei (2) and each lamp be shunted by a reactance of susceptance, b. In each consuming device, comprising lamp and reactance, the admittance thus is, vectorially, Yi^=g^jb (3) if, then, / = current in the series circuit, the voltage consumed by the device comprising lamp and reactance, thus is in a consuming device, however, in which the lamp is burned out, and only the reactance remains ...", "... is, vectorially, Yi^=g^jb (3) if, then, / = current in the series circuit, the voltage consumed by the device comprising lamp and reactance, thus is in a consuming device, however, in which the lamp is burned out, and only the reactance remains, the admittance is Y2= - jb (5) hence, the voltage, with the entire current, /, passing through the admittance, ¥2^ ^. = f^ = j {■ (6) If, then, of the n series lamps, the fraction, p, is burned out, leaving n(l — p) operative lamps, it is: 300 ELECTRIC CIRCUITS ...", "... d by the device comprising lamp and reactance, thus is in a consuming device, however, in which the lamp is burned out, and only the reactance remains, the admittance is Y2= - jb (5) hence, the voltage, with the entire current, /, passing through the admittance, ¥2^ ^. = f^ = j {■ (6) If, then, of the n series lamps, the fraction, p, is burned out, leaving n(l — p) operative lamps, it is: 300 ELECTRIC CIRCUITS voltage consumed by operative devices: n(l - p)Pi = -JZTjT voltage consumed by devices with b ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-04", "section_label": "Chapter 5: Methods Of Approximation", "section_title": "Methods Of Approximation", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 15156-16482", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-04/", "snippets": [ "... Line. Let I be the distance along the line, from some starting point; E^ the voltage; 7, the current at point I, expressed as vector quantities or general numbers; Zo^ro—jxo, the line impedance per unit length (for instance, per mile); Yo=^go—jhQ = Hne admittance, shunted, per unit length; then, rn is the ohmic effective resistance; .To, the self-inductive reactance; &o, the condensive susceptance, that is, wattless charging current divided by volts, and go = energy component of admit- tance, that is, energy compo ...", "... = energy component of admit- tance, that is, energy component of charging current, divided by volts, per unit length, as, per mile. Considering a line element dl, the voltage, dE, consumed by the impedance is ZQidl, and the current, dl, consumed by the admittance is Y^Edl; hence, the following relations may be WTitten : f =^0/; (1) METHODS OF APPROXIMATION. 205 Differentiating (1), and substituting (2) therein gives — ZoYoE, (3) and from (1) it follows that, r '^ dE .. ''-ZoW ''^ Equation (3) is inte ...", "... B=±VZoYo; (6) hence, from (5) and (4), it follows ^_^j^+\\/z^oi4-^42£-v/za^or, (7) / = .^{4l£ + VZoFoi_,l,,_Vz.F„Zl. (8) Next assume I^Iq, the entire length of line; Z=Zo^o, the total line impedance; , . . . (9) and F=ZoFo, the total line admittance; then, substituting (9) into (7) and (8), the following expressions are obtained : Ei = Ais+^^ + A2i-^^^', /i =^^}Ai£+v^- A.s-^^^] (10) as the voltage and current at the generator end of the line. 139. If now ^0 and (0 respectively are the cur ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-10", "section_label": "Chapter 10: Resistance And Reactance Of Transmission", "section_title": "Resistance And Reactance Of Transmission", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6993-9766", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-10/", "snippets": [ "... rent in the receiver circuit. Thus the change of voltage due to a line of given resistance and reactance depends upon the phase difference in the receiver circuit, and can be varied and controlled by varying this phase difference; that is, by varying the admittance, Y = g — jh, of the receiver circuit. The conductance, g, of the receiver circuit depends upon the consumption of power — that is, upon the load on the circuit — and thus cannot be varied for the purpose of regu- lation. Its susceptance, b, however, can ...", "... same so far as the line is concerned, we need not make any assumption as to whether the wattless part of the . receiver circuit is in shunt, or in series, to the power part. Let Zo = To -{- jxo = impedance of the line; Zo = V ro^ + Xo^', Y = g — jb = admittance of receiver circuit; y = ^g' + b'; Eo = Co -{- je'o = impressed voltage at generator end of line ; Eo - Veo' + eo'2; E ^ e -\\- je' = voltage at receiver end of line; E = Ve2 + e'2. h = H + ji'a = current in the line; /o = -nAo- + io'^. The simple ...", "... ' = voltage at receiver end of line; E = Ve2 + e'2. h = H + ji'a = current in the line; /o = -nAo- + io'^. The simplest condition is the non-inductive circuit. 1. Non-inductive Receiver Circuit Supplied over an Inductive Line 66. In this case, the admittance of the receiver circuit is Y = g, since 6 = 0. We have then current, lo ^ Eg; impressed voltage: Eo ^ E + Zoh = E{1 -|- Zog). Hence — voltage at receiver circuit, ^ ^ Eo ^ Eo I -{-Zog I -\\- gro -{- jgxo' current, .° 1 + Zog 1 + f/ro + jgxo 8 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-09", "section_label": "Chapter 9: Kbsistanci: And Kbactance Of Transmission Iine8", "section_title": "Kbsistanci: And Kbactance Of Transmission Iine8", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 6371-8268", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "snippets": [ "... the receiver circuit. Thus the change of potential due to a line of given re- sistance and inductance depends upon the phase difference in the receiver circuit, and can be varied and controlled by varying this phase difference; that is, by varying the admittance, Y = g + Jb, of the receiver circuit. The conductance, g, of the receiver circuit depends upon the consumption of power, — that is, upon the load on the circuit, — and thus cannot be varied for the purpose of reg- ulation. Its susceptance, by however, ca ...", "... ponents is the same so far as the line is concerned, we need not make any assump- tion as to whether the wattless part of the receiver circuit is in shunt, or in series, to the energy part. Let — ^u = ^o — j^o = impedance of the line ; y = ^ -^-j'b = admittance of receiver circuit ; jE^ = ^^ +j^/ = impressed E.M.F. at generator end of line ; E —, c '\\-jt'' — K.M.F. at receiver end of line; E = V^-'' + e'^\\ I,, == /p +yV = current in the line ; /^ = V/V^ + //*''. The simplest condition is that of a non-ind ...", "... I,, == /p +yV = current in the line ; /^ = V/V^ + //*''. The simplest condition is that of a non-inductive receiver circuit, such as a lighting circuit. 1.) XoH-iudnctivc Receiver Circuit Supplied over an Indue til 'c L inc. 58. In this case, the admittance of the receiver circuit IS F = ^, since ^ = 0. ■§58] RESISTANCE OF TRANSMISSION LINES, 85 We have then — •current, /« = Eg\\ impressed E.M.F., ^^ = ^ + Z^/„ = ^ (1 + Z^g). Hence — E.M.F. at receiver circuit, E = ^ = ^ ; 1 + Z,^ l+^r,-/^:r^ c ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-09", "section_label": "Chapter 9: Resistance And Reactance Of Transmission Lines", "section_title": "Resistance And Reactance Of Transmission Lines", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 5334-6956", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "snippets": [ "... the receiver circuit. Thus the change of potential due to a line of given re- sistance and inductance depends upon the phase difference in the receiver circuit, and can be varied and controlled by varying this phase difference ; that is, by varying the admittance, Y = g -f jb, of the receiver circuit. The conductance, gy of the receiver circuit depends upon the consumption of power, — that is, upon the load on the circuit, — and thus cannot be varied for the purpose of reg- ulation. Its susceptance, b, however, c ...", "... same so far as the line is concerned, we need not make any assump- tion as to whether the wattless part of the receiver circuit is in shunt, or in series, to the energy part. Let— Z0 = r0 —,jx0 = impedance of the line ; z0 = Vr02 + ^2; Y = g -\\-jb = admittance of receiver circuit; y = VFTT2; E0 = e0 -f / ...", "... ing-current circuit of resistance, r, inductive re- actance, X, and condensive reactance, Xc, with an exponential decrement a, the apparent impedance, in symbolic expression, is, Z = I r - X (a - j) + j-q^2(- « - i) I dec a = ra +jXa] and, absolute, Admittance 188. Let / = zc\"*** COS (0 — ^) = current. Then from the preceding discussion, the e.m.f. consumed by re- sistance, r, inductive reactance, x, and condensive reactance, Xe, is E = ie-«* cos { - e)^r — a^ — ^ xA - sin (0 - B) = t^oc\"*** cos ...", "... ») +(''-''^-rf^^') dec a. 189. Thus in complex quantities, for oscillating currents, we have: conductance, a r — ax — g = 1 +a' X, (^-rf^)+(''-\"^-rTT^^')\" susceptance. X — X, b = 1 + a2 (^-i^2)+(^-«^-rf^2^0 1> .admittance, in absolute values. y = Vff* + 6* = V (* - rf^^) '+{r-os- rh^^ 350 ELECTRIC CIRCUITS in symbolic expression, Y = S-3b = J. .2 , a TT • Since the impedance is we have = 7; y = T'> 9 = —i> b = T-v mJ Za ^a ^a that is, the same relations as ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-44", "section_label": "Chapter 4: Distributed Capacity Of High-Potential Transformers", "section_title": "Distributed Capacity Of High-Potential Transformers", "kind": "chapter", "sequence": 44, "number": 4, "location": "lines 23179-23585", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "snippets": [ "... t, and of lesser power. 41. Let then, in the high-potential coil of a high- voltage trans- former, e = the e.m.f. generated per unit length of conductor, as, for instance, per turn; Z = r — ' jx = the impedance per unit length; Y = g — jb = the capacity admittance against ground per unit length of conductor, and Y' = pY= the capacity admittance, per unit length of conductor, between conductor elements distant from each other by unit length, as admittance between successive turns. Y' is assumed to represent the tota ...", "... ge trans- former, e = the e.m.f. generated per unit length of conductor, as, for instance, per turn; Z = r — ' jx = the impedance per unit length; Y = g — jb = the capacity admittance against ground per unit length of conductor, and Y' = pY= the capacity admittance, per unit length of conductor, between conductor elements distant from each other by unit length, as admittance between successive turns. Y' is assumed to represent the total effective admittance representing the capacity between successive turns, success ...", "... jx = the impedance per unit length; Y = g — jb = the capacity admittance against ground per unit length of conductor, and Y' = pY= the capacity admittance, per unit length of conductor, between conductor elements distant from each other by unit length, as admittance between successive turns. Y' is assumed to represent the total effective admittance representing the capacity between successive turns, successive layers, and successive coils, as represented by the condensers C2 and C3 in Fig. 89. The charging current ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "... engineering, however, the capacity effect is small enough to be represented by the approximation of one; or, three condensers shunted across the line. 130. {A) Line capacity represented hy one condenser shunted across middle of line. Let Y = g — jh = admittance of receiving circuit; Z = r -\\- jx = impedance of line; he = condenser susceptance of line. iEo Fig. 101. Denoting in Fig. 101. the e.m.f., and current in receiving circuit by E, 7, the e.m.f. at middle of line by E' , the e.m.f., and current at ...", "... solutions of the general differential equation of the circuit offers sufficient exactness. 133. The impedance of an element, dl, of the line is: Zdl and the voltage, dE, consumed by the current, /, in this line ele- ment dl: JE7 VTJ7 dE = Zldl The admittance of the line element, dl, is: Ydl hence the current, dl, consumed by the voltage, dE, of this line element dl: ,^ ,^„ „ dl = YEdl This gives the two equations of the transmission line: Differentiating the first equation, and substituting therein th ...", "... for the exponential function tlie infinite series: ^^ryyi , , ZYX\" , ZYVZYI^ , Z-^YH\" , ±VzH _ 1 + VZFZ + TT,- ± h, V -r-A V ■■■ e gives: 134. If then : I = k is the total length of line, and Zo = loZ — total line impedance, Fo = loY = total line admittance, the equations of voltage Ei and current Ii at the end k of the line are given by substituting I = lo into equations (8), as: (8) ^x = ^0 j 1 + ^ + . . . } + Zo7o { H- ^'p + . . . /x- /o { 1 + ^ + . . . } + Foi^o { 1 + ^-\" + . . . (9) Since Zq ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-18", "section_label": "Chapter 18: Polyphase Induction Motors", "section_title": "Polyphase Induction Motors", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17717-20445", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-18/", "snippets": [ "... secondary induced e.m.f. (reduced to primary system) is Ei = — se. POLYPHASE INDUCTION MOTORS 211 Let 7o = exciting current, or current through the motor, per primary circuit, when doing no work (at synchronism), and F = g — j6 = primary exciting admittance per circuit = — • We thus have, ge = magnetic power current, ge~ = loss of power by hysteresis (and eddy currents) per primary coil. Hence Poge^ = total loss of power by hysteresis and eddies, as calculated according to Chapter XII. he = magnetizing ...", "... .m.fs. V2 of the po-phases, combined by the parallelogram of m.m.fs.^ If (R = reluctance of magnetic circuit per pole, as discussed in Chapter XII, it is V2 Thus, from the hysteretic loss, and the reluctance, the con- stants, g and h and thus the admittance, Y, are derived. Let To = resistance per primary circuit; Xo = reactance per primary circuit; thus, Zo = To -}- jxo = impedance per primary circuit; ri = resistance per secondary circuit reduced to primary system; Xi = reactance per secondary circ ...", "... . 121. 250 300 350 The impressed e.m.f. is 110 volts between lines, and the motor star connected, hence the e.m.f. impressed per circuit: ~% = 63.5; or^o The constants of the motor are: 63.5. POLYPHASE INDUCTION MOTORS 231 Primary admittance, Y = 0.1 — OAj. Primary impedance, Z = 0.03 + 0.09 j. Secondary impedance, Zi = 0.02 + 0.085 j. In Fig. 120 is shown, with the speed in per cent, of synchronism, as abscissas, the torque in kilogram-meters as ordinates in drawn Hnes, for the values of a ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-12", "section_label": "Chapter 14: Phase Conversion And Single-Phase Generation", "section_title": "Phase Conversion And Single-Phase Generation", "kind": "chapter", "sequence": 12, "number": 14, "location": "lines 17125-18412", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-12/", "snippets": [ "... application as singlc- tuCtKM) motor-starting device, is discussed in Chapter V. Tw.> -mil monoeydic triangles combined give the monocyclic square. Fig. (57. 138. Let then, in the monoeydic square shown diagrammalic- ally in Pig. 67: 1\", = g, — j&i = admittance AC and DB; )\", = j,j — fit = admittance CB and AD: Ye = o* — jb* = admittance of the load on PHASE CONVERSION 217 the monocyclic quadrature voltage, #0 = CD, and current, /o. Denoting then : & = e = supply voltage, AB9 and / = supply current, a ...", "... rting device, is discussed in Chapter V. Tw.> -mil monoeydic triangles combined give the monocyclic square. Fig. (57. 138. Let then, in the monoeydic square shown diagrammalic- ally in Pig. 67: 1\", = g, — j&i = admittance AC and DB; )\", = j,j — fit = admittance CB and AD: Ye = o* — jb* = admittance of the load on PHASE CONVERSION 217 the monocyclic quadrature voltage, #0 = CD, and current, /o. Denoting then : & = e = supply voltage, AB9 and / = supply current, and ?it #« = voltages, /i, /i = currents ...", "... Tw.> -mil monoeydic triangles combined give the monocyclic square. Fig. (57. 138. Let then, in the monoeydic square shown diagrammalic- ally in Pig. 67: 1\", = g, — j&i = admittance AC and DB; )\", = j,j — fit = admittance CB and AD: Ye = o* — jb* = admittance of the load on PHASE CONVERSION 217 the monocyclic quadrature voltage, #0 = CD, and current, /o. Denoting then : & = e = supply voltage, AB9 and / = supply current, and ?it #« = voltages, /i, /i = currents in the two sides of the monocyclic squa ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-114", "section_label": "Apparatus Section 8: Induction Machines: Concatenation of Induction Motors", "section_title": "Induction Machines: Concatenation of Induction Motors", "kind": "apparatus-section", "sequence": 114, "number": 8, "location": "lines 21923-22191", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-114/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-114/", "snippets": [ "... motor equals its exciting current plus the transformed exciting current of the second motor, that is, equals twice the exciting current. 161. Henee, comparing the concatenated couple with a single motor, the primary exciting admittance is doubled. The total 358 ELEMENTS OF ELECTRICAL ENGINEERING impedance, primary plus secondary, is that of both motors, that is, doubled also, and the characteristic constant of the con- catenated couple is thus four ti ...", "... tenated couple with a single motor re- wound for twice the number of poles, that is, one-half speed also, such rewinding does not change the self-inductive impe- INDUCTION MACHINES 359 dance, but quadruples the exciting admittance, since one-half as many turns per pole have to produce the same flux in one-half the pole arc, that is, with twice the density. Thus the character- istic constant is increased fourfold also. It follows herefrom that the c ...", "... .2-0.3-0.4-0.5-0.0-0.7 FIG. 193. — Concatenation of induction motors, speed curves. Two motors coupled in concatenation are in the range from standstill to one-half synchronism approximately equivalent to one motor of twice the admittance, three times the primary impedance, and the same secondary impedance as each of the two motors, or more nearly 2.8 times the primary and 1.2 times the secondary impedance of one motor. Such motor is called the equivalent ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-23", "section_label": "Chapter 23: Synchronizing Alternators", "section_title": "Synchronizing Alternators", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 25135-25681", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-23/", "snippets": [ "... zero line, or real axis of coordinates of the complex representation; and let e = difference of potential at the common busbars of the two alternators; SYNCHRONIZING ALTERNATORS 295 Z = r -^ jx = impedance of the external circuit; Y = 9 ~ jb == admittance of the external circuit; hence, the current in the external circuit is e I = r -\\-jx = e(g - jh). Let El = ei -\\- je'i = ai(cos di + j sin di) = generated e.m.f. of first machine; E2 = 62 -{- je'i ^ a2(cos 02. + j sin ^2) = generated e.m ...", "... achine; E2 = 62 -{- je'i ^ a2(cos 02. + j sin ^2) = generated e.m.f. of second machine; /i ^ ii — ji'i = current of the first machine; Jg = 12 — ji'2 = current of the second machine; Zi == ri + jxi = internal impedance, and Yi = Qi — jh\\ = inter- nal admittance of the first machine; ^2 = ^2 + jxi = internal impedance, and Y2 = ^2 — i&2 = inter- nal admittance of the second machine. Fig. 144. Then, er + e'r = al^• 62^ + e'2^ --^ a2^; Ex = e ■\\- hZi, or ei -\\- je\\ = (e + iiVi + i'lXi) -f j(iiXi — i'\\r^; E ...", "... i'i = current of the first machine; Jg = 12 — ji'2 = current of the second machine; Zi == ri + jxi = internal impedance, and Yi = Qi — jh\\ = inter- nal admittance of the first machine; ^2 = ^2 + jxi = internal impedance, and Y2 = ^2 — i&2 = inter- nal admittance of the second machine. Fig. 144. Then, er + e'r = al^• 62^ + e'2^ --^ a2^; Ex = e ■\\- hZi, or ei -\\- je\\ = (e + iiVi + i'lXi) -f j(iiXi — i'\\r^; E2 = e -{- I2Z2, or 62 + je'2 = (e + ^'2^2 + ^'2a;2) + j(i2X2 — ^''2^2) ; / = /i 4- h, or eg — jeb = (h ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-27", "section_label": "Chapter 27: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 33011-34776", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-27/", "snippets": [ "... is equal to the increase of current, or in other words the higher harmonics of current do work with the same efficiency as the fundamental wave. 265. Fourth Example. — In a small three-phase induction motor, the constants per delta circuit are primary admittance Y = 0.002 — 0.03 j, self-inductive impedance Zo = Zi = 0.6 + 2.4 j,: and a sine wave of e.m.f., eo = 110 volts, is impressed upon the motor. The power output, P, current input, Is, and power-factor, p, as function of the slip, s, are given in the firs ...", "... r as wattless, that is, Eo = llOi -1- 13.23 - 25.35 - 14.77 = eo + Eo\\ GENERAL ALTERNATING WAVES 393 where E^^ = 13.23 - 25.35 - 14.77 = component of impressed e.m.f. of higher frequency. The effective value is E(, = 114.5 volts. The condenser admittance for the general alternating wave is Yc = 0.039 7ljn. Since the frequency of rotation of the motor is small com- pared with the frequency of the higher harmonics, as total impedance of the motor for these higher harmonics can be assumed the stationary i ...", "... or is small com- pared with the frequency of the higher harmonics, as total impedance of the motor for these higher harmonics can be assumed the stationary impedance, and by neglecting the resist- ance we have Z^ = nj„(a;o + Xi) = 4.8 njn The exciting admittance of the motor, for these higher har- monics, is, by neglecting the conductance, 71 = _ ^ = - ^M n n and the higher harmonics of counter e.m.f., E^ = — ^• . 2 Thus we have, current input in the condenser, L - EoYc = + 4.28ii + 1.54 i3 - 4.93^5 - ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-15", "section_label": "Chapter 15: Induction Motob", "section_title": "Induction Motob", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 14919-17024", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "snippets": [ "... E.M.F. (reduced to primary system) is -^1 = — se. 210 AL TERN A TING-CURRENT PHENOMENA, [ § 142 Let lo = exciting current, or current passing through the motor, per primary circuit, when doing no work (at synchronism), and Y ^=^g -\\-jb = primary admittance per circuit = — . c It is thus ge = magnetic energy current, ge^ = loss of power by hysteresis (and eddy currents) per primary coil. Hence pgt^= total loss of energy by hysteresis and eddys, as calculated according to Chapter X. b^= magnetizing ...", "... ^ the /-phases, combined by the parallelogram of M.M.Fs.* If (R = reluctance of magnetic circuit per pole, as dis- cussed in Chapter X., it is V2 nbe = (R<^. Thus, from the hysteretic loss, and the reluctance, the constants, g and b, and thus the admittance, K are derived. Let r = resistance per primary circuit ; z = reactance per primary circuit ; thus, Z '=^ r — y .r = impedance per primary circuit ; * Complete discussion hereof, see Chapter XXIII. § 143J INDUCTION MOTOR, 211 ri = resistance pe ...", "... or, of 900 revolutions synchronous speed, 8 poles, fre- quency of 60 cycles. The impressed E.M.F. is 110 volts between lines, and the motor star-connected, hence the E.M.F, impressed per circuit : 110 v5 The constants of the motor are : I'rimary admittance, K Primary impedance, Secondary impedanc r = .1 -I- .4 Z =.03 -.01 Z, = .02 — .086/ 232 ALTERNATTNG-CURRENT PHENOMENA. [§158 In Fig. 107 is shown, with the speed in per cent of synchronism, as abscissae, the torque in kilogrammetres, as ord ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-17", "section_label": "Chapter 17: Synchbonizino Aiitebkatobs", "section_title": "Synchbonizino Aiitebkatobs", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 18829-19345", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-17/", "snippets": [ "... o line, or real axis of coordinates of the complex method ; and let — 252 AL TERN A TING-CURRENT PHENOMENA, [§ 1 74 e = difference of potential at the common bus bars of the two alternators, Z ^= r — jx = impedance of external circuit, K=s^»--|-y^ = admittance of external circuit; hence, the current in external circuit is /- —JX Let £i = fi —/ ^1 = ^1 = 1 — j sin £>i) = induced E.M.F. of first machine ; £2 = e.2 — _/>•/ = a2 (cos w2 — j sin w2) = induced E.M.F. of sec- ond machine ; /! = /! -f-//i' = ...", "... machine ; £2 = e.2 — _/>•/ = a2 (cos w2 — j sin w2) = induced E.M.F. of sec- ond machine ; /! = /! -f-//i' = current of first machine ; /2 = /2 -j-yY2' = current of second machine ; Z^ = T! — jxi = internal impedance, and Yv = gi -\\- jbl = inter- nal admittance, of first machine ; Z2 = r2 — jxz = internal impedance, and K2 =gz ~\\~ jb the impedances divided, the admittances multiplied with I -) . This reduction of the constants of all circuits to the same number of effective turns is convenient by eliminating constant factors from the equations, and so permit- ting a direct comparison. When speaking, therefore, in (he ...", "... : #i = ZJi + Z' (/! + U cos r) - jSZ\"/o sin r. (6) In a structure with uniformly distributed winding, as used in induction motors, etc., Z' = Z\" = Z, that is, the exciting im- pedance is the same in all directions. Z is the reciprocal of the \"exciting admittance,\" Y of the in- duction-motor theory. In the most general case, of a motor containing n circuits, of which some are revolving, some stationary, if: l$k, hy Zk = impressed e.m.f., current and self-inductive im- pedance respectively of any circuit, fc. ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3721-4369", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-06/", "snippets": [ "... ent and the maximum value of transient voltage: '\" \\l^- (9) v/ U V c -^ therefore is of the nature of an impedance z^^ and is called the natural impedance, or the surge im'pedance, of the circuit ; and Ic its reciprocal, \\ j = Vq, is the natural admittance, or the surge admittance, of the circuit. 62 ELECTRIC DISCHARGES, WAVES AND IMPULSES. The maximum transient voltage can thus be calculated from the maximum transient current: eo = ^0 y g = ^'o^Jo, (10) and inversely, fc ^0 = eo y Y = eo2/o. (11 ...", "... of transient voltage: '\" \\l^- (9) v/ U V c -^ therefore is of the nature of an impedance z^^ and is called the natural impedance, or the surge im'pedance, of the circuit ; and Ic its reciprocal, \\ j = Vq, is the natural admittance, or the surge admittance, of the circuit. 62 ELECTRIC DISCHARGES, WAVES AND IMPULSES. The maximum transient voltage can thus be calculated from the maximum transient current: eo = ^0 y g = ^'o^Jo, (10) and inversely, fc ^0 = eo y Y = eo2/o. (11) This relation is very ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "... \"^^0 (1) where Iq = maximum value of transient current, 60 = maximum value of transient voltage. This gives the relation between Bq and Iq, ^^ = Jl ,^ = 1, (2) where Zq is called the natural impedance or surge impedance, 2/0 the natural or surge admittance of the circuit. As the maximum of current must coincide with the zero of voltage, and inversely, if the one is represented by the cosine function, the other is the sine function; hence the periodic com- ponents of the transient are ii = Iq cos (0 — 7) ...", "... Xo (40) and the natural impedance of the line then becomes, in velocity measure, Zq =v/ Co L - ^ - ^ Co 2/0 (41) where eo = maximum voltage, io = maximum current. That is, the natural impedance is the inductance, and the natural admittance is the capacity, per velocity unit of length, and is the main characteristic constant of the line. The equations of the current and voltage of the line oscillation then consist, by (19), of trigonometric terms cos (f) cos CO, sin 0 cos CO, cos (f) sin ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3287-3955", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "snippets": [ "... en the maximum transient current and the maximum transient voltage: v/: -^ therefore is of the nature of an impedance z0, and is called the natural impedance, or the surge impedance, of the circuit ; and fc its reciprocal, V/y = yo, is the natural admittance, or the surge T J j admittance, of the circuit. 62 ELECTRIC DISCHARGES, WAVES AND IMPULSES. The maximum transient voltage can thus be calculated from the maximum transient current: #0 = 'Z'O V/ 7> = i&Qj (10) and inversely, /C io = eo y j = e ...", "... nd the maximum transient voltage: v/: -^ therefore is of the nature of an impedance z0, and is called the natural impedance, or the surge impedance, of the circuit ; and fc its reciprocal, V/y = yo, is the natural admittance, or the surge T J j admittance, of the circuit. 62 ELECTRIC DISCHARGES, WAVES AND IMPULSES. The maximum transient voltage can thus be calculated from the maximum transient current: #0 = 'Z'O V/ 7> = i&Qj (10) and inversely, /C io = eo y j = e02/o. (11) This relation is very ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3956-4744", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "snippets": [ "... Lio2 _ Ceo2 \"2\" ~2~' where i0 = maximum transient current, e0 = maximum transient voltage. This gives the relation between eQ and io, e0 V/L_ 1 i-0 = \\C-ZQ-yQ' where ZQ is called the natural impedance or surge impedance, y0 the natural or surge admittance of the circuit. As the maximum of current must coincide with the zero of voltage, and inversely, if the one is represented by the cosine function, the other is the sine function; hence the periodic com- ponents of the transient are ii = IQ cos ( — 7 ...", "... natural impedance of the line then becomes, in velocity measure, 4 / LQ T 1 1 ^O /A1\\ z° = V r = L° = T = ?T = T (41) ^o ^o 2/o ^o where e0 = maximum voltage, i0 = maximum current. That is, the natural impedance is the inductance, and the natural admittance is the capacity, per velocity unit of length, and is the main characteristic constant of the line. The equations of the current and voltage of the line oscillation then consist, by (19), of trigonometric terms cos 0 cos co, sin 0 cos cu, cos 0 sin co, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-16", "section_label": "Chapter 16: Power, And Double-Frequency Quantities In", "section_title": "Power, And Double-Frequency Quantities In", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 16077-16520", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-16/", "snippets": [ "... absolute values of potential (with regard to any reference point chosen as coordi- nate center), and their connection the difference of potential in phase and intensity. Algebraically these vectors are represented by complex quan- tities. The impedance, admittance, etc., of the circuit is a com- plex quantity also, in symbolic denotation. Thus current, voltage, impedance, and admittance are related by multiplication and division of complex quantities in the same way as current, voltage, resistance, and conductance ...", "... erence of potential in phase and intensity. Algebraically these vectors are represented by complex quan- tities. The impedance, admittance, etc., of the circuit is a com- plex quantity also, in symbolic denotation. Thus current, voltage, impedance, and admittance are related by multiplication and division of complex quantities in the same way as current, voltage, resistance, and conductance are related by Ohm's law in direct-current circuits. In direct-current circuits, power is the product of current into volta ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-36", "section_label": "Chapter 36: Three-Phase System", "section_title": "Three-Phase System", "kind": "chapter", "sequence": 36, "number": 36, "location": "lines 37958-38392", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-36/", "snippets": [ "... Let E = e.m.f. between branches 1 and 2 of a three-phaser. Then e E = e.m.f. between 2 and 3, €^E = e.m.f. between 3 and 1; where e — v^ = —-^ . Let Zi, Z2, Z3 = impedances of the lines issuing from generator terminals 1, 2, 3, and 1^1, Yo, Y3 = admittances of the consumer circuits con- nected between lines 2 and 3, 3 and 1, 1 and 2. If then, Ii, 1 2, 1 3, are the currents issuing from the generator termi- nals into the lines, it is, Ix + h + h = 0. (1) If, I'l, I'l, I's = currents through the admittanc ...", "... mittances of the consumer circuits con- nected between lines 2 and 3, 3 and 1, 1 and 2. If then, Ii, 1 2, 1 3, are the currents issuing from the generator termi- nals into the lines, it is, Ix + h + h = 0. (1) If, I'l, I'l, I's = currents through the admittances, Fi, ¥2, Y3, ' from 2 to 3, 3 to 1, 1 to 2, it is, h = // - /'2, or, h + /'2 - /'a = 0 'h = I'l - 'I'z, or, 72 + I'z - /'i = 0 [ (2) 73=>2-i'x, or, /3 + h-r2 = 0 457 458 ALTERNATING-CURRENT PHENOMENA These three equations (2) added, give (1) as ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... magnetic hysteresis, cause an advance of phase of the current by an a?tgle of advanccy p ; but, unlike hysteresis, eddy currents in general do not dis- tort the current wave. The angle of advance of phase due to eddy currents is, y where y = absolute admittance of the circuit, g = eddy current conductance. While the equivalent conductance, gy due to eddy cur- rents, is a constant of the circuit, and independent of E.M.F., frequency, etc., the loss of power by eddy currents is proportional to the square of the ...", "... constants of the circuit, independent of E.M.F. and fre- quency. The E.M.F. is obviously inversely proportional to the frequency. The true static dielectric hysteresis, observed by Arno as proportional to the 1.6*** power of the density, will enter the admittance and the impedance as a term variable and dependent upon E.M.F. and frequency, in the same manner as discussed in the chapter on magnetic hysteresis. To the magnetic hysteresis corresponds, in the electro- static field, the static component of dielectric ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "section_title": "Dibtbisnted Capacity, Inductance, Besistance, And", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "... owever, the ca- pacity effect is small enough to be represented by the approx- imation of one ; viz., three condensers shunted across the line. 104. A.) Line capacity represented by one condetiser shunted across middle of line. Let — Y == g -{- j'b = admittance of receiving circuit; z =i r — j X = impedance of line ; be = condenser susceptance of line. §105] DISTRIBUTED CAPACITY. 15S Denoting, in Fig. 84, the E.M.F., viz., current in receiving circuit by E^ /, the E.M.F. at middle of line by E\\ the E. ...", "... hase by any desired angle) may be given at the terminals of receiving cir- cuit. To be determined are the E.M.F. and current at any point of the line ; for instance, at the generator terminals. Or, Zi = ri — y xi ; the impedance of receiver circuit, or admittance, and E.M.F\"., E^, at generator terminals iare given. Current and E.M.F\\ at any point of circuit to be determined, etc. 109. Counting now the distance, x, from a point, 0, of the line which has the E.M.F., ^\\ = ^1 +/^i'> and the current : /i = /'i + ji ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-29", "section_label": "Chapter 29: Thbkb-Fhase System", "section_title": "Thbkb-Fhase System", "kind": "chapter", "sequence": 29, "number": 29, "location": "lines 27053-27500", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-29/", "snippets": [ "... .F. between branches 1 and 2 of a three-phasen Then : c ^s = E.M.F. between 2 and 3, ^ E= E.M.F. between 3 and 1, where, e = \"v^i = — — \"^ — - . Let Zi, Z2, Zj = impedances of the lines issuing from genera- tor terminals 1, 2, 3, and Fj, Y^, Yz = admittances of the consumer circuits con- nected between lines 2 and 3, 3 and 1, 1 and 2. If then, Ii, /a, /j, are the currents issuing from the generator termi- nals into the lines, it is, /i+/a + /8 = 0. (1) §263] TIJKEE-P/IASE SYSTEM, 391 If I{,hyU = ...", "... ected between lines 2 and 3, 3 and 1, 1 and 2. If then, Ii, /a, /j, are the currents issuing from the generator termi- nals into the lines, it is, /i+/a + /8 = 0. (1) §263] TIJKEE-P/IASE SYSTEM, 391 If I{,hyU = i'= currents flowing through the admittances Yiy 5, la, from 2 to 3, 3 to 1, 1 to 2, it is, I^^U-J^. or, /i + /2'-// = 0] /o = //-//, or, /« + /3'-// = 0\" (2) /, = //_//, or, /8 + y/~/3' = oJ These three equations (2) added, give (1) as dependent equation. At the ends of the lines 1, 2, 3, i ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-12", "section_label": "Chapter 12: Power, And Double Frequency Quantities In General", "section_title": "Power, And Double Frequency Quantities In General", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 9381-9740", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "snippets": [ "... abso- lute values of potential (with regard to any reference point chosen as co-ordinate center) and their connection the dif- ference of potential in phase and intensity. Algebraically these vectors are represented by complex quantities. The impedance, admittance, etc., of the circuit is a complex quantity also, in symbolic denotation. Thus current, E.M.F., impedance, and admittance are related by multiplication and division of complex quantities similar as current, E.M.F., resistance, and conductance are relate ...", "... if- ference of potential in phase and intensity. Algebraically these vectors are represented by complex quantities. The impedance, admittance, etc., of the circuit is a complex quantity also, in symbolic denotation. Thus current, E.M.F., impedance, and admittance are related by multiplication and division of complex quantities similar as current, E.M.F., resistance, and conductance are related by Ohms law in direct current circuits. In direct current circuits, power is the product of cur- rent into E.M.F. In alt ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "... g, however, the ca- pacity effect is small enough to be represented by the approx- imation of one ; viz., three condensers shunted across the line. 109. A.} Line capacity represented by one condenser shunted across middle of line. Let — Y = g + j b = admittance of receiving circuit ; z = r — j x = impedance of line ; be = condenser susceptance of line. DISTRIBUTED CAPACITY. 161 Denoting, in Fig. 84, the E.M.F., viz., current in receiving circuit by £, It the E.M.F. at middle of line by £', the E.M.F ...", "... in phase by any desired angle) may be given at the terminals of receiving cir- cuit. To be determined are the E.M.F. and current at any point of the line ; for instance, at the generator terminals. Or, Zl=rl— JXl ; the impedance of receiver circuit, or admittance, and E.M.F., E0, at generator terminals are given. Current and E.M.F. at any point of circuit to be determined, etc. 114. Counting now the distance, x, from a point, 0, of the line which has the E.M.F., •Ei = e\\ + Je\\i and the current : /i = i\\ +///, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-15", "section_label": "Chapter 15: The General Alternating-Current Transformer Or Frequency Converter", "section_title": "The General Alternating-Current Transformer Or Frequency Converter", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 12683-13648", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "snippets": [ "... and secondary (thus representing driving by ex- ternal mechanical power). Let «0 = number of primary turns in series per circuit ; /?! = number of secondary turns in series per circuit ; a = — = ratio of turns ; «i Y0 =£\"0 H~./A) = primary exciting admittance per circuit; where gQ = effective conductance ; b0 = susceptance ; Z0 = r0 —jx0 = internal primary self-inductive impedance per circuit, where r0 = effective resistance of primary circuit ; jr0 = reactance of primary circuit ; Zu = TI — jxv = ...", "... hat is, against its torque, by mechanical power. Mostly a synchronous motor is employed, connected to the primary mains, which by over-excitation compensates also for the lagging current of the frequency converter. Let, Y0 = g0 +j&0 = primary exciting admittance per circuit of the frequency converter. Z^ = rt —jx^— internal self inductive impedance per secondary circuit, at the secondary frequency. ALTERNATING-CURRENT TRANSFORMER. 233 Z^ = r0 — jx^ = internal self inductive impedance per primary circuit at ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-31", "section_label": "Chapter 31: Three-Phase System", "section_title": "Three-Phase System", "kind": "chapter", "sequence": 31, "number": 31, "location": "lines 25598-25903", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-31/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-31/", "snippets": [ "... Let: E — E.M.F. between branches 1 and 2 of a three-phaser. Then: « E = E.M.F. between 2 and 3, (*£= E.M.F. between 3 and 1, where, e= ^1= ~ - Let ZD Z2, Zs = impedances of the lines issuing from genera- tor terminals 1, 2, 3, and Yl} Y2, Ys = admittances of the consumer circuits con- nected between lines 2 and 3, 3 and 1, 1 and 2. Jf then, ID It, /8, are the currents issuing from the generator termi- nals into the lines, it is, /I + /2 + /3 = 0. (1) THREE-PHASE SYSTEM. 479 If //, 72', 7/ = curren ...", "... ts con- nected between lines 2 and 3, 3 and 1, 1 and 2. Jf then, ID It, /8, are the currents issuing from the generator termi- nals into the lines, it is, /I + /2 + /3 = 0. (1) THREE-PHASE SYSTEM. 479 If //, 72', 7/ = currents flowing through the admittances Y1, F2, F3, from 2 to 3, 3 to 1, 1 to 2, it is, /! = /,'-/,', or, /1 + /2'_/3' = Ol >,->/-/.', or, /2 + /3'-7/ = o[ (2) >3 = //->/, or, /3 + >1/-// = OJ These three equations (2) added, give (1) as dependent equation. At the ends of the lines 1, 2, ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-05", "section_label": "Chapter 6: Induction-Motor Regulation And Stability", "section_title": "Induction-Motor Regulation And Stability", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 10583-12397", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-05/", "snippets": [ "... is in- creased, that is, the motor characteristic made inferior to that given at constant voltage supply, the more so the higher the voltage drop in the supply circuit. Assuming then a three-phase motor having the following con- stants: primary exciting admittance, Y = 0.01 — 0.1 j; primary self-inductive impedance, Z0 = 0.1 + 0.3 j; secondary self -induc- 123 124 ELECTRICAL APPARATUS tive impedance, Z, = 0.1 + 0.3 j; supply voltage, e0 = 110 volts, and rated output, 5000 waits per phase. Assuming this mo ...", "... ism with smaller motors of good effi- ciency. Any value of torque between the starting torque and the maximum torque is reached at two different speeds. Thus in a three-phase motor having the following constants: impressed e.m.f., eg = 110 volts: exciting admittance, 1\" ~ 0.01 — OAj; primary impedance, Zv = 0.1+ 0.3 j, and secondary impedance, Z\\ = 0.1 + 0.3 j, the torque of 5.5 synchronous kw. is reached at. 54 per cent, of synchronism and also at the speed of 94 per cent, of synchronism, as seen in Fig. 51. When ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-07", "section_label": "Chapter 7: Shaping Of Waves : General", "section_title": "Shaping Of Waves : General", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 12222-12961", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-07/", "snippets": [ "... 100 ohms = re- 122 ELECTRIC CIRCUITS sistance in series to the condenser, the impedance of this circuit, for the n*^ harmonic, would be rz -^ inrk 1000. .-V Z„ = r-j- = 100--^j (7) or, absolute, the impedance. Zn = 1000^^ + 0.01 (8) and, the admittance, _ 0.001 n . . ^'^ \"\" Vl + 0.01 n^ ^ ^ and therefore, the multiplying factor, ^ _yn _ 1.005 n . J — yi Vl + 0.01 n« this gives, for n f n / 1 1.0 13 8.0 3 2.9 15 8.4 5 4.5 25 9.3 7 5 ...", "... 33ii + 0.005 13 + 0.0523 + 0.0426 } SHAPING OF WAVES 123 (where the indices indicate the order of the harmonics) of ejffect- ive value e = VeOO^ + 182 + 122 + 92 + 42 + 22 + 32 + 302 + 242 = 601.7 is impressed upon the condenser resistance of the admittance, ynj the current wave is i = 0.603 { 1 + 0.0878 + 0.09b + 0.0877 + 0.04459 + 0.0247ii + 0.04,3 + 0.4623 + 0.3726 } = 0.603 X 1.173 = 0.707 while with a sine wave of voltage, of 60 = 601.7, the current would be io = 0.599, giving a ratio ^ = 1 ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-12", "section_label": "Chapter 12: Reactance Of Induction Apparatus", "section_title": "Reactance Of Induction Apparatus", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 22634-23465", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-12/", "snippets": [ "... secondary circuit, which supplies power to its external circuit. For convenience, we may assune the secondary circuit as re- duced to the primary circuit by the ratio of turns, that is, assume ratio of turns 1 -^ 1. Let Fo = 17 - j6 = primary exciting admittance; Zo = ro+ jxo = primary self-inductive impedance; Zi = ri + jxi = secondary self-inductive impedance (reduced to the primary). The transformer thus comprises three magnetic fluxes: the mutual magnetic flux, $, which, being interlinked with primary an ...", "... s outside of the secondary circuit, the re- mainder, ^' = ^ — ^'i, passes through the secondary circuit and corresponds to ri/i. 118. Appljdng this to the polyphase induction motor with single squirrel-cage secondary. Let Yo — g — jb = primary exciting admittance; Zo = ro + jxo = primary self-inductive impedance; Zi = ri + jxi = secondary self-inductive impedance at full frequency, reduced to the primary. Let Pi = the true induced voltage in the secondary, at full frequency, corresponding to the magnetic fl ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... nd current (differing in phase by any desired angle) may be given at the terminals of the receiving circuit. To be determined are the e.m.f. and current at any point of the line, for instance, at the generator terminals; or the impedance, Zt = rl - jxv or admittance, Yl = g1 + jblt of the receiver circuit, and e.m.f., E0, at generator terminals are given; the current and e.m.f. at any point of circuit to be deter- mined, etc. 7. Counting- now the distance, I, from a point 0 of the line which has the e.m.f. + je, ...", "... 7 , E are then given by LONG-DISTANCE TRANSMISSION LINE 291 • = \\ and v f )*~ o V |) * +^ o V f)£~a' (cos fti + j sin ~ Sn (26) 10. Assume that the character of the load, that is, the impe- 771 T dance, — -1 =Z.=r,—/jx., or admittance, 77 =F= — = &+$*, Ti • i i of the receiving circuit and the voltage E0 at the generator end of the circuit be given. Let /0 = length of circuit, and counting distance I from the generator end, for I = 0 we have E = E- this substituted in equatio ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-01", "section_label": "Chapter 1: The General Number", "section_title": "The General Number", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 915-3491", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-01/", "snippets": [ "... al diagrams by general numbers, as the polar diagram of alternating currents, those quantities, which are vectors in the polar diagram, as the current, voltage, etc., are represented by dotted capitals: E, I, while those general numbers, as the impedance, admittance, etc. , which appear as operators, that is, as multiphers of one vector, for instance the current, to get another vector, the voltage, are represented algebraically by capitals without dot: Z = r-jx = impedance, etc. This Hmitation of calculation with t ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... + ^/o 1+- ZY + F^oU+^^ (1) where Eo, h are voltage and current, respectively at the step- down end, El, I\\ at the step-up end of the line; and Z = r—jx = Q^—\\Zbj is the total line impedance; Y = g — jh= —0.0012/ is the total shunted line admittance. Herefrom follow the numerical values : ZY (60-135.f)(-0.0012i) ■^2 2 = 1 - 0.036./- 0.081 = 0.919 - 0.036/; ZY 1+- g- = 1 - 0.012/- 0.027 = 0.973 - 0.012/; ryi ZY Z 14--,- -»4'' = (60- 135/) (0.973 -0.012/) = 58.4-0.72/- 131.1/- ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-107", "section_label": "Apparatus Section 1: Induction Machines: General", "section_title": "Induction Machines: General", "kind": "apparatus-section", "sequence": 107, "number": 1, "location": "lines 18949-19165", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-107/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-107/", "snippets": [ "... ses as the primary, or of the ratio of transformation 1 to 1, by multiplying all secondary cur- rents and dividing all secondary e.m.fs. by the ratio of turns, multiplying all secondary impedances and dividing all secondary admittances by the square of the ratio of turns, etc. Thus in the following under secondary current, e.m.f., impe- dance, etc., shall always be understood their values reduced to the primary, or corresponding to a ratio of turns 1 t ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-110", "section_label": "Apparatus Section 4: Induction Machines: Induction Generator", "section_title": "Induction Machines: Induction Generator", "kind": "apparatus-section", "sequence": 110, "number": 4, "location": "lines 21158-21588", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-110/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-110/", "snippets": [ "... nerate. If the power-factor of the external circuit is lower than that of the induction generator, the latter excites and its voltage rises until by saturation of its magnetic circuit and the consequent increase of exciting admittance, that is, decrease of internal power-factor, its power-factor has fallen to equality with that of the external circuit. INDUCTION MACHINES 345 In this respect the induction generator acts like the direct- current shunt ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-112", "section_label": "Apparatus Section 6: Induction Machines: Phase Converter", "section_title": "Induction Machines: Phase Converter", "kind": "apparatus-section", "sequence": 112, "number": 6, "location": "lines 21647-21812", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-112/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-112/", "snippets": [ "... e secondary or armature, and from the secondary to the ter- tiary or generator circuit. Thus, in a quarter-phase motor connected to single-phase mains with one of its circuits, if Y = g — jb = primary polyphase exciting admittance, ZQ = TQ -f- JXQ = self -inductive impedance per primary or ter- tiary circuit, Zi = ri + jxi = resultant single-phase self-inductive impe- dance of secondary circuits. Let e = e.m.f. generated by the mutual flux and Z ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-14", "section_label": "Theory Section 14: Rectangular Coordinates", "section_title": "Rectangular Coordinates", "kind": "theory-section", "sequence": 14, "number": 14, "location": "lines 5264-5831", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-14/", "snippets": [ "... ns 20:1. The primary impedance is ZQ = 2 -f 5 j, the secondary impedance, Zi = 0.004 + 0.01 j, and the exciting current at er = 2000 volts counter-generated e.m.f. is 70o = 0.3 — 0.4 j; thus the exciting admittance, Y = ^ = (0.15 - 0.2 j)10~3. 6 What is the secondary current and secondary terminal voltage and the primary current if the total impedance of the secondary circuit (internal impedance plus external load) consists of (a ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-20", "section_label": "Theory Section 20: Nomenclature", "section_title": "Nomenclature", "kind": "theory-section", "sequence": 20, "number": 20, "location": "lines 7991-8291", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-20/", "snippets": [ "... erence Electromotive force Current Ampere Electrical R,r Resistance Ohm Electrical x Reactance Ohm Electrical Z,z... Impedance Ohm Electrical a Conductance Mho Electrical b Susceptance Mho Electrical Y,y p Admittance Resistivity Mho Ohm-centimeter Electrical Electrical 7 $ Conductivity Magnetic flux Mho-centimeter Line; kiloline; megaline Electrical Magnetic £....... H Magnetic density Magnetic field inten- Lines per cm.2; ki ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-09", "section_label": "Chapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "section_title": "Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 4674-6992", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-09/", "snippets": [ "... undamental laws of alternating- current circuits, when expressed in their complex form, E = ZI, or, 7 = YE, and \"EE = 0 in a closed circuit, S/ = 0 at a distributing point, where E, I, Z, Y, are the expressions of e.m.f., current, impe- dance, and admittance in complex quantities — these values representing not only the intensity, but also the phase, of the alternating wave — we can now — by application of these laws, and in the same manner as with continuous-current circuits, keeping in mind, however, that E ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-13", "section_label": "Chapter 13: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 13484-14333", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-13/", "snippets": [ "... hysteresis, cause an advance of phase of the current by an angle of advance, /3; but unhke hysteresis, eddy currents in general do not distort the current wave. The angle of advance of phase due to eddy currents is sin /3 = ^ » y where y = absolute admittance of the circuit, g = eddy current conductance. While the equivalent conductance, g, due to eddy currents, is a constant of the circuit, and independent of e.m.f., frequency, etc., the loss of power by eddy currents is proportional to the square of the e. ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-19", "section_label": "Chapter 19: Induction Generators", "section_title": "Induction Generators", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 20446-21537", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-19/", "snippets": [ "... acteristic curves of the constant-speed induction generator, due regard has to be taken of the decrease of frequency with increase of load, or what may be called the slip of frequency, s. Let, in an induction generator, Yo = go — jho = primary exciting admittance, Zo = To -\\- jxo = primary self-inductive impedance, Zi = ri + jxi = secondary self-inductive impedance, reduced to primary, all these quantities being reduced to the frequency of synchronism with the speed of the machine, /. Let e = generated em.f., ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-08", "section_label": "Chapter 8: Capacity", "section_title": "Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3872-6370", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "snippets": [ "... laws of alternating-current circuits, or, as expressed in their com- plexform. ^ _^ ' „_ E -= ZJ^ or, / = \\Ey and S-f = in a closed circuit, 5/ = at a distributing point, where J?, /, Z^ V, are the expressions of E.M.F*., current, impedance, and admittance in complex quantities, — these laws representing not only the intensity, but also the phase, of the alternating wave, — we can now — by application of these laws, and in the same manner as with continuous- current circuits, keeping in mind, however, that ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-14", "section_label": "Chapter 14: The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "section_title": "The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14089-14918", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "snippets": [ "... etween primary and secondary (thus representing driving by ex- ternal mechanical power). Let Wo = number of primary turns in series per circuit ; fix = number of secondary turns in series per circuit ; a = — = ratio of turns ; Vq = go +y^o = primary admittance per circuit ; where go '= effective conductance ; do = susceptance ; Zq == Tq — jXo = internal primary impedance per circuit, where To = effective resistance of primary circuit ; Xo = reactance of primary circuit ; Zii = ri — jxi = internal seco ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-19", "section_label": "Chapter 19: Commutatob Motobs", "section_title": "Commutatob Motobs", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 21339-22387", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "snippets": [ "... m, the mag- netism is represented by the primary induced E.M.P\\, E =^ — e\\ the secondary induced E.M.F. : hence, if V2 Zi = /*! — j Xx = secondary impedance reduced to primary circuit, Z =^ r — j X = primary impedance, Y = g -\\- jb = primary admittance, it is, secondary current, r _ E, _ e 1_±j±. -'i — — : — f primary exciting current, 298 AL TERN A TING-CURRENT PHENOMENA. [ § 198 hence, total primary current, Primary impressed E.M.F., or Neglecting in -C© ^^e last term, as of higher or ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-08", "section_label": "Chapter 8: Circuits Containing Resistance, Inductance, And Capacity", "section_title": "Circuits Containing Resistance, Inductance, And Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3577-5333", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "snippets": [ "... fundamental laws of alternating-current circuits, when expressed in their com- plex form, E = ZS, or, / = YE, and *%E = 0 in a closed circuit, S/ = 0 at a distributing point, where E, I, Z, Y, are the expressions of E.M.F., current, impedance, and admittance in complex quantities, — these values representing not only the intensity, but also the phase, of the alternating wave, — we can now — by application of these laws, and in the same manner as with continuous- current circuits, keeping in mind, however, tha ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-20", "section_label": "Chapter 20: Commutator Motors", "section_title": "Commutator Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 19458-20501", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "snippets": [ "... netism is represented by /4>, the primary induced E.M.F., E = — e, the secondary induced E.M.F., £1 = — e {sin X +j\"k cos X|; hence, if Zl = r1—jx1= secondary impedance reduced to primary circuit, Z = r — jx = primary impedance, Y = g —jb = exciting admittance, we have, & sin X -f- jk cos A secondary current, 7X = — L = - e - _ - , primary exciting current, I0 = eY= e (g +jb}, hence, total primary current, Primary impressed E.M.F., E0= — E + IZ\\ = e 1 + (sinX Neglecting in E0 the last term, as of hi ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-14", "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "section_title": "Constant-Potential Constant-Current Trans Formation", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "... duced by the combination of inductive and condensive reactances; and the investigation of different methods of producing constant alternating current from constant alternating voltage, or inversely, constitutes a good application of the terms \"impedance,\" admittance,\" etc., and offers a large number of problems or examples for the symbolic method of dealing with alternating-current phenomena. Even outside of arc lighting, such combinations of inductance and capacity which t«nd toward constant-voltage constant-cur- ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-45", "section_label": "Chapter 5: Distributed Series Capacity", "section_title": "Distributed Series Capacity", "kind": "chapter", "sequence": 45, "number": 5, "location": "lines 23586-23947", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "snippets": [ "... eprinted and enlarged in \" General Lectures on Electrical Engineering,\" by Author. DISTRIBUTED SERIES CAPACITY 351 ground. If then / = the frequency of impressed e.m.f., the series impedance per unit length of circuit is Z'=r-j(x-xc); (1) the shunt admittance per unit length of circuit is Y - g - jb, (2) where x = 2 nfL, 1 b - 2 xfCt; or the absolute values are (3) z = Vr2 + (x~xcy and (4) y = If the distance along the circuit from line L towards ground G is denoted by Z, the potential dif ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-53", "section_label": "Chapter 4: Traveling Waves", "section_title": "Traveling Waves", "kind": "chapter", "sequence": 53, "number": 4, "location": "lines 30244-31450", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "snippets": [ "... here x = 2 TT/L = reactance per unit length. From equation (54), R2 = V(s2 + q2 - m2)2 + 4, and *2 or approximately zero, we would alternate between *i and — *i. On the other hand, the single field-coil construction gives a material advantage in the material economy of the field, and in machines having very many field poles, that is, high-frequency alternators, the economy in the field construction overbalances the lesser economy in the use of the armature, especially as at higli frequencies it is not feasible any more to push the alter- nating flux, $0, up to or near saturation values. Therefore, f ...", "... ternators, the economy in the field construction overbalances the lesser economy in the use of the armature, especially as at higli frequencies it is not feasible any more to push the alter- nating flux, $0, up to or near saturation values. Therefore, for high-frequency generators, the inductor alternator becomes the economically superior types, and is preferred, and for ex- tremely high frequencies (20,000 to 100,000 cycles) the inductor alternator becomes the only feasible type, mechanically, 168. In the calculation o ...", "... y even be smaller than that of the standard type, in spite of the higher hysteresis coefficient, 170. 169. The inductor-machine type, Fig. 136, must have an £—21 \\f\\j\\j\\/\\r\\/\\j\\r ^ :f-A J fttfMtai«4**Aft« ! I >U Fig. 138. — Alexanderson high frequency inductor alternator. auxiliary air gap in the magnetic circuit, separating the revolving from the stationary part, as shown at S. It, therefore, is preferable 10 double the structure, Fig. 136, by using two armatures and inductors, with the field coil b ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... saved in alternating constant potential arc lamps, by using reactance instead of resistance, but the power factor is there- fore greatly lowered ; that is, the constant potential alternating arc lamp rarely has a power factor of over 70%. Where therefore high potential constant current circuits are permissible, as for outdoor or street lighting, arc lamps are usually operated on a constant current circuit, with series connection of from 50 to 100 lamps on one circuit. With the exception of a few of the larger cities, al ...", "... quencies. We can get, if we desire, still very much lower fre- quencies, as electromagnetic waves, such as the radiation sent out by an oscillating current or an alternating current ; but the radiations which we get from heated bodies are all of extremely high frequency, compared with the customary frequencies of electric currents. At the same time they cover a very wide range of frequencies, many octaves, and from all this mass of radiations, from all the frequencies of radiating energy, some- what less than one octave ...", "... energy give high intensi- ties of radiation only for very low frequencies, invisible ultra- red rays, but we are not able to produce anywhere near the same intensities of radiation for higher frequencies. So also, when we speak of ultraviolet, or short, high frequency waves, as chemical waves, thait does not mean that they have a distinctive character in producing chemical action — any form of energy, naturally, can be converted if we know how, into chemical energy, the long ultrared waves just as well as the short ult ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-49", "section_label": "Chapter 9: High-Frequency Conductors", "section_title": "High-Frequency Conductors", "kind": "chapter", "sequence": 49, "number": 9, "location": "lines 27003-27760", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "snippets": [ "CHAPTER IX. HIGH-FREQUENCY CONDUCTORS. 80. As the result of the phenomena discussed in the preceding chapters, conductors intended to convey currents of very high frequency, as lightning discharges, high frequency oscillations of transmission lines, the currents used in wireless t ...", "CHAPTER IX. HIGH-FREQUENCY CONDUCTORS. 80. As the result of the phenomena discussed in the preceding chapters, conductors intended to convey currents of very high frequency, as lightning discharges, high frequency oscillations of transmission lines, the currents used in wireless telegraphy, etc., cannot be calculated by the use of the constants derived at low frequency, but effective resistance and inductance, and therewith ...", "CHAPTER IX. HIGH-FREQUENCY CONDUCTORS. 80. As the result of the phenomena discussed in the preceding chapters, conductors intended to convey currents of very high frequency, as lightning discharges, high frequency oscillations of transmission lines, the currents used in wireless telegraphy, etc., cannot be calculated by the use of the constants derived at low frequency, but effective resistance and inductance, and therewith the power consumed by the conductor, and ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... o (401), is 7 ~ — U(jt, V (404) the current 72, by sub- (405) An inductance discharging into the transmission line thus gives an oscillatory distribution of voltage and current along the line. 68. As example may be considered the three-phase high- potential circuit, comprising a generating system of r = 2 ohms and L = 0.5 henry per phase and connected to a long-distance transmission line of r0= 0.4 ohm, L0 = 0.002 henry, gQ= 0.2 X 10~6 mho, (70= 0.016 X 10~6 farad per mile of conductor or phase, and of 1Q = ...", "... ree-half wave: 541.94°. & = 20,920; UQ = 105.6; 7 = if-** (cos qX- 29.6 sin gd); jE/ = 10,460 v~Wo< (cos g>l + 0.033 sin qX). APPENDIX VELOCITY FUNCTIONS OF THE ELECTRIC FIELD IN the study of the propagation of the electric field through space (wireless telegraphy and telephony), a number of new functions appear (Section III, Chapter VIII). . By the following equations these functions are defined, and related to the \" Sine-Integral\" Si x, the \" Cosine-Integral\" Ci x, and the \" Exponential Integral,\" Ei ...", "... magnetic flux in iron 361 constants 434 of traveling wave, and loading 462 Booster, response to change of load 158 Brush arc machine 221, 230, 242, 248 Building up of direct-current generator 32 of overcompounded direct-current machine 49 Cable, high-potential underground, standing waves 452 opening under load 112, 118 short-circuit oscillation 113, 118 starting 111,117 transient terms and oscillations 98, 102 561 562 INDEX PAGE Capacity, also see Condenser. and inductance, equations 48 and vel ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-03", "section_label": "Lecture 3: Physiological Effects Of Radiation", "section_title": "Physiological Effects Of Radiation", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2366-3638", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-03/", "snippets": [ "... TION, LIGHT, AND ILLUMINATION. in visibility to the orange yellow for long distances, and inversely, the orange yellow is superior for short distances. At the limits of visibility the eye is very many times more sensitive to green light and, in general, high-frequency light, than to orange yellow and, in general, low-frequency light. A necessary result of the higher sensitivity of the eye for green light is the preponderance of green in gas and vapor spectra. As no special reason exists why spectrum lines should appea ...", "... f the eye to light of short wave lengths, even such light which to the normal eye is perfectly harmless, as the mercury lamp. In chronic cases of ultra-violet burn, which may occur when working on unprotected arcs, and especially spark discharges (as in wireless telegraphy), the first symptoms are: occasional headaches, located back of the eyes, that is, pains which may be characterized either as headache or as deep-seated eye ache. These recur with increasing frequency and severity. At the same time the blurring ...", "... ned by severe pains in the eyes, the symptoms of the ultra-violet burn, and had to seek medical attendance. Under proper treatment recovery occurred in a few days, but the blurring of the vision was appreciable for some days longer, and the sensitivity to high-frequency light for some weeks. 28. Arcs produce considerable amount of ultra-violet light,* and in former experiments we have used a high frequency iron arc for producing ultra-violet light and also have seen that even a very thin sheet of glass is opaque for th ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-30", "section_label": "Chapter 8: Low Frequency Surges In High Potential Systems", "section_title": "Low Frequency Surges In High Potential Systems", "kind": "chapter", "sequence": 30, "number": 8, "location": "lines 7826-9227", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "snippets": [ "CHAPTER VIII. LOW FREQUENCY SURGES IN HIGH POTENTIAL SYSTEMS. 64. In electric circuits of considerable capacity, that is, in extended high potential systems, as long distance transmission lines and underground cable systems, occasionally destructive high potential low frequency surges occur; that is, oscil ...", "CHAPTER VIII. LOW FREQUENCY SURGES IN HIGH POTENTIAL SYSTEMS. 64. In electric circuits of considerable capacity, that is, in extended high potential systems, as long distance transmission lines and underground cable systems, occasionally destructive high potential low frequency surges occur; that is, oscillations of the whole system, of the same character as in the case of localized capacity and induc ...", "CHAPTER VIII. LOW FREQUENCY SURGES IN HIGH POTENTIAL SYSTEMS. 64. In electric circuits of considerable capacity, that is, in extended high potential systems, as long distance transmission lines and underground cable systems, occasionally destructive high potential low frequency surges occur; that is, oscillations of the whole system, of the same character as in the case of localized capacity and inductance discussed in the preceding chapter. While a system of distributed capacity has an infinite number of frequen ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "... c- tions of different dissipation constants u. For instance, if in a circuit consisting of an unloaded transformer and a transmission line, as indicated in Fig. 40, at no load on the step-down trans- ^^ Line Transformer Line Fig. 40. former, the high-tension switches are opened at the generator end of the transmission line. The energy stored magnetically and dielectrically in line and transformer then dissipates by a transient, as shown in the oscillogram Fig. 41. This gives the oscillation of a circuit consi ...", "... ntil it becomes equal to the power supply. Such oscillations, which frequently are most destructive ones, are met in electric systems as \"arcing grounds,\" \"grounded phase,\" etc. They are frequently called \"undamped oscillations,\" and as such find a use in wireless telegraphy and telephony. Thus far, the only source of cumulative oscillation seems to be an energy supply over an arc, especially an unstable arc. In the self-limiting cumu- lative oscillation, the so-called damped oscillation, the transient becomes a pe ...", "... und; Fig. 45 the same one minute later, when the ground was fully developed. An oscillogram of a cumulative oscillation in a 2500-kw. 100,000- volt power transformer (60-cycle system) is given in Fig. 46. It is caused by switching off 28 miles of line by high-tension switches, at 88 kilovolts. As seen, the oscillation rapidly increases in in- tensity, until it stops by the arc extinguishing, or by the destruc- tion of the transformer. Of special interest is the limiting case, — s = U) in this case, w + s = 0, and ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 4745-5520", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "snippets": [ "... ions of different dissipation constants u. For instance, if a circuit consists of an unloaded transformer and a transmission line, as indicated in Fig. 40, that is, at no load on the step-down trans- ^> Line Transformer Line Fig. 40. former, the high-tension switches are opened at the generator end of the transmission line. The energy stored magnetically and dielectrically in line and transformer then dissipates by a transient, as shown in the oscillogram Fig. 41. This gives the oscillation of a circuit consi ...", "... ntil it becomes equal to the power supply. Such oscillations, which frequently are most destructive ones, are met in electric systems as \"arcing grounds,\" \"grounded phase,\" etc. They are frequently called \"undamped oscillations,\" and as such find a use in wireless telegraphy and telephony. Thus far, the only source of cumulative oscillation seems to be an energy supply over an arc, especially an unstable arc. In the self-limiting cumu- lative oscillation, the so-called damped oscillation, the transient becomes a pe ...", "... und; Fig. 45 the same one minute later, when the ground was fully developed. An oscillogram of a cumulative oscillation in a 2500-kw. 100,000- volt power transformer (60-cycle system) is given in Fig. 46. It is caused by switching off 28 miles of line by high-tension switches, at 88 kilovolts. As seen, the oscillation rapidly increases in in- tensity, until it stops by the arc extinguishing, or by the destruc- tion of the transformer. Of special interest is the limiting case, — s = u; in this case, u + s = 0, and ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... adiation increases, 'but at the same time radiations of higher and higher frequencies appear, and ultimately the rods become visible in the dark, giving a dark red light; that is, of all the radiations sent out by the rods, a small part is of sufficiently high frequency to be visible. Still further increasing the tempera- ture, the total radiation increases, but the waves of high frequency in- crease more rapidly than those vof lower frequency ; that is, the average frequency of radiation increases or the average wave ...", "... e visible in the dark, giving a dark red light; that is, of all the radiations sent out by the rods, a small part is of sufficiently high frequency to be visible. Still further increasing the tempera- ture, the total radiation increases, but the waves of high frequency in- crease more rapidly than those vof lower frequency ; that is, the average frequency of radiation increases or the average wave length decreases and higher and higher frequencies appear, — orange rays, yellow, green, blue, violet, and the color of t ...", "... ight (red, orange and yellow) with increase in temperature, the light FIG. 10. 12 RADIATION, LIGHT, AND ILLUMINATION. would become bluish. However, we are close to the limit of temperature which even tungsten can stand, and to show you light of high frequency or short wave length I use a different apparatus in which a more direct conversion of electric energy into radiation takes place, — the mercury arc lamp. Here the light is bluish green, containing only the highest frequencies of visible radiation, violet, ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-44", "section_label": "Chapter 4: Distributed Capacity Of High-Potential Transformers", "section_title": "Distributed Capacity Of High-Potential Transformers", "kind": "chapter", "sequence": 44, "number": 4, "location": "lines 23179-23585", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "snippets": [ "CHAPTER IV. DISTRIBUTED CAPACITY OF HIGH-POTENTIAL TRANSFORMERS. 40. In the high-potential coils of transformers designed for very high voltages phenomena resulting from distributed capacity occur. In transformers for very high voltages — 100;000 volts and more, or even considerably less in small tran ...", "CHAPTER IV. DISTRIBUTED CAPACITY OF HIGH-POTENTIAL TRANSFORMERS. 40. In the high-potential coils of transformers designed for very high voltages phenomena resulting from distributed capacity occur. In transformers for very high voltages — 100;000 volts and more, or even considerably less in small transformers — the high- potential coil contai ...", "... 40. In the high-potential coils of transformers designed for very high voltages phenomena resulting from distributed capacity occur. In transformers for very high voltages — 100;000 volts and more, or even considerably less in small transformers — the high- potential coil contains a large number of turns, a great length of conductor, and therefore its electrostatic capacity is appreciable, and such a coil thus represents a circuit of distributed resistance, inductance, and capacity somewhat similar to a transmission l ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-05", "section_label": "Lecture 5: Long Distance Transmission", "section_title": "Long Distance Transmission", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2562-3132", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-05/", "snippets": [ "... ductors = 2 e. For instance, wire No. 0000 D = .46\" ; corona effects begin at the voltage E = 100,000 [) D^ = 46,000. ' ' For 100,000 volts the smallest diameter for which no corona effects occur is : D= ? =1\" 100,000 68 GENERAL LECTURES In high potential transformers in the coils no corona effects may occur, because the diameter of the coil or the thick- ness is large enough, but the leads connecting the coils with each other and with the outside, if not chosen very large in diameter, may give corona effe ...", "... ductor diameter is 2 \"> ^o corona effects occur. If now one terminal is grounded, the other terminal has 100,000 volts to ground and so at 2 \" diameter gives corona effects, that is, glow and streamers which may destroy the insulating material or produce high frequency oscillations. At very high voltages it is therefore necessary to have the system statically balanced or symmetrical, that is, have the same potential differences from all the conductors to the ground. Any electric circuit, and so also the transmission ...", "... as electrostatic energy, or electrostatic charge, due to the voltage. LONG DISTANCE TRANSMISSION 69 If: e = voltage, C = capacity. i = current, L = inductance. the electrostatic energy is : e*C 2 and the electromagnetic energy : i'L 2 In a high potential transmission line both energies are of about the same magnitude, and the energy can therefore see- saw between the two forms and thereby produce oscillations and surges resulting in the production of high voltages, which are not liable to occur in circuit ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-48", "section_label": "Chapter 8: Velocity Of Propagation Of Electric Field", "section_title": "Velocity Of Propagation Of Electric Field", "kind": "chapter", "sequence": 48, "number": 8, "location": "lines 26095-27002", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "snippets": [ "... on, or, in other words, the electric field lags the more, the greater the distance from the conductor. Since the velocity of propagation is very high — about 3 X 1010 centimeters per second — the wave of an alternating or oscillating current even of very high frequency is of considerable length ; at 60 cycles the wave length is 0.5 X 109 centimeters, and even at a million cycles the wave length is 30,000 centimeters, or about 1000 feet, that is, very great compared with the distance to which electric fields usually exte ...", "... propagation has no appreciable effect. Thus, the finite velocity of propagation of the electric field requires consideration only: 387 388 TRANSIENT PHENOMENA (a) At extremely high frequencies, hundreds of millions of cycles per second, as given by Hertzian resonators. (6) In high frequency discharges having no return circuit or no well defined return circuit, as lightning discharges. In this case the effective resistance of radiation may be so large com- pared with the ohmic resistance, even when consideri ...", "... effect. Thus, the finite velocity of propagation of the electric field requires consideration only: 387 388 TRANSIENT PHENOMENA (a) At extremely high frequencies, hundreds of millions of cycles per second, as given by Hertzian resonators. (6) In high frequency discharges having no return circuit or no well defined return circuit, as lightning discharges. In this case the effective resistance of radiation may be so large com- pared with the ohmic resistance, even when considering the unequal current distribution ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "section_label": "Lecture 10: Continual And Cumulative Oscillations", "section_title": "Continual And Cumulative Oscillations", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... equal to the energy supply, and the oscillation becomes continual. A continual or cumulative oscillation thus involves an energy and frequency transformation, from the low-frequency or con- tinuous-current energy of the power supply of the system to the high-frequency energy of the oscillation. 119 120 ELECTRICAL DISCHARGES, WAVES AND IMPULSES This energy transformation may be brought about by the transient of energy readjustment, resulting from a change of circuit conditions, producing again a change of circuit c ...", "... ansformation may be brought about by the transient of energy readjustment, resulting from a change of circuit conditions, producing again a change of circuit conditions and thereby an energy readjustment by transient, etc. For instance, if in an isolated high-potential transmission line, the ground is brought within striking distance of one of the line conductors — as by the puncture of an insulator. A spark dis- charge then occurs to the ground, and the arc following the spark discharges the line by a transient oscilla ...", "... 22,000-volt Three-phase 40-cycle Transmission Line. 122 ELECTRICAL DISCHARGES, WAVES ANDJMPULSES grams, Figs. 62 to 65, were taken on an artificial transmission line.* Oscillations of the type 64 and 65 are industrially used, as ''sing- ing arc, \" in wireless telegraphy, and are produced by shunting a suitable arc by a circuit containing capacity and inductance in series with each other. Fig. 62. — Semi -continuous Recurrent Oscillation of Arcing Ground in Transmission Line. Fig. 63. — Semi-continuous Hec ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... stributed capacity and inductance as so-called \"wave transmission\" and the phenomena thus essentially differ from those in a short energy transmission line. 4. Therefore in very long circuits, as in lines conveying alter- nating currents of high value at high potential over extremely long distances, by overhead conductors or underground cables, or with very feeble currents at extremely high frequency, such as telephone currents, the consideration of the line resistance, which consumes e.m.fs. in phase with the current, ...", "... rgy transmission line. 4. Therefore in very long circuits, as in lines conveying alter- nating currents of high value at high potential over extremely long distances, by overhead conductors or underground cables, or with very feeble currents at extremely high frequency, such as telephone currents, the consideration of the line resistance, which consumes e.m.fs. in phase with the current, and of the line reactance, which consumes e.m.fs. in quadrature with the current, is not sufficient for the explanation of the phenome ...", "... e power component of the charging current. Besides this there is the apparent increase of ohmic resistance due to unequal distribution of current, which, however, is usually not large enough to be noticeable at low frequencies. Also, especially at very high frequency, energy is radiated into space, due to the finite velocity of the electric field, and can be represented by power components of current and of voltage respectively. 5. This gives, as the most general case and per unit length of line, LONG-DISTANCE TR ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-52", "section_label": "Chapter 3: Standing Waves", "section_title": "Standing Waves", "kind": "chapter", "sequence": 52, "number": 3, "location": "lines 29316-30243", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "snippets": [ "... the wave non-oscillatory, and of the frequency /0, which, in an undamped circuit, will correspond to this critical wave length lWo, can best be derived by considering some representative numerical examples. As such may be considered: (1) A high-power high-potential overhead transmission line. (2) A high-potential underground power cable. (3) A submarine telegraph cable. (4) A long-distance overhead telephone circuit. (1) High-power high-potential overhead transmission line. 16. Assume energy to be transmitted ...", "... , which, in an undamped circuit, will correspond to this critical wave length lWo, can best be derived by considering some representative numerical examples. As such may be considered: (1) A high-power high-potential overhead transmission line. (2) A high-potential underground power cable. (3) A submarine telegraph cable. (4) A long-distance overhead telephone circuit. (1) High-power high-potential overhead transmission line. 16. Assume energy to be transmitted 120 miles, at 40,000 volts between line and ground ...", "... merical examples. As such may be considered: (1) A high-power high-potential overhead transmission line. (2) A high-potential underground power cable. (3) A submarine telegraph cable. (4) A long-distance overhead telephone circuit. (1) High-power high-potential overhead transmission line. 16. Assume energy to be transmitted 120 miles, at 40,000 volts between line and ground, by a three-phase system with grounded neutral. The line consists of copper conductors, wire No. 00 B. and S. gage, with 5 feet between con ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-10", "section_label": "Chapter 10: Instability Of Circuits : The Arc", "section_title": "Instability Of Circuits : The Arc", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 17632-21381", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-10/", "snippets": [ "... sually all three may occur, under different circuit conditions. The electric arc is the most frequent and most serious cause of instability of electric circuits, and therefore should first be sus- pected, especially if the instability assumes the form of high- frequency disturbances or abrupt changes of current or voltage, such as is shown for instance in the oscillograms. Figs. 80 and 81. Somewhat similar effects of instability are produced by pyro- electric conductors. Induction motors and synchronous motors may show ...", "... henomena in high-voltage electric circuits. Relatively little exact knowledge exists of their origin. Usually — if not always — an arc somewhere in the system is instrumental in the energy supply which maintains the oscilla- tion. In some instances, as in wireless telegraphy, they have found industrial application. A systematic theoretical investiga- tion of these cumulative electrical oscillations probably is one of the most important problems before the electrical engineer, today. The general nature of these per ...", "... ain itself without external power supply, 188 ELECTRIC CIRCUITS and would even be able to supply the power represented by vol- tage, ei, with current, ii, into an external circuit, as the resistance, r, shown in Fig. 87, or through a transformer into a wireless send- ing circuit, etc. Thus, due to the dropping arc characteristic, an arc shunted by capacity and inductance, on a constant-current supply, be- comes a generator of alternating-current power, of the frequency set by the resonance of C and L. If the ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-07", "section_label": "Lecture 7: High Frequency Oscillations And Surges", "section_title": "High Frequency Oscillations And Surges", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3508-3780", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-07/", "snippets": [ "SEVENTH LECTURE HIGH FREQUENCY OSCILLATIONS AND SURGES 1\"^ N an electric circuit, in addition to the power consump- tion by the resistance of the lines, an energy storage ■^ occurs as electrostatic energy, or electrostatic charge due to the voltage on the line (capacity) ; and as el ...", "... change of conditions, and are dependant upon the stored energy of the circuit, but not upon the generator frequency or wave shape ; therefore they occur in the same manner, and are of the same frequency, in a 25 cycle system as in a 60 cycle system, or a high potential direct current transmission; and occur with sine waves of generator voltage equally as with distorted 92 GENERAL LECTURES generator waves. While the power of these oscillations ulti- mately conies from the generators, it is not the generator wave nor ...", "... ection of the circuit, the wave length is shorter. For instance, if by a thunder cloud a static charge is induced on the trans- mission line, and by a lightning flash in the cloud, the cloud discharges, the electrostatic charge induced by it on the line HIGH FREQUENCY OSCILLATIONS 93 is set free and dissipates by an oscillation. In this case, the length of section on which an abnormal charge existed — one mile for instance — is a half wave of the oscillation, and the complete wave length would thus be two miles. Or, i ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "... e places where the field intensity is highest, as at the needle points, before the disruptive voltage of the spark gap is reached, and then a partial break down occurs at the points of maximum field intensity, as at the needle points, or at the surface of high potential conductors, etc. A blue glow, then, appears at the needle points followed by violet streamers (in air, the color being the nitrogen spectrum; in other gases other colors appear), and gradually increases in extent with increasing voltage, the so-called \" b ...", "... ospheric pressure. By now exhausting the tube, while the voltage is maintained at the terminals, you can watch the gradual change from the static spark to the Geissler tube glow. In this experi- ment, a small condenser, a Leyden jar, is shunted across the high- potential terminals of the transformer, to guard against the disruptive conduction changing to continuous conduction, that is, to an arc, and a reactance inserted into the low-tension pri- mary of the step-up transformer, to limit the discharge current, as shown di ...", "... high voltage is maintained sufficiently long, then pro- duces the vapor stream and starts the arc, that is, the arc follows the spark. If the duration of the high voltage is very short, the energy of the spark may not be sufficient to start the arc. Thus high frequency discharges between live terminals frequently are not followed by an arc, and the lower the voltage between the terminals is, the more powerful a static spark is required to start an arc. (3.) By supplying the conducting vapor stream from another arc, th ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-43", "section_label": "Chapter 3: The Natural Period Of The Transmission Line", "section_title": "The Natural Period Of The Transmission Line", "kind": "chapter", "sequence": 43, "number": 3, "location": "lines 21721-23178", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "snippets": [ "... it. In determining the frequency of the oscillating discharge of such a transmission line, a sufficiently close approximation is 320 NATURAL PERIOD OF TRANSMISSION LINE 321 obtained by neglecting the resistance of the line, which, at the relatively high frequency of oscillating discharges, is small com- pared with the reactance. This assumption means that the dying out of the discharge current through the influence of the resistance of the circuit is neglected, and the current assumed as an alternating current of ...", "... istribution of potential which momentarily is very non-uniform, changes very abruptly along the line, and thus gives rise mainly to very high harmonics, but as a rule does not contain to any appre- ciable extent the lower frequencies; that is, it causes a high- frequency oscillation, more or less local in extent, and while of high voltage, of rather limited power, and therefore less destruc- tive than a low-frequency surge. At the frequencies of the high-frequency oscillation neither capacity nor inductance of the transm ...", "... iable extent the lower frequencies; that is, it causes a high- frequency oscillation, more or less local in extent, and while of high voltage, of rather limited power, and therefore less destruc- tive than a low-frequency surge. At the frequencies of the high-frequency oscillation neither capacity nor inductance of the transmission line is perfectly constant: the inductance varies with the frequency, by the increasing screening effect or unequal current distribution in the conductor; the capacity increases by brush disc ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-50", "section_label": "Chapter 1: General Equations", "section_title": "General Equations", "kind": "chapter", "sequence": 50, "number": 1, "location": "lines 27761-28694", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "snippets": [ "... r be per- fectly correct, — for instance, every resistor has some inductance and every reactor has some resistance, — nevertheless in most cases it is permissible and necessary, and only in some classes of phenomena, and in some kinds of circuits, such as high-frequency phenomena, voltage and current distribution in long-distance, high-potential circuits, cables, telephone circuits, etc., this assumption is not permissible, but r, L, g, C must be treated as distributed throughout the circuit. In the case of a circuit w ...", "... and every reactor has some resistance, — nevertheless in most cases it is permissible and necessary, and only in some classes of phenomena, and in some kinds of circuits, such as high-frequency phenomena, voltage and current distribution in long-distance, high-potential circuits, cables, telephone circuits, etc., this assumption is not permissible, but r, L, g, C must be treated as distributed throughout the circuit. In the case of a circuit with distributed resistance, inductance, conductance, and capacity, as r, L, g, ...", "... ctance, and capacity, as r, L, g, C, are denoted the effec- tive resistance, inductance, conductance, and capacity, respec- tively, per unit length of circuit. The unit of length of the circuit- may be chosen as is convenient, thus : the centimeters in the high- frequency oscillation over the multigap lightning arrester circuit, or a mile in a long-distance transmission circuit or high-potential cable, or the distance of the velocity of light, 300,000 km., etc. The permanent values of current and e.m.f. in such circuits o ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-24", "section_label": "Chapter 2: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 24, "number": 2, "location": "lines 1993-2658", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "snippets": [ "... ries of transient terms is produced, recurring at a frequency depending upon the circuit constants and upon the ratio of the disruptive voltage of the spark gap to the impressed e.m.f. INTRODUCTION 23 >uch a phenomenon for instance occurs when on a high- potential alternating-current system a weak spot appears in the cable insulation and permits a spark discharge to pass to the ground, that is, in shunt to the condenser formed by the cable conductor and the cable armor or ground. 19. In most cases the transient ph ...", "... ile the permanent or stationary short-circuit current is not excessive and represents little power, the very much larger momentary short-circuit current may be beyond the capacity of automatic circuit-opening devices and cause damage by its high power. In high-potential transmissions the potential differences produced by these transient terms may reach values so high above the normal voltage as to cause disruptive effects. (6) Lightning, high-potential surges, etc., are in their nature essentially transient phenomena, ...", "... atic circuit-opening devices and cause damage by its high power. In high-potential transmissions the potential differences produced by these transient terms may reach values so high above the normal voltage as to cause disruptive effects. (6) Lightning, high-potential surges, etc., are in their nature essentially transient phenomena, usually of oscillating character. (c) The periodical production of transient terms of oscillating character is one of the foremost means of generating electric cur- rents of very high fre ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-47", "section_label": "Chapter 7: Distribution Of Alternating-Current Density In Conductor", "section_title": "Distribution Of Alternating-Current Density In Conductor", "kind": "chapter", "sequence": 47, "number": 7, "location": "lines 24981-26094", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "snippets": [ "... considerable, the conductor section is not fully utilized, but the material in the interior of the conductor is more or less wasted. It is of importance, therefore, in alternating- current circuits, especially in dealing with very large currents, or with high frequency, or materials of very high permeability, as iron, to investigate this phenomenon. An approximate determination of this effect for the purpose of deciding whether the unequal current distribution is so small as to be negligible in its effect on the resist ...", "... ease of the effective resistance over the ohmic resistance may be expected in the following cases : (1) In the low-tension distribution of heavy alternating cur- rents by large conductors. (2) When using iron as conductor, as for instance iron wires in high potential transmissions for branch lines of smaller power, or steel cables for long spans in transmission lines. (3) In the rail return of single-phase railways. (4) When carrying very high frequencies, such as lightning discharges, high frequency oscillations. ...", "... iron wires in high potential transmissions for branch lines of smaller power, or steel cables for long spans in transmission lines. (3) In the rail return of single-phase railways. (4) When carrying very high frequencies, such as lightning discharges, high frequency oscillations. In the last two cases, which probably are of the greatest impor- tance, the unequal current distribution usually is such that practically no current exists at the conductor center, and the effective resistance of the track rail even for 25- ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-55", "section_label": "Chapter 6: Transition Points And The Complex Circuit", "section_title": "Transition Points And The Complex Circuit", "kind": "chapter", "sequence": 55, "number": 6, "location": "lines 32709-33527", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "snippets": [ "... never are simple circuits, but are always complex circuits comprising sections of different con- stants, — generator, transformer, transmission lines, and load, — and a simple circuit is realized only by a section of a circuit, as a transmission line or a high-potential transformer coil, which is cut off at both ends from the rest of the circuit, either by open- circuiting, i = 0, or by short-circuiting, e = 0. Approximately, the simple circuit is realized by a section of a complex circuit, connecting to other sections o ...", "... an, approximately, be considered as reflection points. For instance, an underground cable of low L and high (7, when connected to a large reactive coil of high L and low C, may, approximately, at its ends be considered as having reflection points i = 0. A high-potential transformer coil of high L and low C, when connected to a cable of low L and high (7, may at its ends be considered as having reflection points e = 0. In other words, in the first case the reactive coil may be considered as stopping the current, in the la ...", "... n of the constants r, L, g, C of the different sections of the circuit different linear distance measure- ments I may be used. For instance, in the transmission line, the constants may be given per mile, that is, the mile used as unit length, while in the high-potential coil of a transformer the turn, or the coil, or the total transformer may be used as unit of length I, so that the actual linear length of conductor may be unknown. For instance, choosing the total length of conductor in the high-potential transformer as ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "... the usual manner by the vector diagram. This phenomenon is especially noticeable in long-distance lines, in underground cables, and to a certain degree in the high-poten- tial coils of alternating-current transformers for very high vol- tage and also in high frequency circuits. It has the effect that not only the e.m.fs., but also the currents, at the beginning, end, and different points of the conductor, are different in intensity and in phase. Where the capacity effect of the line is small, it may with sufficient a ...", "... ^^ (r+jx) = e{ 1 + (r + jx) [g - jb + ^-^) + ^-jir+jxY (g-jb) 131. Distributed condensive reactance, inductive reactance, leak- age, and resistance. In some cases, especially in very long circuits, as in lines conveying alternating-power currents at high potential over extremely long distances by overhead conductors or under- ground cables, or with very feeble currents at extremely high frequency, such as telephone currents, the consideration of the line resistance— vfhich. consumes e.m.fs. in phase with the curren ...", "... e, and resistance. In some cases, especially in very long circuits, as in lines conveying alternating-power currents at high potential over extremely long distances by overhead conductors or under- ground cables, or with very feeble currents at extremely high frequency, such as telephone currents, the consideration of the line resistance— vfhich. consumes e.m.fs. in phase with the current — and of the line reactance — which consumes e.m.fs. in quadrature with the current — is not sufficient for the explanation of the ph ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-27", "section_label": "Chapter 27: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 33011-34776", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-27/", "snippets": [ "... without corresponding phase displacement, the circuit-factor being less than one-half. Such circuits, for instance, are those including alternating arcs, reaction machines, synchronous induction motors, react- ances with over-saturated magnetic circuit, high potential lines in which the maximum difference of potential exceeds the corona voltage, polarization cells and in general electrolytic conductors above the dissociation voltage of the electrolyte, etc. Such cir- cuits cannot correctly, and in many cases not even a ...", "... tor, for these higher har- monics, is, by neglecting the conductance, 71 = _ ^ = - ^M n n and the higher harmonics of counter e.m.f., E^ = — ^• . 2 Thus we have, current input in the condenser, L - EoYc = + 4.28ii + 1.54 i3 - 4.93^5 - 4.02i7; high-frequency component of motor-impedance current, W ^ ■^ = - 0.92 i3 + 1.06 i5 + 0.44 Jt; high-frequency component of motor-exciting current, ^lyi = ---— = _ 0.07 i3 + O.OSis + 0.03 J7: thus, total high-frequency component of motor current, 7oi =|l -I- E^Y^ = - ...", "... the higher harmonics of counter e.m.f., E^ = — ^• . 2 Thus we have, current input in the condenser, L - EoYc = + 4.28ii + 1.54 i3 - 4.93^5 - 4.02i7; high-frequency component of motor-impedance current, W ^ ■^ = - 0.92 i3 + 1.06 i5 + 0.44 Jt; high-frequency component of motor-exciting current, ^lyi = ---— = _ 0.07 i3 + O.OSis + 0.03 J7: thus, total high-frequency component of motor current, 7oi =|l -I- E^Y^ = - 0.99 i3 + 1.14 J5 + 0.47 iv, 394 ALTERNATING-CURRENT PHENOMENA and total current, without cond ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "... d resistance, vary from point to point ; and it is no longer possible to treat the circuit in the usual manner by the vector diagram. This phenomenon is especially noticeable in long-distance lines, in underground cables, and to a certain degree in the high-potential coils of alternating-current transformers for very high voltage. It has the effect that not only the E.M.Fs., but also the currents, at the beginning, end, and different points of the conductor, are different in intensity and in phase. Where the capacit ...", "... e the same in A.) and in B.). DISTRIBUTED CAPACITY. 163 111. C.) Complete investigation of distributed capacity, inductance, leakage, and resistance. In some cases, especially in very long circuits, as in lines conveying alternating power currents at high potential over extremely long distances by overhead conductors or un- derground cables, or with very feeble currents at extremely high frequency, such as telephone currents, the consideration of the line resistance — which consumes E.M.Fs. in phase with the curren ...", "... , and resistance. In some cases, especially in very long circuits, as in lines conveying alternating power currents at high potential over extremely long distances by overhead conductors or un- derground cables, or with very feeble currents at extremely high frequency, such as telephone currents, the consideration of the line resistance — which consumes E.M.Fs. in phase with the current — and of the line reactance — which con- sumes E.M.Fs. in quadrature with the current — is not sufficient for the explanation of the p ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... shunted capacity to assist the excitation, and not attempting to produce constant potential, single-phase alternators have been built and are in commercial service giving 10,000 and even 100,000 cycles, and 200,000-cycle alternators are being designed for wireless telegraphy and telephony. Still, even going to the limits of peripheral speed, and sacri- ficing everything for high frequency, a limit is reached in the frequency available by electrodynamic generation. It becomes of importance, therefore, to investiga ...", "... been built and are in commercial service giving 10,000 and even 100,000 cycles, and 200,000-cycle alternators are being designed for wireless telegraphy and telephony. Still, even going to the limits of peripheral speed, and sacri- ficing everything for high frequency, a limit is reached in the frequency available by electrodynamic generation. It becomes of importance, therefore, to investigate whether by the use of the condenser discharge the range of frequencies can be extended. Since the oscillating current appro ...", "... y the use of the condenser discharge the range of frequencies can be extended. Since the oscillating current approaches the effect of an alternating current only if the damping is small, that is, the resistance low, the condenser discharge can be used as high frequency generator only by making the circuit of as low resist- ance as possible. 67 68 TRANSIENT PHENOMENA This, however, means limited power. When generating oscillat- ing currents by condenser discharge, the load put on the circuit, that is, the power con ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3721-4369", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-06/", "snippets": [ "... and the maximum voltage which it may produce on the line, as limited by the disruptive strength of the line insulation against momentary voltages, is e^, the maximum discharge current in the line is limited to Iq = eoyo. If L is high but C low, as in the high-potential winding of a high-voltage transformer (which winding can be considered as a circuit of distributed capacity, inductance, and resistance), Zq is high and 2/0 low. That is, a high transient voltage can produce only moderate transient currents, but even a sm ...", "... law of proportionality does not exist, the oscil- lation may not be of constant frequency. Thus in Fig. 31 is shown an oscillogram of the voltage oscillation of the compound circuit consisting of 28 miles of 100,000-volt transmission line and the 2500-kw. high-potential step-up transformer winding, caused by switching transformer and 28-mile line by low-tension switches off a substation at the end of a 153-mile transmission line, at 88 kv. With decreasing voltage, the magnetic density in the transformer DOUBLE-ENERGY T ...", "... ak- age, dielectric induction and dielectric hysteresis, corona, etc.), is negligible. Such is the case in most power circuits and trans- mission lines, except at the highest voltages, where corona appears. It is not always the case in underground cables, high-potential DOUBLE-ENERGY TRANSIENTS. 69 transformers, etc., and is not the case in telegraph or telephone lines, etc. It is very nearly the case if the capacity is due to elec- trostatic condensers, but not if the capacity is that of electrolytic condensers, alu ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 6125-6803", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-09/", "snippets": [ "... venience be considered as one circuit section.) Assume now that the circuit is disconnected from the power sup- ply by low-tension switches, at A. This leaves transformer, line, and load as a compound oscillating circuit, consisting of four sections : the high-tension coil of the step-up transformer, the two lines, and the load. Let then Xi = length of line, X2 = length of transformer circuit, and X3 = length of load circuit, in velocity measure.* If then * If Zi = length of circuit section in any measure, and Lo = i ...", "... In an oscillation of an open compound circuit, the relative intensities of the two component waves are fixed by the condition that at the open ends of the circuit the power transfer must be zero. As illustration may be considered a circuit comprising the high- potential coil of the step-up transformer, and the two lines, which are assumed as open at the step-down end, as illustrated diagram- matically in Fig. 56. 114 ELECTRIC DISCHARGES, WAVES AND IMPULSES. Choosing the same lengths and the same power-dissipation co ...", "... e uniformly distributed throughout the entire circuit, and if it is not so in the beginning of the transient, local traveling waves redistribute the energy throughout the oscillat- ing circuit, as stated before. Such local oscillations are usually of very high frequency, but sometimes come within the range of the oscillograph, as in Fig. 47. During the oscillation of the complex circuit, every circuit element d\\ (in velocity measure), or every wave length or equal part of the wave length, therefore contains the same amo ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3287-3955", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "snippets": [ "... nd the maximum voltage which it may produce on the line, as limited by the disruptive strength of the line insulation against momentary voltages, is e0, the maximum discharge current in the line is limited to i0 = e<>yo. If L is high but C low, as in the high-potential winding of a high-voltage transformer (which winding can be considered as a circuit of distributed capacity, inductance, and resistance), z0 is high and T/O low. That is, a high transient voltage can produce only moderate transient currents, but even a sm ...", "... law of proportionality does not exist, the oscil- lation may not be of constant frequency. Thus in Fig. 31 is shown an oscillogram of the voltage oscillation of the compound circuit consisting of 28 miles of 100,000-volt transmission line and the 2500-kw. high-potential step-up transformer winding, caused by switching transformer and 28-mile line by low-tension switches off a substation at the end of a 153-mile transmission line, at 88 kv. With decreasing voltage, the magnetic density in the transformer DOUBLE-ENERGY T ...", "... ak- age, dielectric induction and dielectric hysteresis, corona, etc.), is negligible. Such is the case in most power circuits and trans- mission lines, except at the highest voltages, where corona appears. It is not always the case in underground cables, high-potential DOUBLE-ENERGY TRANSIENTS. 69 transformers, etc., and is not the case in telegraph or telephone lines, etc. It is very nearly the case if the capacity is due to elec- trostatic condensers, but not if the capacity is that of electrolytic condensers, ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 5521-6088", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "snippets": [ "... nvenience be considered as one circuit section.) Assume now that the circuit is disconnected from the power sup- ply by low-tension switches, at A. This leaves transformer, line, and load as a compound oscillating circuit, consisting of four sections: the high-tension coil of the step-up transformer, the two lines, and the load. Let then Xi = length of line, X2 = length of transformer circuit, and Xs = length of load circuit, in velocity measure.* If then * If Zi = length of circuit section in any measure, and L0 = i ...", "... In an oscillation of an open compound circuit, the relative intensities of the two component waves are fixed by the condition that at the open ends of the circuit the power transfer must be zero. As illustration may be considered a circuit comprising the high- potential coil of the step-up transformer, and the two lines, which are assumed as open at the step-down end, as illustrated diagram- matically in Fig. 56. 114 ELECTRIC DISCHARGES, WAVES AND IMPULSES. Choosing the same lengths and the same power-dissipation co ...", "... e uniformly distributed throughout the entire circuit, and if it is not so in the beginning of the transient, local traveling waves redistribute the energy throughout the oscillat- ing circuit, as stated before. Such local oscillations are usually of very high frequency, but sometimes come within the range of the oscillograph, as in Fig. 47. During the oscillation of the complex circuit, every circuit element d\\ (in velocity measure), or every wave length or equal part of the wave length, therefore contains the same amo ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-02", "section_label": "Lecture 2: Conclusions From The Relativity Theory", "section_title": "Conclusions From The Relativity Theory", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 736-2388", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... thus leads to the conclusion of the existence of abso- lute motion and position and so contradicts the relativity theory. Thus the hypothesis of the ether has been finally dis- proven and abandoned. There is no such thing as the ether, and light and the wireless waves are not wave motions of the ether. CONCLUSIONS FROM RELATIVITY THEORY 17 What, then, is the fallacy in the wave theory of light which has led to the erroneous conception of an ether? The phenomenon of interference proves that light is a wave, ...", "... speed of propagation as the light wave, and has shown that the electromagnetic wave and the (polarized) light wave are identical in all their properties. Hence light is an electromagnetic wave — that is, an alternating electro- magnetic field of extremely high frequency. Electrophysics has been successfully developed to its present high state, and has dealt with alternating currents, voltages and electromag- netic fields, without ever requiring or considering a medium such as the ether. Whatever may be the mechanis ...", "... nd electromag- netic fields, without ever requiring or considering a medium such as the ether. Whatever may be the mechanism of the electro- magnetic wave, it certainly is not a mere transverse wave motion of matter, and the light, being shown to be a high-frequency electro- magnetic wave, cannot be considered any more as a wave motion of the ether. The ether thus vanishes. M Fig. 4. 22 RELATIVITY AND SPACE following the phlogiston and other antiquated physical conceptions. The conception of the field of ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-88", "section_label": "Apparatus Section 10: Synchronous Converters: Frequency", "section_title": "Synchronous Converters: Frequency", "kind": "apparatus-section", "sequence": 88, "number": 10, "location": "lines 15811-15892", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-88/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-88/", "snippets": [ "X. Frequency 101. While converters can be designed for any frequency, the use of high frequency, as 60 cycles, imposes more severe limita- tions on the design, especially that of the commutator, as to make the high-frequency converter inferior to the low-frequency or 25-cycle converter. The commutator surface moves the ...", "X. Frequency 101. While converters can be designed for any frequency, the use of high frequency, as 60 cycles, imposes more severe limita- tions on the design, especially that of the commutator, as to make the high-frequency converter inferior to the low-frequency or 25-cycle converter. The commutator surface moves the distance from brush to next brush, or the commutator pitch, during one-half cycle, that is, 3^50 second with a 25-cycle, J^20 s ...", "... itch must be in- cluded as many commutator segments as necessary to take care of the voltage from brush to brush, and these segments must have a width sufficient for mechanical strength. With the smaller pitch required for high frequency, this may become impossible, and the limits of conservative design thus may have to be exceeded. In a converter, due to the absence of armature reaction and field distortion, a higher voltage per commutator segment can be ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-32", "section_label": "Chapter 32: Transformation Of Polyphase Systems", "section_title": "Transformation Of Polyphase Systems", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 36062-36514", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-32/", "snippets": [ "... lta connection of the primary maintains the balance, in regard to the voltage between the phases at unequal distribution of load. The delta-Y connection of step-up transformers is frequently used in long-distance transmissions, to allow grounding of the high-potential neutral. Under certain conditions — which there- fore have to be guarded against — it is liable to induce excessive voltages by resonance with the line capacity. J_I_i P^^lIM nm Fig. 210. The reverse thereof, or the Y-delta connection, is unde ...", "... the triangle. As result thereof the secondary triangle becomes very greatly distorted even at moderate inequality of load, and the system thus loses all ability to maintain constant voltage at unequal distribution of load, that is, becomes inoperative. In high-potential systems in this case excessive voltages may be induced by resonance with the line capacity. For instance, if only one phase of the secondary triangle is 426 ALTERNATING-CURRENT PHENOMENA loaded, the other two unloaded, the primary current of the load ...", "... ries, hence is less efficient, and is liable to unbalance the system mm) mu Fig. 212. by the internal impedance of the transformers. It is convenient for small powers at moderate voltage, since it requires only two transformers, but is dangerous in high potential circuits, being liable to produce destructive voltages by its electrostatic un- balancing. 5. The main and teaser, or T connection of transformers be- tween three-phase systems, is shown in Fig. 212. One of the 428 ALTERNATING-CURRENT PHENOMENA two ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "section_title": "Dibtbisnted Capacity, Inductance, Besistance, And", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "... to point ; and it is no longer possible to treat the circuit in the usual manner by the vector diagram. This phenomenon is especially noticeable in long-distance lines, in underground cables, especially concentric cables, and to a certain degree in the high-potential coils of alternating- current transformers. It has the effect that not only the E.M.Fs., but also the currents, at the beginning, end, and different points of the conductor, are different in intensity and in phase. Where the capacity effect of the line ...", "... ame in A.) and in B.). § 106] DISTRIBUTED CAPACITY. 155 106. C) Complete investigation of distributed capacity, indnctanccy leakage, and resistattce. In some cases, especially in very long circuits, as in lines conveying alternating power currents at high potential over extremely long distances by overhead conductors or un- derground cables, or with very feeble currents at extremely high frequency, such as telephone currents, the consideration of the line resistance — which consumes E.M.Fs. in phase with the curren ...", "... and resistattce. In some cases, especially in very long circuits, as in lines conveying alternating power currents at high potential over extremely long distances by overhead conductors or un- derground cables, or with very feeble currents at extremely high frequency, such as telephone currents, the consideration of the line resistance — which consumes E.M.Fs. in phase with the current — and of the line reactatice — which con- sumes E.M.Fs. in quadrature with the current — is not sufficient for the explanation of the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "... The exciting admittance of the motor, for these higher harmonics, is, by neglecting the conductance, n and the higher harmonics of counter E.M.F. Thus we have, Current input in the condenser, fc = E, Yc = - 4.28/i - 1.54/3 + 4.93/5 + 4.02/7 High frequency component of motor impedance current, |£ = .92/3 - 1.06y5 - .44/7 High frequency component of motor exciting current, = .07/3 - -08/5 - . 428 AL TERN A TING-CURRENT PHEA'OAIENA. thus, total high frequency component of motor current, /o1 = |f ...", "... ng the conductance, n and the higher harmonics of counter E.M.F. Thus we have, Current input in the condenser, fc = E, Yc = - 4.28/i - 1.54/3 + 4.93/5 + 4.02/7 High frequency component of motor impedance current, |£ = .92/3 - 1.06y5 - .44/7 High frequency component of motor exciting current, = .07/3 - -08/5 - . 428 AL TERN A TING-CURRENT PHEA'OAIENA. thus, total high frequency component of motor current, /o1 = |f + & y1 = .99y3 - 1.14,; - .47/7 and total current, without condenser, 4 = 4 + ...", "... = - 4.28/i - 1.54/3 + 4.93/5 + 4.02/7 High frequency component of motor impedance current, |£ = .92/3 - 1.06y5 - .44/7 High frequency component of motor exciting current, = .07/3 - -08/5 - . 428 AL TERN A TING-CURRENT PHEA'OAIENA. thus, total high frequency component of motor current, /o1 = |f + & y1 = .99y3 - 1.14,; - .47/7 and total current, without condenser, 4 = 4 + 41 = Is + .99/3 - 1.14,; - .47/7 with condenser, = 4 - 4.28,i - . and herefrom the power factor. 3.79,; + 3.55/7 T PER PH ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "... cy reactance, X\\, of the secondary, but only the low-fre- quency reactance, sxi, especially if the commutated winding is in the same slots with the squirrel-cage winding: the short-circuited squirrel-cage winding acts as a short-circuited secondary to the high-frequency pulsation of the commutated current, and there- fore makes the circuit non-inductive for these high-frequency pulsations, or practically so. That is, in the short-circuited con- ductors, local currents are induced equal and opposite to the high-frequency ...", "... winding is in the same slots with the squirrel-cage winding: the short-circuited squirrel-cage winding acts as a short-circuited secondary to the high-frequency pulsation of the commutated current, and there- fore makes the circuit non-inductive for these high-frequency pulsations, or practically so. That is, in the short-circuited con- ductors, local currents are induced equal and opposite to the high-frequency component of the commutated current, and the total resultant of the currents in each slot thus is only the low ...", "... high-frequency pulsation of the commutated current, and there- fore makes the circuit non-inductive for these high-frequency pulsations, or practically so. That is, in the short-circuited con- ductors, local currents are induced equal and opposite to the high-frequency component of the commutated current, and the total resultant of the currents in each slot thus is only the low- frequency current. Such short-circuited squirrel cage in addition to the commu- tated winding, makes the use of a commutator practicable for ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-13", "section_label": "Chapter 9: High-Frequency Conductors. 403", "section_title": "High-Frequency Conductors. 403", "kind": "chapter", "sequence": 13, "number": 9, "location": "lines 1014-1042", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-13/", "snippets": [ "CHAPTER IX. HIGH-FREQUENCY CONDUCTORS. 403 80. Effect of the frequency on the constants of a conductor. 403 81. Thermal resistance and radiation resistance, internal and external reactance, as functions of the frequency. 405 82. Total impedance of high frequency conductor, and ...", "CHAPTER IX. HIGH-FREQUENCY CONDUCTORS. 403 80. Effect of the frequency on the constants of a conductor. 403 81. Thermal resistance and radiation resistance, internal and external reactance, as functions of the frequency. 405 82. Total impedance of high frequency conductor, and its components, discussion. 407 83. Example of copper and iron wire, copper ribbon and iron pipe ; tabulation and discussion of numerical values. 408 84. Continued discussion of results. • 409 85. Potential drop in conductors carrying ...", "... conductor, and its components, discussion. 407 83. Example of copper and iron wire, copper ribbon and iron pipe ; tabulation and discussion of numerical values. 408 84. Continued discussion of results. • 409 85. Potential drop in conductors carrying high frequency currents. Tabulation. Effect of conductor shape and material. 412 CONTENTS. SECTION IV. TRANSIENTS IN TIME AND SPACE. PAGE" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-31", "section_label": "Chapter 9: Divided Circuit", "section_title": "Divided Circuit", "kind": "chapter", "sequence": 31, "number": 9, "location": "lines 9228-10474", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "snippets": [ "... ed e.m.f., e0, it is, and a DIVIDED CIRCUIT 139 pulsation of impressed e.m.f., e0, of a frequency of 120 cycles re- appears in the load current iv reduced to 1 per cent of its value. In cases where from a source of e.m.f., e0, which contains a slight high frequency pulsation — as the pulsation corresponding to the commutator segments of a commutating machine — a current is desired showing no pulsation whatever, as for instance for the operation of a telephone exchange, a very high inductive reactance in series with ...", "... ing machine — a current is desired showing no pulsation whatever, as for instance for the operation of a telephone exchange, a very high inductive reactance in series with the circuit, and a condensive reactance in shunt therewith, entirely eliminates all high frequency pulsa- tions from the current, passing only harmless low frequency pulsations at a greatly reduced amplitude. 81. As a further example is shown in Fig. 37 the pulsation of a non-inductive circuit, xl = 0, of the resistance rl = 4 ohms, shunted by a cond ...", "... t. At 6 = 0.2, the drop of current is 0.23 and 0.95 per cent respectively. For longer times or larger values of 6, the difference produced by the condenser becomes less and less. This effect of a condenser across a direct-current circuit, of suppressing high frequency pulsations from reaching the circuit, requires a very large capacity." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-37", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 37, "number": 1, "location": "lines 15354-15625", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-37/", "snippets": [ "... t, voltage, etc., and the permanent term occasionally is very small compared with the transient term. 4. Periodic transient phenomena are of engineering impor- tance mainly in three cases: (1) in the control of electric circuits; (2) in the production of high frequency currents, and (3) in the rectification of alternating currents. 1. In controlling electric circuits, etc., by some operating mechanism, as a potential magnet increasing and decreasing the resistance of the circuit, or a clutch shifting brushes, etc., the ...", "... erms, any resultant inter- mediary between the two extremes can thus be produced. On this principle, for instance, operated the controlling solenoid of the Thomson-Houston arc machine, and also numerous auto- matic potential regulators. 2. Production of high frequency oscillating currents by period- ically recurring condenser discharges has been discussed under \" oscillating current generator,\" in Section I, paragraph 44. Non-sinusoidal high frequency alternating currents are pro- duced by an arc, when made unstable b ...", "... also numerous auto- matic potential regulators. 2. Production of high frequency oscillating currents by period- ically recurring condenser discharges has been discussed under \" oscillating current generator,\" in Section I, paragraph 44. Non-sinusoidal high frequency alternating currents are pro- duced by an arc, when made unstable by shunting it with a condenser, as discussed before. The Ruhmkorff coil or inductorium also represents an appli- cation of periodically recurring transient phenomena, as also does Prof. ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-41", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 41, "number": 1, "location": "lines 19260-19338", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "snippets": [ "... na in space are of importance in electrical engineering are : (a) Circuits containing distributed capacity and self-induc- tance, as long-distance energy transmission lines, long-distance telephone circuits, multiple spark-gaps, as used in some forms of high potential lightning arresters (multi-gap arrester), etc. (b) The distribution of alternating current in solid conductors and the increase of effective resistance and decrease of effective inductance resulting therefrom. (c) The distribution of alternating magneti ...", "... of a conductor through space, resulting from the finite velocity of propagation of the electric field, and the variation of self-inductance and mutual inductance and of capacity of a conductor without return, as function of the frequency, in its effect on wireless telegraphy. (e) Conductors conveying very high frequency currents, as lightning discharges.", "... te velocity of propagation of the electric field, and the variation of self-inductance and mutual inductance and of capacity of a conductor without return, as function of the frequency, in its effect on wireless telegraphy. (e) Conductors conveying very high frequency currents, as lightning discharges." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "... s oscillations and surges; the former is often more convenient to show the relation to traveling waves. In Figs. 35 and 36 are shown oscillograms of such line oscilla- tions. Fig. 35 gives the oscillation produced by switching 28 miles of 100-kv. line by high-tension switches onto a 2500-kw. step-up transformer in a substation at the end of a 153-mile three- phase line; Fig. 36 the oscillation of the same system caused by switching on the low-tension side of the step-up transformer. 29. As seen, the phase of current ...", "... ferent circuit sections, of different con- stants and therefore different wave lengths, as for instance an overhead line, the underground cable, in which the wave length is about one-half what it is in the overhead line (k = 4) and coiled windings, as the high-potential winding of a transformer, in which the wave length usually is relatively short. In the velocity measure of length, the wave length becomes the same throughout all these circuit sections, and the investigation is thereby greatly simplified. 84 ELECTRIC ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3956-4744", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "snippets": [ "... s oscillations and surges; the former is often more convenient to show the relation to traveling waves. In Figs. 35 and 36 are shown oscillograms of such line oscilla- tions. Fig. 35 gives the oscillation produced by switching 28 miles of 100-kv. line by high-tension switches onto a 2500-kw. step-up transformer in a substation at the end of a 153-mile three- phase line; Fig. 36 the oscillation of the same system caused by switching on the low-tension side of the step-up transformer. 29. As seen, the phase of current ...", "... ferent circuit sections, of different con- stants and therefore different wave lengths, as for instance an overhead line, the underground cable, in which the wave length is about one-half what it is in the overhead line (K = 4) and coiled windings, as the high-potential winding of a transformer, in which the wave length usually is relatively short. In the velocity measure of length, the wave length becomes the same throughout all these circuit sections, and the investigation is thereby greatly simplified. 84 ELECTRIC ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-10", "section_label": "Lecture 10: Inductance And Capacity Of Round Parallel Conductors", "section_title": "Inductance And Capacity Of Round Parallel Conductors", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6089-7274", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "snippets": [ "... the current i. The capacity is the ratio of the dielectric flux to the voltage, where \\f/ is the dielectric flux, or number of lines of dielectric force, and e the voltage which produces it. With a single round conductor without return conductor (as wireless antennae) or with the return conductor at infinite dis- tance, the lines of magnetic force are concentric circles, shown by drawn lines in Fig. 8, page 10, and the lines of dielectric force are straight lines radiating from the conductor, shown dotted in ...", "... equency, etc., given. The same applies for the flux $1, which is reduced by unequal current density due to its screening effect, so that in the limiting case, for conductors of perfect conductivity, that is, zero resistance, or for infinite, that is, very high frequency, only the magnetic flux $1 exists, which is shown shaded in Fig. 5; but 2 and $3 are zero, and the inductance is . (15) ROUND PARALLEL CONDUCTORS. 125 That is, in other words, with small conductors and moderate currents, the total inductance ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... ation from sine shape is suffi- cient to require practical consideration/ especially in those cases, where the electric circuit contains electrostatic capacity, as is for instance, the case with long-distance transmission lines, underground cable systems, high potential transformers, etc. (However, no matter how much the alternating or other periodic wave differs from simple sine shape — ^that is, however much the wave is '' distorted,\" it can always be represented by the trigonometric seriesj(3). As illustration the ...", "... value of the fundamental voltage wave thus is: 25,400 X V2 = 36,000 volts, or 36 kv.; that is, eo = 36, and e = 36{sin 6-0.12 sin (3^-2.3°)-0.23 sin (5^-1.5°) + 0.13 sin (7^-6.2°)}, . (2) would be the voltage supplied to the transmission line at the high potential terminals of the step-up transformers. From the wire tables, the resistance per mile of No. 0 B. & S. copper line wire is ro = 0.52 ohm. The inductance per mile of wire is given by the formula : Lo = 0.7415 log ^+0.0805mh, .... (3) where h is the dis ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-06", "section_label": "Lecture 6: Higher Harmonics Of The Generator Wave", "section_title": "Higher Harmonics Of The Generator Wave", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3133-3507", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-06/", "snippets": [ "... ill low enough so that in case of a ground on one phase, enough current flows over the neutral to open the circuit breaker of the grounded phase. The use of a resistance in the generator neutral is very desirable also, since it eliminates the danger of a high frequency oscillation between line and ground through the generator reactance in the path of the third harmonic, by damping the oscillation in the resistance. For this reason, the resistance should be non-inductive. To ground the gener- ator neutral through a react ...", "... gener- ator neutral through a reactance is very dangerous since it intensifies the danger of a resonance voltage rise. In grounding the generator neutral, special care is neces- sary to get perfect contact, since an arc or loose contact would generate a high frequency in the circuit of the third harmonic and so may lead to a higher frequency oscillation between line and ground." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-08", "section_label": "Lecture 8: Generation", "section_title": "Generation", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 3781-4217", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-08/", "snippets": [ "... f consumption as considera- tions of the cost of property, the availability of condensing water for the engines, the facilities of transportation, etc., per- mit. Transmission lines therefore are less frequently used, but in steam stations of large power, high potential distribution cir- cuits of 6600, 11,000 or 13,200 volts, commonly underground by cables, are used in supplying electric power from the main generating station, to the substations as centres of secondary distribution (New York, Chicago, etc.). As source ...", "... st moment after the short circuit the armature current is limited by self-induction only, and is therefore much larger than afterwards, when self-induction and armature reaction both act. In machines of low armature reaction and high self- induction, as high frequency alternators, the momentary short circuit current is not much larger than the permanent short circuit current. In machines of low self-induction, that is, of a well distributed armature winding, but high armature reac- tion, (that is, very large output per ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... sible ultra-red radiation and the ultra-violet radiation and the non-refrangible radiations, as X-rays, etc., separated from the latter by the second blank space of the radiation spectrum. In the following, mainly the light waves, that is, the second or high frequency range of radiation, will be discussed. The elec- tric waves are usually of importance only in their relation to the radiator or oscillator which produces them, or to the receiver on which they impinge, and thus are treated in connection with the radiator ...", "... second blank space of the radiation spectrum. In the following, mainly the light waves, that is, the second or high frequency range of radiation, will be discussed. The elec- tric waves are usually of importance only in their relation to the radiator or oscillator which produces them, or to the receiver on which they impinge, and thus are treated in connection with the radiator or receiver, that is, the electric conductor, in the theory of transient electric phenomena and oscillations.* The radiation may be of a s ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-19", "section_label": "Theory Section 19: Fields of Force", "section_title": "Fields of Force", "kind": "theory-section", "sequence": 19, "number": 19, "location": "lines 7737-7990", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-19/", "snippets": [ "... masses — which cause the stone to fall toward the earth, and water to run down hill — and this space thus is a field of gravitational force, the earth the gram- motive force. In the space surrounding conductors having a high potential difference, we observe a field of dielectric force, that is, electro- static or dielectric forces are exerted, and the potential difference between the conductors is the electromotive force of the dielectric field. The force ...", "... ability, as used in dealing with magnetic circuits, correspond the terms 118 ELEMENTS OF ELECTRICAL ENGINEERING dielectric flux, dielectric field intensity, permittivity, as used in dealing with the electrostatic fields of high potential apparatus, as transmission insulators, transformer bushings, etc. The fore- most difference is that in the magnetic field, a line of force must always return into itself in a closed circuit, while in the electro- static or d ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-13", "section_label": "Chapter 13: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 13484-14333", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-13/", "snippets": [ "... arge conductors, as the iron rails of the return circuit of alternating-current rail- ways, is given in Section III of \"Theory and Calculation of Tran- sient Electric Phenomena and Oscillations.\" In practice, this phenomenon is observed mainly with very high frequency currents, as lightning discharges, wireless tele- graph and lightning arrester circuits; in power-distribution cir- cuits it has to be avoided by either keeping the frequency suffi- ciently low or having a shape of conductor such that unequal current-dist ...", "... circuit of alternating-current rail- ways, is given in Section III of \"Theory and Calculation of Tran- sient Electric Phenomena and Oscillations.\" In practice, this phenomenon is observed mainly with very high frequency currents, as lightning discharges, wireless tele- graph and lightning arrester circuits; in power-distribution cir- cuits it has to be avoided by either keeping the frequency suffi- ciently low or having a shape of conductor such that unequal current-distribution does not take place, as by using a ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-26", "section_label": "Chapter 26: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 32540-33010", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-26/", "snippets": [ "... The voltage will not exceed twice the normal, even at a fre- quency of complete resonance with the higher harmonic, if none of the higher harmonics amounts to more than 7 per cent, of the fundamental. Herefrom it follows that the danger of resonance in high-potential lines is frequently overestimated, since the conditions assumed in this example are rather more severe than found in hnes of moderate length, the capacity current of such line very seldom reaching 20 per cent, of the main current, 254. The power develope ...", "... constant relation to the output of the secondary circuit, as obvious, since the division of power between the two secondary circuits— the eddy-current circuit and the useful or consumer circuit — is unaffected by wave-shape or intensity of magnetism. In high-potential lines, distorted waves whose maxima are very high above the effective values, as peaked waves, are objectionable by increasing the strain on the insulation. The striking-distance of an alternating voltage depends upon the maximum value, except at extremel ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-33", "section_label": "Chapter 33: Efficiency Of Systems", "section_title": "Efficiency Of Systems", "kind": "chapter", "sequence": 33, "number": 33, "location": "lines 36515-37127", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-33/", "snippets": [ "... circuits, in considering the danger to life from live wires entering buildings or otherwise accessible, the comparison on the basis of maximum potential also appears appropriate. Thus the comparison of different systems of long-distance transmission at high potential or power distribution for motors is to be made on the basis of equality of the maximum difference of potential existing in the system; the comparison of low-poten- tial distribution circuits for lighting on the basis of equality of the minimum difference ...", "... results only in the number of insulators required, etc. Only where the amount of power is so small that mechanical strength, and not power loss, determines the size of the conductor, a saving results by replacing one of the conductors by the ground. The high-tension, direct-current system, whether insulated, or with grounded neutral, or with ground return, appears equal in copper efficiency to a single-phase system of the same character (insulated, or with grounded neutral, or with ground return) and of the same effe ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... g an increase of the ohmic resistance due to unequal current distribution. The general solution of this problem for round conduc- tors leads to complicated equations, and can be found in Maxwell. In practice, this phenomenon is observed only with very high frequency currents, as lightning discharges ; in power distribution circuits it has to be avoided by either keeping the frequency sufficiently low, or having a shape of con- ductor such that unequal current distribution . does not take place, as by using a tubular ...", "... iron, and thus a loss of energy per cycle proportional to the frequency. The existence of a loss of power in the dielectric, pro- portional to the square of the frequency, I observed some time ago in paraffined paper in a high electrostatic field and at high frequency, by the electro-dynamometer method, and other observers under similar conditions have found the same result. Arno of Turin found at low frequencies and low field strength in a larger number of dielectrics, a loss of energy per cycle independent of the f ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-22", "section_label": "Chapter 20: Ri", "section_title": "Ri", "kind": "chapter", "sequence": 22, "number": 20, "location": "lines 24560-25119", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "snippets": [ "... The voltage ^ill not exceed twice the normal, even at a frequency of complete resonance with the higher har- monic, if none of the higher harmonics amounts to more than 7 per cent, of the fundamental. Herefrom it follows that the danger of resonance in high potential lines is in general greatly over-estimated. 226. The power developed by a complex harmonic wave in a non-inductive circuit is the sum of the powers of the individual harmonics. Thus if upon a sine wave of alter- nating E.M.F. higher harmonic waves are su ...", "... ion to the output of the secondary circuit, as obvious, since the division of power between the two secondary circuits — the eddy current circuit, and the useful or consumer cir- cuit — is unaffected by wave-shape or intensity of mag- netism. • 231. In high potential lines, distorted waves whose maxima arc very high above the effective values, as peaked waves, may be objectionable by increasing the strain on the insulation. It is, however, not settled yet beyond doubt whether the striking-distance of a rapidly alterna ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "... an increase of the ohmic resistance due to unequal current distribution. The general solution of this problem for round conduc- tors leads to complicated equations, and can be found else- where. In practice, this phenomenon is observed only with very high frequency currents, as lightning discharges ; in power distribution circuits it has to be avoided by either keeping the frequency sufficiently low, or having a shape of con- ductor such that unequal current distribution does not take place, as by using a tubular or ...", "... iron, and thus a loss of energy per cycle proportional to the frequency. The existence of a loss of power in the dielectric, pro- portional to the square of the frequency, I observed some time ago in paraffined paper in a high electrostatic field and at high frequency, by the electro-dynamometer method, and other observers under similar conditions have found the same result. Arno of Turin found at low frequencies and low field strength in a larger number of dielectrics, a loss of energy per cycle independent of the f ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-23", "section_label": "Chapter 23: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 21983-22448", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "snippets": [ "... the normal, even at a frequency of complete resonance with the higher har- monic, if none of the higher harmonics amounts to more EFFECTS OF HIGHER HARMONICS. 405 than 7 per cent, of the fundamental. Herefrom it follows that the danger of resonance in high potential lines is in general greatly over-estimated, since the conditions assumed in this instance are rather more severe than found in prac- tice, the capacity current of the line very seldom reaching 20% of the main current. 247. The power developed by a compl ...", "... ation to the output of the secondary circuit, as obvious, since the division of power between the two secondary circuits — the eddy current circuit, and the useful or consumer cir- cuit — is unaffected by wave-shape or intensity of mag- netism. 252. In high potential lines, distorted waves whose maxima are very high above the effective values, as peaked waves, may be objectionable by increasing the strain on the insulation. It is, however, not settled yet beyond doubt whether the striking-distance of a rapidly alterna ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-21", "section_label": "Chapter 23: Review", "section_title": "Review", "kind": "chapter", "sequence": 21, "number": 23, "location": "lines 32138-32819", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-21/", "snippets": [ "... tion and of operation, discussed in the preceding, an alphabetical list of them is given in the following, comprising name, definition, principal characteristics, advantages and dis- advantages, and the paragraph in which they are discussed. Alexanderson High-frequency Inductor Alternator. — 159. Comprises an inductor disk of very many teeth, revolving at very high speed between two radial armatures. Used for producing very high frequencies, from 20,000 to 200,000 cycles per second. Amortisseur. — Squirrel-cage winding ...", "... r second. Amortisseur. — Squirrel-cage winding in the pole faces of the synchronous machine, proposed by Leblanc to oppose the hunt- ing tendency, and extensively used. Amplifier. — 161. An apparatus to intensify telephone and radio telephone currents. High-frequency inductor alternator excited by the telephone current, usually by armature reaction through capacity. The generated current is then rectified, be- fore transmission in long-distance telephony, after transmission in radio telephony. Arc Machines. — 138. C ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-22", "section_label": "Chapter 24: Conclusion", "section_title": "Conclusion", "kind": "chapter", "sequence": 22, "number": 24, "location": "lines 32820-33531", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-22/", "snippets": [ "... it is an illustration of the impossibility of a rigid classi- fication of all the machine types. INDEX Also see alphabetical list of apparatus in Chapter XXIII. Acyclic, see Unipolar. Adjustable speed polyphase motor, 321, 378 Alcxanderson very high frequency inductor alternator, 279 Amplifier, 281 Arc rectifier, 248 Armature reaction of regulating pole converter, 426, 437 of unipolar machine, 457 B Balancer, phase, 228 Battery charging rectifier, 244 Brush arc machine as quarterphase rectifier, 2 ...", "... ble squirrel cage induction motor, 29 Double synchronous induction gen- erator, 191, 199, 201 Drum type of unipolar machine, 454 477 478 lUfiEX E Eddy current starting device of in- duction motor, 8 in unipolar machine, 456 Eickemeyer high frequency inductor alternator, 280 F Flashing of rectifier, 249 Frequency converter, 176 pulsation, effect in induction motor, 131 Full wave rectifier, 245 G General alternating current motor, 300 Generator regulation affecting induc- tion motor s ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-01", "section_label": "Chapter 1: Electric Conduction. Soled And Liquid", "section_title": "Electric Conduction. Soled And Liquid", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 959-3894", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-01/", "snippets": [ "... oke, powdered metal, with non-conductors as clay, carborundum, cement, also have pyroelectric conduction. Such are used, for instance, as \"resistance rods\" in lightning arresters, in some rheostats, as ELECTRIC CONDUCTION 13 cement resistances for high-frequency power dissipation in re- actances, etc. Many, if not all so-called \"insulators\" probably are in reality pyroelectric conductors, in which the maximum voltage point 6 is so high, that the range (3) of decreasing charac- teristic can be reached only by the ...", "... that their resistance increases permanently, often by many hundred per cent, when the conductor is for some time exposed to high-fre- quency electrostatic discharges. Coherer action, that is, an abrupt change of conductivity by an electrostatic spark, a wireless wave, etc., also is exhibited by some pyroelectric conductors. 13. Operation of pyroelectric conductors on a constant- voltage circuit, and in the unstable branch (3), is possible by the insertion of a series resistance (or reactance, in alternating-curr ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-16", "section_label": "Chapter 3: Standing Waves. 442", "section_title": "Standing Waves. 442", "kind": "chapter", "sequence": 16, "number": 3, "location": "lines 1087-1111", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-16/", "snippets": [ "CHAPTER III. STANDING WAVES. 442 14. Oscillatory, critical and gradual standing wave. 442 15. The wave length which divides the gradual from the oscillatory wave. 446 16. High-power high-potential overhead transmission line. Character of waves. Numerical example. General equations. 449 17. High-potential underground power cable. Character of waves. Numerical example. General equations. 452 18. Submarine telegraph cable. Existence of logarithmi ...", "... latory, critical and gradual standing wave. 442 15. The wave length which divides the gradual from the oscillatory wave. 446 16. High-power high-potential overhead transmission line. Character of waves. Numerical example. General equations. 449 17. High-potential underground power cable. Character of waves. Numerical example. General equations. 452 18. Submarine telegraph cable. Existence of logarithmic waves. 454 19. Long distance telephone circuit. Numerical example. Effect of leakage. Effect of inductance ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-23", "section_label": "Chapter 1: The Constants Of The Electric Circuit", "section_title": "The Constants Of The Electric Circuit", "kind": "chapter", "sequence": 23, "number": 1, "location": "lines 1317-1992", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "snippets": [ "... t the capacity C can for most purposes be neglected and the circuit treated as containing resistance and inductance only. 14 TRANSIENT PHENOMENA Of approximately equal magnitude is the electromagnetic energy —— and the electrostatic energy - ^ in the high-potential Zi iL long-distance transmission circuit, in the telephone circuit, and in the condenser discharge, and so in most of the phenomena resulting from lightning or other disturbances. In these cases all three circuit constants, r, L, and C, are of essentia ...", "... stop a slowly moving light carriage, the instant stoppage, as by collision, of a fast railway train leads to the usual disastrous result. So also, in electric systems of small stored energy, a sudden change of circuit con- ditions may be safe, while in a high-potential power system of very great stored electric energy any change of circuit conditions requiring a sudden change of energy is liable to be destructive. THE CONSTANTS OF THE ELECTRIC CIRCUIT 15 Where electric energy is stored in one form only, usually littl ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-29", "section_label": "Chapter 7: Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "section_title": "Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "kind": "chapter", "sequence": 29, "number": 7, "location": "lines 6798-7825", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "snippets": [ "... 6°) - £-°-75'(410# - 99). Here also no value of 00 exists at which the transient term disappears. 69. The most important is the oscillating case, r2 < 4 x xc, since it is the most common in electrical circuits, as underground cable systems and overhead high potential circuits, and also is practically the only one in which excessive currents or excessive voltages, and thereby dangerous phenomena, may occur. RESISTANCE, INDUCTANCE, AND CAPACITY 97 If the condensive reactance xc is high compared with the resistan ...", "... ound cables, which are of low inductance, and the inductance is in the generating system, which has practically no capacity. In an underground cable system the tendency therefore is RESISTANCE, INDUCTANCE, AND CAPACITY 103 either towards a local, very high frequency oscillation, or travel- ing wave, of very limited power, in a part of the cables, or a low frequency high power surge, frequently of destructive magnitude, of the joint capacity of the cables, against the inductance of the generating system. 63. The phy ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-40", "section_label": "Chapter 4: Arc Rectification", "section_title": "Arc Rectification", "kind": "chapter", "sequence": 40, "number": 4, "location": "lines 17755-19259", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "snippets": [ "... of constant-current mercury arc rectifier. 24. As illustrations of the above phenomena are shown in Fig. 66 the performance curves of a small constant-current rec- tifier, and in Figs. 67 to 76 oscillograms of this rectifier. Interesting to note is the high frequency oscillation at the ter- mination of the jump of the potential difference cC (Fig. 60) which represents the transient term resulting from the electro- static capacity of the transformer. At the end of the period of overlap of the two rectifying arcs one of ...", "... equal power. The actual current and e.m.f. waves of the arc rectifier thus may be replaced by their equivalent sine waves, for general calculation, except when investigating the phenomena resulting from the discontinuity in the change of current, as the high frequency oscillation at the end and to a lesser extent at the beginning of the period of overlap of the rectifying arcs, and similar phenomena. In a constant-current mercury arc rectifier system, of which the exact equations or rather groups of equations of curre ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-54", "section_label": "Chapter 5: Free Oscillations", "section_title": "Free Oscillations", "kind": "chapter", "sequence": 54, "number": 5, "location": "lines 31451-32708", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "snippets": [ "... nt wave, therefore, are not sym- metrical. From h = 0 follows, by equation (56), s=0, if k2 > LCm\\ ] and (212) 9 = 0, if k2< LCm\\ J The smallest value of k which can exist from equation (210) is and, as discussed in paragraph (15), this value in high-potential high-power circuits usually is very much larger than LCm2, so that the case q = 0 is realized only in extremely long circuits, as long-distance telephone or submarine cable, but not in trans- mission lines, and the first case, s = 0, therefore, is of most ...", "... reases, due to unequal current distribution in the conductor, as discussed in Section III, L slightly decreases hereby, g increases by the energy losses resulting from brush discharges and from electro- static radiation, etc., so that, in general, at very high frequency an increase of y and ^, and therewith of u, may be expected; Li C that is, very high harmonics would die out with greater rapidity, which would result in smoothing out the wave shape with increas- ing decay, making it more nearly approach the fundament ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-02", "section_label": "Chapter 2: Potential Series And Exponential Function", "section_title": "Potential Series And Exponential Function", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3492-6063", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-02/", "snippets": [ "... the exponential function, but that in this function the exponent may be real, or may be imaginary, and in the latter case, the expression is put into real form by intro- ducing the trigonometric functions. EXAMPLE 1. 6o. A condenser (as an underground high-potential cable) of 20 mf. capacity, and of a voltage of eo = 10,000, discharges through an inductance of 50 mh. and of negligible resistance, What is the equation of the discharge current? The current consumed by a condenser of capacity C and potential differen ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-04", "section_label": "Chapter 5: Methods Of Approximation", "section_title": "Methods Of Approximation", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 15156-16482", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-04/", "snippets": [ "... . a J 138. As further example may be considered the equations of an alternating-current electric circuit, containing distributed resistance, inductance, capacity, and shunted conductance, for instance, a long-distance transmission line or an underground high-potential cable. Equations of the Transmission Line. Let I be the distance along the line, from some starting point; E^ the voltage; 7, the current at point I, expressed as vector quantities or general numbers; Zo^ro—jxo, the line impedance per unit length (for ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... derived the Abelian functions. In physics and in engineering, integration of special functions in this manner frequently leads to new special functions. For instance, in the study of the propagation through space, of the magnetic field of a conductor, in wireless telegraphy, lightning protection, etc., we get new functions. If ^=/(0 is the current in the conductor, as function of the time t, at a distance x from the conductor the magnetic field lags by the X time ti = -, where S is the speed of propagation (vel ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-01", "section_label": "Lecture 1: General", "section_title": "General", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 275-735", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-01/", "snippets": [ "... he decrease of length, the slowing down of time, the increase of mass, becomes appreciable only at velocities approaching that of the light. Thus at ordinary every- day velocities length, time and mass are constant; but in the vacuum tubes used in our big wireless stations to pro- duce electrical vibrations which carry the message through space across oceans and continents, or to receive the faint signal arriving from far-distant stations, the current is carried through the empty space of the tube by minute RELA ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-14", "section_label": "Lecture 14: Alternating Current Railway Motor", "section_title": "Alternating Current Railway Motor", "kind": "lecture", "sequence": 14, "number": 14, "location": "lines 8649-9342", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-14/", "snippets": [ "... an in a direct current motor. Good direct current motor design requires a strong field and weak armature, to get little field distortion and therefore good commutation ; that is high n and low m. But such pro- portions, even at low supply frequency N and high frequency of rotation No, would give a hopelessly bad power factor, and ALTERNATING CURRENT MOTOR 179 thus a commercially impractical motor. In the alternating cur- rent commutator motor, it is therefore essential to use as strong an armature and as weak a fiel ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-15", "section_label": "Lecture 15: Electrochemistry", "section_title": "Electrochemistry", "kind": "lecture", "sequence": 15, "number": 15, "location": "lines 9343-9686", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-15/", "snippets": [ "... e, etc., and numerous alloys of refractory metals, mainly with iron; as of vanadium, tungsten, molybdenum, titanium, etc., which are used in steel manufacture. The use of the electric arc for the production of nitric acid and mtraite fertilizers ; of the high potential glow discharge for the production of ozone for water purification, etc., also are applications of electric power, which are of rapidly increas- ing industrial importance." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-08", "section_label": "Lecture 8: Arc Lamps And Arc Lighting", "section_title": "Arc Lamps And Arc Lighting", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 7141-8510", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-08/", "snippets": [ "... he constant-current circuit. In American towns and cities, where arc lamps are used for street lighting, practically always the entire city up to the farthest suburbs is lighted by arc lamps, and frequently arc lamps installed even beyond the reach of the high-potential primary alternating-current supply. To reach such distances with low-voltage constant-potential supply, is impossible, and thus the constant-current series system becomes necessary. In European cities, where a prejudice exists against high-voltage consta ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-105", "section_label": "Apparatus Section 8: Alternating-current Transformer: Autotransformer", "section_title": "Alternating-current Transformer: Autotransformer", "kind": "apparatus-section", "sequence": 105, "number": 8, "location": "lines 18666-18812", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-105/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-105/", "snippets": [ "... interconnects primary and sec- ondary circuit and thereby puts the voltage of the higher voltage circuit onto the lower voltage circuit. Thus, when using auto- transformers, the insulation of the low voltage circuit and the high potential tests of all the apparatus used in the low voltage circuit must be those of the high voltage circuit. Furthermore, a ground in one of the two circuits of an autotransformer also is a ground on the other circuit, while ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-110", "section_label": "Apparatus Section 4: Induction Machines: Induction Generator", "section_title": "Induction Machines: Induction Generator", "kind": "apparatus-section", "sequence": 110, "number": 4, "location": "lines 21158-21588", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-110/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-110/", "snippets": [ "... umber of types of synchronous induction genera- tors have been devised, either with commutator for excitation or without commutator and with excitation by low-frequency synchronous or commutating machine, in the armature, or by high-frequency excitation. For particulars regarding these very interesting machines, see \" Theory and Calculation of Alternat- ing-current Phenomena.\"" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-37", "section_label": "Apparatus Section 16: Synchronous Machines: Higher Frequency Cross Currents Between Synchronous Machines", "section_title": "Synchronous Machines: Higher Frequency Cross Currents Between Synchronous Machines", "kind": "apparatus-section", "sequence": 37, "number": 16, "location": "lines 10124-10189", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-37/", "snippets": [ "... current supplying the losses in the machine. It is only in the parallel operation of very large high-speed machines (steam turbine driven alternators) of high armature reaction and very low armature self-induction that such high- frequency cross currents may require consideration, and even then only in three-phase F-connected generators with grounded neutral, as cross currents between the neutrals of the machines. In a three-phase machine, the voltage between th ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-38", "section_label": "Apparatus Section 17: Synchronous Machines: Short-circuit Currents of Alternators", "section_title": "Synchronous Machines: Short-circuit Currents of Alternators", "kind": "apparatus-section", "sequence": 38, "number": 17, "location": "lines 10190-10429", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-38/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-38/", "snippets": [ "... re x = self-inductive reactance, which is due to a true self-inductance, and x' = effective reactance of armature reaction, which is not instantaneous. 32. In machines of high self-inductance and low armature re- action, as high frequency alternators, this momentary increase of short-circuit current over its normal value is negligible, and moderate in machines in which armature reaction and self-in- ductance are of the same magnitude, as large modern multi- pol ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-89", "section_label": "Apparatus Section 11: Synchronous Converters: Double-current Generators", "section_title": "Synchronous Converters: Double-current Generators", "kind": "apparatus-section", "sequence": 89, "number": 11, "location": "lines 15893-15982", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-89/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-89/", "snippets": [ "... limited to those sizes and speeds at which a good direct-current generator can be built with the same number of poles as a good alternator, that is, low- frequency machines of large output and relatively high speed; while high-frequency low-speed double-current generators are undesirable. The essential difference between double-current generator and converter is, however, that in the former the direct current and the alternating current are not in opposition a ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-90", "section_label": "Apparatus Section 12: Synchronous Converters: Conclusion", "section_title": "Synchronous Converters: Conclusion", "kind": "apparatus-section", "sequence": 90, "number": 12, "location": "lines 15983-16064", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-90/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-90/", "snippets": [ "... al to half that of a direct-current generator. Such motor converters have been recommended for high-fre- quency systems, as their commutating component is of half frequency, and thus affords a better commutator design than a high-frequency converter. They are necessarily much larger than standard converters, but are smaller than motor generator sets, as half the power is converted in either machine. One advantage of this type of machine for phase control is ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1120-1683", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-01/", "snippets": [ "... low-resistance circuits containing large inductive reactance and large condensive reactance in series with each other, so as to produce resonance effects of these higher harmonics, and also under certain conditions of long-distance power transmission and high-potential distribution. 8. Experimentally, the impedance, effective resistance, induc- tance, capacity, etc., of a circuit or a part of a circuit are con- veniently determined by impressing a sine wave of alternating e.m.f. upon the circuit and measuring with alte ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-11", "section_label": "Chapter 11: Phase Control", "section_title": "Phase Control", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 9767-10717", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-11/", "snippets": [ "... ng the field excitation with the load is automatically, by a series field-coil traversed by the direct-current output. The field windings of converters intended for phase control — as for the supply of power to electric railways, from substations fed by a high-potential alternating-current transmission line — ■ are compound-wound, and the shunt field is adjusted for under- excitation, so as to produce at no-load the lagging current, i'o, and the series field adjusted so as to make the reactive compo- nent of current, i', ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-22", "section_label": "Chapter 22: Armature Reactions Of Alternators", "section_title": "Armature Reactions Of Alternators", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 23971-25134", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-22/", "snippets": [ "... erma- nent short-circuit current; many times in a machine of low self-induction and high armature reaction, as a low-frequency, high-speed alternator of large capacity; relatively little in a machine of low armature reaction and high self-induction, as a high-frequency unitooth alternator, 193. Graphically, the internal reactions of the alternating- current generator can be represented as follows: Let the impressed m.m.f., or field excitation, Fo, be repre- sented by the vector OFo, in Fig. 139, chosen for convenience ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-25", "section_label": "Chapter 25: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 29375-32539", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-25/", "snippets": [ "... ve has become very peaked, by a pronounced third harmonic of an effective value of 0.24 E — that is, 38.5 per cent, of the effective value of the total wave. The very high peak of e.m.f. produced by this wave-shape distortion is liable to be dangerous in high-potential, three- phase systems by increasing the strain on the insulation between lines and ground, and leading to resonance phenomena with the third harmonic. The maximum value of the distorted wave of magnetism is 8.89, while with a sine wave it would be 10.0, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-28", "section_label": "Chapter 28: Copper Efficiency Of Systems", "section_title": "Copper Efficiency Of Systems", "kind": "chapter", "sequence": 28, "number": 28, "location": "lines 26584-27052", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-28/", "snippets": [ "... tric strain on the insulation. The same consideration holds in moderate potential power circuits, in considering the danger to life from wires or high differences of potential. Thus the comparison of different systems of long-dis- tance transmission at high potential or power distribution for motors is to be made on the basis of equality of the maximum difference of potential existing in the system. The comparison of low potential distribution circuits for lighting on the basis of equality of the minimum difference o ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-30", "section_label": "Chapter 30: Efficiency Of Systems", "section_title": "Efficiency Of Systems", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 25136-25597", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-30/", "snippets": [ "... ctric strain on the insulation. The same consideration holds in moderate potential power circuits, in considering the danger to life from live wires entering human habitations. Thus the comparison of different systems of long-dis- tance transmission at high potential or power distribution for motors is to be made on the basis of equality of the maximum difference of potential existing in the system. The comparison of low potential distribution circuits for lighting on the basis of equality of the minimum difference o ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-04", "section_label": "Chapter 4: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 6942-9061", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-04/", "snippets": [ "... igh armature reaction and low field excitation, due to the flux distortion, and under certain conditions in the armatures of regulating pole converters. A large number of small unsymmetrical cycles are sometimes superimposed upon the alternating cycle by high-frequency pul- sation of the alternating flux due to the rotor and stator teeth, and then may produce high losses. Such, for instance, is the case in induction machines, if the stator and rotor teeth are not proportioned so as to maintain uniform reluctance, or in ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-07", "section_label": "Chapter 7: Shaping Of Waves : General", "section_title": "Shaping Of Waves : General", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 12222-12961", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-07/", "snippets": [ "... the inductance of the circuit. They may become serious and even dangerous, however, if capacity is present in the circuit, as the current taken by capacity is proportional to the frequency, and even small voltage harmonics, if of very high order, that is, high frequency, produce very large currents, and these in turn may cause dangerous voltages in inductive devices connected in series into the circuit, such as current transformers, or cause resonance effects in transformers, etc. With the increasing extent of very high- ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-13", "section_label": "Chapter 13: Reactance Of Synchronous Machines", "section_title": "Reactance Of Synchronous Machines", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 23466-24022", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-13/", "snippets": [ "... tive effect is represented by a self-inductive reactance, x, the gradual or mutual inductive effect by an armatiu'e reaction. The relation between self-inductive component, x, and mutual inductive component, x\\ varies from about 2 -?- 1 in the unitooth- high frequency alternators of old, to about 1 -5- 20 in some of the earlier turbo-alternators. In those synchronous machines, which contain a squirrel-cage induction-motor winding in the field faces, for starting as motors, or as protection against himting, or to equaU ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-14", "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "section_title": "Constant-Potential Constant-Current Trans Formation", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "... CONSTANT CURRENT ' 8INQIC*PHA8E Fig. 124. the losses in these transformers have not been included, since these transformers are obviously not essential but merely for the convenience of separating electrically the constant-current cir- cuit from the high-potential line. It is evident, for instance, in Fig. 124, that the constant-current and constant-potential cir- g Ul 2 u 5 ^ ^ $-§- f ^'^\"^^ o VTX o 5 o _/ o \"X ^v.. o ^>' o ^ V \\ ^ CONSTANT CURRENT SINOL ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... nnection, 265 Arc as alternating current power generator, 187 characteristics, 34 condition of st^-bility on con- stant current, 173 on constant voltage, 169 conduction, 28, 31, 42 constants, 36 effective negative resistance, 191 equations, 35 as oscillator, 189 parallel operation on constant current, 175 shunted by capacity, 178, 184 and inductance, 184 by resistance on constant current, 172 singing and rasping, 188, 189 tending to unstability, 164 transient characteristic, 192 as unstable conductor, ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-01", "section_label": "Chapter 1: Introduction. 217", "section_title": "Introduction. 217", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 659-674", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-01/", "snippets": [ "... l character of periodically recurring transient phenomena in time. 217 2. Periodic transient phenomena with single cycle. 218 3. Multi-cycle periodic transient phenomena. 218 4. Industrial importance of periodic transient phenomena: circuit control, high frequency generation, rectification. 220 5. Types of rectifiers. Arc machines. 221" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-06", "section_label": "Chapter 2: Long Distance Transmission Line. 279", "section_title": "Long Distance Transmission Line. 279", "kind": "chapter", "sequence": 6, "number": 2, "location": "lines 755-835", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-06/", "snippets": [ "... of negligible resistance. 306 21. Line of quarter-wave length, containing resistance r and conductance g. 309 22. Constant-potential — constant-current transformation by line of quarter-wave length. 310 23. Example of excessive voltage produced in high-potential transformer coil as quarter- wave circuit. 312 24. Effect of quarter-wave phenomena on regulation of long transmission lines; quarter-wave transmission. 313 25. Limitations of quarter-wave transmission. 314 26. Example of quarter-wave transmission o ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-08", "section_label": "Chapter 4: Distributed Capacity Of High-Potential Trans Former. 342", "section_title": "Distributed Capacity Of High-Potential Trans Former. 342", "kind": "chapter", "sequence": 8, "number": 4, "location": "lines 875-887", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-08/", "snippets": [ "CHAPTER IV. DISTRIBUTED CAPACITY OF HIGH-POTENTIAL TRANS- FORMER. 342 40. The transformer coil as circuit of distributed capacity, and the character of its capacity. 342 41. The differential equations of the transformer coil, and their integral equations. 344 42. Terminal conditions and final appro ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-15", "section_label": "Chapter 2: Discussion Of General Equations. 431", "section_title": "Discussion Of General Equations. 431", "kind": "chapter", "sequence": 15, "number": 2, "location": "lines 1063-1086", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-15/", "snippets": [ "CHAPTER II. DISCUSSION OF GENERAL EQUATIONS. 431 7. The two component waves and their reflected waves. Attenuation in time and in space. 431 8. Period, wave length, time and distance attenuation constants. 433 9. Simplification of equations at high frequency, and the velocity unit of distance. 434 10. Decrement of traveling wave. 436 11. Physical meaning of the two component waves. 437 12. Stationary or standing wave. Trigonometric arid logarith- mic waves. 438 13. Propagation constant of wave. 440" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-19", "section_label": "Chapter 6: Transition Points And The Complex Circuit. 498", "section_title": "Transition Points And The Complex Circuit. 498", "kind": "chapter", "sequence": 19, "number": 6, "location": "lines 1187-1227", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-19/", "snippets": [ "... 46. The energy transfer constant of the circuit section, and the transfer of power between the sections. 507 47. The final form of the general equations of the complex circuit, . 508 48. Full-wave, half-wave, quarter-wave oscillation, and gen- eral high-frequency oscillation. 509 49. Determination of the resultant time decrement of the cir- cuit. 510" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-32", "section_label": "Chapter 10: Mutual Inductance", "section_title": "Mutual Inductance", "kind": "chapter", "sequence": 32, "number": 10, "location": "lines 10475-12216", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "snippets": [ "... = mutual inductive reactance; xCi = 4000 ohms = primary condensive reactance of the condenser shunting the break of the interrupter in the battery circuit, and xC2 = 6000 ohms = secondary condensive reactance, due to the capacity of the terminals and the high tension winding. Substituting these values, we have BI = 10 volts i0 = 25 amp. rt = 0.4 ohm xl = 10 ohms xCi = 4000 ohms r2 = 0.2 ohm x2 = 10 ohms xC2 = 6000 ohms xm = 8 ohms. (69) MUTUAL INDUCTANCE 165 These values in equation (61) give / (a) = ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-46", "section_label": "Chapter 6: Alternating Magnetic Flux Distribution", "section_title": "Alternating Magnetic Flux Distribution", "kind": "chapter", "sequence": 46, "number": 6, "location": "lines 23948-24980", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "snippets": [ "... easing depth below the surface of the lamination, so that ultimately hardly any magnetic flux exists in the inside of the laminations, but practically only a surface layer carries magnetic flux. The apparent permeability of the iron thus decreases at very high frequency, and this has led to the opinion that at very high fre- quencies iron cannot follow a magnetic cycle. There is, however, no evidence of such a \" viscous hysteresis,\" but it is probable that iron follows magnetically even at the highest frequencies, traver ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-51", "section_label": "Chapter 2: Discussion Of General Equations", "section_title": "Discussion Of General Equations", "kind": "chapter", "sequence": 51, "number": 2, "location": "lines 28695-29315", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "snippets": [ "... nts of the wave, 1 ) (64) U + S and h is the distance attenuation constant of the wave, L -I. (65) 9. If the frequency of the current and e.m.f. is very high, thousands of cycles and more, as with traveling waves, lightning disturbances, high-frequency oscillations, etc., q is a very large quantity compared with s, u, m, h, k, and k is a large quantity compared with h, then by dropping in equations (50) to (61) the terms of secondary order the equations can be simplified. From (54), ^ = V(s2 + q2 - ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-56", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit", "section_title": "Power And Energy Of The Complex Circuit", "kind": "chapter", "sequence": 56, "number": 7, "location": "lines 33528-34202", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "snippets": [ "... constants per wire :rl = 52;LX = 0.21 jg^ = 40 X 10~6, and Cl = 1.6 X 1Q-6. Further assume this line to be connected to step-up and step- down transformers having the following constants per trans- POWER AND ENERGY OF THE COMPLEX CIRCUIT 523 former high-potential circuit: r2 = 5, L2 = 3; g2 = 0.1 X 10 6, and C2 = 0.3 X 10~6; then A/ = a1 = vT/7i = 0.58 X 10~3, J2' = *2 = 0.95 X 10~3, u, = 136, u2 -= 1. The circuit consists of four sections of the lengths V = 0-58 X 10~3, A2'= 0.95 X 10~3, V =0.58 X 10~3, V = 0 ..." ] } ] }, { "id": "counter-electromotive-force", "label": "Counter-Electromotive Force", "aliases": [ "counter e.m.f.", "counter electromotive force", "counter emf", "counter-electromotive force" ], "total_occurrences": 322, "matching_section_count": 74, "matching_source_count": 9, "source_totals": [ { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 76, "section_count": 16 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 72, "section_count": 15 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 58, "section_count": 13 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 44, "section_count": 13 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 40, "section_count": 9 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 11, "section_count": 4 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 10, "section_count": 2 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 10, "section_count": 1 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-24", "section_label": "Chapter 24: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 25682-29374", "status": "candidate", "occurrence_count": 25, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-24/", "snippets": [ "... is leading, in the other lagging. Fig. 154. In Figs. 155 to 158 are shown diagrams, giving the points £\"0 = impressed e.m.f., assumed as constant = 1000 volts, E = e.m.f. consumed by impedance, E^ = e.m.f. consumed by resistance (not numbered). The counter e.m.f. of the motor, Ei, is OEi, equal and parallel -£'£'0, but not shown in the diagrams, to avoid complication. The four diagrams correspond to the values of power, or motor output. P = 1,000, P = 1,000 P = 6,000 P = 9,000 P = 12,000 6,000, 9,000, 1 ...", "... 6,000, 9,000, 12,000 watts, and give: 46 < £1 < 2,200, 1 < / < 49 340 < El < 1,920, 540 < El < 1,750, 920 < El < 1,320, 7 < / < 43 11.8 < / < 38.2 20 < / < 30 Fig. 155. Fig. 156. Fig. 157. Fig. 158. As seen, the permissible value of counter e.m.f., Ei, and of current, /, becomes narrower with increasing output. SYNCHRONOUS MOTOR 313 Eo=lOOO P = 1000 46 where tQ is time of one 1 complete period, = -v or by the time angle 6 = 90°. FIG. 11. — Self-induction effects produced by an alternating sine wave of current. This e.m.f. is called the counter e.m.f. of inductance. It is .'•'• '•••• e'*=-Ljt = - 2 TT/L/O cos 2 irft. It is shown in dotted line in Fig. 11 as e'2. The quantity 2 irfL is called the inductive reactance of the circuit, and denoted by x. It ...", "... e quantity 2 irfL is called the inductive reactance of the circuit, and denoted by x. It is of the nature of a resistance, and expressed in ohms. If L is given in 109 absolute units or henrys, x appears in ohms. The counter e.m.f. of inductance of the current, i = /o sin 2 irft = /o sin 0) of effective value , V\"2 IS e'2 = — xI0 cos 2 irft = — xIQ cos 6, having a maximum value of X!Q and an effective value of xh T E, = ...", "... ue , V\"2 IS e'2 = — xI0 cos 2 irft = — xIQ cos 6, having a maximum value of X!Q and an effective value of xh T E, = -- = xl; ALTERNATING-CURRENT CIRCUITS 33 that is, the effective value of the counter e.m.f. of inductance equals the reactance, x, times the effective value of the current, /, and lags 90 time degrees, or a quarter period, behind the current. 35. By the counter e.m.f. of inductance, e'z = — xIQ cos 0, whic ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-04", "section_label": "Chapter 4: Vector Representation", "section_title": "Vector Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2149-2759", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-04/", "snippets": [ "... hase with the current, represented by OEi in the diagram. The inductive reactance of the hne generates an e.m.f. which is pro- portional to the current, /, and the reactance, x, and lags a quarter of a period, or 90°, behind the current. To overcome this counter e.m.f. of inductive reactance, a voltage of the value Ix is required, in phase 90° ahead of the current, hence represented by vector 0E2- Thus resistance consumes voltage in phase, and reactance voltage 90° ahead of the current. The voltage of the generator, Eo ...", "... by the reactance (90° ahead of the current) as parts, or components, of the impressed volt- age, ^0, and have derived E^ by combining Er, Ex, and E. 20. We may, however, introduce the effect of the inductive react- ance directly as an e.m.f., E'l, the counter e.m.f. of inductive react- ance = Ix, and lagging 90° behind the current; and the e.m.f. con- ^ , . , . Fig. 13. sumed by the resistance as a counter e.m.f., E'l =Ir, in opposition to the current, as is done in Fig. 13; and combine the three voltages Eq, ...", "... e may, however, introduce the effect of the inductive react- ance directly as an e.m.f., E'l, the counter e.m.f. of inductive react- ance = Ix, and lagging 90° behind the current; and the e.m.f. con- ^ , . , . Fig. 13. sumed by the resistance as a counter e.m.f., E'l =Ir, in opposition to the current, as is done in Fig. 13; and combine the three voltages Eq, E\\, E'2, to form a resultant voltage E, which is left at the end of the line. E\\ and E'2 combine to form E'3, the counter e.m.f. of impedance; and since ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-04", "section_label": "Chapter 4: Graphic Befrisxintation", "section_title": "Graphic Befrisxintation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2122-2743", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "snippets": [ "... equired in phase with the current, repre- sented by OE^ in the diagram. The self-inductance of the line induces an E.M.F. which is proportional to the current / and reactance -r, and lags a quarter of a period, or 90°, behind the current. To overcome this counter E.M.F. /' 24 ALTERNATING-CURRENT PHENOMENA. [§18 of self-induction, an E.M.F. of the value Ix is required, in phase 90® ahead of the current, hence represented by- vector OEj^. Thus resistance consumes E.M.F. in phase,, and reactance an E.M.F. 90° ...", "... .F. consumed by the reactance (90? ahead of the current) as parts, or components, of the impressed E.M.F., E^t and have derived E^ by combining E^., E^, and E, 18. We may, howeyer, introduce the effect of the induc- tance directly as an E.M.F., E^ , the counter E.M.F. of self-induction = I,j and lagging 90° behind the current ; and the E.M.F. consumed by the resistance as a counter E.M.F., -£*/ = /r, but in opposition to the current, as is done in Fig. 18 ; and combine the three E.M.Fs. E^j if/, EJ, to form a resulta ...", "... ived E^ by combining E^., E^, and E, 18. We may, howeyer, introduce the effect of the induc- tance directly as an E.M.F., E^ , the counter E.M.F. of self-induction = I,j and lagging 90° behind the current ; and the E.M.F. consumed by the resistance as a counter E.M.F., -£*/ = /r, but in opposition to the current, as is done in Fig. 18 ; and combine the three E.M.Fs. E^j if/, EJ, to form a resultant E.M.F., /:, which is left at the end of the line. 118] GRAPHIC REPRESENTATIO^r, 2& E^ and E^ combine to form E ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-04", "section_label": "Chapter 4: Graphic Representation", "section_title": "Graphic Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 1743-2321", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "snippets": [ "... required in phase with the current, repre- sented by OEr in the diagram. The self-inductance of the line induces an E.M.F. which is proportional to the current / and reactance x, and lags a quarter of a period, or 90°, behind the current. To overcome this counter E.M.F. 24 ALTERNA TING-CURRENT PHENOMENA. of self-induction, an E.M.F. of the value Ix is required, in phase 90° ahead of the current, hence represented by vector OEX. Thus resistance consumes E.M.F. in phase, and reactance an E.M.F. 90° ahead of the cu ...", "... nce (90° ahead of the current) as parts, or components, of the impressed E.M.F., E0, and have derived E0 by combining Er, Ex, and E. E'. E? 0 Fig. 13. 18. We may, however, introduce the effect of the induc- tance directly as an E.M.F., Ex , the counter E.M.F. of self-induction = Ix, and lagging 90° behind the current ; and the E.M.F. consumed by the resistance as a counter E.M.F., Ef = Ir, but in opposition to the current, as is done in Fig. 13 ; and combine the three E.M.Fs. E0, EJ, Ex , to form a resultant ...", "... x, and E. E'. E? 0 Fig. 13. 18. We may, however, introduce the effect of the induc- tance directly as an E.M.F., Ex , the counter E.M.F. of self-induction = Ix, and lagging 90° behind the current ; and the E.M.F. consumed by the resistance as a counter E.M.F., Ef = Ir, but in opposition to the current, as is done in Fig. 13 ; and combine the three E.M.Fs. E0, EJ, Ex , to form a resultant E.M.F., E, which is left at the end of the line- GRAPHIC REPRESENTA TION. 25 Ef and £a! combine to form Eg) the cou ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "section_label": "Chapter 16: Induction Motor", "section_title": "Induction Motor", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "... imary and secondary) passes through zero, in complex quantities, the magnetic flux is denoted by and the primary induced E.M.F., 240 ALTERNATING-CURRENT PHENOMENA. where e= V2irrt7V10-8 maybe considered as the \"Active E.M.F. of the motor,\" or \" Counter E.M.F.\" Since the secondary frequency is s N, the secondary in- duced E.M.F. (reduced to primary system) is El = — se. Let I0 = exciting current, or current passing through the motor, per primary circuit, when doing no work (at synchronism), and K= g -j- ...", "... pri- mary reactance 90° ahead of OG, and represented by OIxv and their resultant Ofz0 is the E.M.F. consumed by the INDUCTION MOTOR. 245 primary impedance. The E.M.F. induced in the primary circuit is OE', and the E.M.F. required to overcome this counter E.M.F. is OE equal and opposite to OE1. Com- bining OE with OIzQ gives the primary terminal voltage represented by vector OEy and the angle of primary lag, EOG Fig. 115. 156. Thus far the diagram is essentially the same as the diagram of the stationary al ...", "... slip s, the frequency N, and the number of poles q, the linear speed at unit radius is hence the output of the motor, P= TV or, substituted, is the Power of the Induction Motor. 158. We can arrive at the same results in a different way : By the counter E.M.F. e of the primary circuit with current / ' = f0 + 7X the power is consumed, e I = e I0 + e 7r The power e I0 is that consumed by the primary hysteresis and eddys. The power e 1^ disappears in the primary circuit by being transmitted to the secondary syste ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-12", "section_label": "Chapter 12: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 10718-13483", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-12/", "snippets": [ "... ce of the circuit, but the impedance, z = \\/f^ + x^. 3. By the ratio: Power consumed, (Current) 2 where, however, the \"power\" does not include the work done by the circuit, and the counter e.m.fs. representing it, as, for instance, in the case of the counter e.m.f. of a motor. In alternating-current circuits, this value of resistance is the power coefficient of the e.m.f.. Power component of e.m.f. Total current It is called the elective resistance of the circuit, since it represents the effect, or power, expen ...", "... surrounded by iron, as, for instance, the primary circuit of an alternating-current transformer with open secondary circuit. The wave of current produces in the iron an alternating mag- netic flux which generates in the electric circuit an e.ni.f. — the counter e.m.f. of self-induction. If the ohmic resistance is negligible, that is, practically no e.m.f. consuzned by the resist- ance, all the impressed e.m.f. must be consumed by the counter e.m.f. of self-induction, that is, the counter e.m.f. equals the impressed e. ...", "... ag- netic flux which generates in the electric circuit an e.ni.f. — the counter e.m.f. of self-induction. If the ohmic resistance is negligible, that is, practically no e.m.f. consuzned by the resist- ance, all the impressed e.m.f. must be consumed by the counter e.m.f. of self-induction, that is, the counter e.m.f. equals the impressed e.m.f.; hence, if the impressed e.m.f. is a sine wave, the counter e.m.f., and, therefore, the magnetic flux which generates the counter e.m.f., must follow a sine wave also. The alterna ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "section_label": "Chapter 10: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "... esistance of the circuit, but the impedance, 3.) By the ratio : r__ Power consumed . (Current)2 where, however, the \"power\" does not include the work done by the circuit, and the counter E.M.Fs. representing it, as, for instance, in the case of the counter E.M.F. of a motor. In alternating-current circuits, this value of resistance is the energy coefficient of the E.M.F., _ Energy component of E.M.F. Total current It is called the effective resistance of the circuit, since it represents the effect, or powe ...", "... ely surrounded by iron, as, for instance, the primary circuit of an alternating-current transformer with open secondary circuit. The wave of current produces in the iron an alternating magnetic flux which induces in the electric circuit an E.M.F., — the counter E.M.F. of self-induction. If the ohmic re- sistance is negligible, that is, practically no E.M.F. con- sumed by the resistance, all the impressed E.M.F. must be consumed by the counter E.M.F. of self-induction, that is, the counter E.M.F. equals the impressed E ...", "... magnetic flux which induces in the electric circuit an E.M.F., — the counter E.M.F. of self-induction. If the ohmic re- sistance is negligible, that is, practically no E.M.F. con- sumed by the resistance, all the impressed E.M.F. must be consumed by the counter E.M.F. of self-induction, that is, the counter E.M.F. equals the impressed E.M.F. ; hence, if EFFECTIVE RESISTANCE AND REACTANCE. 107 the impressed E.M.F. is a sine wave, the counter E.M.F., and, therefore, the magnetic flux which induces the counter E. ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-21", "section_label": "Chapter 21: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 20502-21189", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-21/", "snippets": [ "... reactance. It is known that synchronous motors of large and variable reactance keep in synchronism, and are able to do a considerable amount of work, and even carry under circumstances full load, if the field-exciting circuit is broken, and thereby the counter E.M.F. E± reduced to zero, and sometimes even if the field circuit is reversed and the counter E.M.F. E± made negative. Inversely, under certain conditions of load, the current and the E.M.F. of a generator do not disappear if the gene- rator field is broken, ...", "... onism, and are able to do a considerable amount of work, and even carry under circumstances full load, if the field-exciting circuit is broken, and thereby the counter E.M.F. E± reduced to zero, and sometimes even if the field circuit is reversed and the counter E.M.F. E± made negative. Inversely, under certain conditions of load, the current and the E.M.F. of a generator do not disappear if the gene- rator field is broken, or even reversed to a small negative value, in which latter case the current flows against the ...", "... t magnetism of the field poles de- stroyed beforehand by application of an alternating current. 226. These phenomena cannot be explained under the assumption of a constant synchronous reactance; because in this case, at no-field excitation, the E.M.F. or counter E.M.F. of the machine is zero, and the only E.M.F. exist- ing in the alternator is the E.M.F. of self-induction; that is, the E.M.F. induced by the alternating current upon itself. If, however, the synchronous reactance is constant, the counter E.M.F. of self-i ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-14", "section_label": "Chapter 16: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 14, "number": 16, "location": "lines 19374-20293", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-14/", "snippets": [ "... is known that synchronous motors or converters of large and variable reactance keep in synchronism, and are able to do a considerable amount of work, and even carry under circum- stances full load, if the field-exciting circuit is broken, and thereby the counter e.m.f., E,, reduced to zero, and sometimes even if the field circuit is reversed and the counter e.m.f., £.',. made negative. Inversely, under certain conditions of load, the current and the e.m.f. of a generator do not disappear if the generator field circui ...", "... sm, and are able to do a considerable amount of work, and even carry under circum- stances full load, if the field-exciting circuit is broken, and thereby the counter e.m.f., E,, reduced to zero, and sometimes even if the field circuit is reversed and the counter e.m.f., £.',. made negative. Inversely, under certain conditions of load, the current and the e.m.f. of a generator do not disappear if the generator field circuit is broken, or even reversed to a small negative value, in which tatter case the current is agai ...", "... nent magnetism of the field poles destroyed beforehand by application of an alternating current. These phenomena can uol be explained under the assump- tion of a constant synchronous reactance: because in ilu- oast al no-field excitation, the e.m.f. or counter e.m.f. of the machine REACTION MACHINES 2fil let mi mi H MVO, ;md the only cm. I', existing in tlic- al tern (it in1 is the e.m.f. of self-induction; that is, the e.m.f. induced by the alternating current upon itself. If, however, the synchronous r ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-01", "section_label": "Chapter 1: Electric Conduction. Soled And Liquid", "section_title": "Electric Conduction. Soled And Liquid", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 959-3894", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-01/", "snippets": [ "... ergy, and as the rate of electrical energy supply is given by current times vol- tage, it follows that a voltage drop or potential difference occurs at the electrodes in the electrolyte. This is in opposition to the ELECTRIC CONDUCTION 7 current, or a counter e.m.f., the \"counter e.m.f. of electrochem- ical polarization,\" and thus consumes energy, if the chemical reaction requires energy — ^as the deposition of copper from a solu- tion of a copper salt. It is in the same direction as the current, thus producing elec ...", "... e of electrical energy supply is given by current times vol- tage, it follows that a voltage drop or potential difference occurs at the electrodes in the electrolyte. This is in opposition to the ELECTRIC CONDUCTION 7 current, or a counter e.m.f., the \"counter e.m.f. of electrochem- ical polarization,\" and thus consumes energy, if the chemical reaction requires energy — ^as the deposition of copper from a solu- tion of a copper salt. It is in the same direction as the current, thus producing electric energy, if the c ...", "... c acid. During the passage of the current, hydrogen is given off at the cathode and oxygen at the anode, but terminals and electrolyte remain the same (assuming that the small amount of dissociated water is replaced). In such a polarization cell, if eo = counter e.m.f . of polarization (corresponding to the chemical energy of dissociation of water, and approximately 1.6 volts) at constant temperature and thus constant resistance of the electrolyte, the current, i, is proportional to the voltage, e, minus the counter e. ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... MINATION 243 radiation. The question whether an illuminant owes its high efficiency to selective radiation, depends largely on the defini- tion of the term \"selective radiation\". We have here a simi- lar case to that of the much discussed problem of the \"counter electromotive force of the electric arc\". Whether the electric arc has a counter e. m. f. or not, entirely depends on the defini- tion of counter e. m. f. In the same way, the decision on the question of selective radiation depends upon what you define as selective radiation ...", "... ncy to selective radiation, depends largely on the defini- tion of the term \"selective radiation\". We have here a simi- lar case to that of the much discussed problem of the \"counter electromotive force of the electric arc\". Whether the electric arc has a counter e. m. f. or not, entirely depends on the defini- tion of counter e. m. f. In the same way, the decision on the question of selective radiation depends upon what you define as selective radiation. If you define as selective radiation any radiation in which the int ...", "... f the term \"selective radiation\". We have here a simi- lar case to that of the much discussed problem of the \"counter electromotive force of the electric arc\". Whether the electric arc has a counter e. m. f. or not, entirely depends on the defini- tion of counter e. m. f. In the same way, the decision on the question of selective radiation depends upon what you define as selective radiation. If you define as selective radiation any radiation in which the intensity of radiation is distributed through the total spectrum dif ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-10", "section_label": "Chapter 10: F", "section_title": "F", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 8269-10499", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "snippets": [ "... \\ 3.) By the ratio : __ Power consumed __ (E.M.F.)' . (Current)* Power consumed ' where, however, the \"power*' and the \"E.M.F.\" do not include the work done by the circuit, and the counter E.M.Fs. representing it, as, for instance, in the case of the counter E.M.F. of a motor. In alternating-current circuits, this value of resistance is the energy coefficient of the E.M.F., — Energy compon ent of E.M.F. Total current It is called the effective resistance of the circuit, since it represents the effect, or powe ...", "... ely surrounded by iron, as, for instance, the primary circuit of an alternating-current transformer with open secondary circuit. The wave of current produces in the iron an alternating magnetic flux which induces in the electric circuit an E.M.F., — the counter E.M.F. of self-induction. If the ohmic resistance is negligible, the counter E.M.F. equals the impressed E.M.F. ; hence, if the impressed E.M.F. is §75] EFFECTIVE RESISTANCE AND REACTANCE, 107 a sine wave, the counter E.M.F., and, therefore, the mag- netic ...", "... ng-current transformer with open secondary circuit. The wave of current produces in the iron an alternating magnetic flux which induces in the electric circuit an E.M.F., — the counter E.M.F. of self-induction. If the ohmic resistance is negligible, the counter E.M.F. equals the impressed E.M.F. ; hence, if the impressed E.M.F. is §75] EFFECTIVE RESISTANCE AND REACTANCE, 107 a sine wave, the counter E.M.F., and, therefore, the mag- netic flux which induces the counter E.M.F. must follow sine waves also. The altern ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-20", "section_label": "Chapter 20: Beactiox Machines", "section_title": "Beactiox Machines", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 22388-23273", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "snippets": [ "... reactance. It is known that synchronous motors of large and variable reactance keep in synchronism, and are able to do a considerable amount of work, and even carry under circumstances full load, if the field-exciting circuit is broken, and thereby the counter E.M.F. E^ reduced to zero, and sometimes even if the field circuit is reversed and the counter E.M.F. E^ made negative. Inversely, under certain conditions of load, the current and the E.M.F. of a generator do not disappear if the gene- rator field is broken, ...", "... onism, and are able to do a considerable amount of work, and even carry under circumstances full load, if the field-exciting circuit is broken, and thereby the counter E.M.F. E^ reduced to zero, and sometimes even if the field circuit is reversed and the counter E.M.F. E^ made negative. Inversely, under certain conditions of load, the current and the E.M.F. of a generator do not disappear if the gene- rator field is broken, or even reversed to a small negative value, in which latter case the current flows against the ...", "... magnetism of the field poles de- stroyed beforehand by application of an alternating current. 205. These phenomena cannot be explained under the assumption of a constant synchronous reactance ; because in this case, at no-field excitation, the E.M.F. or counter E.M.F. of the machine is zero, and the only E.M.F. exist- ing in the alternator is the E.M.F. of self-induction; that is, the E.M.F. induced by the alternating current upon itself. If, however, the synchronous reactance is constant, the counter E.M.F. of self-i ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-109", "section_label": "Apparatus Section 3: Induction Machines: Single -phase Induction Motor", "section_title": "Induction Machines: Single -phase Induction Motor", "kind": "apparatus-section", "sequence": 109, "number": 3, "location": "lines 20428-21157", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-109/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-109/", "snippets": [ "... cuit of the starting device, and thus changes the distribution of currents and e.m.fs. in the starting device. The Circuits of the starting device then contain, besides the motor admittance and external admittance, an active counter e.m.f., changing with the speed. Inversely, the currents produced by the counter e.m.f. of the motor in the auxiliary circuit react upon the counter e.m.f., that is, upon the quadrature component or main flux, and change it. Th ...", "... .m.fs. in the starting device. The Circuits of the starting device then contain, besides the motor admittance and external admittance, an active counter e.m.f., changing with the speed. Inversely, the currents produced by the counter e.m.f. of the motor in the auxiliary circuit react upon the counter e.m.f., that is, upon the quadrature component or main flux, and change it. Thus during acceleration we have to consider — 1. The effect of the change of to ...", "... en contain, besides the motor admittance and external admittance, an active counter e.m.f., changing with the speed. Inversely, the currents produced by the counter e.m.f. of the motor in the auxiliary circuit react upon the counter e.m.f., that is, upon the quadrature component or main flux, and change it. Thus during acceleration we have to consider — 1. The effect of the change of total motor admittance and its power-factor upon the starting device. 2 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-14", "section_label": "Chapter 14: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 11605-12682", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "snippets": [ "... impressed E.M.F. by combina- tion of OEr0, OEx0, and OE' by means of the parallelo- gram of E.M.Fs. is, E0 = ~OE0, and the difference of phase between the primary impressed E.M.F. and the primary current is ft0 = E0O50. In the secondary circuit : Counter E.M.F. of resistance is 1^ in opposition with Iv and represented by the vector OJS'r^ ; 198 AL TERNA TING-CURRENT PHENOMENA, 90° behind 7X, and Counter E.M.F. of reactance is represented by the vector OE^x^ Induced E.M.Fs., E( represented by the vec ...", "... mary impressed E.M.F. and the primary current is ft0 = E0O50. In the secondary circuit : Counter E.M.F. of resistance is 1^ in opposition with Iv and represented by the vector OJS'r^ ; 198 AL TERNA TING-CURRENT PHENOMENA, 90° behind 7X, and Counter E.M.F. of reactance is represented by the vector OE^x^ Induced E.M.Fs., E( represented by the vector OE-[. Hence, the secondary terminal voltage, by combination of OEr^ OEx{ and OE^ by means of the parallelogram of E.M.Fs. is -==• A = M»II and the diffe ...", "... ually, and with sufficient .exactness, be considered as constant. Let n0 = number of primary turns in series ; #1 = number of secondary turns in series ; a = — = ratio of turns ; Y0 = g0 4- jb0 = primary admittance Exciting current . ~i I Primary counter E.M.F. ' .VVWvVl rw^ww ALTERNATING-CURRENT TRANSFORMER. 205 Z0 = r0 — j x0 = primary impedance 7. — — E.M.F. consumed in primary coil by resistance and reactance. ^ -n-f '\" ' j**/\\. Primary current ~ / Z± = r± —jx1= secondary impedance __ E.M.F. ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "... Total power consumed in field excitation : P = 2 t»r„ (2) where i = field exciting current. Power consumed by hysteresis: P - e*g. (3) it is then: or: 60 ELECTRICAL APPARATUS 42. Let, in a synchronous motor: E0 = impressed voltage, E = counter e.m.f., or nominal induced voltage, Z — r + jx = synchronous impedance, / = i\\ — 3H = current, #o = $ + ZJ = # + (n'i + xi2) + j (xt\\ - n2), (4) $ = $q — Zf = #o - (n'i + xz2) ~ j (xii - ri2), (5) or, reduced to absolute values, and choosing: g = e ...", "... duced voltage and thus of the field excitation, required to maintain unity power- factor at all loads, that is, currents, ix. From (8) follows: re0 ± \\/z2e2 — xV ,nx '* = - - -o - • W zl INDUCTION MOTOR 61 Thus, the minimum possible value of the counter e.m.f., e, is given by equating the square root to zero, as: x e = - e<>. z For a given value of the counter e.m.f., e, that is, constant field excitation, it is, from (7) : xe0 , /e* 7. re0\\* , . or, if the synchronous impedance, x, is very large compa ...", "... rrents, ix. From (8) follows: re0 ± \\/z2e2 — xV ,nx '* = - - -o - • W zl INDUCTION MOTOR 61 Thus, the minimum possible value of the counter e.m.f., e, is given by equating the square root to zero, as: x e = - e<>. z For a given value of the counter e.m.f., e, that is, constant field excitation, it is, from (7) : xe0 , /e* 7. re0\\* , . or, if the synchronous impedance, x, is very large compared with r, and thus, approximately : z = x: ii = ei± 4i ~ ^ (11) The maximum value, which the energy current ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-09", "section_label": "Theory Section 9: Vector Diagrams", "section_title": "Vector Diagrams", "kind": "theory-section", "sequence": 9, "number": 9, "location": "lines 2865-3233", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-09/", "snippets": [ "... ez = x!0 cos 0, is repre- sented by a vector OEZ equal in length to x!Q, and located so that at 0 = 0, its projection on the horizontal is a maximum. That is, it is the zero vector OE2 in Fig. 18. Analogously, the counter e.m.f. of self-inductance E'2 is represented by vector OE'Z on the negative horizontal of Fig. 18; the voltage consumed by the resistance r, e\\ — e!Q sin 0, is represented by vector OEi equal to r/0, and located on the nega- ...", "... r OE'Z on the negative horizontal of Fig. 18; the voltage consumed by the resistance r, e\\ — e!Q sin 0, is represented by vector OEi equal to r/0, and located on the nega- VECTOR DIAGRAMS 45 tive vertical, and the counter e.m.f. of resistance by vector OE'i on the positive vertical. The counter e.m.f. of impedance: — (r/o sin 0 + x!Q cos 0) - ?Jn sin (ft -\\- fi»} sin (6 + 00) then is represented graphically as the resultant, by the ...", "... resistance r, e\\ — e!Q sin 0, is represented by vector OEi equal to r/0, and located on the nega- VECTOR DIAGRAMS 45 tive vertical, and the counter e.m.f. of resistance by vector OE'i on the positive vertical. The counter e.m.f. of impedance: — (r/o sin 0 + x!Q cos 0) - ?Jn sin (ft -\\- fi»} sin (6 + 00) then is represented graphically as the resultant, by the parallelo- gram of sine waves of OE\\ and OE'2} that is, by a vector OE', ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-110", "section_label": "Apparatus Section 4: Induction Machines: Induction Generator", "section_title": "Induction Machines: Induction Generator", "kind": "apparatus-section", "sequence": 110, "number": 4, "location": "lines 21158-21588", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-110/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-110/", "snippets": [ "... case if the circuit consists of a syn- chronous motor or contains synchronous motors or synchronous converters. In the synchronous motor the current is in phase with the impressed e.m.f. if the impressed e.m.f. equals the counter e.m.f. of the motor plus the internal loss of voltage. It is leading if the impressed e.m.f. is less, and lagging if the impressed e.m.f. is more. Thus when connecting an induction generator with a synchronous motor, at constan ...", "... 19 IjO 11. 12 13 14 lf.5 FIG. 190. — Induction generator and synchronous converter, phase control, no line impedance. voltage of the induction generator rises until it is as much below the counter e.m.f. of the synchronous motor as required to give the leading current corresponding to the power-factor of the generator. Thus a system consisting of a constant-speed induc- tion generator and a synchronous motor at constant fiel ...", "... cita- tion is absolutely stable. At constant field excitation of the synchronous motor\", at no load the synchronous motor runs practically at synchronism with the induction generator, with a terminal voltage slightly below the counter e.m.f. of the syn- chronous motor. With increase of load the frequency and thus the speed of the synchronous motor drops, due to the slip of frequency in the induction generator, and the voltage drops, INDUCTION MACHINES 347 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-17", "section_label": "Chapter 17: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16521-17716", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-17/", "snippets": [ "... primary impressed e.m.f. by combination of OErQ, OEzQ, and OE' by means of the parallelogram of e.m.fs. is E, - OE,, and the difference of phase between the primary impressed e.m.f. and the primary current is ^0 = EqOFq, In the secondary circuit: Counter e.m.f. of resistance is IiVi in opposition with /i, and represented by the vector, OE'r^; Counter e.m.f. of reactance is IiXi, 90° behind h, and repre- sented by the vector, OE'x^. Generated e.m.fs., E'l, represented by the vector, 0E\\. Hence, the secondary ...", "... .fs. is E, - OE,, and the difference of phase between the primary impressed e.m.f. and the primary current is ^0 = EqOFq, In the secondary circuit: Counter e.m.f. of resistance is IiVi in opposition with /i, and represented by the vector, OE'r^; Counter e.m.f. of reactance is IiXi, 90° behind h, and repre- sented by the vector, OE'x^. Generated e.m.fs., E'l, represented by the vector, 0E\\. Hence, the secondary terminal voltage, by combination of OE'r^, OE'xi and ()E\\ by means of the parallelogram of e.m.fs. ...", "... flux passing between primary and second- ary coils; that is, interlinked with one coil only. Let also Y = g —jb = total admittance of secondary circuit, in- cluding the internal impedance; £\"0 = primary impressed e.m.f.; E' = e.m.f. consumed by primary counter e.m.f.; El = secondary terminal voltage; E'l = secondary generated e.m.f.; 7o = primary current, total; Zoo = primary exciting current; 1 1 = secondary current. Since the primary counter e.m.f., Eo', and the secondary generated e.m.f., E\\, are proportional ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-18", "section_label": "Chapter 18: Polyphase Induction Motors", "section_title": "Polyphase Induction Motors", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17717-20445", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-18/", "snippets": [ "... ic circuits, primary and secondary), passes through zero, in complex quantities, the magnetic flux is denoted by $ = - i$, and the primary generated e.m.f., E = - e; where e = \\/2 xn/$ 10~* may be considered as the \"active e.m.f. of the motor,\" or \"counter e.m.f.\" Since the secondary frequency is sf, the secondary induced e.m.f. (reduced to primary system) is Ei = — se. POLYPHASE INDUCTION MOTORS 211 Let 7o = exciting current, or current through the motor, per primary circuit, when doing no work (at synchro ...", "... e e.m.f. consumed by the primary reactance 90° ahead of OG, and represented by OIxo, and their resultant, OIzo, is the e.m.f. consumed by the primary impedance. The e.m.f. gener- ated in the primary circuit is OE', and the e.m.f. required to overcome this counter e.m.f. is OE equal and opposite to OE'. Combining OE with OIzo gives the primary terminal voltage represented by vector OEo, and the angle of primary lag, EoOG - 6*0. POLYPHASE INDUCTION MOTORS 215 160. Thus far the diagram is essentially the same as th ...", "... and the number of poles, q, the linear speed at unit radius is q ' hence the output of the motor, P - Dv, or, substituted, „ Pirie-s{\\ — s) 2S sv,^^ ^ Sy^ EflOOO P=6000 340 = $x I G(x = 2 Trixdx / 10. Hence, the total magnetic flux inside the conductor is , 27T . CR . TTiR* I From this we get, as the excess of counter E.M.F. at the axis of the conductor over that at the surface — &E = V27r^0> 10 ~8 = V27r7W10 -9, per unit length, and the reactivity, or specific reactance at the center of the conductor, becomes k = &E / i = V2 i^NR* 10 ~9. Let p = resistivity, or specific ...", "... can be considered as a constant, consisting of a wattless component, the condensance proper, and an energy com- ponent, the dielectric hysteresis. The condensance of a polarization cell, however, begins to decrease at very low potentials, as soon as the counter E.M.F. of chemical dissociation is approached. The condensance of a synchronizing alternator is of the nature of a variable quantity ; that is, the effective reactance changes gradually, according to the relation of impressed and of counter E.M.F., from induct ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-16", "section_label": "Chapter 18: Surging Of Synchronous Motors", "section_title": "Surging Of Synchronous Motors", "kind": "chapter", "sequence": 16, "number": 18, "location": "lines 20975-21712", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-16/", "snippets": [ "... ment the power prod wed by the motor exceeds the mechanical load (as in the moment of throwing off a part of the load), the excess power is consumed by the momentum as acceleration, causing an increase of speed. The result thereof is that the phase of the counter e.m.f., c, is not constant, but its vector, e, moves backward to earlier time, or counter-clockwise, at a rate depending upon the momentum. Thereby the current changes and the power developed changes and decreases. As soon as the power produced equals the load, ...", "... non, a surging by what may be called electro- mechanical resonance, must be taken into consideration in a complete theory of the synchronous motor. 167. Let: E0 = e0 = impressed e.m.f. assumed as zero vector. E = e (cos P — j sin P) = e.m.f. consumed by counter e.m.f. of motor, where: P = phase angle between E0 and E. Let: Z = r + jx, and z = Vr2 + x2 = impedance of circuit between Eo and E, and x tan a = — r The current in the system is: e0 — E eo — e cos P + je sin P /o = r + jx = - {[e0 cos a ...", "... motor is: Po = [EI]1 = - {[cos p [e0 cos a - e cos (a + 0)] z + sin 0 [e0 sin a — e sin (a + 0)] J = {[e0 cos (a — 0) — e cos a]). (2) If, now, a pulsation of the synchronous motor occurs, resulting in a change of the phase relation, 0, between the counter e.m.f., e, and the impressed e.m.f., e0 (the latter being of constant fre- quency, thus constant phase), by an angle, 5, where 8 is a periodic function of time, of a frequency very low compared with the impressed frequency, then the phase angle of the counter e ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-17", "section_label": "Chapter 19: Alternating- Current Motors In General", "section_title": "Alternating- Current Motors In General", "kind": "chapter", "sequence": 17, "number": 19, "location": "lines 21713-23905", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-17/", "snippets": [ "... 0: h Eo ~ Z'+'Zo u = 0; /oo \" fa V 2?oZ £10 Z + Zo t , Zo 1 + z At standstill: 8 • - i; u> £» (Z + zo . ZZo H~ ZZi -f- ZoZi * h _ 2?oZ ZZo \"h ZZi + ZoZi EqZi ZZo + ZZi + ZoZi #' = 0. Introducing as parameter the counter e.m.f ., or e.m.f. of mutual induction : # = #o — Zo/o, (21) or: #o = # + Zo/o, (22) it is, substituted : Counter e.m.f. : v = ^° zZoT+zz\\ + ZoZV (23) hence: Primary impressed e.m.f.: « „ ZZos + Zi + ZZoZi ,0 .v #o = # 22 ' '**' E.m.f. of rota ...", "... (Z + zo . ZZo H~ ZZi -f- ZoZi * h _ 2?oZ ZZo \"h ZZi + ZoZi EqZi ZZo + ZZi + ZoZi #' = 0. Introducing as parameter the counter e.m.f ., or e.m.f. of mutual induction : # = #o — Zo/o, (21) or: #o = # + Zo/o, (22) it is, substituted : Counter e.m.f. : v = ^° zZoT+zz\\ + ZoZV (23) hence: Primary impressed e.m.f.: « „ ZZos + Zi + ZZoZi ,0 .v #o = # 22 ' '**' E.m.f. of rotation: #' = #S = # (1 - s). (25) Secondary current: h = Jj- (26) Primary current: /o \" ^~zzT' z; + z (27) 310 ...", "... y current: /. = E° * = Eo ! (40) 41 Z sXo + Xi + XoXi Z 5X0 + Xi v ' Exciting current: r _ -Bo Xi __ Eo Xi . /0° \" Z sXo + X~i + XoXi ~~ Z 5X0 + Xi' l l) E.m.f . of rotation : W = QoS .— ,-^ r .-. = VoS -\\ - - (42) sXo + Xi + X0X1 5X0 + Xi ' Counter e.m.f.: sXo + Xi + X0X1 sXo + Xi v ' ALTERNATING-CURRENT MOTORS 313 177. As an example are shown, in Fig. 149, with the speed as abscissae, the curves of a polyphase induction motor of the constants: e0 = 320 volts, Z = 1 + 10j ohms, Z0 = Zl = 0. ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-18", "section_label": "Chapter 20: Single-Phase Commutator Motors", "section_title": "Single-Phase Commutator Motors", "kind": "chapter", "sequence": 18, "number": 20, "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "... While in its general principle of operation the alternating- current commutator motor is identical with the direct-cums! motor, in the relative proportioning of the parts a great differ- ence exists. In the direct-current motor, voltage is consumed by the counter e.m.f. of rotation, which represents the power output of the motor, and by the resistance, which represents the power loss. In addition thereto, in the alternating-cur rent motor voltage is consumed by the inductance, which is wattless or reactive and therefore ...", "... gnetic field oppo- site to that of the armature reaction and proportional to the armature current. Such a field is produced by overcompensa- tion or by the use of a commutating pole or interpole. As seen in the foregoing, in the direct-current motor t he counter e.m.f. of self-inductance of commutation opposes the reversal of current in the armature coil under the commutator brush, and this can be mitigated in its effect by the use of high-resistance brushes, and overcome by the commutating field of overcompen- sation. ...", "... use the motor to lose its torque, is not sufficient, for the reason that the resistance of the brush contact is not high enough and also is not constant. The brush contact resistance is not of the nature of an ohmic resistance, but more of the nature of a counter e.m.f.; that is, for large currents the potential drop at the brushes becomes approximately constant, as seen from the volt-ampere characteristics of different brushes given in Figs. 167 and 168. Fig. 167 gives the voltage consumed by the brush contact of a cop ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-82", "section_label": "Apparatus Section 3: Synchronous Converters: Variation of the Ratio of Electromotive Forces", "section_title": "Synchronous Converters: Variation of the Ratio of Electromotive Forces", "kind": "apparatus-section", "sequence": 82, "number": 3, "location": "lines 13796-13888", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-82/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-82/", "snippets": [ "... e.m.f. they are higher, by as much as 10 per cent, in extreme cases. In determining the wave shape of impressed e.m.f. at the con- verter terminals, not only the wave of generator e.m.f., but also that of the converter counter e.m.f., may be instrumental. Thus, with a converter connected directly to a generating system of very large capacity, the impressed e.m.f. wave will be practically identical with the generator wave, while at the terminals of a co ...", "... enerator wave, while at the terminals of a converter connected to the generator over long lines with re- active coils or inductive regulators interposed, the wave of im- pressed e.m.f. may be so far modified by that of the counter e.m.f. of the converter as to resemble the latter much more than the generator wave, and thereby the ratio of conversion may be quite different from that corresponding to the generator wave. Furthermore, for instance, in three-p ...", "... e.m.f. wave. With an impressed wave differing from the sine shape, there is a current of higher frequency, but generally of negligible mag- nitude, through the converter armature, due to the difference between impressed and counter e.m.f. wave." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-22", "section_label": "Chapter 22: Armature Reactions Of Alternators", "section_title": "Armature Reactions Of Alternators", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 23971-25134", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-22/", "snippets": [ "... d excitation to the resultant m.m.f., which produces the resultant magnetic field in the field poles and generates in the armature an e.m.f. called the \"virtual generated e.m.f.,\" since it has no actual existence, but is merely a mathematical fiction. The counter e.m.f. of self-induction of the armature current, that is, e.m.f. generated by the armature current by a local magnetic flux, combines with the virtual generated e.m.f. to the actual generated e.m.f. of the armature, which corresponds to the magnetic flux in th ...", "... f design, frequently the self-induction is represented by an increase of the armature reaction, that is, an effective armature reaction used which com- bines the effect of the true armature reaction and the armature self-induction. That is, instead of the counter e.m.f. of self- induction, a counter m.m.f. is used, which would produce the magnetic flux which would generate the e.m.f. of self-induction. For theoretical investigations usually the armature reaction is represented by an effective self-induction, that is, in ...", "... en change of the field generates an e.m.f. in the field circuit, which temporarily increases or decreases the field current, and so retards the change of the field flux. So, for instance, a sudden increase of load results in a simultaneous increase of the counter e.m.f. of self-induction and counter m.m.f. of armature reaction. With the armature reaction demagnetizing the field, the field flux begins to decrease, and thus generates an e.m.f. in the field-exciting circuit, which increases the field current and retards th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-14", "section_label": "Chapter 14: The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "section_title": "The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14089-14918", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "snippets": [ "... urrounds the one circuit without interlinking with the other, and is thus produced by the M.M.F. of one circuit only. 133. The common magnetic flux of the transformer is produced by the resultant M.M.F. of both electric circuits. It is determined by the counter E.M.F., the number of turns, and the frequency of the electric circuit, by the equation : ^ Where E = effective E.M.F. iV= frequency. n = number of turns. * = maximum magnetic flux. The M.M.F. producing this flux, or the resultant M.M.F. of primary and s ...", "... ] ALTERNATING-CURRENT TRANSFORMER. 197 by X at frequency N, then at frequency sN, or slip j, it will be = J ;r, and thus : Z ■= r — jsx = external secondary impedance.* Let -5*0 = primary impressed E.M.F. per circuit, E^ = E.M.F. consumed by primary counter E.M.F., Ex = secondary terminal E.M.F., E( = secondary induced E.M.F., e = E.M.F. induced per turn by the mutual magnetic flux, at full frequency N^ I^ = primary current, J^^ = primary exciting current, /i = secondary current. It is then : Secondary ...", "... that part of the reactance which is inversely proportional to the frequency ; and have thus, at slip J, or frequency sN^ the external secondary reactance jjt' -|- jc\" -|- X*\" 198 AL TERN A TING-CURRENT PHENOMENA. [§ 1 35^ E.M.F. consumed by primary counter E.M.F, hence, primary exciting current : Component of primary current corresponding to second- ary current /^ : j' ^ — Ix a n^se a^{{r^^ + ^) - js (^1 + X)) ' hence, total primary current, = «,«,,jl 1 ^ioJUlh I ai(ri + r) —js(xi + x) s Primary impr ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-19", "section_label": "Chapter 19: Commutatob Motobs", "section_title": "Commutatob Motobs", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 21339-22387", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "snippets": [ "... primary current, Primary impressed E.M.F., or Neglecting in -C© ^^e last term, as of higher order, xSq — ^ ■^ -*- \"1 _- : ( » or, eliminating imaginary quantities, ^ ^ ^ V(^ + nV^ + kxf + (x + x^V2 - krf ^ 198. The power consumed by the primary counter E.M.F., r, that is, transferred into the secondary circuit, is or, eliminating the imaginary quantities. 7^' = n + '^-''^i V2 n' + -^'i The power consumed by the secondary resistance is 2 n^ + ^/^ ' Hence, the difference, or the mechanical power at ...", "... teresis), ri = resistance of armature (effective resistance, including hys- teresis), iV = frequency of alternations, JVi = speed in cycles per second. It is then, E.M.F. induced in armature conductors by their rotation through the magnetic field (counter E.M.F. of motor). £ =4;/,i\\^i*10-» E.M.F. of self-induction of field, J5\" = 2fl-///i\\'^*10-«, E.M.F. of self-induction of armature, E.M.P\\ consumed by resistance, where / = current passing through motor, in amperes effective. Further, it is : Fiel ...", "... ate satisfactorily in an alternating-current circuit. It will start with good torque, since in starting the current in armature, as well as in field, are greatly lagging, and thus approximately in phase with each other. With increasing speed, however, the counter E.M.F. of the armature should be in phase with the impressed E.M.F., and thereby the armature current lag less, to represent power. Since how- ever, the field current, and thus the field magnetism, lag nearly 00°, the induced E.M.F, of the armature will lag ne ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-15", "section_label": "Chapter 15: The General Alternating-Current Transformer Or Frequency Converter", "section_title": "The General Alternating-Current Transformer Or Frequency Converter", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 12683-13648", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "snippets": [ "... urrounds the one circuit without interlinking with the other, and is thus produced by the M.M.F. of one circuit only. 143. The mutual magnetic flux of the transformer is produced by the resultant M.M.F. of both electric circuits. It is determined by the counter E.M.F., the number of turns, and the frequency of the electric circuit, by the. equation: Where E = effective E.M.F. JV= frequency. n = number of turns. <£ == maximum magnetic flux. The M.M.F. producing this flux, or the resultant M.M.F. of primary and ...", "... r ALTERNATING-CURRENT TRANSFORMER, 223 by x at frequency N, then at frequency s N, or slip s, it will be = s x, and thus : Z = r — jsx = external secondary impedance.* Let £0 = primary impressed E.M.F. per circuit, E ' = E.M.F. consumed by primary counter E.M.F., £1 = secondary terminal E.M.F., EI = secondary induced E.M.F., e = E.M.F. induced per turn by the mutual magnetic flux, at full frequency JY, IQ = primary current, ^0 = primary exciting current, 7i = secondary current. It is then : Secondary ind ...", "... quency, and x'\" that part of the reactance which is inversely proportional t6 the frequency ; and have thus, at slip s, or frequency sN, the external secondary reactance sx' + x\" -f- — — . 224 AL TERNA TING-CURRENT PHENOMENA, E.M.F. consumed by primary counter E.M.F. £'= -«<>'; hence, primary exciting current : 700 = E ' YQ = — «0 e (g0 + /£<))• Component of primary current corresponding to second- ary current 7X : hence, total primary current, // 1 Primary impressed E.M.F., We get thus, as the Equa ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-02", "section_label": "Chapter 2: Multiple Squirrel-Cage Induction Motor", "section_title": "Multiple Squirrel-Cage Induction Motor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3543-5554", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-02/", "snippets": [ "... tic flux which passes beyond the cir- cuit in which e\\ is induced. In the usual induction-motor theory, the mutual magnetic flux, , induces a voltage, E} which produces a current, and this current produces a self-inductive flux, 'j, giving rise to a counter e.m.f. of self-induction I\\X\\, which sub- tracts from E. However, the self -inductive flux, 'i, interlinks with the same conductors, with which the mutual flux, , inter- links, and the actual or resultant flux interlinkage thus is i = $ — 'i, and th ...", "... + jxi = self-inductive impedance of first motor second- ary; Z\\ = r'i + jx\\ = self-inductive impedance of second motor secondary. Assuming all these quantities reduced to the same number of turns per circuit, and to full frequency, as usual. If: e = counter e.m.f . generated in the second motor by its mutual magnetic flux, reduced to full frequency. It is then: secondary current of second motor: r/ _ *'* [« (1 + a) - a] e 1 * \"\" PT+ fix>\\ - ?;+j\\MV+ a) - a] x\\ = e(fll \" Ja'^ (8) 46 ELECTRICAL APPARATUS ...", "... /i = /] + /' 00 = e (bi - j6a)> bi = ax + g', bt = a* + 6', (12) (13) the impedance of the circuit comprising the primary of the second, and the secondary of the first motor, is: Z = Z/ + ZV - (n + r'0) + js (*, + x'0), (14) hence, the counter e.m.f., or induced voltage in the -secondary of the first motor, of frequency is: s$i = se + IiZ, hence, reduced to full frequency : where: C - 1 + *!-« + — = e (ci + jc2), ri + r-6i + (x1 + x/0)6a (15) 8 c% = (xj + x'o) 6i - ri + r'0 ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-11", "section_label": "Chapter 12: Frequency Converter Or General Alternating Current Transformer", "section_title": "Frequency Converter Or General Alternating Current Transformer", "kind": "chapter", "sequence": 11, "number": 12, "location": "lines 14897-17124", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-11/", "snippets": [ "... duction motor magnetically represent transformers of high ex- citing admittance and high self-inductive impedance. 104. The mutual magnetic flux of the transformer is pro- duced by the resultant m.m.f. of both electric circuits. It is determined by the counter e.m.f., the number of turns, and the frequency of the electric circuit, by the equation : E = V2 rfnQ 10\"8, where E = effective e.m.f., / = frequency, n = number of turns, $ = maximum magnetic flux. The m.m.f. producing this flux, or the resultant m.m.f ...", "... external reactance, and denote the latter by x at frequency, /, then at frequency, «/, or slip, s, it will be = *x, and thus: Z = r + jsx = external secondary impedance.1 Let: #o = primary impressed e.m.f. per circuit, J$' = e.m.f. consumed by primary counter e.m.f., #i = secondary terminal e.m.f., #\\ = secondary generated e.m.f., e = e.m.f. generated per turn by the mutual magnetic flux, at full frequency, /, /o = primary current, /oo = primary exciting current, /i = secondary current. It is then: Secondary ...", "... the external secondary reactance, sx' -f x\" -f x,n % 180 ELECTRICAL APPARATUS Secondary terminal voltage : #i = #'i ~ JiZi = fiZ = N rt + jgxi I = sntf (r + jsx) 1 1 0i + r) + js (xi + x) J \\rx + r) + j* (xi + x) e.m.f. consumed by primary counter e.m.f. $' = n0e; hence, primary exciting current: /oo = #'Fo = no« (flf - jb). Component of primary current corresponding to secondary current, /\\: aMCri + O+^Cxi + x)}' hence, total primary current: /o = /oo + / 0 f 1 1 , g - jb lfl2 (n + r) + js ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-34", "section_label": "Chapter 12: Magnetic Saturation And Hysteresis In Alternat Ing-Current Circuits", "section_title": "Magnetic Saturation And Hysteresis In Alternat Ing-Current Circuits", "kind": "chapter", "sequence": 34, "number": 12, "location": "lines 12885-13935", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-34/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-34/", "snippets": [ "... flux and the magnetic flux density also be at their negative maximum value - ^>0 and - (B0 — that is, in an inductive circuit, near the zero value of the decreasing e.m.f. wave — during the first half wave of e.m.f. the magnetic flux, which generates the counter e.m.f., should vary from — 4>0 to + 0, or by 2 4>0; hence, starting with 0, to generate the same counter e.m.f., it must rise to + 2 0, that is, twice its permanent value, and so the current i also rises, at constant inductance L, from zero to twice its m ...", "... inductive circuit, near the zero value of the decreasing e.m.f. wave — during the first half wave of e.m.f. the magnetic flux, which generates the counter e.m.f., should vary from — 4>0 to + 0, or by 2 4>0; hence, starting with 0, to generate the same counter e.m.f., it must rise to + 2 0, that is, twice its permanent value, and so the current i also rises, at constant inductance L, from zero to twice its maximum permanent value, 2 70. Since the e.m.f. consumed by the current during the variation from 0 to 2 70 i ...", "... its negative maximum value, — OJ0 = -- 10,000, the actual density at this moment may be <$>r = + 7600, the remanent magnetism of the cycle. During the first half wave of impressed e.m.f. the variation of flux density by 2 (B0, as required to generate the counter e.m.f., when neglecting the resistance, would bring the positive maximum of flux density up to (Br + 2 (B0 = 27,600, requiring 1880 amperes maximum current, or 420 times the normal current. Obviously, no such rise could occur, since the resistance of the circui ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-10", "section_label": "Theory Section 10: Hysteresis and Effective Resistance", "section_title": "Hysteresis and Effective Resistance", "kind": "theory-section", "sequence": 10, "number": 10, "location": "lines 3234-3585", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-10/", "snippets": [ "... reactance x = 2 irfL and of negligible resistance, the HYSTERESIS AND EFFECTIVE RESISTANCE 49 magnetic flux produced by the current, 0$ = $, is in phase with the current, and the e.m.f. generated by this flux, or counter e.m.f. of self-inductance, OE'\" = E'\" = xl, lags 90 degrees be- hind the current. The e.m.f. consumed by self-inductance or impressed e.m.f. OE\" = E\" = xl is thus 90 degrees ahead of the current. Inversely, if the e.m.f. OE\" ...", "... cuit. As seen in Fig. 24, in a circuit whose ohmic resistance is not negligible, the hysteresis current and the magnetizing current are not in phase and in quadrature respectively with the im- pressed e.m.f., but with the counter e.m.f. of inductance or e.m.f. consumed by inductance. Obviously the magnetizing current is not quite wattless, since HYSTERESIS AND EFFECTIVE RESISTANCE 51 energy is consumed by this current in the ohmic resistance of the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-16", "section_label": "Theory Section 16: Phase Control of Transmission Lines", "section_title": "Phase Control of Transmission Lines", "kind": "theory-section", "sequence": 16, "number": 16, "location": "lines 6222-6813", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-16/", "snippets": [ "... il of impedance Z\\ = r\\ + jx\\ = 0.5 -f- 10 j and run light, as compensator (that is, generator of reactive currents). How will the voltage at the synchronous motor terminals e\\, at constant excitation, that is, constant counter e.m.f. e = 2000, vary as function of e$ at no load and at a load of i = 100 amp. power current, and what will be the reactive current in the synchronous motor? Let I = ii — jiz = current in receiving circuit of voltage ...", "... i = 100 amp. power current, and what will be the reactive current in the synchronous motor? Let I = ii — jiz = current in receiving circuit of voltage e\\. Of this current 1,—jiz is taken by the synchronous motor of counter e.m.f. 'e, and thus EI = e — Zoji2 = e + X0i2 - jr0i2'} or, reduced, e^= (e + xoit)2 + rjif. In the supply circuit the voltage is Eo = Ei + IZl = e + xoi* - jrQi2 + (ii-jiz) (TI + jxi) = [e + riii + (xQ + xi) ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-17", "section_label": "Theory Section 17: Impedance and Admittance", "section_title": "Impedance and Admittance", "kind": "theory-section", "sequence": 17, "number": 17, "location": "lines 6814-7380", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-17/", "snippets": [ "... ng from the impressed e.m.f. and all e.m.fs. produced by the current i in the circuit. Such counter e.m.fs. may be due to inductance, as self-induc- tance, or mutual inductance, to capacity, chemical polarization, etc. The counter e.m.f. of self-induction, or e.m.f. generated by the magnetic field produced by the alternating current i, is repre- sented by a quantity of the same dimensions as resistance, and measured in ohms: reactance x. The e.m.f. consumed ...", "... e reactance of the circuit. And the quantity 21 = Vr!2 + x2 or, in symbolic representation, Zi = ri + jxi is the impedance of the circuit. If power is consumed in the circuit only by the ohmic resist- ance r, and counter e.m.f. produced only by self-inductance, the effective resistance TI is the true or ohmic resistance r, and the effective reactance Xi is the true or inductive reactance x. 100 ELEMENTS OF ELECTRICAL ENGINEERING By means of ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-20", "section_label": "Chapter 20: Single-Phase Induction Motors", "section_title": "Single-Phase Induction Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 21538-22301", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-20/", "snippets": [ "... ry circuit. Since the e.m.f. generated in the tertiary circuit decreases from e at synchronism to he at standstill, the effective tertiary admittance or admittance reduced to a generated e.m.f., e, is at slip s, F4I = [1 - (1 - h)s]}\\. Let then, e = counter e.m.f. of primary circuit, s = slip. We have, the secondary load current, J se S se / • N Zi^ (1 + s) (ri + jsxi) the secondary exciting current, /ii = eYi' = 1.5eFo[l - (1 - t) [s; the secondary condenser current; /, = er,i = eYi[l - (1 - /i) s]; ...", "... tal secondary current, I' = h +/1I + /4; the primary exciting current, W = eYo' = 1.5 e Fo, thus, the total primary current, /o = /I + h' = /i + /4 + Ii' + lo' = e(6i - M; the primary impressed e.m.f., Eo = e + Zo^/o = e(ci - JC2) ; thus, the main counter e.m.f., Eo e Cl - JC2 or, eo E = Cl - JC2 252 ALTERNATING-CURRENT PHENOMENA and the absolute value, hence, the primary current, J eo(fei - jbj) -«o — '• , Ci - JC2 or, ^0 = eo lb? -\\-b, The volt-ampere input, the power in ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-27", "section_label": "Chapter 27: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 33011-34776", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-27/", "snippets": [ "... of the third harmonic. The fifth and seventh harmonics do not give any power, since they are not contained in the synchronous motor wave. Sub- stituting now different numerical values for 6, the phase angle between generator e.m.f. and synchronous motor counter e.m.f., corresponding values of the. currents, /, Jo, and the powers, P^, Pi^, Ps', are derived. These are plotted in Fig. 190 with the total current, I, as abscissas. To each value of the total current, /, correspond two values of the total power, P^, a positi ...", "... the stationary impedance, and by neglecting the resist- ance we have Z^ = nj„(a;o + Xi) = 4.8 njn The exciting admittance of the motor, for these higher har- monics, is, by neglecting the conductance, 71 = _ ^ = - ^M n n and the higher harmonics of counter e.m.f., E^ = — ^• . 2 Thus we have, current input in the condenser, L - EoYc = + 4.28ii + 1.54 i3 - 4.93^5 - 4.02i7; high-frequency component of motor-impedance current, W ^ ■^ = - 0.92 i3 + 1.06 i5 + 0.44 Jt; high-frequency component of motor-exci ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 3230-3545", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-06/", "snippets": [ "... diagram, a certain ambiguity exists, in so far as one and the same quantity — an E.M.F., for in- stance — can be represented by two vectors of opposite •direction, according as to whether the E.M.F. is considered as a part of the impressed E.M.F., or as a counter E.M.F. This is analogous to the distinction between action and reaction in mechanics. Fig. 25. Further, it is obvious that if in the circuit of a gener- ator, G (Fig. 25), the current flowing from terminal A over resistance R to terminal B, is represented ...", "... f potential between any pair of termi- nals — for instance E^ and E^ — is then the distance E^E^^ or E^E^y according to the direction considered. Fig, 30. 35. If, now, in Fig. 29, a current, /j, in phase with E.M.F., E^, passes through a circuit, the counter E.M.F. of resistance, r, is E^ = /r, in opposition to /^ or E^^ 135] TOPOGRAPHIC METHOD. 47 and hence represented in the diagram by point £\",, and its combination with E^ by E(. The counter E,M.F. of reactance, x, is E^ = Ix, 90' behind the current / ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-15", "section_label": "Chapter 15: Induction Motob", "section_title": "Induction Motob", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 14919-17024", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "snippets": [ "... G, the E.M.F. consumed by the pri- mary reactance 90° ahead of OGy and represented by OIx^ and their resultant Ola is the E.M.F. consumed by the primary impedance. The E.M.F. induced in the primary circuit is OE^y and the E.M.F. required to overcome this counter E.M.F. is OE equal and opposite to OE^, Com- bining OE with OIs gives the primary terminal voltage represented by vector OE^^ and the angle of primary lag, ^,(9(7 = ^,. 145. Thus far the diagram is essentially the same as the diagram of the stationary alterna ...", "... ius is V = — ^ (1 - ^) ; hence the output of the motor, P= TS or, substituted, p^ P^\\^s(\\ -s) 218 AL TERN A TING-CURRENT PHENOMENA, [ § 147 The Power of the Induction Motor. 147. We can arrive at the same results in a different way: By the counter E.M.F. e of the primary circuit with current I = I^-^- 1^ the power is consumed, el = el^ + el^. The power el^ is that consumed by the primary hysteresis and eddys. The power e I^ disappears in the primary circuit by being transmitted to the secondary system. ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-20", "section_label": "Chapter 20: Commutator Motors", "section_title": "Commutator Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 19458-20501", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "snippets": [ "... e 1 + (sinX Neglecting in E0 the last term, as of higher order, £0 = e j 1 + sin X +jk cos X ^ ^4^ j ; or, eliminating imaginary quantities, e V(?i + r sin X -f- kx cos X)2 + (x^ + x sin X — kr cos X)2 The power consumed by the component of primary counter E.M.F., whose flux is interlinked with the secondary e sin X, is, f = [e sin X /]' = ^inXfosuiX-^cosX) , r\\ + x\\ the power consumed by the secondary resistance is, _ 2 _ **ri (sin2 x + ^ cos2 x) hence the difference, or the mechanical power developed by ...", "... teresis), rj = resistance of armature (effective resistance, including hys- teresis), N = frequency of alternations, N± = speed in cycles per second. It is then, E.M.F. induced in armature conductors by their rotation through the magnetic field (counter E.M.F. of motor). E =4 E.M.F. of self-induction of field, E' = E.M.F. of self-induction of armature, ^/ = 27r«1^V110-8, E.M.F. consumed by resistance, Er = (r + *i) I, where / = current passing through motor, in amperes effective. Further, it i ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "... e power of the third harmonic. The 5th and 7th harmonics do not give any power, since they are not contained in the synchronous motor wave. Substituting now different numerical values for u> the phase angle between generator E.M.F. and synchronous motor counter E.M.F., corresponding values of the currents / 70, and the powers P\\ P*, /Y are derived. These are plotted in Fig. 180 with the total current /as abcissae. To each value of the total current / correspond two values of the total power P\\ a positive value plotted ...", "... ics can be assumed the stationary impedance, and by neglecting the resistance it is Z1 = - njn (XQ + XJ = - 4.8 njn The exciting admittance of the motor, for these higher harmonics, is, by neglecting the conductance, n and the higher harmonics of counter E.M.F. Thus we have, Current input in the condenser, fc = E, Yc = - 4.28/i - 1.54/3 + 4.93/5 + 4.02/7 High frequency component of motor impedance current, |£ = .92/3 - 1.06y5 - .44/7 High frequency component of motor exciting current, = .07/3 - -0 ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-39", "section_label": "Chapter 3: Mechanical Rectification", "section_title": "Mechanical Rectification", "kind": "chapter", "sequence": 39, "number": 3, "location": "lines 15963-17754", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-39/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-39/", "snippets": [ "... the current not controlled thereby, as when rectifying for the supply of series fields of alternators. 2. r = r0 = oo , or open circuit rectification. This is feasible only if the rectified circuit contains practically no self -inductance, but a constant counter e.m.f., e, (charging storage batteries), so that in the moment when the alternating impressed e.m.f. falls to e, and the current disappears, the circuit is opened, and closed again in opposite direction when after reversal the alter- nating impressed e.m.f. has ...", "... stant-potential rectification. 12. Let the alternating e.m.f. eQ sin 0 of the alternating cir- cuit of impedance Z0 = r0 — jx0 .be rectified by connecting it at the moment 01 with the direct-current receiver circuit of impedance Z = r — jx and continuous counter e.m.f. e, dis- connecting it therefrom at the moment TT - 02, and closing during the time from n — 02 to n + Ol the alternating circuit by the resistance rv the direct-current circuit by the resistance r2, then connecting the circuits again in series in opposit ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-05", "section_label": "Chapter 6: Empirical Curves", "section_title": "Empirical Curves", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 16483-21988", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-05/", "snippets": [ "... , log e, as IV. Neither of these curves is a straight line. Curve IV is relatively the straightest, especially for high values of e. This points toward the existence of a constant term. The existence of a constant term in the arc voltage, the so-called \" counter e.m.f. of the arc \" is physically probable. In Table IV thus are given the values (e— 40) and log (e— 40), and plotted as curve V. This shows the opposite curvature of IV. Thus the. constant term is less than 40. Estimating by interpolation, and calculating in ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-11", "section_label": "Lecture 11: Lightning Protection", "section_title": "Lightning Protection", "kind": "lecture", "sequence": 11, "number": 11, "location": "lines 4931-5294", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-11/", "snippets": [ "... minum cells, over a path of practically no resistance; but the volume of the discharge which passes, is not that given by the voltage on*the system, but is merely that due to the excess voltage over the normal, since the normal voltage is held back by the counter e. m. f. of the aluminum cells. As a result — with strokes following each other, thousands per second, that is, with a recurrent surge — the aluminum arrester discharges continu- ously; but it can stand the continuous discharge for half an hour or more without da ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-04", "section_label": "Theory Section 4: Power and Effective Values", "section_title": "Power and Effective Values", "kind": "theory-section", "sequence": 4, "number": 4, "location": "lines 1244-1572", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-04/", "snippets": [ "... onsumed by resistance r is P = 72r. Either EI = E, then, the total power in the circuit is con- sumed by the resistance, or EI < E} then only a part of the power is consumed by the resistance, the remainder by some counter e.m.f., E — EI. If an alternating current i = I0 sin 6 passes through a resist- ance r, the power consumed by the resistance is, i*r = 702r sin2 0 = ^r C1 ~ cos 2 0), & thus varies with twice the frequency of the cur ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-13", "section_label": "Theory Section 13: Alternating-current Transformer", "section_title": "Alternating-current Transformer", "kind": "theory-section", "sequence": 13, "number": 13, "location": "lines 4465-5263", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-13/", "snippets": [ "... 1 1 Primary load current, /' = -a/i Primary excit- ing current, 70o Total primary current, /o . . . . Primary resist- ance, voltage, /oPo Primary react- ance, voltage, Iox0 E.m.f. consum- ed by primary counter e.m.f., -El a Total primary impressed e.m.f., E° Hence, Non-inductive, 0i = 0 Lag, 0i = + 60° Lead, 0! = - 60° Resultant Eo .... 2040 1 2098 3 1944 2 Resultant /o 10 32 1 ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-25", "section_label": "Apparatus Section 4: Synchronous Machines: Self-inductance", "section_title": "Synchronous Machines: Self-inductance", "kind": "apparatus-section", "sequence": 25, "number": 4, "location": "lines 8907-9034", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-25/", "snippets": [ "... n loaded generator, in the same manner. If EI = real generated voltage, 0i = lag of current behind generated voltage EI, the magnetic flux produced by the arma- ture current I is in phase with the current, and thus the counter e.m.f. of self-inductance is in quadrature behind the current, and therefore the e.m.f. consumed by self-inductance is in quadrature ahead of the current. Thus in Fig. 50, denoting OEi = EI the generated e.m.f., the current is 0 ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-28", "section_label": "Apparatus Section 7: Synchronous Machines: Synchronous Motor", "section_title": "Synchronous Machines: Synchronous Motor", "kind": "apparatus-section", "sequence": 28, "number": 7, "location": "lines 9292-9398", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-28/", "snippets": [ "... ELEMENTS OF ELECTRICAL ENGINEERING bining OE'i and OE'o gives OE', the e.m.f. consumed by the synchronous impedance. The e.m.f. consumed by the synchro- nous impedance OE' and the e.m.f. consumed by the nominal generated or counter e.m.f. of the synchronous motor OEo, combined, give the impressed e.m.f. OE. Hence OEo is one side of a parallelogram, with OE' as the other side, and OE as diagonal. OEoo .(not shown), equal and opposite OE0, would thus be t ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-33", "section_label": "Apparatus Section 12: Synchronous Machines: Starting of Synchronous Motors", "section_title": "Synchronous Machines: Starting of Synchronous Motors", "kind": "apparatus-section", "sequence": 33, "number": 12, "location": "lines 9749-9820", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-33/", "snippets": [ "... impressed voltage required in starting is higher and the current lower than with solid field poles. In either case, at full impressed e.m.f. the starting current of a synchronous motor is large, since in the absence of a counter e.m.f. the total impressed e.m.f. has to be consumed by the impedance of the armature cir- cuit. Since the starting torque of the synchronous motor is due to the magnetic flux produced by the alternating armature cur- rents, or ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1120-1683", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-01/", "snippets": [ "... The power equation: Po = ei, where Po is the power expended in the circuit of e.m.f., e, and current, i. 4. Kirchhoff's laws: (a) The sum of all the e.m.fs. in a closed circuit = 0, if the e.m.f. consumed by the resistance, ir, is also considered as a counter e.m.f., and all the e.m.fs. are taken in their proper direction. (b) The sum of all the currents directed toward a distributing point = 0. In alternating-current circuits, that is, in circuits in which the currents rapidly and periodically change their direc ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-05", "section_label": "Chapter 5: Symbolic Method", "section_title": "Symbolic Method", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2760-3266", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-05/", "snippets": [ "... e voltage consumed by the resistance is in phase with the current, and equal to the product of the current and resistance. Or rl = ri -\\- jri'. If L is the inductance, and x = 2x/L the inductive react- ance, the e.m.f. produced by the reactance, or the counter e.m.f. 1 In this representation of the sine wave by the exponential expression of the complex quantity, the angle 0 necessarily must be expressed in radians, and not in degrees, that is, with one complete revolution or cycle as 2 tt. or 180 with — = 57.3° as ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 3267-3618", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-06/", "snippets": [ "... by vectors, a certain ambiguity exists, in so far as one and the same quantity — voltage, for instance — can be represented by two vectors of opposite direction, according as to whether the e.m.f , is considered as a part of the impressed voltage or as a counter e.m.f. This is analogous to the distinction between action and reaction in mechanics. Further, it is obvious that if in the circuit of a generator, G (Fig. 25), the current in the direction from terminal A over re- sistance R to terminal B is represented by a ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-13", "section_label": "Chapter 13: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 13484-14333", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-13/", "snippets": [ "... he alternating current in the conductor produces a magnetic field, not only outside of the conductor, but inside of it also; and the lines of magnetic force which close themselves inside of the con- ductor generate e.m.fs. in their interior only. Thus the counter e.m.f. of self-induction is largest at the axis of the conductor, and least at its surface; consequently, the current density at the sur- face will be larger than at the axis, or, in extreme cases, the cur- rent may not penetrate at all to the center, or a rever ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "... m- ber of infinitely small condensers infinitely near together, as diagrammatically shown in Fig, 100. liiilliiiiiiiiiiiiiiiiiii JTTTTTTTTTTTTTTTTTTTTTTT- Fig. 100. In this case the intensity as well as phase of the current, and consequently of the counter e.m.f. of inductive reactance and resistance, vary from point to point; and it is no longer possible to treat the circuit in the usual manner by the vector diagram. This phenomenon is especially noticeable in long-distance lines, in underground cables, and to ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-26", "section_label": "Chapter 26: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 32540-33010", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-26/", "snippets": [ "... gnetic circuit, as, for instance, a transformer, the wave of magnetism in the primary will repeat in shape the wave of magnetism interlinked with the armature coils of the alternator, and consequently with a lesser maximum magnetic flux the same effective counter e.m.f. will be produced, that is, the same power converted in the transformer. Since the hysteretic loss in the transformer depends upon the maximum value of mag- netism, it follows that the hysteretic loss in a transformer is less with a distorted wave of a un ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... current from constant po- tential, 76 synchronous motor, 337 potential constant current trans- formation, 76 Consumed voltage, by resistance, re- actance, impedance, 23 Control of voltage by shunted sus- ceptance, 89 Corona, 112, 161 of line, 174 Counter e.m.f. of impedance, react- a,nce, resistance, self-induc- tion, 23 of synchronous motor, 24, 315 Crank diagram, 19 and polar diagram, comparison, 51 Critical voltage of corona, 166 Cross currents in alternators, 293 Cross flux, magnetic of transformer, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1224-1727", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "snippets": [ "... ower equation : P^ = ei, where P^ is the power expended in the circuit of E.M.F., .admittance, in absolute values. y = Vff* + 6* = V (* - rf^^) '+{r-os- rh^^ 350 ELECTRIC CIRCUITS in symb ...", "... ations as in the complex quantities in alter- nating-current circuits, except that in the present case all the constants, Va, Xa, Zay g, Zj y, depend upon the decrement, a. It is interesting to note that with oscillating currents, resist- ance as well as conductance have a negative term added, which depends on the decrement a. Such a negative resistance repre- sents energy production, and its meaning in the present case is, that with the decrease of the oscillating current and voltage, their stored magnetic and diele ...", "... magnetic properties, 80 Coefficient of hysteresis, 61 Coherer action of pyroelectric con- ductor, 19 Compensating voltage balancing un- balanced power, 320 Condenser, electrostatic, 9 power equation, 319 tending to instability, 164. See Capacity, Conductance with oscillating cur- rents, 349 Conduction, electric, 1 Conductors, mechanical magnetic forces, 106 Constant component of power in general system, 317 current arc, stability condition, 172 constant potential transfor- mation, 243, 286 reactance, ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-43", "section_label": "Chapter 3: The Natural Period Of The Transmission Line", "section_title": "The Natural Period Of The Transmission Line", "kind": "chapter", "sequence": 43, "number": 3, "location": "lines 21721-23178", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "snippets": [ "... the problem is essentially simplified. 28. Let 10 = total length of a transmission line; I = the dis- tance from the beginning of the line; r = resistance per unit length; x = reactance per unit length = 2 nfL, where L = inductance per unit length; g = conductance from line to return (leakage and discharge into the air) per unit length; b = capacity susceptance per unit length = 2 nfC, where C = capacity per unit length. Neglecting the line resistance and line conductance, r = 0 and g = 0, the line constants a ...", "... where L = inductance per unit length; g = conductance from line to return (leakage and discharge into the air) per unit length; b = capacity susceptance per unit length = 2 nfC, where C = capacity per unit length. Neglecting the line resistance and line conductance, r = 0 and g = 0, the line constants a and /?, by equations (14), Chapter II, then assume the form a = 0 and ft = Vxb, (1) and the line equations (17) of Chapter II become / = (AA - A2) cos pi - j (Aj + A,) sin pi and E = V ^ (A, + A2)cos fl - / ...", "... t in space as well as in time, which are discussed in Section IV. 39. In the equations discussed in the preceding, of the free oscillations of a circuit containing uniformly distributed resist- 340 TRANSIENT PHENOMENA ance, inductance, capacity , and conductance, the energy losses in the circuit have been neglected, and voltage and current therefore appear alternating instead of oscillating. That is, these equations represent only the initial or maximum values of the phenomenon, but to represent it completely an ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-52", "section_label": "Chapter 3: Standing Waves", "section_title": "Standing Waves", "kind": "chapter", "sequence": 52, "number": 3, "location": "lines 29316-30243", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "snippets": [ "... WAVES 447 hence, from (62), '•-,Vr.- <125> The frequency at the wave length lWo is zero, since at this wave length the phenomenon ceases to be oscillatory ; that is, due to the energy losses in the circuit, by the effective resistance r and effective conductance g, the frequency / of the wave is reduced below the value corresponding to the wave length lw, the more, the greater the wave length, until at the wave length lWo the frequency becomes zero and the phenomenon thereby non-oscillatory. This means that with ...", "... ent. Substituting £0, and reducing to one mile and common loga- rithm, gives mf.; (134) logf lr hence, in this instance, C = 0.0162 mf. Estimating the loss in the static field of the line as 400 watts per mile of conductor gives an effective conductance, which gives the line constants per mile as r = 0.41 ohm; L = 1.95X10-3 henry; g = 0.25 X 10~6 mho, and C = 0.0162 X lO\"6 farad. Herefrom then follows :>-i.S-.S-'* a- = VLC = V31.6 X 10~6 = 5.62 X lO\"6, &0 = ra\\/57 = 545 X 10~6; hence, the critic ...", "... g of two wires No. 4 B. and S. G., 24 inches distant from each other. Calculating in the same way as discussed under (1), the follow- ing constants per mile of conductor are obtained: r = 1.31 ohms, L = 1.84 X 10~3 henry, and C = .0172 X 10~6 farad. As conductance, g, we may assume (a) g = 0; that is, very perfect insulation, as in dry weather. (6) g = 2.5 X HT6; that is, slightly leaky line. STANDING WAVES 455 (c) g = 12 X 10~6; that is, poor insulation, or a leaky line. (d) g = 40 X 10~6; that is, extr ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-56", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit", "section_title": "Power And Energy Of The Complex Circuit", "kind": "chapter", "sequence": 56, "number": 7, "location": "lines 33528-34202", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "snippets": [ "... conductor element dX is dp? = Mdl (327) 2r hence, substituting herein equation (318) gives the power con- sumed by resistance of the circuit element dX as ^ 2r (flfojo du/ _-a) is of the low frequency of the beat, or the current fluctuation betwee ...", "... of no further interest. The second term p\"i=- cos a [[END_PDF_PAGE:29]] [[PDF_PAGE:30]] 24 Report of Charles P. Steinmetz gives, substituting cos a = - ; z E 2g P\"i=2? 2 where g is the conductance of the circuit. That is, this term is the energy loss in the conductance, that is, the resistance of the circuit, and thus also is of no further interest. The third term: p'Y=-!|cos(2a>-a) is of the low frequency of the beat, or the current fluctuation between the two alternators: pf. It thus represents the energy transfer between ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "... O fl bC -^^ 78 ELECTRIC DISCHARGES, WAVES AND IMPULSES. Instead of L and C, thus enter into the equation of the double- energy oscillation of the line the values — and — ^ IT IT In the same manner, instead of the total resistance r and the total conductance g, the values — and —^ appear. TT IT The values of Zq, yo, u, 4>, and co are not changed hereby. The frequency /, however, changes from the value correspond- ing to the circuit of massed capacity, / = 7= , to the value 2 7r vLC 4:VLC Thus the fre ...", "... ation of a transmission line is / = — 7= = T-^ ■ (20) where a = VlC. (21) If h is the length of the line, or of that piece of the line over which the oscillation extends, and we denote by Lo,Co,ro,go (22) the inductance, capacity, resistance, and conductance per unit length of line, then that is, the rate of decrease of the transient is independent of the length of the line, and merely depends on the line constants per unit length. It then is (T = ll & 3. Resistance r = r0 + r', consuming the power, tfr = ? 4. Conductance ...", "... conductance g. In its most general form the electric circuit therefore contains the constants : 1. Inductance L, storing 'the energy, -— , ft 2. Capacity C, storing the energy, - — > & 3. Resistance r = r0 + r', consuming the power, tfr = ? 4. Conductance g} consuming the power, ezg, where r0 is the resistance of the conductor, r' the effective resist- ance representing the power loss in the magnetic field L, and g represents the power loss in the electrostatic field C. 9. If of the three components of t ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-45", "section_label": "Chapter 5: Distributed Series Capacity", "section_title": "Distributed Series Capacity", "kind": "chapter", "sequence": 45, "number": 5, "location": "lines 23586-23947", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "snippets": [ "... ining distributed series capacity thus leads to an under- standing of the phenomena occurring in the thunder cloud during the lightning discharge.* Only a general outline can be given in the following. 45. In a circuit containing distributed resistance, conductance, inductance, shunt, and series capacity, as the multigap lightning arrester, Fig. 90, represented electrically as a circuit in Fig. 91, let r = the effective resistance per unit length of circuit, or per circuit element, that is, per arrester cylinder; g ...", "... , shunt, and series capacity, as the multigap lightning arrester, Fig. 90, represented electrically as a circuit in Fig. 91, let r = the effective resistance per unit length of circuit, or per circuit element, that is, per arrester cylinder; g = the shunt conductance per unit length, representing leakage, brush dis- charge, electrical radiation, etc.; L = the inductance per unit length of circuit; C = the series capacity per unit length of cir- cuit, or circuit element, that is, capacity between adjacent arrester cyli ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-53", "section_label": "Chapter 4: Traveling Waves", "section_title": "Traveling Waves", "kind": "chapter", "sequence": 53, "number": 4, "location": "lines 30244-31450", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "snippets": [ "... e can be reduced, that is, the wave caused to travel a greater distance / with the same decrease of amplitude. As function of the inductance L, the attenuation constant (155) is a minimum for — °=o- dL hence, rO - gL = 0, or (156) and if the conductance g = 0 we have L = ; hence, in a per- fectly insulated circuit, or rather a circuit having no energy losses depending on the voltage, the attenuation decreases with increase of the inductance, that is, by \"loading the line,\" and the more inductance is ...", "... ncy may appear which has the time decrement, that is, dies out at the rate In this decrement the factor 474 TRANSIENT PHENOMENA is the usual decrement of a circuit of resistance r and inductance Lj while the other factor, may be attributed to the conductance and capacity of the circuit, and the total decrement is the product, A further discussion of the equations (176) and (177) and the meaning of their transient term requires the consideration of the terminal conditions of the circuit. 27. The alternatin ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... a transmission line may be considered as an illustration of the phenomena in a complex circuit comprising sections of very different constants; that is, a combination of a circuit section of high inductance and small resistance and negligible capacity and conductance, as a generating station, with a circuit of distributed capacity and inductance, as a transmission line. The extreme case of such a discharge would occur if a short circuit at the busbars of a gen- erating station opens while the transmission line is conn ...", "... ce 55 equations 48 oscillation, effective value of voltage, current and power. ... 70 efficiency, decrement and output 72 frequency 62 general equations 60 size and rating 69 starting on alternating voltage 94 voltage in inductive circuit 49 Conductance, shunted, effective 12 Conductors at high frequency 403 Constant-current mercury arc rectifier 250 rectification 221, 230 potential-constant-current transformation by quarter-wave line 308 mercury arc rectifier 251 rectification 221, 230 INDEX ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1003-1658", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-02/", "snippets": [ "... current): current): = lines of magnetic ^ = lines of dielectric i = electric cur- force. force. rent. Magnetomotive force: Electromotive force: Voltage: F = ni ampere turns. e = volts. e = volts. Permeance: Permittance or capacity: Conductance: Inductance: C = — farads. a = - mhos. 71\"$ n^ e e henry. Reluctance: (Elastance) : Resistance: R = ^. 1 e r = - ohms. $ C ^' I Magnetic energy: Dielectric energy: Electric power: Li2 F^,^ ,. , Ce^ e^ . , p = ri^ = ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 883-1530", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "snippets": [ "... t) : <£ = lines of magnetic ^ = lines of dielectric i = electric cur- force. force. rent. Magnetomotive force: Electromotive force: Voltage: F = ni ampere turns. e = volts. e = volts. Permeance: M = 4?F Permittance or capacity: Conductance: Inductance: 4irV2f , i Q — - mnos. ~~F~ ' ~T henry. Reluctance: (Elastance ?): Resistance: F 1 e e & C 4*v*l>- T ~~\" T OIIIXIS. Magnetic energy: Dielectric energy: Electric power: w=— = — !Q-* joules. Ce2 e^ . , w = - ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-04", "section_label": "Chapter 5: Methods Of Approximation", "section_title": "Methods Of Approximation", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 15156-16482", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-04/", "snippets": [ "... xaV4x(l+2^)(l-2j) (1 _ \\4a2 a a J a3/2(l-3s2+2-- + S2--) \\ a a / \\ 4 a. a J 138. As further example may be considered the equations of an alternating-current electric circuit, containing distributed resistance, inductance, capacity, and shunted conductance, for instance, a long-distance transmission line or an underground high-potential cable. Equations of the Transmission Line. Let I be the distance along the line, from some starting point; E^ the voltage; 7, the current at point I, expressed as vector ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-108", "section_label": "Apparatus Section 2: Induction Machines: Polyphase Induction Motor", "section_title": "Induction Machines: Polyphase Induction Motor", "kind": "apparatus-section", "sequence": 108, "number": 2, "location": "lines 19166-20427", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-108/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-108/", "snippets": [ "... induction motor de- pends upon two complex imaginary constants, Y and Z, or four real constants, g, 6, r, x, the same terms which characterize the stationary alternating-current transformer on non-inductive load. Instead of conductance g, susceptance 6, resistance r, and react- ance x, as characteristic constants may be chosen: the absolute exciting admittance y = \\/g2 -f- &2; the absolute self-inductive impedance z — \\/r2-}-x2', the power-factor of admitta ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-20", "section_label": "Theory Section 20: Nomenclature", "section_title": "Nomenclature", "kind": "theory-section", "sequence": 20, "number": 20, "location": "lines 7991-8291", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-20/", "snippets": [ "... Character E, e. Voltage Volt Electrical I, i. . Potential difference Electromotive force Current Ampere Electrical R,r Resistance Ohm Electrical x Reactance Ohm Electrical Z,z... Impedance Ohm Electrical a Conductance Mho Electrical b Susceptance Mho Electrical Y,y p Admittance Resistivity Mho Ohm-centimeter Electrical Electrical 7 $ Conductivity Magnetic flux Mho-centimeter Line; kiloline; megaline Electrical Magnetic £....... ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-16", "section_label": "Chapter 16: Power, And Double-Frequency Quantities In", "section_title": "Power, And Double-Frequency Quantities In", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 16077-16520", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-16/", "snippets": [ "... admittance, etc., of the circuit is a com- plex quantity also, in symbolic denotation. Thus current, voltage, impedance, and admittance are related by multiplication and division of complex quantities in the same way as current, voltage, resistance, and conductance are related by Ohm's law in direct-current circuits. In direct-current circuits, power is the product of current into voltage. In alternating-current circuits, if the product, is not the power; that is, multiplication and division, which are correct ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-17", "section_label": "Chapter 17: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16521-17716", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-17/", "snippets": [ "... s derived by calculating the total exciting current from the ampere-turns excitation, the mag- netic characteristic of the iron and the dimensions of the main magnetic circuit, that is the magnetic circuit interlinked with primary and secondary coils. The conductance, go, is derived from the hysteresis loss in the iron, as given by magnetic density, hysteresis coefficient and dimensions of magnetic circuit, allow- ance being made for eddy currents in the iron. The ohmic resistances, ro and ri, are found from the dime ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-27", "section_label": "Chapter 27: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 33011-34776", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-27/", "snippets": [ "... impedance of the motor for these higher harmonics can be assumed the stationary impedance, and by neglecting the resist- ance we have Z^ = nj„(a;o + Xi) = 4.8 njn The exciting admittance of the motor, for these higher har- monics, is, by neglecting the conductance, 71 = _ ^ = - ^M n n and the higher harmonics of counter e.m.f., E^ = — ^• . 2 Thus we have, current input in the condenser, L - EoYc = + 4.28ii + 1.54 i3 - 4.93^5 - 4.02i7; high-frequency component of motor-impedance current, W ^ ■^ = - 0 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "section_title": "Dibtbisnted Capacity, Inductance, Besistance, And", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "... or of dielectric hysteresis. Currents consumed in quadrature to the E.M.F., E, and = bE, being wattless, and due to : Capacity and Electrostatic influence. Hence we get four constants : — Effective resistance, r. Effective reactance, x. Effect iv'e conductance, g^ Effective susceptance, ^ = — b^y 158 ALTERJ^ATING-CURRENT PHENOMENA. [§§108,109 per unit length of line, which represent the coefficients, per unit length of line, of E.M.F. consumed in phase with current ; E.M.P\\ consumed in quadrature with cur ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-14", "section_label": "Chapter 14: The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "section_title": "The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14089-14918", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "snippets": [ "... riving by ex- ternal mechanical power). Let Wo = number of primary turns in series per circuit ; fix = number of secondary turns in series per circuit ; a = — = ratio of turns ; Vq = go +y^o = primary admittance per circuit ; where go '= effective conductance ; do = susceptance ; Zq == Tq — jXo = internal primary impedance per circuit, where To = effective resistance of primary circuit ; Xo = reactance of primary circuit ; Zii = ri — jxi = internal secondary impedance per circuit at standstill, or for ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "section_label": "Chapter 30: Quartbr-Fhase System", "section_title": "Quartbr-Fhase System", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... a; K Z^ Za ) S288] OSCILLATING CURRENTS. 417 or, substituting, I^E r -^ ax — 1 + tf^ K'-if5)+(— rf?'.)' X — +y 1 +'»* ^FM'^{—.hA dec a* + 288. Thus in complex quantities, for oscillating cur- rents, we have : conductance, r — ajc — a ^ = \\-\\- a^ \" I X — ■ +[r — ax^ Xg 55 susceptance, b = X — 1 + g^ , (\"-riv^) +('•-\"\"-- rf^\"')\"^ admittance, in absolute values, ^ = vV* + />« = v/(\"-i+7^)+(''-''*-iT7»\"')' ■ in symbolic expression, [r — ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-12", "section_label": "Chapter 12: Power, And Double Frequency Quantities In General", "section_title": "Power, And Double Frequency Quantities In General", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 9381-9740", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "snippets": [ "... e impedance, admittance, etc., of the circuit is a complex quantity also, in symbolic denotation. Thus current, E.M.F., impedance, and admittance are related by multiplication and division of complex quantities similar as current, E.M.F., resistance, and conductance are related by Ohms law in direct current circuits. In direct current circuits, power is the product of cur- rent into E.M.F. In alternating current circuits, if The product, P0 = EI= (Ml - *\"/\") +j (W POWER, AND DOUBLE FREQUENCY QUANTITIES. 151 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-15", "section_label": "Chapter 15: The General Alternating-Current Transformer Or Frequency Converter", "section_title": "The General Alternating-Current Transformer Or Frequency Converter", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 12683-13648", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "snippets": [ "... ternal mechanical power). Let «0 = number of primary turns in series per circuit ; /?! = number of secondary turns in series per circuit ; a = — = ratio of turns ; «i Y0 =£\"0 H~./A) = primary exciting admittance per circuit; where gQ = effective conductance ; b0 = susceptance ; Z0 = r0 —jx0 = internal primary self-inductive impedance per circuit, where r0 = effective resistance of primary circuit ; jr0 = reactance of primary circuit ; Zu = TI — jxv = internal secondary self -inductive impedance pe ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "section_label": "Chapter 16: Induction Motor", "section_title": "Induction Motor", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "... ltampere, of the magnetic cycle, it follows that the apparent efficiency of such a motor can never exceed the value (1 — s) sin a, or a fraction of the primary hysteretic energy. The primary hysteretic energy of an induction motor, as represented by its conductance, g, being a part of the loss in the motor, and thus a very small part of its output only, it follows that the output of a hysteresis motor is a very small fraction only of the output which the same magnetic structure could give with secondary short-circui ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "... impedance of the motor for these higher harmonics can be assumed the stationary impedance, and by neglecting the resistance it is Z1 = - njn (XQ + XJ = - 4.8 njn The exciting admittance of the motor, for these higher harmonics, is, by neglecting the conductance, n and the higher harmonics of counter E.M.F. Thus we have, Current input in the condenser, fc = E, Yc = - 4.28/i - 1.54/3 + 4.93/5 + 4.02/7 High frequency component of motor impedance current, |£ = .92/3 - 1.06y5 - .44/7 High frequency com ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-32", "section_label": "Chapter 32: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 25904-27405", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "snippets": [ "... p \\ cos (9 — to ) -j sin (9 — hence in complex quantities, E = e (cos u> -\\-j sin oi) dec a, + sin OSCILLATING CURRENTS. 505 or, substituting, r — ax — I =E I- dec a. 317. Thus in complex quantities, for oscillating cur- rents, we have : conductance, susceptance, admittance, in absolute values, / o i To 1 in symbolic expression, Y=g+J» 1 + a2/ \\ 1 + a2 ' Since the impedance is Z = ir — ax — we have 506 APPENDIX II. that is, the same relations as in the complex quantities in al ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-01", "section_label": "Chapter 1: Speed Control Of Induction Motors", "section_title": "Speed Control Of Induction Motors", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1368-3542", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-01/", "snippets": [ "... uced voltage, and thus also the voltage producing the eddy currents, is proportional to the frequency. The currents are proportional to the voltage, and the eddy-current losses, there- fore, are proportional to the square of the voltage. The eddy- current conductance, gf thus is independent of the frequency. The admittance of a magnetic circuit consuming energy by eddy currents (and other secondary currents in permanent closed circuits), of negligible hysteresis loss, thus is represented, as function of the slip, by ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "... reactance of synchronous-motor armature reaction, is the reciprocal of the exciting acceptance of the induction machine. The total or synchronous reactance of the induction machine as synchronous motor thus is: * - x« + x' .1 = x. + r The exciting conductance, g, represents the loss by hysteresis, etc., in the iron of the machine. As synchronous machine, this loss is supplied by the mechanical power, and not electrically, and the hysteresis loss in the induction machine as synchronous motor thus is: e*g. We ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-04", "section_label": "Chapter 5: Single-Phase Induction Motor", "section_title": "Single-Phase Induction Motor", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 8555-10582", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-04/", "snippets": [ "... om follows t, q and v. As instance consider a motor of effective admittance per cir- cuit: Y = g-jb = l-3j, with the two circuits connected in series between single-phase mains of voltage, e<>, and one circuit shunted by a non-inductive resistance of conductance, gim What value of g\\ gives maximum starting torque, and what is this torque? It is: (53}' ' \" 1 , __J_ \" 2g + gx - 2j6 ~ (5b} ff + flfi — jb 0 - J& (54). *-— -—^ *__.___, (57) (55) : m (cos * + j sin 0) - *-±-«L^ = [^+_^)^Hl^; hence: gi& ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-09", "section_label": "Chapter 10: Hysteresis Motor", "section_title": "Hysteresis Motor", "kind": "chapter", "sequence": 9, "number": 10, "location": "lines 14551-14761", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-09/", "snippets": [ "... nergy of the mag- netic cycle, it follows that the apparent efficiency of such a motor can never exceed the value (1 — s) sin a, or a fraction of the primary hysteretic energy. The primary hysteretic energy of an induction motor, as repre- sented by its conductance, ij, being a part of the loss in the motor, and thus a very small part of its output only, it follows that the output of a hysteresis motor is a small fraction only of the output which the same magnetic structure could give with secondary short-circuited ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-11", "section_label": "Chapter 12: Frequency Converter Or General Alternating Current Transformer", "section_title": "Frequency Converter Or General Alternating Current Transformer", "kind": "chapter", "sequence": 11, "number": 12, "location": "lines 14897-17124", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-11/", "snippets": [ "... g by external mechanical power). Let: n0 = number of primary turns in series per circuit; nx = number of secondary turns in series per circuit; a = = ratio of turns; Til Y = g — jb = primary exciting admittance per circuit; where: g = effective conductance; b = susceptance; Zq = r0 + jxo = internal primary self-inductive impedance per circuit, where: r0 = effective resistance of primary circuit; Xq = self-inductive reactance of primary circuit; Zn = n + jx\\ = internal secondary self-inductive im- peda ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-06", "section_label": "Chapter 2: Long Distance Transmission Line. 279", "section_title": "Long Distance Transmission Line. 279", "kind": "chapter", "sequence": 6, "number": 2, "location": "lines 755-835", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-06/", "snippets": [ "... 18. Special case : Infinitely long conductor. 305 19. Special case: Generator feeding into closed circuit. 306 20. Special case: Line of quarter-wave length, of negligible resistance. 306 21. Line of quarter-wave length, containing resistance r and conductance g. 309 22. Constant-potential — constant-current transformation by line of quarter-wave length. 310 23. Example of excessive voltage produced in high-potential transformer coil as quarter- wave circuit. 312 24. Effect of quarter-wave phenomena on re ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-20", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit. 513", "section_title": "Power And Energy Of The Complex Circuit. 513", "kind": "chapter", "sequence": 20, "number": 7, "location": "lines 1228-1261", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-20/", "snippets": [ "... its compo- nents. Transfer of energy between electrostatic and electromagnetic field. 517 53. Energy stored in a circuit section by the total electric field, and power supplied to the circuit by it. 518 54. Power dissipated in the resistance and the conductance of a circuit section. 519 55. Relations between power supplied by the electric field of a circuit section, power dissipated in it, and power transferred to, or received by other sections. 520 56. Flow of energy, and resultant circuit decrement. 521 ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-47", "section_label": "Chapter 7: Distribution Of Alternating-Current Density In Conductor", "section_title": "Distribution Of Alternating-Current Density In Conductor", "kind": "chapter", "sequence": 47, "number": 7, "location": "lines 24981-26094", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "snippets": [ "... effective internal inductance inversely proportional, to the square root of the electric conductivity, of the magnetic permeability, and of the frequency. From equation (40) it follows that with a change of conduc- tivity A of the material the apparent conductance, and therewith the apparent resistance of the conductor, varies proportionally to the square root of the true conductivity or resistivity. Curves of distribution of current density throughout the sec- tion of the conductor are identical with the curves o ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-55", "section_label": "Chapter 6: Transition Points And The Complex Circuit", "section_title": "Transition Points And The Complex Circuit", "kind": "chapter", "sequence": 55, "number": 6, "location": "lines 32709-33527", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "snippets": [ "... tion, of time constant u, the time decrement, from Chapters III and V, is, however, e~ut; that is, with the decrement e~ut the wave dies out in the isolated sec- tion at the rate at which its stored energy is dissipated by the power lost in resistance and conductance. In a section of the circuit connected to other sections the time decrement e~U(* does not correspond to the power dissipation in the section; that is, the wave does not die out in each section at the rate as given by the power consumed in this section, o ..." ] } ] }, { "id": "wave-length", "label": "Wave Length", "aliases": [ "Wave length", "wave length", "wave lengths", "wave-length", "wave-lengths", "wavelength" ], "total_occurrences": 279, "matching_section_count": 39, "matching_source_count": 9, "source_totals": [ { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 118, "section_count": 19 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 85, "section_count": 7 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 34, "section_count": 2 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 15, "section_count": 3 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 15, "section_count": 3 }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 6, "section_count": 2 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 3, "section_count": 1 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 2, "section_count": 1 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 36, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... ves are in phase, as Al and B^ in Fig. 3 add to Cr If, however, the two beams A2 and B2 are not in phase, their resultant C2 is less than their sum, and if the two beams A3 and B3 in Fig. 3 happen to be in opposition (180 degrees apart), that is, one-half wave length out of phase with each other, their resultant is zero, that is, they blot each other out. Assuming now we take a plain glass plate A (Fig. 4) and a slightly curved plate B, touching each other at (7, and illuminate them by a beam of uniform light — as t ...", "... am b and a beam c. The two beams of light which combine to a single one, a, differ from each other in phase by twice the distance between the two glass plates. At those points dv dv etc. at which the distance FIG. 4. between the two glass plates is J wave length, or j, J, etc., the two component beams of a would differ by \\, f , |, etc. wave lengths, and thus would blot each other out, producing darkness, 6 RADIATION, LIGHT, AND ILLUMINATION. while at those points where the distance between the glass plates i ...", "... each other in phase by twice the distance between the two glass plates. At those points dv dv etc. at which the distance FIG. 4. between the two glass plates is J wave length, or j, J, etc., the two component beams of a would differ by \\, f , |, etc. wave lengths, and thus would blot each other out, producing darkness, 6 RADIATION, LIGHT, AND ILLUMINATION. while at those points where the distance between the glass plates is J, 1, lj, etc. wave lengths, and the two component beams a thus differ in phase by a ful ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-52", "section_label": "Chapter 3: Standing Waves", "section_title": "Standing Waves", "kind": "chapter", "sequence": 52, "number": 3, "location": "lines 29316-30243", "status": "candidate", "occurrence_count": 34, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "snippets": [ "... e, two different cases exist, depending upon the rela- tive values of Ar* and LCm2, and in addition thereto the inter- mediary or critical case, in which k2 = LCm2. These three cases require separate consideration. is a circuit constant, while k is the wave length constant, that is, the higher k the shorter the wave length. A. Short waves, k2 > LCm2, (99) hence, R2 = k2 - LCm2 (100) and q = V ^ - ™\\ 442 STANDING WAVES 443 or approximately, for very large k, Herefrom then follows and VLC ...", "... values of Ar* and LCm2, and in addition thereto the inter- mediary or critical case, in which k2 = LCm2. These three cases require separate consideration. is a circuit constant, while k is the wave length constant, that is, the higher k the shorter the wave length. A. Short waves, k2 > LCm2, (99) hence, R2 = k2 - LCm2 (100) and q = V ^ - ™\\ 442 STANDING WAVES 443 or approximately, for very large k, Herefrom then follows and VLC °l= k c' mL c, -T-c, -1± - 2\" k c'=---c' 2 k ...", "... estigate the conditions under which these two different cases occur. The transition from gradual to oscillatory takes place at k* = m2LC; (121) for larger values of k the phenomenon is oscillatory; for smaller, exponential or gradual. Since k is the wave length constant, the wave length, at which the phenomenon ceases to be oscillatory in time and becomes a gradual dying out, is given by (63) as 27T 2, (122) m Vie In an undamped wave, that is, in a circuit of zero r and zero g, in which no energy los ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... ce, from heat energy by raising a body to a 230 GENERAL LECTURES high temperature. Then the heat energy is converted into radi- ation and issues from the heated body, as for instance an incan- descent lamp filament, as a mass of radiations of different wave lengths, that is, different frequencies. All kinds of frequencies appear : from very low frequencies, that is only a few millions of millions of cycles per second, up to many times higher frequencies. We can get, if we desire, still very much lower fre- quencies, ...", "... ury arc at low temperature gives. Possibly, since the oxygen atom is so much lighter than the silver atom, its fre- quency of vibration is much higher, which means that resonance effects and destruction of the molecules take place only with a much shorter wave length of radiation, or much higher frequency. Vice versa, it seems that these frequencies which are chemically active in organic life, which give the energy absorbed from radiation by plants, and so the chemical activity utilized in building up the growth of ...", "... ween heat waves, chemical waves and light waves, therefore is not a physical distinction, destruction down to the atom. death; one splits up into carbon groups and the other carries but all are radiating energy of the same character, differing merely in wave length, and the visible range is somewhat less than one octave, rather at the upper end, at the higher fre- quencies, which are difficult to produce. This makes the prob- lem of investigating and dealing with light difficult for the engi- neer, because it is not ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-03", "section_label": "Lecture 3: Physiological Effects Of Radiation", "section_title": "Physiological Effects Of Radiation", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2366-3638", "status": "candidate", "occurrence_count": 19, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-03/", "snippets": [ "LECTURE III. PHYSIOLOGICAL EFFECTS OF RADIATION. Visibility. 20. The most important physiological effect is the visibility of the narrow range of radiation, of less than one octave, between wave length 76 X 10~6 and 39 X 1Q-6. The range of intensity of illumination, over which the eye can see with practically equal comfort, is enormous: the average intensity of illumination at noon of a sunny day is nearly one million times greater than the illuminatio ...", "... is, to be near the limits of permissi- bility. This law of sensation (Fechner's Law) means : If i = intensity of illumination, as physical quantity, that is, 40 RADIATION, LIGHT, AND ILLUMINATION. in meter-candles or in watts radiation of specified wave length, the physiological effect given thereby is : L = A log V %> where A is a proportionality constant (depending on the physio- logical measure of L) and \\ is the minimum perceptible value of illumination or the \"threshold value,\" below which sensation ...", "... in most cases seems to be very small. 22. It is found, however, that the sensitivity curve for different colors of radiation is a function of the intensity of radiation; that is, the maximum sensitivity point of the eye is not at a definite frequency or wave length, but varies with the intensity of illumi- nation and shifts more towards the red end of the spectrum for high, towards the violet end of the spectrum for low intensity of illumination, and for illumination of very high intensity the maxi- mum physiologica ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... the number of periods, or frequency of the impressed alternating e.m.fs., in resonance condition, is the velocity of light divided by four times the length of the line; or, in free oscillation or resonance condition, the length of the line is one quarter wave length. 279 280 TRANSIENT PHENOMENA If then I = length of line, S = speed of light, the frequency of oscillations or natural period of the line is — '• \"4? or, with I given in miles, hence S = 188,000 miles per second, it is , 47,000 /o = — j- cycles ...", "... onance frequency as low as commercial frequencies, as 25 or 60 cycles, would require Z == 1880 miles for /0 = 25 cycles, and Z = 783 miles for./, - 60 cycles. It follows herefrom that many existing transmission lines are such small fractions of a quarter-wave length of the impressed frequency that the change of voltage and current along the line can be assumed as linear, or at least as parabolic; that is, the line capacity can be represented by a condenser in the middle of the line, or by condensers in the middle and ...", "... becomes of importance with reference to the investigation of the effects of higher harmonics of the generator wave. In long-distance telephony the important frequencies of speech probably range from 100 to 2000 cycles. For these fre- er quencies the wave length varies from — = 1880 miles down to L 94 miles, and a telephone line of 1000 miles length would thus LONG-DISTANCE TRANSMISSION LINE 281 contain from about one-half to 11 complete waves of the im- pressed frequency. For long-distance telephony the ph ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-54", "section_label": "Chapter 5: Free Oscillations", "section_title": "Free Oscillations", "kind": "chapter", "sequence": 54, "number": 5, "location": "lines 31451-32708", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "snippets": [ "... ions of the electric circuit, (50) and (51), contain eight terms: four waves: two main waves and their reflected waves, and each wave consists of a sine term and a cosine term. The equations contain five constants, namely: the frequency constant, g; the wave length constant, &; the time attenuation constant, u\\ the distance attenuation constant, h, and the time acceleration constant, s ; among these, the time attenuation, uy is a constant of the circuit, independent of the character of the wave. By the value of the ...", "... 0 at both ends of the circuit or i = 0 at both ends of the circuit. 32. From (210) it follows that or an odd multiple thereof; that is, the longest wave which can exist in the circuit is that which makes the circuit a quarter- FREE OSCILLATIONS 483 wave length. Besides this fundamental wave, all its odd multi- ples can exist. Such an oscillation may be called a quarter-wave oscillation. The oscillation of a circuit which is open at one end, grounded at the other end, is a quarter-wave oscillation, which can co ...", "... ve oscillation, which can contain only the odd harmonics of the fundamental wave of oscillation. From (211) it follows that or a multiple thereof; that is, the longest wave which can exist in such a circuit is that wave which makes the circuit a half- wave length. Besides this fundamental wave, all its multiples, odd as well as even, can exist. Such an oscillation may be called a half-wave oscillation. The oscillation of a circuit which is open at both ends, or grounded at both ends, is a half-wave oscillation, a ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "... se of current i and voltage e changes pro- gressively along the line I, so that at some distance Iq current and voltage are 360 degrees displaced from their values at the starting point, that is, are again in the same phase. This distance Zo is called the wave length, and is the distance which the electric field travels during one period to — -j. of the frequency of oscillation. As current and voltage vary in phase progressively along the line, the effect of inductance and of capacity, as represented by the inductan ...", "... this circuit section is short compared with the entire length of the circuit, that is, the frequency high compared with the frequency which the oscillation would have if the entire line oscillates as a whole). If li is the oscillating line section, the wave length of this oscilla- tion is four times the length Zo = 4/i. (27) This can be seen as follows : At any point I of the oscillating line section k, the effective power Pq = avg ei = 0 (28) is always zero, since voltage and current are 90 degrees apart. ...", "... f li is a node or point of zero power, and the oscillating unit again is a quarter- wave. In the same way, in Fig. SSB, the section h consists of 4 quarter- wave units, etc. Fig. 37. Fig. 38. The same applies to case 1, and it thus follows that the wave length lo is four times the length of the oscillation k. 30. Substituting U = 4:li into (26) gives as the frequency of oscillation / = A • (30) Iqcfq 1 However, if / = frequency, and v = - , velocity of propagation, the wave length U is the distance ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3956-4744", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "snippets": [ "... se of current i and voltage e changes pro- gressively along the line Z, so that at some distance 1Q current and voltage are 360 degrees displaced from their values at the starting point, that is, are again in the same phase. This distance Z0 is called the wave length, and is the distance which the electric field travels during one period to = j of the frequency of oscillation. As current and voltage vary in phase progressively along the line, the effect of inductance and of capacity, as represented by the inductance ...", "... this circuit section is short compared with the entire length of the circuit, that is, the frequency high compared with the frequency which the oscillation would have if the entire line oscillates as a whole). If Zi is the oscillating line section, the wave length of this oscilla- tion is four times the length Z0 = 4 ZL (27) This can be seen as follows: At any point I of the oscillating line section Zi, the effective power Po = avg ei = 0 (28) is always zero, since voltage and current are 90 degrees apart. ...", "... f li is a node or point of zero power, and the oscillating unit again is a quarter-wave. In the same way, in Fig. 385, the section /i consists of 4 quarter- wave units, etc. Fig. 37. Fig. 38. The same applies to case 1, and it thus follows that the wave length 10 is four times the length of the oscillation l\\. 30. Substituting /0 = 4 li into (26) gives as the frequency of oscillation / = ^r • (30) However, if / = frequency, and v = - , velocity of propagation, the wave length 1Q is the distance traveled d ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-09", "section_label": "Lecture 9: Measurement Of Light And Radiation", "section_title": "Measurement Of Light And Radiation", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 8511-9388", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-09/", "snippets": [ "... e produced by the energy of the incident beam of radia- tion is observed. Probably the most sensitive method of measuring even very small amounts of radiation is the bolometer. The beam of the radiation (or after dissolving the beam into a spectrum, the wave length of which the power is to be measured) impinges upon a narrow and thin strip of metal, as platinum, and thereby raises its temperature by conversion of the radiation energy into heat. A rise of temperature, however, produces a rise of electric resistance, ...", "... ws the values of radiation power of the components. 75. Light, however, cannot be measured by any of the pre- ceding methods, since light, in the sense in which it is con- sidered photometrically, is not power, but is the physiological effect of certain wave lengths of radiation, and therefore can- not be measured, physically, as power, but only physiologically, 168 RADIATION, LIGHT, AND ILLUMINATION. by comparison with other physiological effects of the same nature. The power of visible radiation obviously can ...", "... y of the effect, the individuality of the observer, etc. It appears, however, that at higher intensities the relation is very nearly constant and the same with differ- ent observers, so that it is possible to express the physiological effect of a definite wave length of radiation, within the accuracy of physiological measurements, by the power consumed in pro- ducing this wave length of radiation; but it becomes entirely impossible to compare physiological effects of widely different wave lengths by comparing the powe ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-46", "section_label": "Chapter 6: Alternating Magnetic Flux Distribution", "section_title": "Alternating Magnetic Flux Distribution", "kind": "chapter", "sequence": 46, "number": 6, "location": "lines 23948-24980", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "snippets": [ "... equations of the distribution of alternating magnetic flux in a laminated conductor are of the same form as the equations of distribution of current and voltage in a transmission line, but more special in form, that is, the attenuation constant a and the wave length constant /? have the same value, c. As result, the distribution of the alternating magnetic flux in the lamina depends upon one constant only, clQ. The wave length is given by cZ = 2 * ALTERNATING MAGNETIC FLUX DISTRIBUTION 361 i hence and by ( ...", "... a transmission line, but more special in form, that is, the attenuation constant a and the wave length constant /? have the same value, c. As result, the distribution of the alternating magnetic flux in the lamina depends upon one constant only, clQ. The wave length is given by cZ = 2 * ALTERNATING MAGNETIC FLUX DISTRIBUTION 361 i hence and by (9) 10,000 and the attenuation during one wave length, or decrease of intensity of magnetism, per wave length, is £- 2- = 0.0019, and per half-wave length is ...", "... , the distribution of the alternating magnetic flux in the lamina depends upon one constant only, clQ. The wave length is given by cZ = 2 * ALTERNATING MAGNETIC FLUX DISTRIBUTION 361 i hence and by (9) 10,000 and the attenuation during one wave length, or decrease of intensity of magnetism, per wave length, is £- 2- = 0.0019, and per half-wave length is e- - = 0.043. At the depth -j below the surface, the magnetic flux lags 90 degrees and has considerably decreased; at the depth -^ it lags Zi ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-48", "section_label": "Chapter 8: Velocity Of Propagation Of Electric Field", "section_title": "Velocity Of Propagation Of Electric Field", "kind": "chapter", "sequence": 48, "number": 8, "location": "lines 26095-27002", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "snippets": [ "... e greater the distance from the conductor. Since the velocity of propagation is very high — about 3 X 1010 centimeters per second — the wave of an alternating or oscillating current even of very high frequency is of considerable length ; at 60 cycles the wave length is 0.5 X 109 centimeters, and even at a million cycles the wave length is 30,000 centimeters, or about 1000 feet, that is, very great compared with the distance to which electric fields usually extend. The important part of the electric field of a conduc ...", "... gation is very high — about 3 X 1010 centimeters per second — the wave of an alternating or oscillating current even of very high frequency is of considerable length ; at 60 cycles the wave length is 0.5 X 109 centimeters, and even at a million cycles the wave length is 30,000 centimeters, or about 1000 feet, that is, very great compared with the distance to which electric fields usually extend. The important part of the electric field of a conductor extends to the return conductor, which usually is only a few feet d ...", "... r, which usually is only a few feet distant; beyond this, the field is the differential field of conductor and return conductor. Hence, the intensity of the electric field has usually already become inappreciable at a distance very small compared with the wave length, so that within the range in which an appreciable field exists this field is practically in phase with the flow of energy in the conductor, that is, the velocity of propagation has no appreciable effect. Thus, the finite velocity of propagation of the el ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-07", "section_label": "Lecture 7: High Frequency Oscillations And Surges", "section_title": "High Frequency Oscillations And Surges", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3508-3780", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-07/", "snippets": [ "... open circuit, and the instantaneous opening of a short circuit on a transmission line — as it occasionally occurs by the sudden rupture of a short circuiting arc — ^therefore gives rise to the most powerful, and thereby most destructive oscillation. The wave length of oscillation thus depends on the length of the circuit in which the stored energy readjusts itself. For instance, in the short circuit oscillation of the system, the wave extends over the entire circuit, including generators and trans- formers ; and the ...", "... tored energy readjusts itself. For instance, in the short circuit oscillation of the system, the wave extends over the entire circuit, including generators and trans- formers ; and the entire circuit so represents one wave, or one- half wave, that is, the wave length is very considerable. If the readjustment of stored energy takes place only over a section of the circuit, the wave length is shorter. For instance, if by a thunder cloud a static charge is induced on the trans- mission line, and by a lightning flash in t ...", "... re circuit, including generators and trans- formers ; and the entire circuit so represents one wave, or one- half wave, that is, the wave length is very considerable. If the readjustment of stored energy takes place only over a section of the circuit, the wave length is shorter. For instance, if by a thunder cloud a static charge is induced on the trans- mission line, and by a lightning flash in the cloud, the cloud discharges, the electrostatic charge induced by it on the line HIGH FREQUENCY OSCILLATIONS 93 is se ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-51", "section_label": "Chapter 2: Discussion Of General Equations", "section_title": "Discussion Of General Equations", "kind": "chapter", "sequence": 51, "number": 2, "location": "lines 28695-29315", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "snippets": [ "... o, k = 0 and to h = 0, s = 0. 8. In the equations (50) and (51) qt = 2x gives the time of a complete cycle, that is, the period of the wave, and the frequency of the wave is / = -L 2 kl = 27T gives the distance of a complete cycle, that is, the wave length, W 7 7 k (u — s) t = 1 and (u + s) t = 1 give the time, */'- — and t\"= -*—, during which the wave decreases to - = 0.3679 of its value, and hi = 1 gives the distance, over which the wave decreases to - = 0.3679 of its value; £ that is, q ...", "... reases to - = 0.3679 of its value, and hi = 1 gives the distance, over which the wave decreases to - = 0.3679 of its value; £ that is, q is the frequency constant of the wave, f - - I I: «'—'•• (62) > 2V °~' 434 TRANSIENT PHENOMENA k is the wave length constant, (63) (u - s) and (u -f s) are the time attenuation constants of the wave, 1 ) (64) U + S and h is the distance attenuation constant of the wave, L -I. (65) 9. If the frequency of the current and e.m.f. is very high, thousa ...", "... frequency of propagation (velocity of light), we have h = o-s, k = o-q, (69) and m — c q (70) and introducing the new independent variable, as distance, we have and hi = si;. (71) (72) 436 TRANSIENT PHENOMENA hence, the wave length is given by qX = 2n as V-^j (73) and since the period is it follows that by the introduction of the denotation (71) dis- tances are measured with the velocity of propagation as unit length, and wave length /„, and period t0 thus have the same num ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "... ally comprised by the name luminescence. Some special cases of luminescence have already been discussed in the phe- nomena of fluorescence and phosphorescence, represented by the conversion of the radiation absorbed by a body into radiation of a different wave length. Usually luminescence at ordinary temperature, or at moderate temperatures, that is, temperatures below incandescence, is called fluorescence or phosphorescence. Fluorescence and Phosphorescence. Fluorescence is the production of radiation from the en ...", "... sphorescence persists as long as these chemical changes can occur. The different forms of luminescence may be distinguished by the character of the energy which is converted into radiation. The conversion of radiation energy into radiation of different wave length, either immediately, or after storage in the body, thus may be called radio-fluorescence and radio-phosphorescence. It was discussed in Lecture II. The same bodies, exposed to an electric discharge in a vacuum (Geissler tube or Crooke tube) show electro- ...", "... f the characteristic forms of luminescence at higher temperatures are pyro-luminescence, chemical-luminescence, and electro-luminescence. As pyro-luminescence or heat-luminescence, must be considered all radiation, produced by heat, which exceeds at some wave length the intensity of the black body radiation at the same temperature. Whether real pyro-luminescence exists, is uncertain, but by an extension of the definition any colored temperature radiation may be considered as heat luminescence of a grey body of an a ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-53", "section_label": "Chapter 4: Traveling Waves", "section_title": "Traveling Waves", "kind": "chapter", "sequence": 53, "number": 4, "location": "lines 30244-31450", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "snippets": [ "CHAPTER IV. TRAVELING WAVES. 20. As seen in Chapter III, especially in electric power cir- cuits, overhead or underground, the longest existing standing wave has a wave length which is so small compared with the critical wave length — where the frequency becomes zero — that the effect of the damping constant on the frequency and the wave length is negligible. The same obviously applies also to traveling waves, generally to a st ...", "CHAPTER IV. TRAVELING WAVES. 20. As seen in Chapter III, especially in electric power cir- cuits, overhead or underground, the longest existing standing wave has a wave length which is so small compared with the critical wave length — where the frequency becomes zero — that the effect of the damping constant on the frequency and the wave length is negligible. The same obviously applies also to traveling waves, generally to a still greater extent, since the lengths of traveling waves ...", "... power cir- cuits, overhead or underground, the longest existing standing wave has a wave length which is so small compared with the critical wave length — where the frequency becomes zero — that the effect of the damping constant on the frequency and the wave length is negligible. The same obviously applies also to traveling waves, generally to a still greater extent, since the lengths of traveling waves are commonly only a small part of the length of the circuit. Usually, therefore, in the discussion of traveling wa ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-55", "section_label": "Chapter 6: Transition Points And The Complex Circuit", "section_title": "Transition Points And The Complex Circuit", "kind": "chapter", "sequence": 55, "number": 6, "location": "lines 32709-33527", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "snippets": [ "... ther words, the frequency of oscillation, as represented by q, and the rate of decay of the oscillation, as represented by the exponential function of time, must be the same throughout the entire circuit. Not so, however, with the distance variable Z; the wave length of the oscillation and its rate of building up or down along the circuit need not be the same, and usually are not, but in some sections of the circuit the wave length may be far shorter, as in coiled circuits as transformers, due to the higher L, or in c ...", "... same throughout the entire circuit. Not so, however, with the distance variable Z; the wave length of the oscillation and its rate of building up or down along the circuit need not be the same, and usually are not, but in some sections of the circuit the wave length may be far shorter, as in coiled circuits as transformers, due to the higher L, or in cables, due to the higher C. To extend the same equations over the entire complex circuit, it therefore becomes necessary to substitute for the distance variable / anothe ...", "... sformers, due to the higher L, or in cables, due to the higher C. To extend the same equations over the entire complex circuit, it therefore becomes necessary to substitute for the distance variable / another distance variable X of such character that the wave length has the same value in all sections of the complex circuit. As the wave length of the section i is — = > this is done by changing the unit distance by the factor cr = VLf!^ The distance unit of 502 TRANSIENT PHENOMENA the new distance variable ^ the ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... may be of a single frequency, that is, a single wave; or a mixture of different frequencies, that is, a mixture of different and frequently of an infinite number of waves. Electric radiation usually is of a single frequency, that is, of the frequency or wave length determined by the constants of the electric circuit which produces the radiation, mainly the induct- ance L and the capacity C. They may, however, have different wave shapes, that is, comprise, in adolition to the fundamental wave, higher harmonics or mul ...", "... e refractive index d varies with the frequency and is derived for the extremely high frequencies of light radiation, while K refers to stationary conditions. A better agreement is thus reached when using as d the refractive index extrapolated for infinite wave lengths. 12. It is found that the different component frequencies of a beam of radiation are deflected differently when passing from one medium into another, and the higher frequencies are deflected FIG. 16. more than the lower frequencies, thus showing that ...", "... ted differently when passing from one medium into another, and the higher frequencies are deflected FIG. 16. more than the lower frequencies, thus showing that the velocity of propagation decreases with an increase of frequency, that is, a decrease of wave length. This gives a means of resolving a mixed radiation into its com- ponent waves, that is, into a spectrum, by refraction. A narrow beam of light B (Fig. 16) is passed through a prism P of transparent material, and the component frequencies then appear on ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-05", "section_label": "Lecture 5: Temperature Radiation", "section_title": "Temperature Radiation", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3946-5076", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-05/", "snippets": [ "... iation curve; that is, the same distribution of intensity as function of the frequency and thus the same fraction of visible to total radia- tion, that is, the same efficiency of light production. If T is the absolute temperature in deg. cent, and lw the wave length of radiation, the power radiated at wave length /„, and temperature T1 by normal temperature radiation is : b P (IJ = c,Alw % ^ , (Wien's law) ; or' r • i. * r1 P (U = c,Alw a\\e V-l\\ (Planck's law) ; TEMPERATURE RADIATION. 75 where a = 5 for norm ...", "... intensity as function of the frequency and thus the same fraction of visible to total radia- tion, that is, the same efficiency of light production. If T is the absolute temperature in deg. cent, and lw the wave length of radiation, the power radiated at wave length /„, and temperature T1 by normal temperature radiation is : b P (IJ = c,Alw % ^ , (Wien's law) ; or' r • i. * r1 P (U = c,Alw a\\e V-l\\ (Planck's law) ; TEMPERATURE RADIATION. 75 where a = 5 for normal temperature radiation or black body radiatio ...", "... of the radiator. Integrating the formula of Wien's law over lw from 0 to oo , gives the total radiation : P- f °°P (lw)dlw = Mr-1; «/o thus, for a = 5; or, Stephan's law, as discussed above. The maximum energy rate at temperature T occurs at the wave length lw = lm given by: dP (lw) ~Ji — = °> dlw which gives: lmT =- = 0.284; a or, 0.284 = 50 X 10~6 thus gives: T - = 5680 deg. With normal temperature radiation the efficiency of light pro- duction is thus merely a function of the temperatur ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-06", "section_label": "Chapter 2: Long Distance Transmission Line. 279", "section_title": "Long Distance Transmission Line. 279", "kind": "chapter", "sequence": 6, "number": 2, "location": "lines 755-835", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-06/", "snippets": [ "CHAPTER II. LONG DISTANCE TRANSMISSION LINE. 279 3. Relation of wave length of impressed frequency to natural frequency of line, and limits of approximate line cal- culations. 279 4. Electrical and magnetic phenomena in transmission line. 281 5. The four constants of the transmission line : r, L, g, C. 282 6. The problem of ...", "... end of the line. 289 10. Equations with generator voltage, and load on receiving circuit given. 291 CONTENTS. xix PAGE 11. Example of 60,000-volt 200-mile line. 292 12. Comparison of result with different approximate calcula- tions. 294 13. Wave length and phase angle. 295 14. Zero phase angle and 45-degree phase angle. Cable of negligible inductance. 296 15. Examples of non-inductive, lagging and leading load, and discussion of flow of energy. 297 16. Special case: Open circuit at end of line. 29 ...", "... ergy. 297 16. Special case: Open circuit at end of line. 299 17. Special case: Line grounded at end. 304 18. Special case : Infinitely long conductor. 305 19. Special case: Generator feeding into closed circuit. 306 20. Special case: Line of quarter-wave length, of negligible resistance. 306 21. Line of quarter-wave length, containing resistance r and conductance g. 309 22. Constant-potential — constant-current transformation by line of quarter-wave length. 310 23. Example of excessive voltage produced i ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-02", "section_label": "Lecture 2: Conclusions From The Relativity Theory", "section_title": "Conclusions From The Relativity Theory", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 736-2388", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... power transmission line) are therefore periodic alternations of the electromagnetic energy field in space, and the differ- ences are merely those due to the differences of frequency. Thus the electromagnetic field of the 60-cycle transmission line has a wave length of 3 X lO^V^O cm. = 5000 km. Its extent is limited to the space between the conductors and their immediate surroundings, being therefore extremely small compared with the wave length, and under these conditions the part of the electromagnetic energy which ...", "... Thus the electromagnetic field of the 60-cycle transmission line has a wave length of 3 X lO^V^O cm. = 5000 km. Its extent is limited to the space between the conductors and their immediate surroundings, being therefore extremely small compared with the wave length, and under these conditions the part of the electromagnetic energy which is radiated into space is extremely small. It is so small that it may be neglected and that it may be said that all the energy supplied by the source of power which is consumed in pr ...", "... ll that it may be neglected and that it may be said that all the energy supplied by the source of power which is consumed in produc- ing the electromagnetic field is returned to the supply circuit at the disappearance of the field. In radio communication wave lengths of 15,000 to 200 meters and less^ — that is, fre- quencies of 20,000 to 1,500,000 cycles and more — are used, and the circuit is arranged so as to give the electromagnetic field the greatest possible extent, it being the field which carries the message. ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 6125-6803", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-09/", "snippets": [ "... as stated before. Such local oscillations are usually of very high frequency, but sometimes come within the range of the oscillograph, as in Fig. 47. During the oscillation of the complex circuit, every circuit element d\\ (in velocity measure), or every wave length or equal part of the wave length, therefore contains the same amount of stored energy. That is, if eo = maximum voltage, ^o = maximum current, and Xo = wave length, the average energy \" ° must be constant throughout the entire circuit. Since, however, i ...", "... llations are usually of very high frequency, but sometimes come within the range of the oscillograph, as in Fig. 47. During the oscillation of the complex circuit, every circuit element d\\ (in velocity measure), or every wave length or equal part of the wave length, therefore contains the same amount of stored energy. That is, if eo = maximum voltage, ^o = maximum current, and Xo = wave length, the average energy \" ° must be constant throughout the entire circuit. Since, however, in velocity measure, Xo is constan ...", "... cillation of the complex circuit, every circuit element d\\ (in velocity measure), or every wave length or equal part of the wave length, therefore contains the same amount of stored energy. That is, if eo = maximum voltage, ^o = maximum current, and Xo = wave length, the average energy \" ° must be constant throughout the entire circuit. Since, however, in velocity measure, Xo is constant and equal to the period Tq through- out all the sections of the circuit, the product of maximum voltage and of maximum current, eo ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 5521-6088", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "snippets": [ "... as stated before. Such local oscillations are usually of very high frequency, but sometimes come within the range of the oscillograph, as in Fig. 47. During the oscillation of the complex circuit, every circuit element d\\ (in velocity measure), or every wave length or equal part of the wave length, therefore contains the same amount of stored energy. That is, if e0 = maximum voltage, i0 = maximum current, and X0 = wave length, the average energy ° ° Q must be constant throughout the entire circuit. Since, however, ...", "... llations are usually of very high frequency, but sometimes come within the range of the oscillograph, as in Fig. 47. During the oscillation of the complex circuit, every circuit element d\\ (in velocity measure), or every wave length or equal part of the wave length, therefore contains the same amount of stored energy. That is, if e0 = maximum voltage, i0 = maximum current, and X0 = wave length, the average energy ° ° Q must be constant throughout the entire circuit. Since, however, in velocity measure, Xo is const ...", "... cillation of the complex circuit, every circuit element d\\ (in velocity measure), or every wave length or equal part of the wave length, therefore contains the same amount of stored energy. That is, if e0 = maximum voltage, i0 = maximum current, and X0 = wave length, the average energy ° ° Q must be constant throughout the entire circuit. Since, however, in velocity measure, Xo is constant and equal to the period TO through- out all the sections of the circuit, the product of maximum voltage and of maximum current, ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-04", "section_label": "Lecture 4: Chemical And Physical Effects Of Radiation", "section_title": "Chemical And Physical Effects Of Radiation", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3639-3945", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-04/", "snippets": [ "... ing action of radiation on silver salts, the chloride in ordinary photographic paper, the bromide and iodide in the negative plate and the quick printing papers. This chemical action is greatest in the violet and ultra-violet and decreases with increasing wave length, hence is less in the green, small in the yellow, and almost absent in the red and ultra-red, so that the short waves, blue, violet and ultra-violet, have sometimes been called \" chemical rays.\" This, however, is a misnomer, just as the term \"heat rays\" s ...", "... ical effects of radiation are those by which it is converted into another form of radiation : fluorescence and phosphorescence. Many substances have the property of converting some of the radiation which is absorbed by them into radiation of a different wave length, that is, act as frequency converter of radiation, fluorescence. Many bodies when exposed to radiation store some of the energy of radiation in such a manner as to give it out again afterwards and thus, after exposure to light, glow in the darkness with g ...", "... ce also is usually CHEMICAL AND PHYSICAL EFFECTS OF RADIATION. 67 so weak as to escape notice, although in a few bodies it is very strong. The change of frequency in fluorescence always seems to be a lowering of the frequency, that is, an increase of wave length, and in phosphorescence also the light given out seems always to be of lower frequency than the light absorbed and indeed, fluores- cence and phosphorescence seem to be essentially the same phenomenon, radiation is absorbed and its energy given out again ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "... ngth of line, we get at hence g — jbc or a-; ft At X = /, E0 sin/?/}. (19) Equations (18) and (19) determine the constants A and B, which, substituted in (14), give the final integral equations. The length, X0 = 2 TT / ft is a complete wave length (20), ,vhich means, that in the distance 2 IT / ft the phases of the components of current and E.M.F. repeat, and that in half this distance, they are just opposite. Hence the remarkable condition exists that, in a very long line, at different points th ...", "... iffer by £th period. D.) Generator feeding into closed circuit : Let x = 0 be the center of cable ; then, hence : E — 0 at x = 0 ; which equations are the same as in B, where the line is grounded at x = 0. E.) Let the length of a line be one-quarter wave length; and assume the resistance r and conductance g as negligible 180 AL TERN A TING-CURRENT PHENOMENA. compared with x and bc. r=0=g These values substituted in (11) give a=0. (3= V^ Let the E.M.F. at the receiving end of the line be assumed zer ...", "... 181 Then at x Hence also •£\"„ and 70 are both in quadrature ahead of r ** The equ ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-03", "section_label": "Lecture 3: Gravitation And The Gravitational Fleld", "section_title": "Gravitation And The Gravitational Fleld", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2389-3594", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-03/", "snippets": [ "... the electromagnetic field^ — and the difference between the alternating fields of our transmission lines, the electro- magnetic waves of our radio stations, the waves of visible light and the X-rays are merely those due to the differences of frequency or wave length. The energy field at any point of space is determined by two constants, the intensity and the direction, and the force exerted by the field on a susceptible body is proportional to the field intensity and is in the direction of the energy field. Thus ...", "... tire universe, then the world's radius would be: R^ = 1.08 X 10\" cm. R = S& X 10>2 cm. = 225,000,000 miles. 68 RELATIVITY AND SPACE electrical constants of the hydrogen atom and showing us the exact rate of its vibration in the spectroscope by the wave length or frequency of its spectrum lines. Thus in a strong gravitational field the frequency of luminous vibrations of the atoms should be found slowed down; in other words, the spectrum lines should be shifted towards the red end of the spectrum. The amount of ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-35", "section_label": "Chapter 35: Balanced Symmetrical Polyphase Systems", "section_title": "Balanced Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 35, "number": 35, "location": "lines 37453-37957", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-35/", "snippets": [ "... iently it may be derived from the inductance. If C is the capacity of the circuit, of which the inductance is L, then is the fundamental frequency of oscillation, or natural period, that is, the frequency which makes the length, I, of the line a quarter-wave length. Since the velocity of propagation of the electric field is the ve- ^ \"Theoretical Elements of Electrical Engineering.\" BALANCED SYMMETRICAL POLYPHASE SYSTEMS 451 locity of light, v, with a wave-length, 4 I, the number of waves per second, or freque ...", "... hich makes the length, I, of the line a quarter-wave length. Since the velocity of propagation of the electric field is the ve- ^ \"Theoretical Elements of Electrical Engineering.\" BALANCED SYMMETRICAL POLYPHASE SYSTEMS 451 locity of light, v, with a wave-length, 4 I, the number of waves per second, or frequency of oscillation of the line, is f - — and herefrom then follows: hence, for V I Vlc I = 100 miles, V = 186,000 miles per second, L = 0.23 henry, C = 1.26 mf. and the capacity susceptan ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-10", "section_label": "Chapter 6: Alternating Magnetic Flux Distribution. 355", "section_title": "Alternating Magnetic Flux Distribution. 355", "kind": "chapter", "sequence": 10, "number": 6, "location": "lines 904-937", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-10/", "snippets": [ "... urrents in alternating fields. 355 49. The differential equations of alternating magnetic flux in a lamina. 356 50. Their integral equations. 357 51. Terminal conditions, and the final equations. 358 52. Equations for very thick laminae. 360 53. Wave length, attenuation, depth of penetration. 361 54. Numerical example, with frequencies of 60, 1000 and 10,000 cycles per second. 362 55. Depth of penetration of alternating magnetic flux in different metals. 363 56. Wave length, attenuation, and velocity o ...", "... ery thick laminae. 360 53. Wave length, attenuation, depth of penetration. 361 54. Numerical example, with frequencies of 60, 1000 and 10,000 cycles per second. 362 55. Depth of penetration of alternating magnetic flux in different metals. 363 56. Wave length, attenuation, and velocity of penetration. 365 57. Apparent permeability, as function of frequency, and damping. 366 58. Numerical example and discussion. 367" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... n of appreciable power which can be produced by a condenser discharge reaches billions of cycles per second, thus is enormously higher than the highest frequencies which can be produced by electrodynamic machinery. At five billion cycles per second, the wave length is about 6 cm., that is, the frequency only a few octaves lower than the lowest frequencies observed as, heat radiation or ultra red light. The average wave length of visible light, 55 X 10~6 cm., corresponding to a frequency of 5.5 X 1014 cycles, would ...", "... ich can be produced by electrodynamic machinery. At five billion cycles per second, the wave length is about 6 cm., that is, the frequency only a few octaves lower than the lowest frequencies observed as, heat radiation or ultra red light. The average wave length of visible light, 55 X 10~6 cm., corresponding to a frequency of 5.5 X 1014 cycles, would require spheres 10~5 cm. in diameter, that is, approaching molecular dimensions. OSCILLATING-CURRENT GENERATOR. 49. A system of constant impressed e.m.f., e, char ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-43", "section_label": "Chapter 3: The Natural Period Of The Transmission Line", "section_title": "The Natural Period Of The Transmission Line", "kind": "chapter", "sequence": 43, "number": 3, "location": "lines 21721-23178", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "snippets": [ "... ively low fundamental frequency and its overtones, but can also oscillate with any frequency whatever, provided that this frequency is very high. This is analogous to waves formed in a body of water of regular shape : large standing waves have a definite wave length, depending upon the dimensions of the body of water, but very short waves, ripples in the water, can have any wave length, and do not depend on the size of the body of water. A further investigation of oscillations in conductors with distributed capacit ...", "... frequency is very high. This is analogous to waves formed in a body of water of regular shape : large standing waves have a definite wave length, depending upon the dimensions of the body of water, but very short waves, ripples in the water, can have any wave length, and do not depend on the size of the body of water. A further investigation of oscillations in conductors with distributed capacity, inductance, and resistance requires, how- ever, the consideration of the resistance, and so leads to the investigation ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-56", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit", "section_title": "Power And Energy Of The Complex Circuit", "kind": "chapter", "sequence": 56, "number": 7, "location": "lines 33528-34202", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "snippets": [ "... in the magnetic field at point A as a w j j. i*u/j 7 7T == ^ I — TT~ Ctfr (A - 2 [(AC - BD) cos 2qX+ (AD + BC) sin 2 ql]}, (312) POWER AND ENERGY OF THE COMPLEX CIRCUIT 517 and integrating over one complete period of distance A, or one complete wave length, this gives (313) The energy stored by the inductance L, or in the magnetic field of the conductor, thus consists of a constant part, dl a part which is a function of (X — t) and (X + t), (A2 - B2) cos 2 q (X - t) (C2 - D2) cos 2 q (X + 0] n2 ...", "... -s- s thus is the ratio of the power supplied to the sec- tion by its electric field, dissipated in the section, and transferred from the section to adjoining sections. These relations obviously are approximate only, and applicable to the case where the wave length is short. 56. Equation (306), of the power transferred from a section to the adjoining section, can be arranged in the form (A2 + B2) - e-2 (C2 + D2)] (A2 + B2) - £-2sA' ((T2 + Z)2)]} ; (342) that is, it consists of two parts, thus : Po> - li/5f-** ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "... length, that is, measure the length with the distance of propagation during unit time (3 X 10^° cm. with a straight con- ductor in air) as unit of length. This allows the use of the same distance unit through all sections of the circuit, and expresses the wave length Xo and the period To by the same numerical values, Xo = Tq = -j., and makes the time angle and the distance angle co directly comparable : (^ = 2 Tt/^ = 2 TT CO = 27r— = 2 7r/X. Xo (8) 34. If power flows along the circuit, three cases may ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 4745-5520", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "snippets": [ "... length, that is, measure the length with the distance of propagation during unit time (3 X 1010 cm. with a straight con- ductor in air) as unit of length. This allows the use of the same distance unit through all sections of the circuit, and expresses the wave length X0 and the period T0 by the same numerical values, X0 = TQ = -, and makes the time angle 0 and the distance angle co directly comparable: 0 = 2vft = 27T— , AO CO = 2 7T — = 2 7T/X. A (8) 34. If power flows along the circuit, three cases may o ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "section_title": "Dibtbisnted Capacity, Inductance, Besistance, And", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "... {(^c«'-^c-«0cos/8/-y(/^€«^ + Bc-^^ (19) sinp/}. 162 ALTERNATING-CURRENT PHENOMENA. [§ 113 Equations (18) and (10) determine the constants^ and B, which, substituted in (14), give the final integral equations. The length, x^ = 2ir/^ is a complete wave length (20), which means, that in the distance 2ir/^ the phases of cur- rent and E.M.F. repeat, and that in half this distance, they are just opposite. Hence the remarkable condition exists that, in a very long line, at different points the currents at the sam ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-15", "section_label": "Chapter 2: Discussion Of General Equations. 431", "section_title": "Discussion Of General Equations. 431", "kind": "chapter", "sequence": 15, "number": 2, "location": "lines 1063-1086", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-15/", "snippets": [ "CHAPTER II. DISCUSSION OF GENERAL EQUATIONS. 431 7. The two component waves and their reflected waves. Attenuation in time and in space. 431 8. Period, wave length, time and distance attenuation constants. 433 9. Simplification of equations at high frequency, and the velocity unit of distance. 434 10. Decrement of traveling wave. 436 11. Physical meaning of the two component waves. 437 12. Stationary or stan ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-16", "section_label": "Chapter 3: Standing Waves. 442", "section_title": "Standing Waves. 442", "kind": "chapter", "sequence": 16, "number": 3, "location": "lines 1087-1111", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-16/", "snippets": [ "CHAPTER III. STANDING WAVES. 442 14. Oscillatory, critical and gradual standing wave. 442 15. The wave length which divides the gradual from the oscillatory wave. 446 16. High-power high-potential overhead transmission line. Character of waves. Numerical example. General equations. 449 17. High-potential underground power cable. Character of waves. Numeric ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-18", "section_label": "Chapter 5: Free Oscillations. 478", "section_title": "Free Oscillations. 478", "kind": "chapter", "sequence": 18, "number": 5, "location": "lines 1148-1186", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-18/", "snippets": [ "... ditions. 480 31. Free oscillation as standing wave. 481 32. Quarter-wave and half-wave oscillation, and their equa- tions. 482 33. Conditions under which a standing wave is a free oscilla- tion, and the power nodes of the free oscillation. 485 34. Wave length, and angular measure of distance. 487 35. Equations of quarter-wave and half-wave oscillation. 489 36. Terminal conditions. Distribution of current and voltage at start, and evaluation of the coefficients of the trigo- nometric series. 491 37. Final ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-45", "section_label": "Chapter 5: Distributed Series Capacity", "section_title": "Distributed Series Capacity", "kind": "chapter", "sequence": 45, "number": 5, "location": "lines 23586-23947", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "snippets": [ "... of many spark-gaps in series may be many times the resultant voltage, and a lightning flash may pass possibly for miles through clouds with a total potential of only a few hundred million volts. In the above example the 300 cylinders include 7.86 complete wave-lengths of the discharge." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... ain axes of electric field 46 wave at transition point 531 Massed inductance and electric wave 537 Mechanical rectification 221, 229 Mercury arc rectifier 250 INDEX 567 PAGE Metallic conductors, resistivities 8 magnetic induction 10 Minimum wave length of oscillating currents 74 Motor circuit, alternating, starting 44 field, excitation 27 Multigap lightning arrester '. 348 Mutual impedance and velocity of propagation 399 inductance, equations 143 and velocity of propagation 397 inductive circu ..." ] } ] }, { "id": "field-stress", "label": "Field Stress, Strain, Pressure, and Tension", "aliases": [ "elastic", "pressure", "strain", "stress", "tension" ], "total_occurrences": 260, "matching_section_count": 60, "matching_source_count": 14, "source_totals": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 62, "section_count": 8 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 54, "section_count": 8 }, 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gas between the terminals, current exists, but the terminal voltage is apparently indepen- dent of the current, that is, if the other conditions as temperature, gas pressure, etc., remain the same, the terminal voltage of the Geissler tube or the spark gap remains the same and independent of the current, and the current is determined by the impedance between the. Geissler tube or spark gap and the source of 100 RADIATION, L ...", "... - pedance in series with it, or a source of limited power, that is, a source in which the voltage drops with increase of cur- rent, as a constant current transformer or an electrostatic machine, etc. The disruptive voltage essentially depends on the gas pressure in the space between the electrodes, and also on the chemical nature, and on the temperature of the gas. It is over a wide range, directly proportional to the gas pressure. Thus, at n atmospheres pressure the voltage required to jump a spark between two ...", "... electrostatic machine, etc. The disruptive voltage essentially depends on the gas pressure in the space between the electrodes, and also on the chemical nature, and on the temperature of the gas. It is over a wide range, directly proportional to the gas pressure. Thus, at n atmospheres pressure the voltage required to jump a spark between two terminals is n times as great as at one atmosphere. This law seems to hold from the highest pressures which have been investigated down to pressures of a few mm. mercury, th ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-02", "section_label": "Chapter 2: Electric Conduction. Gas And Vapor", "section_title": "Electric Conduction. Gas And Vapor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3895-5444", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-02/", "snippets": [ "... d at the terminals (hot cathode), are the conductors. Such conduction thus exists also in a perfect vacuum, and may be accompanied by practically no luminescence. 28 ELECTRIC CONDUCTION . 29 Disruptive Conduction 19. Spark conduction at atmospheric pressure is the disruptive spark, streamers, and corona. In a partial vacuum, it is the Geissler discharge or glow discharge. Spark conduction is dis- continuous, that is, up to a certain voltage, the \"disruptive voltage,\" no conduction exists, except perhaps the ...", "... e of maintaining considerable current, the spark conduction changes to arc conduction, by the heat de- veloped at the negative terminal supplying the conducting arc vapor stream. The current usually is small and the voltage high. Especially at atmospheric pressure, the drop of the volt- ampere characteristic is extremely steep, so that it is practically impossible to secure stability by series resistance, but the con- duction changes to arc conduction, if sufficient current is avail- able, as from power generators, ...", "... n by the recovery of voltage, as with an electrostatic machine. Thus spark conduction also is called disruptive conduction and discon- tinuous conduction. Apparently continuous — though still interipittent — spark con- duction is produced at atmospheric pressure by capacity in series to the gaseous conductor, on an alternating-voltage supply, as corona, and as Geissler tube conduction at a partial vacuum, by an alternating-supply voltage with considerable reactance or resistance in series, or from a direct-curren ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-33", "section_label": "Chapter 33: Efficiency Of Systems", "section_title": "Efficiency Of Systems", "kind": "chapter", "sequence": 33, "number": 33, "location": "lines 36515-37127", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-33/", "snippets": [ "... minimum potential difference in the system, or the potential difference per circuit or phase of the system. 431 432 ALTERNATING-CURRENT PHENOMENA In low-potential circuits, as secondary networks, where the potential is not limited by the insulation strain, but by the potential of the apparatus connected into the system, as incan- descent lamps, the proper basis of comparison is equality of the potential per branch of the system, or per phase. On the other hand, in long-distance transmissions where the po ...", "... l only, but where the limitation of potential depends upon the problem of insulating the conductors against disruptive discharge, the proper com- parison is on the basis of equality of the maximum difference of potential; that is, equal maximum dielectric strain on the insulation. In this case, the comparison voltage may be either the poten- tial difference between any two conductors of the system, or it may be the potential difference between any conductor of the system and the ground, depending on the charact ...", "... the comparison voltage may be either the poten- tial difference between any two conductors of the system, or it may be the potential difference between any conductor of the system and the ground, depending on the character of the circuit. The dielectric stress is from conductor to conductor, or be- tween any two conductors, in a system which is insulated from the ground, as is mostly the case in medium voltage overhead transmissions, and frequently in underground cables. In an ungrounded cable system, in which ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-05", "section_label": "Lecture 5: Temperature Radiation", "section_title": "Temperature Radiation", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3946-5076", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-05/", "snippets": [ "... ist between different bodies regarding their rate of evaporation. Thus water and benzine have practically the same boiling point, but at the same distance below the boiling point, benzine evaporates much faster than water; that is, has a much higher vapor tension. Carbon has a very high vapor tension, that is, shows a very rapid evaporation far below the boiling point, and since in the incan- descent lamp the carbon vapor condenses and is deposited on the globe and carbon is black, it blackens the globe and obstru ...", "... their rate of evaporation. Thus water and benzine have practically the same boiling point, but at the same distance below the boiling point, benzine evaporates much faster than water; that is, has a much higher vapor tension. Carbon has a very high vapor tension, that is, shows a very rapid evaporation far below the boiling point, and since in the incan- descent lamp the carbon vapor condenses and is deposited on the globe and carbon is black, it blackens the globe and obstructs the light. Also, the decrease of t ...", "... This limitation of carbon lead to the revival of the metal fila- ment lamps in recent years. First arrived the osmium lamp, with 1.5 watts per candle power. The melting point of osmium is very high, but still very much below that of carbon, but the vapor tension of osmium is very low even close to its melting point, so 80 RADIATION, LIGHT, AND ILLUMINATION. that osmium could be operated at temperatures far closer to its melting point without appreciable evaporation; that is, without blackening and falling off ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... liquid body the vibrating particles are so close together as to interfere with each other. If you could set a body in vibration, in which the vibrating particles, atoms or molecules, are so far apart as not to interfere with each other, as in a gas at low pressure, then they would execute their own periods of vibration, and then the light from such a body would not be a radiation of all wave lengths, but we would get radiations of 244 GENERAL LECTURES only a few definite wave lengths, or a line spectrum. So in- ...", "... in addition thereto a number of utrared and ultraviolet rays. Since the spectrum light is based on the non-interference of the vibrating particles, it is easy to understand, that when you bring the atoms or molecules closely together — as at atmospheric pressure — interference may begin, and the lines of the spectrum become more confused and blurr into bands. Therefore, we see in the mercury arc spectrum, which is at low vapor pressure, a small number of definite, sharply definite lines. In the calcium spectrum o ...", "... at when you bring the atoms or molecules closely together — as at atmospheric pressure — interference may begin, and the lines of the spectrum become more confused and blurr into bands. Therefore, we see in the mercury arc spectrum, which is at low vapor pressure, a small number of definite, sharply definite lines. In the calcium spectrum of the flame carbon arc, we get a large number of lines blurring into each other to an almost continuous spectrum ; so also in the white spectrum of the magnetite-titanium arc. ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-01", "section_label": "Lecture 1: General Review", "section_title": "General Review", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 154-565", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-01/", "snippets": [ "... verter substation. The use of direct current is therefore restricted to those places where a fairly concentrated load exists, as in large cities; while in the suburbs, and in small cities and villages, where the load is too scattered to reach from one low tension supply point, sufficient customers to load a substation, the alternating current must be used, as it requires merely a step- down transformer which needs no attention. In the interior of large cities, the alternating current system is at a disadvantage, ...", "... ernating current system is at a disadvantage, because in addition to the voltage consumed by resistance, an additional drop of voltage occurs by self-induction, or by reactance ; and with the large conduc- tors required for the distribution of a large low tension current, the drop of voltage by self-induction is far greater than that by resistance, and the regulation of the system therefore is serious- ly impaired, or at least the voltage regulation becomes far more difficult than with direct current. A second dis ...", "... tor service essentially consists in starting at heavy torque, and rapid acceleration, and in both of these features the direct current motor with compound field winding is superior, and easier to control. Where therefore direct current can be used in low tension distribution, it is preferable to use it, and to relegate alternat- ing current low tension distribution to those cases where direct I pliOPERVY OF ELCCTRICAL LABORATOKY, ] I FACULTY OF AfPLieO SCItNCE. J 1 8 GENERAL LECTURES current cannot be use ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "... ions of different dissipation constants u. For instance, if in a circuit consisting of an unloaded transformer and a transmission line, as indicated in Fig. 40, at no load on the step-down trans- ^^ Line Transformer Line Fig. 40. former, the high-tension switches are opened at the generator end of the transmission line. The energy stored magnetically and dielectrically in line and transformer then dissipates by a transient, as shown in the oscillogram Fig. 41. This gives the oscillation of a circuit consi ...", "... mer then dissipates by a transient, as shown in the oscillogram Fig. 41. This gives the oscillation of a circuit consisting of 28 miles of line and 2500-kw. 100-kv. step-up and step-down transformers, and is produced by discon- necting this circuit by low-tension switches. In the transformer, the duration of the transient would be very great, possibly several seconds, as the stored magnetic energy (L) is very large, the dis- sipation of power (r and g) relatively small; in the line, the tran- sient is of fairly sh ...", "... Fig. 45 the same one minute later, when the ground was fully developed. An oscillogram of a cumulative oscillation in a 2500-kw. 100,000- volt power transformer (60-cycle system) is given in Fig. 46. It is caused by switching off 28 miles of line by high-tension switches, at 88 kilovolts. As seen, the oscillation rapidly increases in in- tensity, until it stops by the arc extinguishing, or by the destruc- tion of the transformer. Of special interest is the limiting case, — s = U) in this case, w + s = 0, and ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 4745-5520", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "snippets": [ "... of different dissipation constants u. For instance, if a circuit consists of an unloaded transformer and a transmission line, as indicated in Fig. 40, that is, at no load on the step-down trans- ^> Line Transformer Line Fig. 40. former, the high-tension switches are opened at the generator end of the transmission line. The energy stored magnetically and dielectrically in line and transformer then dissipates by a transient, as shown in the oscillogram Fig. 41. This gives the oscillation of a circuit consi ...", "... mer then dissipates by a transient, as shown in the oscillogram Fig. 41. This gives the oscillation of a circuit consisting of 28 miles of line and 2500-kw. 100-kv. step-up and step-down transformers, and is produced by discon- necting this circuit by low-tension switches. In the transformer, the duration of the transient would be very great, possibly several seconds, as the stored magnetic energy (L) is very large, the dis- sipation of power (r and g) relatively small; in the line, the tran- sient is of fairly sh ...", "... Fig. 45 the same one minute later, when the ground was fully developed. An oscillogram of a cumulative oscillation in a 2500-kw. 100,000- volt power transformer (60-cycle system) is given in Fig. 46. It is caused by switching off 28 miles of line by high-tension switches, at 88 kilovolts. As seen, the oscillation rapidly increases in in- tensity, until it stops by the arc extinguishing, or by the destruc- tion of the transformer. Of special interest is the limiting case, — s = u; in this case, u + s = 0, and ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-05", "section_label": "Lecture 5: Long Distance Transmission", "section_title": "Long Distance Transmission", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2562-3132", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-05/", "snippets": [ "... nce of the transformer building up with the line capacity. In those transformer connections in which several high 74 GENERAL LECTURES potential coils of different transformers are connected between the transmission wires, this may occur if the low tension coil of one of the transformers accidentally opens and the high potential coil of this transformer then acts as inductive react- ance in series with the line capacity in the circuit of the other transformer. ~r I ^ T Fife. 21. This may occur for ...", "... l of this transformer then acts as inductive react- ance in series with the line capacity in the circuit of the other transformer. ~r I ^ T Fife. 21. This may occur for instance in transformer connection 2, Fig. 19, if as shown in Fig. 21, the low tension coil c opens. Then the high tension coil C is an inductive reactance in series ;c<> Fife. 22. with the line capacity from 3 to i, energized by transformer A; and C is a high inductive reactance in series with the line capacity from 3 to 2 in a circ ...", "... ductive react- ance in series with the line capacity in the circuit of the other transformer. ~r I ^ T Fife. 21. This may occur for instance in transformer connection 2, Fig. 19, if as shown in Fig. 21, the low tension coil c opens. Then the high tension coil C is an inductive reactance in series ;c<> Fife. 22. with the line capacity from 3 to i, energized by transformer A; and C is a high inductive reactance in series with the line capacity from 3 to 2 in a circuit of voltage B. That is, from 3 to ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-11", "section_label": "Lecture 11: Lightning Protection", "section_title": "Lightning Protection", "kind": "lecture", "sequence": 11, "number": 11, "location": "lines 4931-5294", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-11/", "snippets": [ "... arrester. Series resistance, however, also limited the discharge current, and with very heavy discharges, such lightning arresters with series resistance failed to protect the circuits, that is, failed to discharge the abnormal voltage without destructive pressure rise. This difficulty was solved by the introduction of shunted resistances, that is, resistances shunt- ing a part of the spark gaps. All the minor discharges then pass over the resistances and the unshunted spark gaps, the LIGHTNING PROTECTION 139 r ...", "... is essentially that of protecting against excessive voltages. The performance of the lightning arrester on an electric circuit is analogous to that of the safety valve on the steam boiler, that is, to protect against dangerous pressures — whether steam pressure or electric pressure — ^by opening a discharge path as soon as the pressure approaches the danger limit. Therefore absolute reliability is required in its operation, and discharge with as little shock as possible, but over a path amply large to discharge ...", "... of protecting against excessive voltages. The performance of the lightning arrester on an electric circuit is analogous to that of the safety valve on the steam boiler, that is, to protect against dangerous pressures — whether steam pressure or electric pressure — ^by opening a discharge path as soon as the pressure approaches the danger limit. Therefore absolute reliability is required in its operation, and discharge with as little shock as possible, but over a path amply large to discharge practically unlimited ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-28", "section_label": "Chapter 28: Copper Efficiency Of Systems", "section_title": "Copper Efficiency Of Systems", "kind": "chapter", "sequence": 28, "number": 28, "location": "lines 26584-27052", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-28/", "snippets": [ "... n the system ; or 2d. On the basis of the minimum potential difference in the system, or the potential difference per circuit or phase of the system. In low potential circuits, as secondary networks, where the potential is not limited by the insulation strain, but by the potential of the apparatus connected into the system, as incandescent lamps, the proper basis of comparison is equality of the potential per branch of the system, or per phase. On the other hand, in long distance transmissions where the pot ...", "... here the limitation of potential depends upon the problem of insulating the conductors against disruptive discharge, the proper comparison is on the basis of equality of the maximum difference of potential in the system ; that is, equal maximum dielectric strain on the insulation. The same consideration holds in moderate potential power circuits, in considering the danger to life from wires or high differences of potential. Thus the comparison of different systems of long-dis- tance transmission at high potent ...", "... TING-CURRENT PHENOMENA. [§261 261. Comparison on the Basis of Equality of the Maximum Differetice of Potential in the System^ in Long- Distance Trafismissiofij Power Distribution^ etc. Wherever the potential is so high as to bring the ques- tion of the strain on the insulation into consideration, or in other cases, to approach the danger limit to life, the proper comparison of different systems is on the basis of equality of maximum potential in the system. Hence in this case, since the maximum potential is ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-30", "section_label": "Chapter 30: Efficiency Of Systems", "section_title": "Efficiency Of Systems", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 25136-25597", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-30/", "snippets": [ "... n the system ; or 2d. On the basis of the minimum potential difference in the system, or the potential difference per circuit or phase of the system. In low potential circuits, as secondary networks, where the potential is not limited by the insulation strain, but by the potential of the apparatus connected into the system, as incandescent lamps, the proper basis of comparison is equality of the potential per branch of the system, or per phase. On the other hand, in long distance transmissions where the pot ...", "... ere the limitation of potential depends upon the problem of insulating the conductors against disruptive discharge, the proper comparison is on the basis of equality of the maximum difference of potential in the system ; that is, •equal maximum dielectric strain on the insulation. The same consideration holds in moderate potential power circuits, in considering the danger to life from live wires entering human habitations. Thus the comparison of different systems of long-dis- tance transmission at high potenti ...", "... AL TERNA TING-CURRENT PHENOMENA. 290. Comparison on the Basis of Equality of the Maximum Difference of Potential in the System, in Long- Distance Transmission, Power Distribution, etc. Wherever the potential is so high as to bring the ques- tion of the strain on the insulation into consideration, or in other cases, to approach the danger limit to life, the proper comparison of different systems is on the basis of equality of maximum potential in the system. Hence in this case, since the maximum potential is ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-08", "section_label": "Lecture 8: Arc Lamps And Arc Lighting", "section_title": "Arc Lamps And Arc Lighting", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 7141-8510", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-08/", "snippets": [ "... n of arc length and current, i, the voltage of the arc stream is ex- pressed by : k (I + I) ei = TT1-' (1 and the total arc voltage by : , *(*+*,: (2) where e0, k and Zt are constants of the terminal material (k, how- ever, varies with the gas pressure in the space in which the arc exists). This equation (2) represents the arc characteristics with good approximation, except for long low-current arcs, which usually require a higher voltage than calculated, as might be expected from the unsteady nature ...", "... of the current, and absence of drifting, a supply voltage is used which exceeds the arc voltage by from 75 per cent to 100 per cent or more of the voltage, ev of the arc stream. 65. The preceding consideration applies only to those arcs in which the gas pressure in the space surrounding the arc, and thereby the arc vapor pressure and temperature, are constant and independent of the current, as is the case with arcs in air (even \" enclosed\" arcs, as the enclosure cannot be absolutely air- tight), as it is based on ...", "... ch exceeds the arc voltage by from 75 per cent to 100 per cent or more of the voltage, ev of the arc stream. 65. The preceding consideration applies only to those arcs in which the gas pressure in the space surrounding the arc, and thereby the arc vapor pressure and temperature, are constant and independent of the current, as is the case with arcs in air (even \" enclosed\" arcs, as the enclosure cannot be absolutely air- tight), as it is based on the assumption that the section of the vapor stream is proportional ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "section_label": "Chapter 14: Dielectric Losses", "section_title": "Dielectric Losses", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "... ux density in the insulating material. Thus, for instance, in the dielectric field between parallel con- ductors, at a voltage far below that which would jump from conductor to conductor, locally at the conductor surface the concentration of electrostatic stress exceeds the dielectric strength of air, and causes it to break down as corona. In solid dielectrics, under similar conditions, the breakdown due to local over-stress DIELECTRIC LOSSES 161 often may change the flux distribution so as to gradually extend ...", "... onductor to conductor, locally at the conductor surface the concentration of electrostatic stress exceeds the dielectric strength of air, and causes it to break down as corona. In solid dielectrics, under similar conditions, the breakdown due to local over-stress DIELECTRIC LOSSES 161 often may change the flux distribution so as to gradually extend throughout the entire dielectric, until puncture results. Corona 123. — In the magnetic field, with increasing magnetizing force, /, or magnetic field intensity, ...", "... uct- ing, that is, punctures, and thereby short-circuits the dielectric field. The voltage gradient, go, at which disruption of the dielectric occurs is called the \"disruptive strength\" or \"dielectric strength\" of the dielectric. With air at atmospheric pressure and temperature, it is go = 30 kv. per centimeter. Thus under alternating electric stress, air punctures at 21 kv. effective per / 30 \\ centimeter I ~-y= I . The dielectric strength of air is over a very wide range proportional to the air density, and ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... two pressures between which the nozzle operates, is given in Fig. 54, as determined by experiment. As abscissas are used the nozzle mouth opening, that is, the widest part of the nozzle at the exhaust end, as fraction of that corresponding to the exhaust pressure, while the nozzle throat, that is, the narrowest part of the nozzle, is assumed as constant. As ordinates are plotted the efficiencies. This curve is not symmetrical, 'but falls off from the maximum, on the sides of larger nozzle mouth, far more rapidly t ...", "... is not symmetrical, 'but falls off from the maximum, on the sides of larger nozzle mouth, far more rapidly than on the side of smaller nozzle mouth. The reason is that wdth too large a nozzle mouth the expansion in the nozzle is carried below the exhaust pressure p2, and steam eddies are produced by this overexpansion. The maximum efficiency of 94.6 per cent is found at the point Po, at which the nozzle mouth corresponds to the exhaust pressure. If, however, the maximum is determined as mid- way between two poin ...", "... ozzle mouth the expansion in the nozzle is carried below the exhaust pressure p2, and steam eddies are produced by this overexpansion. The maximum efficiency of 94.6 per cent is found at the point Po, at which the nozzle mouth corresponds to the exhaust pressure. If, however, the maximum is determined as mid- way between two points Pi and P2, on each side of the maximum, MAXIMA AND MINIMA, 151 at which the efficiency is the same, 93 per cent, a point Po' is obtained, which lies on one side of the maximum. ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-08", "section_label": "Lecture 8: Generation", "section_title": "Generation", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 3781-4217", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-08/", "snippets": [ "... ndustry; while the steam turbine in the last ten years of its development has practically replaced the steam engine in large electric generating plants. The cause of the disadvantages of the gas engine is the high maximum temperature and the high maximum pressure compared with the mean pressure in the cylinders, which is necessary to get the greater temperature range and thus the efficiency, therefore is inherent in this type of apparatus. The output depends upon the mean pressure in the cylinder, which is low; ...", "... in the last ten years of its development has practically replaced the steam engine in large electric generating plants. The cause of the disadvantages of the gas engine is the high maximum temperature and the high maximum pressure compared with the mean pressure in the cylinders, which is necessary to get the greater temperature range and thus the efficiency, therefore is inherent in this type of apparatus. The output depends upon the mean pressure in the cylinder, which is low; the strains on the maximum pressu ...", "... temperature and the high maximum pressure compared with the mean pressure in the cylinders, which is necessary to get the greater temperature range and thus the efficiency, therefore is inherent in this type of apparatus. The output depends upon the mean pressure in the cylinder, which is low; the strains on the maximum pressure, which is very high ; and the gas engine therefore must be very large, and its moving parts very strong and heavy, for its out- put. The impulse due to the rapid pressure change is very j ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-23", "section_label": "Chapter 1: The Constants Of The Electric Circuit", "section_title": "The Constants Of The Electric Circuit", "kind": "chapter", "sequence": 23, "number": 1, "location": "lines 1317-1992", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "snippets": [ "... ergy always decreases from generating to receiving circuit, and the power gradient therefore is characteristic of the direc- tion of the flow of energy.) In the space outside of the conductor, during the flow of energy through the circuit, a condition of stress exists which is called the electric field of the conductor. That is, the surrounding space is not uniform, but has different electric and magnetic properties in different directions. No power is required to maintain the electric field, but energy 3 ...", "... , (9) l Ll W K = — = energy stored in the dielectric field of the cir- £t cuit, (14) 8 TRANSIENT PHENOMENA and the three circuit constants r, L, C therefore appear as the components of the energy conversion into heat, magnetism, and electric stress, respectively, in the circuit. 4. The circuit constant, resistance r, depends only on the size and material of the conductor, but not on the position of the conductor in space, nor on the material filling the space surrounding the conductor, nor on the s ...", "... eturned at the disappearance of the electric field, but a part is consumed by conversion into heat in producing or in any other way changing the electric field. That is, the conversion of electric energy into and from the electromagnetic and electrostatic stress is not complete, but a loss of energy occurs, especially with the magnetic field in the so-called magnetic materials, and with the electrostatic field in unhomogeneous dielectrics. The energy loss in the production and reconversion of the magnetic compo ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-02", "section_label": "Lecture 2: General Distribution", "section_title": "General Distribution", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 566-982", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-02/", "snippets": [ "... .109 ohms, and so 1.88 times as great as the reactance of two con- ductors of No. I in multiple, which latter is half that of one conductor No. i, or .058 ohms, provided that the two con- ductors are used as separate circuits. In alternating current low tension distribution, the size of the conductor and so the current per conductor, is limited by the self -inductive drop, and alternating current low tension networks are therefore of necessity of smaller size than those of direct current distribution. As regar ...", "... .058 ohms, provided that the two con- ductors are used as separate circuits. In alternating current low tension distribution, the size of the conductor and so the current per conductor, is limited by the self -inductive drop, and alternating current low tension networks are therefore of necessity of smaller size than those of direct current distribution. As regards economy of distribution, this is not a serious objection, as the alternating current transformer and primary distribution permits the use of numero ...", "... lts is used, feeding step-down transformers. The different arrangements are — a. A separate transformer for each customer. This is necessary in those cases where the customers are so far apart from each other that they cannot be reached by the same low tension or secondary circuit ; every alternating current system therefore has at least a number of instances where individual transformers are used. This is the most uneconomical arrangement. It requires the use of small transformers, which are necessarily less ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-02", "section_label": "Chapter 2: Potential Series And Exponential Function", "section_title": "Potential Series And Exponential Function", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3492-6063", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-02/", "snippets": [ "... e voltage at the condenser dropped to 0.1 its initial value? A condenser acts as a reser- voir of electric energy, similar to a tank as water reservoir. If in a water tank, Fig. 27, A is the sectional area of the tank, e, the height of water, or water pressure, and water flows out of the tank, then the height e decreases by the flow of water; that is the tank empties, and the current of water, i, is proportional to the change of the de water level or height of water, — , and to the area A of the Fig. 27. ...", "... ' de dt' (72) The minus sign stands on the right-hand side, as for positive i; that is, out-flow, the height of the water decreases; that is, de is negative. POTENTIAL SERIES AND EXPONENTIAL FUNCTION. 77 In an electric reservoir, the electric pressure or voltage e corresponds to the water pressure or height of the water, and to the storage capacity or sectional area A of the water tank corresponds the electric storage capacity of the condenser, called capacity C. The current, or, flow out of an electri ...", "... the right-hand side, as for positive i; that is, out-flow, the height of the water decreases; that is, de is negative. POTENTIAL SERIES AND EXPONENTIAL FUNCTION. 77 In an electric reservoir, the electric pressure or voltage e corresponds to the water pressure or height of the water, and to the storage capacity or sectional area A of the water tank corresponds the electric storage capacity of the condenser, called capacity C. The current, or, flow out of an electric condenser, thus is, --4I (-3) The capacit ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-06", "section_label": "Lecture 6: Higher Harmonics Of The Generator Wave", "section_title": "Higher Harmonics Of The Generator Wave", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3133-3507", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-06/", "snippets": [ "... es the maximum e. m. f. ; that is, the e. m. f. wave is very low for a large part of the cycle and then rises to a very high peak, as shown by Fig. 23 ; and the maximum e. m. f . may exceed that of a sine wave by 50% and more, thus giving high insulation stress and the possibility of resonance voltages. EFFECTS OF HIGHER HARMONICS In a three-phase system the three phases are 120° apart, and their third harmonics are 3 x 120° = 360° apart, that is, in phase with each, and for the third harmonic the three-phase ...", "... oltage divided by V3, that is, the true Y voltage of the system ; but superimposed upon it is this single-phase triple frequency voltage; and the voltage from line to ground, especially its maximum, may be greatly increased, thus increasing the insulation strain. For this single-phase voltage all three lines go together, and so may cause static induction on other circuits, as telephone lines. A circuit of this single-phase triple frequency voltage then exists frcmi the generator neutral over the inductance of all ...", "... n a circuit of the triple har- monic, and if capacity and inductance are high enough, we may get a dangerous voltage rise. In this case of grounded generator neutral, if the neutral of the Y connected step-down transformers is grounded also, and the low tension side of these transformers connected in Y, the third harmonic of the generator has no path; the cur- rent produced by it would have to return over the open circuit reactance of the step-down transformer, and is limited there- by to a negligible value. I ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-07", "section_label": "Chapter 7: Shaping Of Waves : General", "section_title": "Shaping Of Waves : General", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 12222-12961", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-07/", "snippets": [ "... developed by the cur- rent in a resistance is the object, as for incandescent lighting, heating, etc., any wave form is equally satisfactory, as the energy of the wave depends only on its effective value, but not on it^ shape. With regards to insulation stress, as in high-voltage systems, a flat-top wave of voltage and current, such as shown in Fig. 47, would be preferable, as it has a higher effective value, with tho same maximimi value and therefore with the same strain on tho insulation, and therefore transm ...", "... it^ shape. With regards to insulation stress, as in high-voltage systems, a flat-top wave of voltage and current, such as shown in Fig. 47, would be preferable, as it has a higher effective value, with tho same maximimi value and therefore with the same strain on tho insulation, and therefore transmits more energy than the sine wave. Fig. 46. Inversely, a peaked wave of voltage, such as Fig. 48, and such as the common saw-tooth wave of the uni tooth alternator, is superior in transformers and similar devices, ...", "... ss may amount to as much as 15 to 25 p(;r cent, of the ^^otal hysteresis loss, in extreme cases. Inversely, a peaked voltage wave like Fig. 48 would be obj(i(j- t-xonable in high- voltage transmission apparatus, by giving an un- necessary high insulation strain, and a flat-top wave of voltage ^vke Fig. 47, when impressed upon a transformer, would give a ^^^ed wave of magnetism and thereby an increased hyHteresis Ill 112 ELECTRIC CIRCUITS The advantage of the sine wave is, that it remains unch&nged in s ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-18", "section_label": "Chapter 17: Conclusion", "section_title": "Conclusion", "kind": "chapter", "sequence": 18, "number": 17, "location": "lines 7568-8027", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-18/", "snippets": [ "... at first; by his greater initiative, by his control of much of the political and indus- trial machinery, he would, by organizing the Slav and Mediterranean, by political, indus- ^2i / CONCLUSION trial, anu social pressure, drive tlie citizens of Celtic and German descent from power, and practically, if not even legally, disfranchise them. But then, deprived of the organizing ability of the German, the administrative ability of the Celt, and ...", "... system by the political government, as it exists, for instance, in Germany. However, it will be a matter of generations before our national temperament, by collectiv- istic immigration and elimination of the individ- ualistic strain, has changed sufficiently; and industrial progress and reorganization in the co-operative era is so rapid abroad, that long 226 \\ t CONCLUSION before America's national character could have changed so far as to mak ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 557-1002", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-01/", "snippets": [ "... n the supply pipe represents a considerable amount of stored mechanical energy, when flowing at velocity, under load. If, then, full load is suddenly thrown off, it is not possible to suddenly stop the flow of water, since a rapid stopping would lead to a pressure transient of destructive value, that is, burst the pipe. Hence the use of surge tanks, relief valves, or deflecting nozzle governors. Inversely, if a heavy load comes on suddenly, opening the nozzle wide does not immediately take care of the load, but mom ...", "... value, that is, burst the pipe. Hence the use of surge tanks, relief valves, or deflecting nozzle governors. Inversely, if a heavy load comes on suddenly, opening the nozzle wide does not immediately take care of the load, but momentarily drops the water pressure at the nozzle, while gradually the water column acquires velocity, that is, stores energy. The fundamental condition of the appearance of a transient thus is such a disposition of the stored energy in the system as differs from that required by the exis ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "... illations and surges; the former is often more convenient to show the relation to traveling waves. In Figs. 35 and 36 are shown oscillograms of such line oscilla- tions. Fig. 35 gives the oscillation produced by switching 28 miles of 100-kv. line by high-tension switches onto a 2500-kw. step-up transformer in a substation at the end of a 153-mile three- phase line; Fig. 36 the oscillation of the same system caused by switching on the low-tension side of the step-up transformer. 29. As seen, the phase of current ...", "... e oscillation produced by switching 28 miles of 100-kv. line by high-tension switches onto a 2500-kw. step-up transformer in a substation at the end of a 153-mile three- phase line; Fig. 36 the oscillation of the same system caused by switching on the low-tension side of the step-up transformer. 29. As seen, the phase of current i and voltage e changes pro- gressively along the line I, so that at some distance Iq current and voltage are 360 degrees displaced from their values at the starting point, that is, are a ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 6125-6803", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-09/", "snippets": [ "... -up transformer, transmission line, and load. (The load, consisting of step-down transformer and its secondary cir- cuit, may for convenience be considered as one circuit section.) Assume now that the circuit is disconnected from the power sup- ply by low-tension switches, at A. This leaves transformer, line, and load as a compound oscillating circuit, consisting of four sections : the high-tension coil of the step-up transformer, the two lines, and the load. Let then Xi = length of line, X2 = length of transform ...", "... nce be considered as one circuit section.) Assume now that the circuit is disconnected from the power sup- ply by low-tension switches, at A. This leaves transformer, line, and load as a compound oscillating circuit, consisting of four sections : the high-tension coil of the step-up transformer, the two lines, and the load. Let then Xi = length of line, X2 = length of transformer circuit, and X3 = length of load circuit, in velocity measure.* If then * If Zi = length of circuit section in any measure, and Lo = i ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 460-882", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "snippets": [ "... n the supply pipe represents a considerable amount of stored mechanical energy, when flowing at velocity, under load. If, then, full load is suddenly thrown off, it is not possible to suddenly stop the flow of water, since a rapid stopping would lead to a pressure transient of destructive value, that is, burst the pipe. Hence the use of surge tanks, relief valves, or deflecting nozzle governors. Inversely, if a heavy load comes on suddenly, opening the nozzle wide does not immediately take care of the load, but mom ...", "... value, that is, burst the pipe. Hence the use of surge tanks, relief valves, or deflecting nozzle governors. Inversely, if a heavy load comes on suddenly, opening the nozzle wide does not immediately take care of the load, but momentarily drops the water pressure at the nozzle, while gradually the water column acquires velocity, that is, stores energy. The fundamental condition of the appearance of a transient thus is such a disposition of the stored energy in the system as differs from that required by the exis ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3956-4744", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "snippets": [ "... illations and surges; the former is often more convenient to show the relation to traveling waves. In Figs. 35 and 36 are shown oscillograms of such line oscilla- tions. Fig. 35 gives the oscillation produced by switching 28 miles of 100-kv. line by high-tension switches onto a 2500-kw. step-up transformer in a substation at the end of a 153-mile three- phase line; Fig. 36 the oscillation of the same system caused by switching on the low-tension side of the step-up transformer. 29. As seen, the phase of current ...", "... e oscillation produced by switching 28 miles of 100-kv. line by high-tension switches onto a 2500-kw. step-up transformer in a substation at the end of a 153-mile three- phase line; Fig. 36 the oscillation of the same system caused by switching on the low-tension side of the step-up transformer. 29. As seen, the phase of current i and voltage e changes pro- gressively along the line Z, so that at some distance 1Q current and voltage are 360 degrees displaced from their values at the starting point, that is, are a ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 5521-6088", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "snippets": [ "... -up transformer, transmission line, and load. (The load, consisting of step-down transformer and its secondary cir- cuit, may for convenience be considered as one circuit section.) Assume now that the circuit is disconnected from the power sup- ply by low-tension switches, at A. This leaves transformer, line, and load as a compound oscillating circuit, consisting of four sections: the high-tension coil of the step-up transformer, the two lines, and the load. Let then Xi = length of line, X2 = length of transforme ...", "... ence be considered as one circuit section.) Assume now that the circuit is disconnected from the power sup- ply by low-tension switches, at A. This leaves transformer, line, and load as a compound oscillating circuit, consisting of four sections: the high-tension coil of the step-up transformer, the two lines, and the load. Let then Xi = length of line, X2 = length of transformer circuit, and Xs = length of load circuit, in velocity measure.* If then * If Zi = length of circuit section in any measure, and L0 = i ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-03", "section_label": "Lecture 3: Physiological Effects Of Radiation", "section_title": "Physiological Effects Of Radiation", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2366-3638", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-03/", "snippets": [ "... en continued too long, or in poor light, as in artificial illumination, leads to blurring of the vision and head or eye ache. Practically complete recovery occurs only after some years, and even then some care is necessary, as any very severe and extended strain on the eyes temporarily brings back the symptoms. Especially is this the case when looking at a light of short wave length, as the mercury arc; that is, there remains an abnormal sensitivity of the eye to light of short wave lengths, even such light which ...", "... ays have so far only been observed in the radiation of a low temperature mercury arc in a quartz tube : quartz being transparent to these rays while glass is opaque. The high temperature mercury arc in a quartz tube, that is, arc operated near atmospheric pressure as it is used to some extent for illumination, especially abroad, seems to be much less dan- gerous than the low temperature or vacuum arc, but it also requires a protecting glass globe. In general, no metal arc, spark discharge, or glow discharge shoul ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-09", "section_label": "Lecture 9: Measurement Of Light And Radiation", "section_title": "Measurement Of Light And Radiation", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 8511-9388", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-09/", "snippets": [ "... ply voltage eliminate by appearing in both sources L and S. MEASUREMENT OF LIGHT AND RADIATION. 171 For similar reasons, when testing gas lamps or other flames, L, as S, a flame standard, as the pentane lamp, is used, so that the effect of barometric pressure, humidity of the air, etc., appears in both lamps and thereby does not appreciably affect the comparison of their light. A quick and approximate method of comparison of sources of light is given by the shadow photometer by moving an object between the t ...", "... d which has found extensive and international use is the amyl-acetate lamp of Hefner. This is a lamp burning arnyl acetate at a definite rate, with a definite 178 RADIATION, LIGHT, AND ILLUMINATION. height of flame and definite conditions regarding air pressure and humidity. This Hefner lamp, or German candle, equals about 90 per cent of the British candle and equals 90 per cent of the international candle. Amyl acetate has been chosen, as it can easily be produced in chemical purity, and gives a good luminous ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-12", "section_label": "Lecture 12: Illumination And Illuminating Engineering", "section_title": "Illumination And Illuminating Engineering", "kind": "lecture", "sequence": 12, "number": 12, "location": "lines 16485-17445", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-12/", "snippets": [ "... artificial light, the sensitivity of the eye decreases, the illumination appears less bright, and thus a higher illumination is required than would be sufficient in the absence of fatigue, and the continuous use and absence of rest cause the sensation of strain, that is, irritation or an uncomfortable feeling, as especially noticeable when working or reading for a considerable length of time in rooms having a high uniform intensity of illumination, as meeting-rooms, some libraries, etc. If, however, the eye can ...", "... ct, is sharply defined, while the other edge of the shadow, which ter- minates on the flat surrounding surface, should gradually fade or blur. If we have to look closely to determine that the outer edge of the shadow is not the edge of another object, the strain of distinguishing between the edge of an object and the edge of a shadow makes the illumination uncomfortable and thus unsatisfactory. In the shadows cast by a single arc in a clear glass globe, this difficulty of distinguishing between the edge of a sha ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-22", "section_label": "Chapter 20: Ri", "section_title": "Ri", "kind": "chapter", "sequence": 22, "number": 20, "location": "lines 24560-25119", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "snippets": [ "... nd the useful or consumer cir- cuit — is unaffected by wave-shape or intensity of mag- netism. • 231. In high potential lines, distorted waves whose maxima arc very high above the effective values, as peaked waves, may be objectionable by increasing the strain on the insulation. It is, however, not settled yet beyond doubt whether the striking-distance of a rapidly alternat- ing j)otential dej)ends upon the maximum value or upon the effective value. Since disruptive phenomena do not §231] EFFECTS OF HIGHER H ...", "... value or upon the effective value. Since disruptive phenomena do not §231] EFFECTS OF HIGHER HARMONICS. 345 always take place immediately after application of the potential, but the time element plays an important part, it is possible that insulation-strain and striking-distance is, in a certain range, dependent upon the effective potential, and thus independent of the wave-shape. In general, as conclusions may be derived that the im- portance of a proper wave-shape is generally greatly over- rated, but th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-23", "section_label": "Chapter 23: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 21983-22448", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "snippets": [ "... and the useful or consumer cir- cuit — is unaffected by wave-shape or intensity of mag- netism. 252. In high potential lines, distorted waves whose maxima are very high above the effective values, as peaked waves, may be objectionable by increasing the strain on the insulation. It is, however, not settled yet beyond doubt whether the striking-distance of a rapidly alternat- ing potential depends upon the maximum value or upon EFFECTS OF HIGHER HARMONICS. 409 some value between effective and maximum. Since ...", "... EFFECTS OF HIGHER HARMONICS. 409 some value between effective and maximum. Since dis- ruptive phenomena do not always take place immediately after application of the potential, but the time element plays ari important part, it is possible that insulation-strain and striking-distance is, in a certain range, dependent upon the effective potential, and thus independent of the wave-shape. In this respect it is quite likely that different insulating materials show a different behavior, and homogeneous solid substan ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-01", "section_label": "Chapter 1: Electric Conduction. Soled And Liquid", "section_title": "Electric Conduction. Soled And Liquid", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 959-3894", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-01/", "snippets": [ "... ON. SOLED AND LIQUID CONDUCTORS 1, When electric power flows through a circuit, we find phe- nomena taking place outside of the conductor which directs the flow of power, and also inside thereof. The phenomena outside of the conductor are conditions of stress in space which are called the electric field, the two main components of the electric field being the electromagnetic component, characterized by the cir- cuit constant inductance, L, and the electrostatic component, characterized by the electric circuit ...", "... onduction is reached, though even these show the high negative temperature coefficient- With some, as varnishes, etc., the conductivity becomes sufficient, at high temperatures, though still below carbonization tempera- ture, that under high electrostatic stress, as in the insulation of high-voltage apparatus, appreciable energy is represented by the leakage current through the insulation, and in this case rapid i^r heating and final destruction of the material may result. That is, such materials, while excellent ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... self inductive and mutual in- ductive, of alternator arma- ture, 239 shunt in series circuit, 298 regulating series circuit by saturation, 302 of synchronous machines, 232 total, of transformer, 224 of transformer, measurement, 227 and short-circuit stress, 100 as wave screen, 153 Reactive power of system, total and resultant, 317 Recovery of induction motor after overload, 204 Rectification by arc, 32 by electronic conduction, 40 giving even harmonics, 159 Rectifying voltage range of alter- nating ...", "... ctance shunting series circuit, 302 value, magnetic, 46 Screen, wave-, 153 Secondary cell, 8 Self inductive armature flux of alternator, 234 Series operation, constant current, 297 constant voltage, 297 Shape of hysteresis curve, 68 Short circuit stress in transformer, 99 third harmonic in alternator, 244 Shunt protective device in series circuits, 298 Silicon as pyroelectric conductor, 13 steel, hysteresis, 62 magnetic properties, 79 Sine wave as standard, 111 Singing arc, 188 Singlephase load ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... 0 to dissipate. This latter takes a con- siderable time, and an air blast directed against the spark gap e0, by carrying away the products of the discharge, permits a more rapid recurrence of the discharge. The velocity of the air blast (and therefore the pressure of the air) must be such as to carry the ionized air or the metal vapors which the discharge forms in the gap e0 out of the discharge path faster than the con- denser recharges. Assuming, for instance, the spark gap, e0, set for 20,000 volts, or about 0 ...", "... ed with 0.75 in., hence at least 3 to 6 in. With 1000 discharges per second, this would require an air velocity of v = 250 to 500 feet per second, with 5000 discharges per second an air velocity of v = 1250 to 2500 feet per second, corresponding to an air pressure of approximately p = 14.7 { (1 + 2 w2 10 - 7)3'5 - 1 } lb. per sq. in., or 0.66 to 2.75 Ib. in the first, 23 to 230 lb. in the second case. 76 TRANSIENT PHENOMENA While the condenser charge may be oscillatory or logarithmic, efficiency requires a low ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-43", "section_label": "Chapter 3: The Natural Period Of The Transmission Line", "section_title": "The Natural Period Of The Transmission Line", "kind": "chapter", "sequence": 43, "number": 3, "location": "lines 21721-23178", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "snippets": [ "... nverter, causes the circuit to open at the generating station, the dissipation of the stored energy — in this case that of the excessive current in the system — occurs as a full-wave oscillation, if the line cuts off from the generating station on the low-tension side of the step-up transformers, and the oscillating circuit comprises the high-tension coils of the step-up trans- formers, the transmission line, step-down transformers, and load. If the line disconnects from the generating system on the high- NATURA ...", "... red energy — in this case that of the excessive current in the system — occurs as a full-wave oscillation, if the line cuts off from the generating station on the low-tension side of the step-up transformers, and the oscillating circuit comprises the high-tension coils of the step-up trans- formers, the transmission line, step-down transformers, and load. If the line disconnects from the generating system on the high- NATURAL PERIOD OF TRANSMISSION LINE 341 potential side of the step-up transformers, the oscill ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-04", "section_label": "Chapter 3: The Individualistic Era: From Competition to Co-operation", "section_title": "The Individualistic Era: From Competition to Co-operation", "kind": "chapter", "sequence": 4, "number": 3, "location": "lines 874-1745", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-04/", "snippets": [ "... all is the welfare of societj^ \\ The realization of \"social work\" as one of the essential activities of the corporation has come last. It is just being approached by many corporations. Sometimes it is the result of the pressure exerted by independent and often hostile employees' associations — labor unions. Or where the corporation has succeeded in suppressing organized action of its employees, by spontaneous outbreaks — syndicalism. But whatever the rea ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-08", "section_label": "Chapter 7: The Other European Nations in the Individualistic Era", "section_title": "The Other European Nations in the Individualistic Era", "kind": "chapter", "sequence": 8, "number": 7, "location": "lines 3207-3740", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-08/", "snippets": [ "... y her two stronger neighbors, Germany 9G OTHER EUROPEAN NATIONS and Hungary. Thus when in the first year of the war Austria's military organization broke down, Germany reorganized the armies; when, later on, the economic pressure resulting from the food blockade threatened Austria, Germany again had to organize Austria's internal economy. Austria, however, was the leading nation in central Europe before Germany. Her emperor is of the oldest and most ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-16", "section_label": "Chapter 15: The American Nation", "section_title": "The American Nation", "kind": "chapter", "sequence": 16, "number": 15, "location": "lines 6598-6974", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-16/", "snippets": [ "... mperament and characteristic like the British-American, will have the British view- point— or that of any other constituent nation — however much this may disappoint us. Inversely, however, we must realize that the Anglo-Saxon strain is one of the largest in the composition of the American race; that his- torically, by the previous preponderance of the Anglo-Saxon, it has exerted more influence on the molding of the new nation than any other race, and ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-17", "section_label": "Chapter 16: The Future Corporation", "section_title": "The Future Corporation", "kind": "chapter", "sequence": 17, "number": 16, "location": "lines 6975-7567", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-17/", "snippets": [ "... ld's history; the creation of prosperous industrial cities in the sandy deserts of the lake shore; the control in the service of man, for power production in the steam-turbine, of the steam jet which issues from the high- pressure steam-boiler at speeds so terrific that, compared with it, the monster shells of the high- power guns which have smashed Europe's ii5 AMERICA AND THE NEW EPOCH strongest fortifications are crawling with a snail's pace, ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-appendix-01-synchronous-operation", "section_label": "Mathematical Appendix 5: Appendix: Synchronous Operation", "section_title": "Appendix: Synchronous Operation", "kind": "mathematical-appendix", "sequence": 5, "number": 5, "location": "PDF pages 27-68, lines 2165-5013", "status": "pdf-text-extracted-candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "snippets": [ "... ble magnitude. The voltage across the power limiting reactors, in Column (10). and the phase angles between the stations, in Column (11), are very moderate: only a little over 5 degrees maximum phase displacement between Fisk A and Quarry Street. That is, the strain is very moderate, and very far from the limits of synchronizing power. Assuming now the second explanation, hunting of the stations. Column (12) then gives the estimated values of the quadrature voltage resulting from the swing of the machines, which would be ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3721-4369", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-06/", "snippets": [ "... ig. 31 is shown an oscillogram of the voltage oscillation of the compound circuit consisting of 28 miles of 100,000-volt transmission line and the 2500-kw. high-potential step-up transformer winding, caused by switching transformer and 28-mile line by low-tension switches off a substation at the end of a 153-mile transmission line, at 88 kv. With decreasing voltage, the magnetic density in the transformer DOUBLE-ENERGY TRANSIENTS. 65 decreases, and as at lower magnetic densities the permeability of the iron is ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3287-3955", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "snippets": [ "... ig. 31 is shown an oscillogram of the voltage oscillation of the compound circuit consisting of 28 miles of 100,000-volt transmission line and the 2500-kw. high-potential step-up transformer winding, caused by switching transformer and 28-mile line by low-tension switches off a substation at the end of a 153-mile transmission line, at 88 kv. With decreasing voltage, the magnetic density in the transformer DOUBLE-ENERGY TRANSIENTS. 65 decreases, and as at lower magnetic densities the permeability of the iron is ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-02", "section_label": "Lecture 2: Conclusions From The Relativity Theory", "section_title": "Conclusions From The Relativity Theory", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 736-2388", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... gth of a body and the time on it change with the relative velocity of the observer. The highest velocities which we can produce (outside of ionic velocities) are the velocity of the rifle bullet (1000 meters per second) , the velocity of expansion of high-pressure steam into a vacuum (2000 meters per second), and the velocity of propagation of the detonation in high explosives (6000 meters per second). At these velocities the change of length and time is one part in 180,000 millions, 22,000 millions and 5000 milli ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-03", "section_label": "Lecture 3: Light And Power Distribution", "section_title": "Light And Power Distribution", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 983-1526", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-03/", "snippets": [ "... onductors is 4500, and the copper economy of the system therefore is that of a 45CX) volt three-phase system. 5. Polyphase primary and polyphase secondary distri- bution, with the motor connected to the same secondary mains as the lights. SYSTEMS OF LOW TENSION DISTRIBUTION FOR LIGHTING AND POWER. I. Two- Wire Direct Current or Singi.e-Phase ho Volts. Fig 6. This can can be used only for very short distances, since its copper economy is very low, that is, the amount of conduc- tor material is very high for ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... ble and set for about ^ in. gap. This lamp is connected across a high voltage 0.2-mf. mica condenser C, which is connected to the high voltage terminal of a small step-up trans- former T giving about 15,000 volts (200 watts, 110 •*- 13,200 volts). The low tension side of the transformer is connected to the 240-volt 60-cycle circuit through a rheostat R to limit the current. The transformer charges the condenser, and when the voltage of the condenser has risen sufficiently high it discharges through the spark gaps ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... a number or range of frequencies in each band, where the line RELATION OF BODIES TO RADIATION. 27 spectrum has only 'one single frequency in each line. Such band spectra are usually characteristic of luminescent compounds or of gases and vapors at high pressure, while elementary gases or vapors give line spectra. Absorption and fluorescence also give band spectra, and I thus show you a band spectrum by opera- ting a mercury lamp in a tube of uranium glass, behind a trans- parent screen colored by rhodamine (an a ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-103", "section_label": "Apparatus Section 6: Alternating-current Transformer: Heating and Ventilation", "section_title": "Alternating-current Transformer: Heating and Ventilation", "kind": "apparatus-section", "sequence": 103, "number": 6, "location": "lines 18461-18520", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-103/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-103/", "snippets": [ "... through a system of pipes located under the oil at the top of the trans- former tank. This is the most common design of large trans- formers. (c) Air blast. Coils and iron are subdivided by ventilating ducts, and a low-pressure air blast forced through the ventilating ducts. This is the cleanest method, as no oil is used. However, it is limited to low and moderate voltages — up to about 33,000; at higher voltage, the mechanical and chemical actio ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-81", "section_label": "Apparatus Section 1: Synchronous Converters: General", "section_title": "Synchronous Converters: General", "kind": "apparatus-section", "sequence": 81, "number": 1, "location": "lines 13189-13795", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-81/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-81/", "snippets": [ "... ts, either polyphase or single-phase, are extensively used. For many applications, however, as especially for electrolytic work, direct currents are required, and are usually preferred also for electrical railroading and for low-tension distribution on the Edison three- wire system. Thus, where power is derived from an alternating system, transforming devices are required to convert from alternating to direct current. This can be done either by a direct-curr ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-87", "section_label": "Apparatus Section 9: Synchronous Converters: Inverted Converters", "section_title": "Synchronous Converters: Inverted Converters", "kind": "apparatus-section", "sequence": 87, "number": 9, "location": "lines 15735-15810", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-87/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-87/", "snippets": [ "... rect current or as inverted converters from direct to alternating current. While the former use is by far the more 256 ELEMENTS OF ELECTRICAL ENGINEERING frequent, sometimes inverted converters are desirable. Thus in low-tension direct-current systems outlying districts have been supplied by converting from direct to alternating, transmitting as alternating, and then reconverting to direct current. Or in a station containing direct-current generators for ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-25", "section_label": "Chapter 25: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 29375-32539", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-25/", "snippets": [ "... ic of an effective value of 0.24 E — that is, 38.5 per cent, of the effective value of the total wave. The very high peak of e.m.f. produced by this wave-shape distortion is liable to be dangerous in high-potential, three- phase systems by increasing the strain on the insulation between lines and ground, and leading to resonance phenomena with the third harmonic. The maximum value of the distorted wave of magnetism is 8.89, while with a sine wave it would be 10.0, that is, the maxi- mum of the wave of magnetis ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-26", "section_label": "Chapter 26: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 32540-33010", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-26/", "snippets": [ "... rrent circuit and the useful or consumer circuit — is unaffected by wave-shape or intensity of magnetism. In high-potential lines, distorted waves whose maxima are very high above the effective values, as peaked waves, are objectionable by increasing the strain on the insulation. The striking-distance of an alternating voltage depends upon the maximum value, except at extremely high frequencies, such as oscillating discharges. In the latter, the very short duration of the voltage peak may reduce the disruptive s ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-28", "section_label": "Chapter 28: General Polyphase Systems", "section_title": "General Polyphase Systems", "kind": "chapter", "sequence": 28, "number": 28, "location": "lines 34777-34928", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-28/", "snippets": [ "... ved from two phases of a three-phase system by transformation with two transformers, of which the secondary of one is reversed with regard to its primary (thus changing the phase difference from 120° to 180° — 120° = 60°) finds a hmited application in low-tension distribution." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-20", "section_label": "Chapter 20: Beactiox Machines", "section_title": "Beactiox Machines", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 22388-23273", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-20/", "snippets": [ "... le has been widened, representing not only the electrical energy consumed by molecular magnetic friction, but also the me- chanical output. Hence, ruch a synchronous motor can be called \" hyste- resis motor,\" since the mechanical work is done by an ex- tension of the loop of hysteresis. 208. It is evident that the variation of reluctance must bo symmetrical with regard to the field poles ; that is, that the two extreme values of reluctance, maximum and mini- 5 208] REACTION MACHINES. mum, will take pl ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-25", "section_label": "Chapter 25: General Polyphase Systems", "section_title": "General Polyphase Systems", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 23643-23780", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-25/", "snippets": [ "... from two phases of a three-phase system by transformation with two transformers, of which the secondary of one is reversed with regard to its primary (thus changing the phase difference from 120° to 180° - 120° = 60°), finds a limited application in low tension distribution. 434 ALTERNATING-CURRENT PHENOMENA." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-32", "section_label": "Chapter 10: Mutual Inductance", "section_title": "Mutual Inductance", "kind": "chapter", "sequence": 32, "number": 10, "location": "lines 10475-12216", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "snippets": [ "... ual inductive reactance; xCi = 4000 ohms = primary condensive reactance of the condenser shunting the break of the interrupter in the battery circuit, and xC2 = 6000 ohms = secondary condensive reactance, due to the capacity of the terminals and the high tension winding. Substituting these values, we have BI = 10 volts i0 = 25 amp. rt = 0.4 ohm xl = 10 ohms xCi = 4000 ohms r2 = 0.2 ohm x2 = 10 ohms xC2 = 6000 ohms xm = 8 ohms. (69) MUTUAL INDUCTANCE 165 These values in equation (61) give / (a) = ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-40", "section_label": "Chapter 4: Arc Rectification", "section_title": "Arc Rectification", "kind": "chapter", "sequence": 40, "number": 4, "location": "lines 17755-19259", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "snippets": [ "... ally withdrawing the terminals derive the energy of the arc flame by means of the current, from the electric circuit, as is done in practically all arc lamps. Or by increasing the voltage across the gap between the terminals so high that the electrostatic stress in the gap repre- sents sufficient energy to establish a path for the current, i.e., by jumping an electrostatic spark across the gap, this spark is fol- lowed by the arc flame. An arc can also be established between two terminals by supplying the arc fla ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-47", "section_label": "Chapter 7: Distribution Of Alternating-Current Density In Conductor", "section_title": "Distribution Of Alternating-Current Density In Conductor", "kind": "chapter", "sequence": 47, "number": 7, "location": "lines 24981-26094", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "snippets": [ "... re calculation and methods of avoiding it, is given in \" Alternating-Current Phe- nomena,\" Chapter XIV, paragraph 133. An appreciable increase of the effective resistance over the ohmic resistance may be expected in the following cases : (1) In the low-tension distribution of heavy alternating cur- rents by large conductors. (2) When using iron as conductor, as for instance iron wires in high potential transmissions for branch lines of smaller power, or steel cables for long spans in transmission lines. (3) ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... . 1 77 79 - .008 267 + .008 057 1 1 80 + .007 957 1 81 - .007 858 0 x> 80 j»fe 79 X sil|s=(-l) + 1 2~2 INDEX PAGE Acceleration constant of traveling wave 466 Air blast, action in oscillating-current generator 75 pressure required in oscillating-current generator 75 Alternating-current circuit and transient term of fundamental frequency 473 distribution in conductor 369 transformer operating oscillating-current generator 87 transmission, equations of traveling wave 477 ..." ] } ] }, { "id": "susceptance", "label": "Susceptance", "aliases": [ "susceptance", "susceptances" ], "total_occurrences": 220, "matching_section_count": 38, "matching_source_count": 8, "source_totals": [ { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 68, "section_count": 9 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 58, "section_count": 8 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 54, "section_count": 7 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 16, "section_count": 2 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 12, "section_count": 4 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 6, "section_count": 3 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 4, "section_count": 3 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 2, "section_count": 2 } ], "section_hits": [ { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-10", "section_label": "Chapter 10: Resistance And Reactance Of Transmission", "section_title": "Resistance And Reactance Of Transmission", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6993-9766", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-10/", "snippets": [ "... s, by varying the admittance, Y = g — jh, of the receiver circuit. The conductance, g, of the receiver circuit depends upon the consumption of power — that is, upon the load on the circuit — and thus cannot be varied for the purpose of regu- lation. Its susceptance, b, however, can be changed bj' shunt- ing the circuit with a reactance, and will be increased by a shunted inductive reactance, and decreased by a shunted con- densive reactance. Hence, for the purpose of investigation, the receiver circuit can be assume ...", "... unted inductive reactance, and decreased by a shunted con- densive reactance. Hence, for the purpose of investigation, the receiver circuit can be assumed to consist of two branches, a conductance, g, — the non-inductive part of the circuit — shunted by a susceptance, h, which can be varied without expenditure of energy. The two components of current can thus be considered separately, the energy component as deter- 78 TRANSMISSION LINES 79 mined by the load on the circuit, and the wattless component, which can b ...", "... ; efficiency of transmission, (Curve III). The same quantities for a non-inductive line of resistance, To = 2.5 ohms, Xo = 0, are shown in Curves IV, V, and VI. 2. Maximum Power Supplied over an Inductive Line 68. If the receiver circuit contains the susceptance, b, in addition to the conductance, g, its admittance can be written thus: Y = g - jh, y = Vg^ + b^. Then, current, /o = EY; Impressed voltage, E^ =^ E -\\- IqZq = £\"(1 + YZq). Hence, voltage at receiver terminals, p, _ __j^0 Eq . ^ ~ 1 + FZo \" ( ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-09", "section_label": "Chapter 9: Resistance And Reactance Of Transmission Lines", "section_title": "Resistance And Reactance Of Transmission Lines", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 5334-6956", "status": "candidate", "occurrence_count": 23, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "snippets": [ "... by varying the admittance, Y = g -f jb, of the receiver circuit. The conductance, gy of the receiver circuit depends upon the consumption of power, — that is, upon the load on the circuit, — and thus cannot be varied for the purpose of reg- ulation. Its susceptance, b, however, can be changed by shunting the circuit with a reactance, and will be increased by a shunted inductance, and decreased by a shunted con- densance. Hence, for the purpose of investigation, the 84 ALTERNATING-CURRENT PHENOMENA. receiver circ ...", "... decreased by a shunted con- densance. Hence, for the purpose of investigation, the 84 ALTERNATING-CURRENT PHENOMENA. receiver circuit can be assumed to consist of two branches, a conductance, g, — the non-inductive part of the circuit, — shunted by a susceptance, b, which can be varied without expenditure of energy. The two components of current can thus be considered separately, the energy component as determined by the load on the circuit, and the wattless component, which can be varied for the purpose of regu- ...", "... \\y n& 100 1 cu ^RE NT N L !NE AMF ERE s \\ 10 20 30 40 50 60 70 80 Fig. 57. Non-inductive Receiver Circuit Supplied Over Inductive Line. 2.) Maximum Power Supplied over an Inductive Line. 60. If the receiver circuit contains the susceptance, b, in addition to the conductance, g, its admittance can be written thus : — Then — current, Impressed E.M.F., /„ = E Y; E0 = E + I0Z0 == E (1 + KZ0). 88 AL TERNA TING-CURRENT PHENOMENA. Hence — E.M.F. at receiver terminals, 1 + FZ0 (1 + r ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-09", "section_label": "Chapter 9: Kbsistanci: And Kbactance Of Transmission Iine8", "section_title": "Kbsistanci: And Kbactance Of Transmission Iine8", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 6371-8268", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "snippets": [ "... by varying the admittance, Y = g + Jb, of the receiver circuit. The conductance, g, of the receiver circuit depends upon the consumption of power, — that is, upon the load on the circuit, — and thus cannot be varied for the purpose of reg- ulation. Its susceptance, by however, can be changed by shunting the circuit with a reactance, and will be increased by a shunted inductance, and decreased by a shunted con- densance. Hence, for the purpose of investigation, the 84 AL TERN A TIXG-CURRENT PHENOMENA, [§ 68 rece ...", "... d by a shunted con- densance. Hence, for the purpose of investigation, the 84 AL TERN A TIXG-CURRENT PHENOMENA, [§ 68 receiver circuit can be assumed to consist of two branches, a conductance, g^ — the non-inductive part of the circuit, — shunted by a susceptance, by which can be varied without expenditure of energy. The two components of current can thus be considered separately, the energy component as determined by the load on the circuit, and the wattless component, which can be varied for the purpose of regu- ...", "... ^^ 35-ffi\". . J^ ^-^ ^ Ss- t N, r^™ . / \\^\\a» T ^^»» , / .„,.,,„uL.: ,....,.„ ^r'\" n^ S7. Uan-lnAatliit Mtttlatr t It Suppliti Ootr /ndMt/M U 2.) Maximnm Pomer Snpplitd over an Inductive Line. 60. If the receiver circuit contains the susceptance, b, in addition to the conductance, g, its admittance can be written thus: — Then — current, /„ = EY\\ Impressed E.M.F., E, = B ■\\- I„Z, = £ (1 + l'-?.)- 88 AL TERN A TING-CURRENT PHENOMENA. [§61 Hence — E.M.F. at receiver terminals, 1 + KZ, ( ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-08", "section_label": "Chapter 8: Admittance, Conductance, Susceptance", "section_title": "Admittance, Conductance, Susceptance", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 4088-4673", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-08/", "snippets": [ "CHAPTER VIII ADMITTANCE, CONDUCTANCE, SUSCEPTANCE 48. If in a continuous-current circuit, a number of resistances, Ti, r2, ?'3, . . ., are connected in series, their joint resistance, R, is the sum of the individual resistances, K = ri + r2 + ra + . . . If, however, a number of resistances are connecte ...", "... tance of a number of series-connected resistances is equal to the sum of the individual resistances; the joint conduct- ance of a number of parallel-connected conductances is equal to the sum of the individual conductances. 64 ADMITTANCE, CONDUCTANCE, SUSCEPTANCE 55 49. In alternating-current circuits, instead of the term resist- ance we have the term impedance, Z = r -\\- jx, with its two components, the resistance, r, and the reactance, x, in the formula of Ohm's law, E = IZ. The resistance, r, gives the compone ...", "... the current, in the equation of Ohm's law, I =YE ={g- jh)E, and the component, h, which represents the coefficient of current in quadrature with the e.m.f., or wattless or reactive component, hE, of the current. g is called the conductance, and h the susceptance, of the cir- cuit. Hence the conductance, g, is the power component, and 56 ALTERNATING-CURRENT PHENOMENA the susceptance, h, the wattless component, of the admittance, Y = g ~ jb, while the numerical value of admittance is y = Vg' + h^; the resist ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-07", "section_label": "Chapter 7: Admittance, Conductance, Susceptance", "section_title": "Admittance, Conductance, Susceptance", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 3132-3576", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-07/", "snippets": [ "CHAPTER VII. ADMITTANCE, CONDUCTANCE, SUSCEPTANCE. 38. If in a continuous-current circuit, a number of resistances, ?\\, r%, r3, . . . are connected in series, their joint resistance, R, is the sum of the individual resistances If, however, a number of resistances are connected in multiple or in parall ...", "... series connection, and the use of the reciprocal term conductance in parallel connections ; therefore, The joint resistance of a number of series-connected resis- tances is equal to the sum of the individual resistances ; the ADMITTANCE, CONDUCTANCE, SUSCEPTANCE. 53 joint conductance of a number of parallel-connected conduc~ tances is equal to the sum of the individual conductances. 39. In alternating-current circuits, instead of the term resistance we have the term impedance, Z = r —Jx, with its two component ...", "... hase with the E.M.F., or energy current, gEt in the equation of Ohm's law, — and the component b, which represents the coefficient of current in quadrature with the E.M.F., or wattless com- ponent of current, bE. g is called the conductance, and b the susceptance, of the circuit. Hence the conductance, g, is the energy com- ponent, and the susceptance, b, the wattless component, of the admittance, Y = g -f jb, while the numerical value of admittance is — y = Vr1 + P ; the resistance, r, is the energy componen ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-07", "section_label": "Chapter 7: Admittance, Conductance, Susceftance", "section_title": "Admittance, Conductance, Susceftance", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 3546-3871", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-07/", "snippets": [ "... connection, and the use of the reciprocal term conductance in parallel connections ; therefore, The joint resistance of a number of series -connected resis- tances is equal to the sum of the individual resistances ; the § 30] ADMITTANCE, CONDUCTANCE, SUSCEPTANCE. 53 joint conductance of a number of parallel-connected conduc- tances is equal to the sum of the individual conductances, 39. In alternating-current circuits, instead of the term resistance we have the term impedance , Z = r —jx, with its two componen ...", "... nent ^, which represents the coefficient of current in quadrature with the K.M.F., or wattless com- ponent of current, bE, g may be called the conductance^ and b the susceptanccy of the circuit. Hence the conductance, g^ is the energy component, and the susceptance, by the wattless component, of the admittance, Y = g -\\-jby while the numerical value of admittance is — the resistance, r, is the energy component, and the reactance^ Xy the wattless component, of the impedance, Z = r — jx\\ the numerical value of imped ...", "... the resistance, but depends upon the resistance as well as upon the reactance. Only when the reactance ^ = 0, or in continuous-current circuits, is the conductance the reciprocal of resistance. Again, only in circuits with zero resistance (r = 0) is the susceptance the reciprocal of reactance ; otherwise, the susceptance depends upon reactance and upon resistance. The conductance is zero for two values of the resistance : — 1.) If r = oc , or ^ = 00 , since in this case no current passes, and either component of t ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-15", "section_label": "Chapter 15: Constant-Voltage Series Operation", "section_title": "Constant-Voltage Series Operation", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 27996-29301", "status": "candidate", "occurrence_count": 14, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-15/", "snippets": [ "... on the same circuit, from constant-voltage supply. 156. Let n lamps of voltage, ei, and current, ii, thus conductance ff = j^ (1) ei be connected in series into a circuit of supply voltage, eo = nei (2) and each lamp be shunted by a reactance of susceptance, b. In each consuming device, comprising lamp and reactance, the admittance thus is, vectorially, Yi^=g^jb (3) if, then, / = current in the series circuit, the voltage consumed by the device comprising lamp and reactance, thus is in a consuming de ...", "... om p = or full-load, to p = 1 or no-load, and no value of shunted reactance, 6, exists, which maintains constant current. With de- creasing load, the current, f i, decreases the slower, the higher 6 is, that is, the more current is shunted by the reactive susceptance, 6, and the poorer therefore the power-factor is. Thus shunted constant reactance can not give constant-voltage regulation. However, with 6 = 0.2 gf, at no-load the shunted reactance would get five times as much current as at load, and thus have five ...", "... however, is not feasible, except by making the reactance abnormally large and therefore uneconomical. In general, long before five times normal voltage is reached, magnetic saturation will have occurred, and the reactance thereby decreased, that is, the susceptance, 6, increased, as more fully dis- cussed in Chapter VIII. This actual condition would correspond to a value, 6i, of the shunted susceptance when shunted by the lamp^ and a different, higher value, 62, of the shunted susceptance when the lamp is burned o ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... and the E.M.F. induced in the primary circuit by the secon- dary current, /^ is £= ^^/; or, expanded, (V + ^V n^ + xi') ' Hence, ^ = —-^ — ^- = effective conductance of mutual inductance ; r,» + jf« — »f », Xi b = — ^-^^^ — ■* = effective susceptance of mutual inductance. The susceptance of mutual inductance is negative, or of opposite sign from the susceptance of self-inductance. Or, Mutual itidtutance consumes energy and decreases the self- inductatice. Dielectric and Electrostatic Phenomena, ...", "... ircuit by the secon- dary current, /^ is £= ^^/; or, expanded, (V + ^V n^ + xi') ' Hence, ^ = —-^ — ^- = effective conductance of mutual inductance ; r,» + jf« — »f », Xi b = — ^-^^^ — ■* = effective susceptance of mutual inductance. The susceptance of mutual inductance is negative, or of opposite sign from the susceptance of self-inductance. Or, Mutual itidtutance consumes energy and decreases the self- inductatice. Dielectric and Electrostatic Phenomena, 98. While magnetic hysteresis and eddy c ...", "... V n^ + xi') ' Hence, ^ = —-^ — ^- = effective conductance of mutual inductance ; r,» + jf« — »f », Xi b = — ^-^^^ — ■* = effective susceptance of mutual inductance. The susceptance of mutual inductance is negative, or of opposite sign from the susceptance of self-inductance. Or, Mutual itidtutance consumes energy and decreases the self- inductatice. Dielectric and Electrostatic Phenomena, 98. While magnetic hysteresis and eddy currents can be considered as the energy component of inductance, cori- den ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "section_label": "Chapter 14: Dielectric Losses", "section_title": "Dielectric Losses", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "... very low) and specific capacity or permittivity k, if: I = thickness of the dielectric, A = area or cross-section, e = impressed alternating-current voltage, effective value, the dielectric capacity of the material is: JcA ^ ~~ I and the capacity susceptance: 152 ALTERNATING-CURRENT PHENOMENA hence the current passing through the dielectric as capacity- current or \"displacement current,\" is: ^ ^^ 2 7r//cA iQ = eo — 2 TTjCe = — -. — e The conductance of the dielectric is: yA hence, the current, con ...", "... r of the dielectric, and 72, k-z, h, Ao the corresponding values of the second layer. It is then : yA g = -y- = electric conductance kA C = -J- = electrostatic capacity of the layer of dielectric, hence: 2 irfk A b = 2irfC = — J — = capacity susceptance, and (1) 154 AL TERN A TING-C URREN T PHENOMENA Y = g -\\- jh = admittance, thus : Z =y = r — jx = impedance, where: 9 r = ^ = vector resistance (not ohmic resistance, but energy component of impedance, T see paragraph 89.) X = r = ...", "... X2 Substituting now for the impedance quantities Z= r — jx, which have no direct physical meaning in the dielectric field, the admittance quantities Y = g -{- jh, which have the physical meaning that g is the effective ohmic conductance, b the capacity susceptance, it is: g negligible compared with h and y, and b = y. Thus, by (2) : . ebM _ 2x/CiC2e ' ~ 61 + 62 ~ C1 + C2 ^ ^ hence proportional to the frequency /: (61 + b.y (Ci + c,r hence, the loss of power by current leakage in the dielectric in this ca ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-17", "section_label": "Theory Section 17: Impedance and Admittance", "section_title": "Impedance and Admittance", "kind": "theory-section", "sequence": 17, "number": 17, "location": "lines 6814-7380", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-17/", "snippets": [ "... impedance z — - with its components, I? the resistance and reactance, its reciprocal can be introduced. e \" z ' which is called the admittance. The components of the admittance are called the conduc- tance and the susceptance. Resolving the current i into a power component i\\ in phase with the e.m.f. and a wattless component iz in quadrature with the e.m.f., the quantity i\\_ _ power current, or current in phase with e.m.f. e e.m.f. . = ...", "... e.m.f., the quantity i\\_ _ power current, or current in phase with e.m.f. e e.m.f. . = 9 is called the conductance. The quantity _*2_ _ reactive current, or current in quadrature with e.m.f. e e.m.f. is called the susceptance of the circuit. The conductance represents the current in phase with the IMPEDANCE AND ADMITTANCE 101 e.m.f., or power current, the susceptance the current in quad- rature with the e.m.f., or reactive current. Conductance ...", "... active current, or current in quadrature with e.m.f. e e.m.f. is called the susceptance of the circuit. The conductance represents the current in phase with the IMPEDANCE AND ADMITTANCE 101 e.m.f., or power current, the susceptance the current in quad- rature with the e.m.f., or reactive current. Conductance g and susceptance b combined give the admittance y = Vg2 + 62; (7) or, in symbolic or vector representation, Y = g - jb. (8) Thus Ohm's ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... ents, 112 admittance, 137 coefficient, 138 conductance, 137 in conductor, 144 loss with distorted wave, 377 of power, 136 Effective circuit constants, 168 Effective circuit conductance, 111 power, 180 reactance, 112 resistance, 2, 5, 9, 111 susceptance, 112 value of wave, 11 in polar diagram, 53 Efficiency of circuit with inductive line, 88, 95 induction motor, 234 Electrostatic, see Dielectric E.m.f. of self-induction, 123 Energy distance of dielectric field, 165 flow in polyphase system, 406 an ...", "... 5 Resolution of sine waves, 31 Resonance of condenser with dis- torted wave, 387 by harmonics, 373 Ring connection of polyphase sys- tem, 416 current in polyphase system, 417 voltage in polyphase system, 417 Rise of voltage of circuit by shunted susceptance, 94 Rotating field of symmetrical poly- phase system, 401 Ruhmkorff coil, 7 Saturation, magnetic, induction gen- erator, 238 Saw-tooth wave, 370 Screening effect of eddy currents, 142 Secondary impedance of trans- former, 198 Self-excitation of in ...", "... duction motor, 238 Star connection of polyphase system, 415 current in polyphase system, 417 voltage in polyphase system, 417 Starting devices of single-phase in- duction motor, 245 torque of induction motor, 223 single-phase induction motor, 252 Susceptance, 55 of circuit with inductive line, 82 480 INDEX Susceptance, effective, 112 Susceptivity, dielectric, 153, 160 Symbolic expression of power, 181 Symmetrical polyphase system, 396 Synchronizing power of alternators, 294 Synchronous condenser ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "... ircuit by the secon- dary current, 7l is or, expanded, Y zr j~. 2 xm^ JXm 2 _i_ r 2 r2 i JT T^ ^i \"l \" •* 2 Hence, the E.M.F. consumed thereby effective resistance of mutual inductance ; ^ = effective reactance of mutual inductance. The susceptance of mutual inductance is negative, or of opposite sign from the reactance of self-inductance. Or, Mutual inductance consumes energy and decreases the self- inductance. Dielectric and Electrostatic Phenomena. 98. While magnetic hysteresis and eddy curren ...", "... con- 146 AL TERNA TING-CURRENT PHENOMENA. ditions of alternating-current condensers, — then it is pro- portional to the square of the E.M.F., that is, the effective conductance, g, due to dielectric hysteresis is a constant ; and, since the condenser susceptance, — b= b', is a constant also, — unlike the magnetic inductance, — the ratio of con- ductance and susceptance, that is, the angle of difference of phase due to dielectric hysteresis, is a constant. This I found proved by experiment. This would mean that th ...", "... ortional to the square of the E.M.F., that is, the effective conductance, g, due to dielectric hysteresis is a constant ; and, since the condenser susceptance, — b= b', is a constant also, — unlike the magnetic inductance, — the ratio of con- ductance and susceptance, that is, the angle of difference of phase due to dielectric hysteresis, is a constant. This I found proved by experiment. This would mean that the dielectric hysteretic admittance of a condenser, Y=g+jb=g-jb', where : g = hysteretic conductance, b' = ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-12", "section_label": "Chapter 12: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 10718-13483", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-12/", "snippets": [ "... ch way as to represent a larger expenditure of power. In dealing with alternating-current circuits, it is necessarj-, therefore, to substitute everywhere the values \"effective re- sistance,\" \"effective reactance,\" \"effective conductance,\" and \"effective susceptance,\" to make the calculation applicable to general alternating-current circuits, such as inductive reactances containing iron, etc. While the true ohmic resistance is a constant of the circuit, depending only upon the temperature, but not upon the e.m.f., ...", "... g is negligible compared with b, and b is practically equal to y. 132 ALTERNATING-CURRENT PHENOMENA Therefore, in an electric circuit containing iron, but forming an open magnetic circuit whose air-gap is not less than Koo the length of the iron, the susceptance is practically constant and equal to the admittance, so long as saturation is not yet ap- proached, or, , (R. / b ^ J, or: .: = ^-- The angle of hysteretic advance is small, and the hysteretic con- ductance is JC 0 ~ ^0.4/0.6' The current wave ...", "... icient of hysteresis, the loss of power by hysteresis due to molecular magnetic friction is P = vfVB'-'; P hence the hysteretic conductance is g = i^, and variable with the e.m.f., E. The angle of hysteretic advance is 9 . sm a = - , y the susceptance. b = Vif- - g^; the effective resistance, ^ _ fiL. and the reactance, h 103. As conclusions, we derive from this chapter the following: 1. In an alternating-current circuit surrounded by iron, the current produced by a sine wave of e.m.f. is not ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-10", "section_label": "Chapter 10: F", "section_title": "F", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 8269-10499", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "snippets": [ "... nductance of the circuit. § 733 EFFECTIVE RESISTANCE AND REACTANCE. 105 In the same way, the value, _ Wattless component of E.M.F. Total current is the effective reactance, and , _ Wattless compo nent of current ■\" Total E.M.F. is the effective susceptance of the circuit. While the true ohmic resistance represents the expendi- ture of energy as heat inside of the electric conductor by a current of uniform density, the effective resistance repre- sents the total expenditure of energy. Since, in an alterna ...", "... h way as to represent a larger expenditure of energy. In dealing with alternating-current circuits, it is necessary, therefore, to substitute everywhere the values \"effective re- sistance,\" \"effective reactance,\" \"effective conductance,'* and \" effective susceptance,\" to make the calculation appli- cable to general alternating-current circuits, such as ferric inductances, etc. While the true ohmic resistance is a constant of the circuit, depending only upon the temperature, but not upon the E.M.F., etc., the effect ...", "... sin a = .035 to sin a = .064. Thus g is negligible compared with ^, and b is practically equal to y. Therefore, in an electric circuit containing iron, but forming an open* magnetic circuit whose air-gap is not less than yij> the length of the iron, the susceptance is practi- cally constant and equal to the admittance, so long as saturation is not yet approached, or, . (Rrt5 N b = — , or : a: = — . N (Rtf The angle of hysteretic advance is small, below 4**, and the hysteretic conductance is. The current wav ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "section_label": "Chapter 10: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "... ffective conductance of the circuit. EFFECTIVE RESISTANCE AND REACTANCE. 105 In the same way, the value, _ Wattless component of E.M.F. Total current is the effective reactance, and , _ Wattless component of current TotafE.M.F. is the effective susceptance of the circuit. While the true ohmic resistance represents the expendi- ture of energy as heat inside of the electric conductor by a current of uniform density, the effective resistance repre- sents the total expenditure of energy. Since, in an alterna ...", "... ch way as to represent a larger expenditure of energy. In dealing with alternating-current circuits, it is necessary, therefore, to substitute everywhere the values \"effective re- sistance,\" \"effective reactance,\" \"effective conductance,\" and \" effective susceptance,\" to make the calculation appli- cable to general alternating-current circuits, such as induc- tances, containing iron, etc. While the true ohmic resistance is a constant of the circuit, depending only upon the temperature, but not upon the E.M.F., etc. ...", "... om sin a = .035 to sin a = .064. Thus g is negligible compared with b, and b is practically equal to j. Therefore, in an electric circuit containing iron, but forming an open magnetic circuit whose air-gap is not less than T^ the length of the iron, the susceptance is practi- cally constant and equal to the admittance, so long as saturation is not yet approached, or, b = = 4- Instance* = 4, bc = 20 X 10 ~5, E0 = 10,000 V. Hence / = 55.5, *0 = 222, b0 = .0111, 7j = 70.7, 70 = .00707 e. 122. An interesting application of this method is the determination of the natural period of a transmission line ; ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-01", "section_label": "Chapter 1: Speed Control Of Induction Motors", "section_title": "Speed Control Of Induction Motors", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1368-3542", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-01/", "snippets": [ "... agnetic circuit, are independent of the frequency, and vary relatively little with the magnetic density and thus the current, over a wide range,1 thus may approxi- mately be assumed as constant. That is, the hysteretic con- ductance is proportional to the susceptance : g' = V tan a. ((>) Thus, the exciting admittance, of a closed magnetic circuit of negligible resistance and negligible eddy-current losses, at the frequency of slip, «, is given by: Y' = g' - jb' = V (tan a - j) = - J = (tan a - j) (7) 8 8 8 1 ...", "... losses: very thick laminations or solid iron, or we directly provide a closed high-resistance secondary wii-ing around the magnetic circuit, which is inserted into the ir.d lotion-motor secondary for increasing the starting torque. SPEED CONTROL 9 The susceptance of the magnetic circuit obviously follows the same law as when there are no eddy currents. That is: &' = 6- (10) s At a given current, ih energizing the magnetic circuit, the in- duced voltage, and thus also the voltage producing the eddy currents, i ...", "... urns per pole are inverse proportional to the number of poles : N' n N n' In consequence hereof, the exciting currents, at the name impressed voltage, are proportional to the square of the number of poles: t'oo _ n'2 too n2 ' and thus the exciting susceptances are proportional to the square of the number of poles : b n2' The magnetic flux per pole remains the same, and thiiM the magnetic-flux density, and with it the hystereHin Iohh in the primary core, remain the same, at a change of the number of poles. T ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "... f., in quadrature with current, and = current X effective reactance, or x; power component of current, in phase with e.m.f., and = e.m.f. X effective conductance, or g; reactive component of current, in quadrature with e.m.f., and = e.m.f. X effective susceptance, or b. In many cases the exact calculation of the quantities, r, x, g, h, is not possible in the present state of the art. In general, r, x, g, b, are not constants of the circuit, but depend — besides upon the frequency — more or less upon e.m.f., curr ...", "... approximation of one; or, three condensers shunted across the line. 130. {A) Line capacity represented hy one condenser shunted across middle of line. Let Y = g — jh = admittance of receiving circuit; Z = r -\\- jx = impedance of line; he = condenser susceptance of line. iEo Fig. 101. Denoting in Fig. 101. the e.m.f., and current in receiving circuit by E, 7, the e.m.f. at middle of line by E' , the e.m.f., and current at generator by Ea, h; we have, I = E(g-jh); E' = E + \"^i^/ pJi , (r + jx) (g - ...", "... radiation. Currents consumed in quadrature to the e.m.f., E, and = bE, being wattless, and due to: Capacity and electrostatic influence. Hence we get four constants: Effective resistance, r, Effective reactance, x, Effective conductance, g, Effective susceptance, — h, per unit length of line, which represents the coefficients, per unit lenght of line, of e.m.f. consumed in phase with current; e.m.f. consumed in quadrature with current; current consumed in phase with e.m.f.; current consumed in quadrature with ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-109", "section_label": "Apparatus Section 3: Induction Machines: Single -phase Induction Motor", "section_title": "Induction Machines: Single -phase Induction Motor", "kind": "apparatus-section", "sequence": 109, "number": 3, "location": "lines 20428-21157", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-109/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-109/", "snippets": [ "... two impedances to the third terminal of a three- phase induction motor, which is connected with its other two terminals to the single-phase lines, as shown diagrammatically in Fig. 184, for a conductance a and an inductive susceptance -jo,. This starting device, when using an inductance and a conden- sance of proper size, can be made to give an apparent starting torque efficiency superior to that of the polyphase induction motor. Usually a resistance a ...", "... 84, M represents a three-phase induction motor of which two terminals, 1 and 2, are connected to single-phase mains and the terminal 3 to the common connection of a conduct- ance a (that is, a resistance - j and an equal susceptance — ja (thus a reactance H — ) connected in series across the mains. Let Y = g — jb = total admittance of motor between termi- INDUCTION MACHINES 337 nals 1 and 2 while at rest. We then have HY = total admit- tance ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "section_title": "Dibtbisnted Capacity, Inductance, Besistance, And", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "... n of one ; viz., three condensers shunted across the line. 104. A.) Line capacity represented by one condetiser shunted across middle of line. Let — Y == g -{- j'b = admittance of receiving circuit; z =i r — j X = impedance of line ; be = condenser susceptance of line. §105] DISTRIBUTED CAPACITY. 15S Denoting, in Fig. 84, the E.M.F., viz., current in receiving circuit by E^ /, the E.M.F. at middle of line by E\\ the E.M.F., viz., current at generator by EoyJo\\ t r n Fig. 84. Capacity Shmrttd acro ...", "... is. Currents consumed in quadrature to the E.M.F., E, and = bE, being wattless, and due to : Capacity and Electrostatic influence. Hence we get four constants : — Effective resistance, r. Effective reactance, x. Effect iv'e conductance, g^ Effective susceptance, ^ = — b^y 158 ALTERJ^ATING-CURRENT PHENOMENA. [§§108,109 per unit length of line, which represent the coefficients, per unit length of line, of E.M.F. consumed in phase with current ; E.M.P\\ consumed in quadrature with current ; Current consumed in ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-14", "section_label": "Chapter 14: The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "section_title": "The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14089-14918", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "snippets": [ "... sonable limits. An iron- clad construction again greatly increases the self-induction of primary and secondary circuit. Thus the induction motor is a transformer of large magnetizing current and large self-induction ; that is, comparatively large primary susceptance and large reactance. The general alternating-current transformer transforms between electrical and mechanical power, and changes not only E.M.Fs. and currents, but frequencies also. 132. Besides the magnetic flux interlinked with both primary and secon ...", "... mechanical power). Let Wo = number of primary turns in series per circuit ; fix = number of secondary turns in series per circuit ; a = — = ratio of turns ; Vq = go +y^o = primary admittance per circuit ; where go '= effective conductance ; do = susceptance ; Zq == Tq — jXo = internal primary impedance per circuit, where To = effective resistance of primary circuit ; Xo = reactance of primary circuit ; Zii = ri — jxi = internal secondary impedance per circuit at standstill, or for x = 1, where ri = ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-15", "section_label": "Chapter 15: The General Alternating-Current Transformer Or Frequency Converter", "section_title": "The General Alternating-Current Transformer Or Frequency Converter", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 12683-13648", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "snippets": [ "... limits. An iron- clad construction again greatly increases the self-induction of primary and secondary circuit. Thus the induction motor is a transformer of large magnetizing current and large self-induction; that is, comparatively large primary exciting susceptance and large reactance. The general alternating-current transformer transforms between electrical and mechanical power, and changes not only E.M.Fs. and currents, but frequencies also, and may therefore be called a \"frequency converter.\" Obviously, it also ...", "... er). Let «0 = number of primary turns in series per circuit ; /?! = number of secondary turns in series per circuit ; a = — = ratio of turns ; «i Y0 =£\"0 H~./A) = primary exciting admittance per circuit; where gQ = effective conductance ; b0 = susceptance ; Z0 = r0 —jx0 = internal primary self-inductive impedance per circuit, where r0 = effective resistance of primary circuit ; jr0 = reactance of primary circuit ; Zu = TI — jxv = internal secondary self -inductive impedance per circuit at standsti ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... (^ - r?-^.) +('• - «^ - rTT*=^«)* x — Xe -J 1 + a 2 (^-m\"») +(''-''^-rf^^') dec a. 189. Thus in complex quantities, for oscillating currents, we have: conductance, a r — ax — g = 1 +a' X, (^-rf^)+(''-\"^-rTT^^')\" susceptance. X — X, b = 1 + a2 (^-i^2)+(^-«^-rf^2^0 1> .admittance, in absolute values. y = Vff* + 6* = V (* - rf^^) '+{r-os- rh^^ 350 ELECTRIC CIRCUITS in symbolic expression, Y = S-3b = J. .2 , a TT • Since the impedance is we have ...", "... of arc, 175 of synchronous machine, 215 curves of arc, 36, 168 of pyroelectric conductor, 20 Stable magnetic characteristic, 54 Storage battery, 8 Streak conduction of pyroelectric conductor, 18, 42 Stream voltage of arc, 35 of Geissler tube, 29 Susceptance with oscillating cur- rents, 350 Symmetrical wave, 114 Synchronizing force and power, 210 Synchronous reactance of alter- nator, 236 machines, hunting, 208 reactance, 232 motor tending to instability, 164 T-connection of constant current transfo ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... drature with tJw e.m.f., E, and = bE, being reactive, and due to capacity and electrostatic influence. Hence we get four constants per unit length of line, namely: Effective resistance, r; effective reactance, x; effective conduc- tance, g, and effective susceptance, b = - bc (bc being the absolute value of susceptance). These constants represent the coefficients per unit length of line of the following: e.m.f. consumed in phase with the current; e.m.f. consumed in quadra- ture with the current; current consumed in p ...", "... and due to capacity and electrostatic influence. Hence we get four constants per unit length of line, namely: Effective resistance, r; effective reactance, x; effective conduc- tance, g, and effective susceptance, b = - bc (bc being the absolute value of susceptance). These constants represent the coefficients per unit length of line of the following: e.m.f. consumed in phase with the current; e.m.f. consumed in quadra- ture with the current; current consumed in phase with the e.m.f., and current consumed in quadratu ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-04", "section_label": "Chapter 5: Methods Of Approximation", "section_title": "Methods Of Approximation", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 15156-16482", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-04/", "snippets": [ "... quantities or general numbers; Zo^ro—jxo, the line impedance per unit length (for instance, per mile); Yo=^go—jhQ = Hne admittance, shunted, per unit length; then, rn is the ohmic effective resistance; .To, the self-inductive reactance; &o, the condensive susceptance, that is, wattless charging current divided by volts, and go = energy component of admit- tance, that is, energy component of charging current, divided by volts, per unit length, as, per mile. Considering a line element dl, the voltage, dE, consumed by ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... t convenient way usually is the arrangement in tabular form. As example, consider the problem of calculating the regula- tion of a 6(),000-volt transmission line, of r = 60 ohms resist- ance, a;= 135 ohms inductive reactance, and 6 = 0.0012 conden- sive susceptance, for various values of non-inductive, inductive, and condensive load. Starting with the complete equations of the long-distance transmission line, as given in \"Theory and Calculation of Transient Electric Phenomena and Oscillations,\" Section III, paragr ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-108", "section_label": "Apparatus Section 2: Induction Machines: Polyphase Induction Motor", "section_title": "Induction Machines: Polyphase Induction Motor", "kind": "apparatus-section", "sequence": 108, "number": 2, "location": "lines 19166-20427", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-108/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-108/", "snippets": [ "... r de- pends upon two complex imaginary constants, Y and Z, or four real constants, g, 6, r, x, the same terms which characterize the stationary alternating-current transformer on non-inductive load. Instead of conductance g, susceptance 6, resistance r, and react- ance x, as characteristic constants may be chosen: the absolute exciting admittance y = \\/g2 -f- &2; the absolute self-inductive impedance z — \\/r2-}-x2', the power-factor of admittance 0 = g/y, ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-20", "section_label": "Theory Section 20: Nomenclature", "section_title": "Nomenclature", "kind": "theory-section", "sequence": 20, "number": 20, "location": "lines 7991-8291", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-20/", "snippets": [ "... t Electrical I, i. . Potential difference Electromotive force Current Ampere Electrical R,r Resistance Ohm Electrical x Reactance Ohm Electrical Z,z... Impedance Ohm Electrical a Conductance Mho Electrical b Susceptance Mho Electrical Y,y p Admittance Resistivity Mho Ohm-centimeter Electrical Electrical 7 $ Conductivity Magnetic flux Mho-centimeter Line; kiloline; megaline Electrical Magnetic £....... H Magnetic density Magnetic f ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-20", "section_label": "Chapter 20: Single-Phase Induction Motors", "section_title": "Single-Phase Induction Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 21538-22301", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-20/", "snippets": [ "... a- tion can be secured, that is, the conditions brought about: El = E2 = 6 The starting by condenser in the tertiary circuit, of a three- phase motor, can be considered as a special case of the mono- cyclic starting device, for Yi = 0 and F2 = capacity susceptance. A further extension of the monocyclic starting device is, to use another induction motor, which is running at speed, to supply the quadrature voltage, E3. Thus, if a number of single-phase induction motors are oper- ated near each other, as in the sam ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-27", "section_label": "Chapter 27: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 33011-34776", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-27/", "snippets": [ "... on Induction Motors. To improve the power-factor of the motor and bring it to unity at an output of 500 watts, a condenser capacity is required giving 4.28 amp. leading current at 110 volts, that is, neglecting the power loss in the condenser, capacity susceptance 4.28 110 0.039. In this case, let Is = current input into the motor per delta cir- cuit at slip s, as given in the following table. The total current supplied by the circuit with a sine wave of impressed e.m.f. is /' = 7,-1-4.28 i, power cu ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-35", "section_label": "Chapter 35: Balanced Symmetrical Polyphase Systems", "section_title": "Balanced Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 35, "number": 35, "location": "lines 37453-37957", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-35/", "snippets": [ "... ve-length, 4 I, the number of waves per second, or frequency of oscillation of the line, is f - — and herefrom then follows: hence, for V I Vlc I = 100 miles, V = 186,000 miles per second, L = 0.23 henry, C = 1.26 mf. and the capacity susceptance, 6 = 2 tt/C = 475 X 10-«. Representing, as approximation, the line capacity by a con- denser shunted across the middle of the line We have, impedance of half the line, Z = ^ +j| = 26 + 44johms. Choosing the voltage at the receiving end as zero vecto ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "section_label": "Chapter 30: Quartbr-Fhase System", "section_title": "Quartbr-Fhase System", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... r -^ ax — 1 + tf^ K'-if5)+(— rf?'.)' X — +y 1 +'»* ^FM'^{—.hA dec a* + 288. Thus in complex quantities, for oscillating cur- rents, we have : conductance, r — ajc — a ^ = \\-\\- a^ \" I X — ■ +[r — ax^ Xg 55 susceptance, b = X — 1 + g^ , (\"-riv^) +('•-\"\"-- rf^\"')\"^ admittance, in absolute values, ^ = vV* + />« = v/(\"-i+7^)+(''-''*-iT7»\"')' ■ in symbolic expression, [r — ax -xA +J\\x ^ — -) y=s+jf>=j Y , r,- Since the impedance is Z = ( r — ax Xr ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "... Induction Motors. To improve the power factor of the motor and bring it to unity at an output of 500 watts, a condenser capacity is required giving 4.28 amperes leading current at 110 volts, that is, neglecting the energy loss in the condenser, capacity susceptance In this case, let Is = current input into the motor per delta circuit at slip s, as given in the following table. The total current supplied by the circuit with a sine wave of impressed E.M.F., is /i = ls - 4.28/ energy current and heref rom the p ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-32", "section_label": "Chapter 32: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 25904-27405", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "snippets": [ "... ) -j sin (9 — hence in complex quantities, E = e (cos u> -\\-j sin oi) dec a, + sin OSCILLATING CURRENTS. 505 or, substituting, r — ax — I =E I- dec a. 317. Thus in complex quantities, for oscillating cur- rents, we have : conductance, susceptance, admittance, in absolute values, / o i To 1 in symbolic expression, Y=g+J» 1 + a2/ \\ 1 + a2 ' Since the impedance is Z = ir — ax — we have 506 APPENDIX II. that is, the same relations as in the complex quantities in alternating-curren ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "... ine would have to be redesigned with 70 poles, giving: n = 19, ' * = 0.05, 70 ELECTRICAL APPARATUS With the same rotor diameter of the induction machine, the pole pitch would be increased inverse proportional to the number of poles, and the exciting susceptance decreased with the square thereof, thus giving the constants: Y0 = g -jb = 0.02 - 0.54 j; Z0 = r0+jxo = 0.1 + 0.3j; Zi = ri+jxt = 0.1 + 0.3./. Assuming as synchronous motor synchronous impedance, reduced to full frequency: Z2 = r2 + jx2 = 0.02 + 0.2 ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-11", "section_label": "Chapter 12: Frequency Converter Or General Alternating Current Transformer", "section_title": "Frequency Converter Or General Alternating Current Transformer", "kind": "chapter", "sequence": 11, "number": 12, "location": "lines 14897-17124", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-11/", "snippets": [ "... hanical power). Let: n0 = number of primary turns in series per circuit; nx = number of secondary turns in series per circuit; a = = ratio of turns; Til Y = g — jb = primary exciting admittance per circuit; where: g = effective conductance; b = susceptance; Zq = r0 + jxo = internal primary self-inductive impedance per circuit, where: r0 = effective resistance of primary circuit; Xq = self-inductive reactance of primary circuit; Zn = n + jx\\ = internal secondary self-inductive im- pedance per circuit at ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-32", "section_label": "Chapter 10: Mutual Inductance", "section_title": "Mutual Inductance", "kind": "chapter", "sequence": 32, "number": 10, "location": "lines 10475-12216", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-32/", "snippets": [ "... lly preferable to separate the total reactance z, into the self-inductive reactance, x81 referring to the magnetic flux interlinked with the inducing circuit only, but with no other circuit, and the mutual inductive reactance, xm, usually represented as a susceptance, which refers to the mutual induc- tive component of the total inductance; in which case x = xs + xm. This is not done in the present case. Furthermore it is assumed that the circuits are inductively related to each other symmetrically, or reduced theret ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-43", "section_label": "Chapter 3: The Natural Period Of The Transmission Line", "section_title": "The Natural Period Of The Transmission Line", "kind": "chapter", "sequence": 43, "number": 3, "location": "lines 21721-23178", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "snippets": [ "... dis- tance from the beginning of the line; r = resistance per unit length; x = reactance per unit length = 2 nfL, where L = inductance per unit length; g = conductance from line to return (leakage and discharge into the air) per unit length; b = capacity susceptance per unit length = 2 nfC, where C = capacity per unit length. Neglecting the line resistance and line conductance, r = 0 and g = 0, the line constants a and /?, by equations (14), Chapter II, then assume the form a = 0 and ft = Vxb, (1) and the lin ..." ] } ] }, { "id": "energy-storage-fields", "label": "Energy Storage in Fields", "aliases": [ "energy of the field", "energy stored", "stored energy", "stored in the field" ], "total_occurrences": 213, "matching_section_count": 42, "matching_source_count": 12, "source_totals": [ { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 75, "section_count": 10 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 71, "section_count": 9 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 43, "section_count": 11 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 11, "section_count": 2 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 3, "section_count": 1 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 3, "section_count": 3 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 2, "section_count": 1 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 1, "section_count": 1 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 1, "section_count": 1 }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 1, "section_count": 1 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 1, "section_count": 1 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 557-1002", "status": "candidate", "occurrence_count": 25, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-01/", "snippets": [ "... re phenome- non. While electric power flows over the line A, there is a magnetic field surrounding the line conductors, and an electrostatic field issuing from the line conductors. The magnetic field and the electrostatic or \" dielectric \" field represent stored energy. Thus, during the permanent conditions of the flow of power through the circuit Fig. 3, there is electric energy stored in the space surround- ing the line conductors. There is energy stored also in the genera- tor and in the load ; for instance, the mech ...", "... and an electrostatic field issuing from the line conductors. The magnetic field and the electrostatic or \" dielectric \" field represent stored energy. Thus, during the permanent conditions of the flow of power through the circuit Fig. 3, there is electric energy stored in the space surround- ing the line conductors. There is energy stored also in the genera- tor and in the load ; for instance, the mechanical momentum of the revolving fan in Fig. 1, and the heat energy of the incandescent lamp filaments. The permanent co ...", "... ic field and the electrostatic or \" dielectric \" field represent stored energy. Thus, during the permanent conditions of the flow of power through the circuit Fig. 3, there is electric energy stored in the space surround- ing the line conductors. There is energy stored also in the genera- tor and in the load ; for instance, the mechanical momentum of the revolving fan in Fig. 1, and the heat energy of the incandescent lamp filaments. The permanent condition of the circuit Fig. 3 thus represents not only flow of power, b ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 460-882", "status": "candidate", "occurrence_count": 25, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "snippets": [ "... re phenome- non. While electric power flows over the line A , there is a magnetic field surrounding the line conductors, and an electrostatic field issuing from the line conductors. The magnetic field and the electrostatic or \"dielectric \" field represent stored energy. Thus, during the permanent conditions of the flow of power through the circuit Fig. 3, there is electric energy stored in the space surround- ing the line conductors. There is energy stored also in the genera- tor and in the load ; for instance, the mech ...", "... and an electrostatic field issuing from the line conductors. The magnetic field and the electrostatic or \"dielectric \" field represent stored energy. Thus, during the permanent conditions of the flow of power through the circuit Fig. 3, there is electric energy stored in the space surround- ing the line conductors. There is energy stored also in the genera- tor and in the load ; for instance, the mechanical momentum of the revolving fan in Fig. 1, and the heat energy of the incandescent lamp filaments. The permanent co ...", "... tic field and the electrostatic or \"dielectric \" field represent stored energy. Thus, during the permanent conditions of the flow of power through the circuit Fig. 3, there is electric energy stored in the space surround- ing the line conductors. There is energy stored also in the genera- tor and in the load ; for instance, the mechanical momentum of the revolving fan in Fig. 1, and the heat energy of the incandescent lamp filaments. The permanent condition of the circuit Fig. 3 thus represents not only flow of power, b ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "... al short circuit a quantity of magnetic energy is impressed upon a part of the circuit. This energy then gradually distributes over the circuit, as indicated by the curves B, C, etc., of Fig. 39, that is, moves along the circuit, and the dissipation of the stored energy thus occurs by a flow of power along the circuit. 90 ELECTRIC DISCHARGES, WAVES AND IMPULSES. Such a flow of power must occur in a circuit containing sec- tions of different dissipation constants u. For instance, if in a circuit consisting of an unloa ...", "... ting of an unloaded transformer and a transmission line, as indicated in Fig. 40, at no load on the step-down trans- ^^ Line Transformer Line Fig. 40. former, the high-tension switches are opened at the generator end of the transmission line. The energy stored magnetically and dielectrically in line and transformer then dissipates by a transient, as shown in the oscillogram Fig. 41. This gives the oscillation of a circuit consisting of 28 miles of line and 2500-kw. 100-kv. step-up and step-down transformers, an ...", "... ge, the dis- sipation of power (r and g) relatively small; in the line, the tran- sient is of fairly short duration, as r (and g) are considerable. Left to themselves, the line oscillations thus would die out much more rapidly, by the dissipation of their stored energy, than the transformer oscillations. Since line and transformer are connected together, both must die down simultaneously by the same tran- sient. It then follows that power must flow during the transient from the transformer into the line, so as to have b ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 4745-5520", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "snippets": [ "... al short circuit a quantity of magnetic energy is impressed upon a part of the circuit. This energy then gradually distributes over the circuit, as indicated by the curves B, C, etc., of Fig. 39, that is, moves along the circuit, and the dissipation of the stored energy thus occurs by a flow of power along the circuit. 90 ELECTRIC DISCHARGES, WAVES AND IMPULSES. Such a flow of power must occur in a circuit containing sections of different dissipation constants u. For instance, if a circuit consists of an unloaded tra ...", "... n unloaded transformer and a transmission line, as indicated in Fig. 40, that is, at no load on the step-down trans- ^> Line Transformer Line Fig. 40. former, the high-tension switches are opened at the generator end of the transmission line. The energy stored magnetically and dielectrically in line and transformer then dissipates by a transient, as shown in the oscillogram Fig. 41. This gives the oscillation of a circuit consisting of 28 miles of line and 2500-kw. 100-kv. step-up and step-down transformers, an ...", "... ge, the dis- sipation of power (r and g) relatively small; in the line, the tran- sient is of fairly short duration, as r (and g) are considerable. Left to themselves, the line oscillations thus would die out much more rapidly, by the dissipation of their stored energy, than the transformer oscillations. Since line and transformer are connected together, both must die down simultaneously by the same tran- sient. It then follows that power must flow during the transient from the transformer into the line, so as to have b ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-23", "section_label": "Chapter 1: The Constants Of The Electric Circuit", "section_title": "The Constants Of The Electric Circuit", "kind": "chapter", "sequence": 23, "number": 1, "location": "lines 1317-1992", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "snippets": [ "... t elapse during which the energy of the electric field is stored, and the generator therefore gives more power than consumed in the conductor and delivered at the receiving end; again, the flow of electric energy cannot be stopped instantly, but first the energy stored in the electric field has to be expended. As result hereof, where the flow of electric energy pulsates, as in an alternating- current circuit, continuously electric energy is stored in the field during a rise of the power, and returned to the circuit aga ...", "... flow of electric energy cannot be stopped instantly, but first the energy stored in the electric field has to be expended. As result hereof, where the flow of electric energy pulsates, as in an alternating- current circuit, continuously electric energy is stored in the field during a rise of the power, and returned to the circuit again during a decrease of the power. The electric field of the conductor exerts magnetic and elec- trostatic actions. The magnetic action is a maximum in the direction concen- tric, or approximat ...", "... *n The power consumed in the conductor by its resistance r is Pr = ieh (15) and thus, by equation (4), Pr = tV. (16) That is, when the electric power P = ei (1) exists in a circuit, it is pr = tfr = power lost in the conductor, (16) WM = l— = energy stored in the magnetic field of the circuit, (9) l Ll W K = — = energy stored in the dielectric field of the cir- £t cuit, (14) 8 TRANSIENT PHENOMENA and the three circuit constants r, L, C therefore appear as the components of the energy conversion ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-07", "section_label": "Lecture 7: High Frequency Oscillations And Surges", "section_title": "High Frequency Oscillations And Surges", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3508-3780", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-07/", "snippets": [ "... age ■^ occurs as electrostatic energy, or electrostatic charge due to the voltage on the line (capacity) ; and as electromag- netic energy, or magnetic field of the current in the line (inductance). In the long distance transmission line, both amounts of stored energy are very considerable, and of about equal magnitude; the former varying with the voltage, the latter with the current in the line. Any change of the voltage on the line, or the current in the line, or the relation between volt- age and current, therefore ...", "... ual magnitude; the former varying with the voltage, the latter with the current in the line. Any change of the voltage on the line, or the current in the line, or the relation between volt- age and current, therefore requires a corresponding change of the stored energy; that is, a readjustment of the stored energy e^C in the system, the electrostatic energy and the electro- i'L magnetic energy — — , from the previous to the changed cir- cuit conditions. This readjustment occurs by an oscillation, that is, a series o ...", "... tage, the latter with the current in the line. Any change of the voltage on the line, or the current in the line, or the relation between volt- age and current, therefore requires a corresponding change of the stored energy; that is, a readjustment of the stored energy e^C in the system, the electrostatic energy and the electro- i'L magnetic energy — — , from the previous to the changed cir- cuit conditions. This readjustment occurs by an oscillation, that is, a series of waves of voltage and of current, which grad ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-56", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit", "section_title": "Power And Energy Of The Complex Circuit", "kind": "chapter", "sequence": 56, "number": 7, "location": "lines 33528-34202", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "snippets": [ "... ction of length A' to the rest of the circuit, or received by the section from the rest of the circuit, is proportional to the length of the section, A', to its trans- fer constant, s, and to the sum of the power of main wave and reflected wave. 51. The energy stored by the inductance L of a circuit element dXj that is, in the magnetic field of the circuit, is 'LV dwl =-^~A where U = inductance per unit length of circuit expressed by the distance coordinate A. Since L = the inductance per unit length of circuit, ...", "... 0 + fi-^C8- D2) cos 2 ^ (4 + 0] + 2 [A£e+2sA sin 2 0 (4 - 0 + CDe~2sX sin 2 g (4 + 0] - 2 [(AC - BD) cos 2 04 + (AD + BC) sin 2 g/l] - 2 [(AC + £D) cos 2qt+ (AD - BC) sin 2qt]}. (311) Integrating over a complete period in time gives the effective energy stored in the magnetic field at point A as a w j j. i*u/j 7 7T == ^ I — TT~ Ctfr (A - 2 [(AC - BD) cos 2qX+ (AD + BC) sin 2 ql]}, (312) POWER AND ENERGY OF THE COMPLEX CIRCUIT 517 and integrating over one complete period of distance A, or one complete ...", "... a w j j. i*u/j 7 7T == ^ I — TT~ Ctfr (A - 2 [(AC - BD) cos 2qX+ (AD + BC) sin 2 ql]}, (312) POWER AND ENERGY OF THE COMPLEX CIRCUIT 517 and integrating over one complete period of distance A, or one complete wave length, this gives (313) The energy stored by the inductance L, or in the magnetic field of the conductor, thus consists of a constant part, dl a part which is a function of (X — t) and (X + t), (A2 - B2) cos 2 q (X - t) (C2 - D2) cos 2 q (X + 0] n2g(/l - 0 n2g(yl + 01} , (315) a part ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3721-4369", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-06/", "snippets": [ "LECTURE VI. DOUBLE-ENERGY TRANSIENTS. 24. In a circuit in which energy can be stored in one form only, the change in the stored energy which can take place as the result of a change of the circuit conditions is an increase or decrease. The transient can be separated from the permanent condition, and then always is the representation of a gradual decrease of energy. Even if the stored ene ...", "... red energy which can take place as the result of a change of the circuit conditions is an increase or decrease. The transient can be separated from the permanent condition, and then always is the representation of a gradual decrease of energy. Even if the stored energy after the change of circuit conditions is greater than before, and during the transition period an increase of energy occurs, the representation still is by a decrease of the transient. This transient then is the difference between the energy storage in t ...", "... y, and would be given by v = Vo[l-e~'^). (6) In a system in which energy can be stored in two different forms, as for instance as magnetic and as dielectric energy in a circuit containing inductance and capacity, in addition to the gradual decrease of stored energy similar to that represented by the single-energy transient, a transfer of energy can occur between its two different forms. Thus, if i = transient current, e = transient voltage (that is, the difference between the respective currents and voltages exist- ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 6125-6803", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-09/", "snippets": [ "... ms of such circuits have been shown in the previous lecture. If we have a circuit consisting of sections 1, 2, 3 . . . , of the respective lengths (in velocity measure) Xi, X2, X3 . . . , this entire circuit, when left to itself, gradually dissipates its stored energy by a transient. As function of the time, this transient must decrease at the same rate Uq throughout the entire circuit. Thus the time decrement of all the sections must be Every section, however, has a power-dissipation constant, Ui, U2, U3 . . . , whic ...", "... time, this transient must decrease at the same rate Uq throughout the entire circuit. Thus the time decrement of all the sections must be Every section, however, has a power-dissipation constant, Ui, U2, U3 . . . , which represents the rate at which the stored energy of the section would be dissipated by the losses of power in the section, t , t , t ... But since as part of the whole circuit each section must die down at the same rate e~\"o', in addition to its power-dissipation decrement e\"\"'^, e~\"2< , . . ^ each ...", "... tant: s = Uo-u= -100 +700 -100 -800 The transformer thus dissipates power at the rate U2 = 100, while it sends out power into the other sections at the rate of S2 = 700, or seven times as much as it dissipates. That is, it sup- plies seven-eighths of its stored energy to other sections. The load dissipates power at the rate uz = 1600, and receives power at the rate —s = 800; that is, half of the power which it dissipates is supplied from the other sections, in this case the transformer. The transmission line dissipate ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3287-3955", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "snippets": [ "LECTURE VI. DOUBLE-ENERGY TRANSIENTS. 24. In a circuit in which energy can be stored in one form only, the change in the stored energy which can take place as the result of a change of the circuit conditions is an increase or decrease. The transient can be separated from the permanent condition, and then always is the representation of a gradual decrease of energy. Even if the stored ene ...", "... red energy which can take place as the result of a change of the circuit conditions is an increase or decrease. The transient can be separated from the permanent condition, and then always is the representation of a gradual decrease of energy. Even if the stored energy after the change of circuit conditions is greater than before, and during the transition period an increase of energy occurs, the representation still is by a decrease of the transient. This transient then is the difference between the energy storage in t ...", "... ty, and would be given by v = v0(l-6~r}. (6) In a system in which energy can be stored in two different forms, as for instance as magnetic and as dielectric energy in a circuit containing inductance and capacity, in addition to the gradual decrease of stored energy similar to that represented by the single-energy transient, a transfer of energy can occur between its two different forms. Thus, if i = transient current, e = transient voltage (that is, the difference between the respective currents and voltages exist- ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 5521-6088", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "snippets": [ "... ms of such circuits have been shown in the previous lecture. If we have a circuit consisting of sections 1, 2, 3 . . . , of the respective lengths (in velocity measure) Xi, X2, X3 . . . , this entire circuit, when left to itself, gradually dissipates its stored energy by a transient. As function of the time, this transient must decrease at the same rate u0 throughout the entire circuit. Thus the time decrement of all the sections must be 6-**. Every section, however, has a power-dissipation constant, u\\t Uz, u3 . . ...", "... his transient must decrease at the same rate u0 throughout the entire circuit. Thus the time decrement of all the sections must be 6-**. Every section, however, has a power-dissipation constant, u\\t Uz, u3 . . . , which represents the rate at which the stored energy of the section would be dissipated by the losses of power in the section, €-\"»', €-«*', €-\"*' . . . But since as part of the whole circuit each section must die down at the same rate e~Uot, in addition to its power-dissipation decrement e~Ul*, e~\"2' . ...", "... tant: S = MO-M= -100 +700 -100 -800 The transformer thus dissipates power at the rate u2 = 100, while it sends out power into the other sections at the rate of s2 = 700, or seven times as much as it dissipates. That is, it sup- plies seven-eighths of its stored energy to other sections. The load dissipates power at the rate Uz = 1600, and receives power at the rate —s = 800; that is, half of the power which it dissipates is supplied from the other sections, in this case the transformer. The transmission line dissipate ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-55", "section_label": "Chapter 6: Transition Points And The Complex Circuit", "section_title": "Transition Points And The Complex Circuit", "kind": "chapter", "sequence": 55, "number": 6, "location": "lines 32709-33527", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "snippets": [ "... ch is the same throughout the entire circuit. In an isolated section, of time constant u, the time decrement, from Chapters III and V, is, however, e~ut; that is, with the decrement e~ut the wave dies out in the isolated sec- tion at the rate at which its stored energy is dissipated by the power lost in resistance and conductance. In a section of the circuit connected to other sections the time decrement e~U(* does not correspond to the power dissipation in the section; that is, the wave does not die out in each section ...", "... nd the wave dies out in that particular section at a lesser rate than corresponds to the power consumed in the section, or, in other words, in this section of the complex circuit more power is consumed by r and g than is sup- plied by the decrease of the' stored energy, and this section, therefore, must receive energy from adjoining sections. Inversely, if s is positive, u0 > u, the wave dies out more rapidly in that section than its stored energy is consumed by r and g] that is, a part of the stored energy of this sect ...", "... e power is consumed by r and g than is sup- plied by the decrease of the' stored energy, and this section, therefore, must receive energy from adjoining sections. Inversely, if s is positive, u0 > u, the wave dies out more rapidly in that section than its stored energy is consumed by r and g] that is, a part of the stored energy of this section is transferred to the adjoining sections, and only a part — occasionally a very small part — dissipated in the section, and this section acts as a store of energy for supplying t ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1003-1658", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-02/", "snippets": [ "... electric field of the conductor. 8. The magnetic field or magnetic flux of the circuit, $, is pro- portional to the current, i, with a proportionality factor, L, which is called the inductance of the circuit. $ = L^.* (1) The magnetic field represents stored energy ly. To produce it, power, p, must therefore be supplied by the circuit. Since power is current times voltage : P = e'i, (2) * n^, if the flux interlinks the circuit n fold. 12 ELECTRIC DISCHARGES, WAVES AND IMPULSES. to produce the magnetic fie ...", "... ^, if the flux interlinks the circuit n fold. 12 ELECTRIC DISCHARGES, WAVES AND IMPULSES. to produce the magnetic field $ of the current i, a voltage e' must be consumed in the circuit, which with the current i gives the power p, which supplies the stored energy w of the magnetic field $. This voltage e' is called the inductance voltage, or voltage consumed hy self-induction. Since no power is required to maintain the field, but power is required to produce it, the inductance voltage must be propor- tional to t ...", "... alogous relations exist in the dielectric field. The dielectric field, or dielectric flux-, ^, is proportional to the voltage e, with a proportionality factor, C, which is called the capacity of the circuit: ^ = Ce. (6) The dielectric field represents stored energy, w. To produce it, power, p, must, therefore, be supplied by the circuit. Since power is current times voltage: p = i'e, (7) to produce the dielectric field ^¥ of the voltage e, a current i^ must be consumed in the circuit, which with the voltage e gi ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1659-2484", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-03/", "snippets": [ "LECTURE III. SINGLE-ENERGY TRANSIENTS IN CONTINUOUS- CURRENT CIRCUITS. 13. The simplest electrical transients are those in circuits in which energy can be stored in one form only, as in this case the change of stored energy can consist only of an increase or decrease ; but no surge or oscillation between several forms of energy can exist. Such circuits are most of the low- and medium-voltage circuits, — 220 volts, 600 volts, and 2200 volts. In them the capac- ity is small, d ...", "... tance by short- circuiting the terminals of the coil, as indicated at A. With no voltage impressed upon the coil, and thus no power supplied to it, current i and magnetic flux $ of the coil must finally be zero. However, since the magnetic flux represents stored energy, it cannot instantly vanish, but the magnetic flux must gradually decrease from its initial value $0, by the dissipation of its stored energy in the resistance of the coil circuit as i-r. Plotting, there- fore, the magnetic flux of the coil as function of ...", "... o it, current i and magnetic flux $ of the coil must finally be zero. However, since the magnetic flux represents stored energy, it cannot instantly vanish, but the magnetic flux must gradually decrease from its initial value $0, by the dissipation of its stored energy in the resistance of the coil circuit as i-r. Plotting, there- fore, the magnetic flux of the coil as function of the time, in Fig. 11 A, the flux is constant and denoted by $0 up to the moment of *o I 1 ^^\"^^-5 A K-L__ B io 1 1 C ^0 ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 883-1530", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "snippets": [ "... ctric field of the conductor. 8. The magnetic field or magnetic flux of the circuit, <£, is pro- portional to the current, i, with a proportionality factor, L, which is called the inductance of the circuit. = Li. (1) The magnetic field represents stored energy w. To produce it, power, p, must therefore be supplied by the circuit. Since power is current times voltage, p = e'i. (2) 12 ELECTRIC DISCHARGES, WAVES AND IMPULSES. To produce the magnetic field $ of the current i, a voltage ef must be consumed in ...", "... e power is current times voltage, p = e'i. (2) 12 ELECTRIC DISCHARGES, WAVES AND IMPULSES. To produce the magnetic field $ of the current i, a voltage ef must be consumed in the circuit, which with the current i gives the power p, which supplies the stored energy w of the magnetic field . This voltage er is called the inductance voltage, or voltage consumed by self-induction. Since no power is required to maintain the field, but power is required to produce it, the inductance voltage must be propor- tional to ...", "... alogous relations exist in the dielectric field. The dielectric field, or dielectric flux, ty} is proportional to the voltage 6, with a proportionality factor, C, which is called the capacity of the circuit: f = Ce. (6) The dielectric field represents stored energy, w. To produce it, power, p, must, therefore, be supplied by the circuit. Since power is current times voltage, p = i'e. (7) To produce the dielectric field ty of the voltage e, a current ir must be consumed in the circuit, which with the voltage e giv ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-03", "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "section_title": "Single-Energy Transients In Continuous Current Circuits", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 1531-2161", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "snippets": [ "LECTURE III. SINGLE-ENERGY TRANSIENTS IN CONTINUOUS- CURRENT CIRCUITS. 13. The simplest electrical transients are those in circuits in which energy can be stored in one form only, as in this case the change of stored energy can consist only of an increase or decrease ; but no surge or oscillation between several forms of energy can exist. Such circuits are most of the low- and medium-voltage circuits, — 220 volts, 600 volts, and 2200 volts. In them the capac- ity is small, d ...", "... ance by short- circuiting the terminals of the coil, as indicated at A, with no voltage impressed upon the coil, and thus no power supplied to it, current i and magnetic flux <£ of the coil must finally be zero. However, since the magnetic flux represents stored energy, it cannot instantly vanish, but the magnetic flux must gradually decrease from its initial value 3>o, by the dissipation of its stored energy in the resistance of the coil circuit as i~r. Plotting, there- fore, the magnetic flux of the coil as function o ...", "... it, current i and magnetic flux <£ of the coil must finally be zero. However, since the magnetic flux represents stored energy, it cannot instantly vanish, but the magnetic flux must gradually decrease from its initial value 3>o, by the dissipation of its stored energy in the resistance of the coil circuit as i~r. Plotting, there- fore, the magnetic flux of the coil as function of the time, in Fig. 11 A, the flux is constant and denoted by $0 up to the moment of Fig. 11. — Characteristics of Magnetic Single-energy Tran ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... an effective resistance, which increases the rapidity of the decay of the oscillation, and thus limits the power, and, when approaching the critical value, also lowers the frequency. This is obvious, since the oscillating current is the dissipation of the energy stored electrostatically in the condenser, and the higher the resistance of the circuit, the more rapidly is this energy dissipated, that is, the faster the oscillation dies out. With a resistance of the circuit sufficiently low to give a fairly well sustained ...", "... d pencil scratch on a piece of porcelain. Therefore the size or bulk of condensers and reactors depends not only on C and L but also on the voltage and current which can be applied continuously, that is, it is approximately pro- Ce2 W portional to the energy stored, - and — , or since in electrical OSCILLATING CURRENTS 69 engineering energy is a quantity less frequently used than power, condensers and reactors are usually characterized by the power or rather apparent power which can be impressed upon them contin ...", "... ondenser, gives since r = 0.05 x, r - 0.05 V x = 2 xfL, 1 and the energy of the discharge, by (65), is W = — - \\^LC = 10 6* C volt-ampere-seconds; — T thus the power factor is cos 00 = 0.05. 72 . TRANSIENT PHENOMENA Since the energy stored in the capacity is WQ = ^ joules, the critical resistance is hence, r. - „ 0 7 = 0.025, *'4 and the decrement of the oscillation is A = 0.92, that is, the decay of the wave is very slow at no load. Assuming, however, as load an external ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2485-3386", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-04/", "snippets": [ "LECTURE IV. SINGLE-ENERGY TRANSIENTS IN ALTERNATING- CURRENT CIRCUITS. 17. Whenever the conditions of an electric circuit are changed in such a manner as to require a change of stored energy, a transi- tion period appears, during which the stored energy adjusts itself from the condition existing before the change to the condition after the change. The currents in the circuit during the transition period can be considered as consisting of the ...", "LECTURE IV. SINGLE-ENERGY TRANSIENTS IN ALTERNATING- CURRENT CIRCUITS. 17. Whenever the conditions of an electric circuit are changed in such a manner as to require a change of stored energy, a transi- tion period appears, during which the stored energy adjusts itself from the condition existing before the change to the condition after the change. The currents in the circuit during the transition period can be considered as consisting of the superposition of the permanent current, corresponding to the co ...", "... by a concen- tric circle a, Fig. 18. This, however, applies only to the permanent condition. In the moment of start, all the three currents are zero, and their resultant magnetic field thus also zero, as shown above. Since the magnetic field represents stored energy and thus cannot be produced instantly, a transient must appear in the building up of the rotating field. This can be studied by considering separately SINGLE-ENERGY TRANSIENTS. 35 the permanent and the transient components of the three currents, a ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "section_label": "Lecture 10: Continual And Cumulative Oscillations", "section_title": "Continual And Cumulative Oscillations", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "LECTURE X. CONTINUAL AND CUMULATIVE OSCILLATIONS. 43. A transient is the phenomenon by which the stored energy readjusts itself to a change of circuit conditions. In an oscilla- tory transient, the difference of stored energy of the previous and the after condition of the circuit, at a circuit change, oscillates between magnetic and dielectric energy. As there alw ...", "LECTURE X. CONTINUAL AND CUMULATIVE OSCILLATIONS. 43. A transient is the phenomenon by which the stored energy readjusts itself to a change of circuit conditions. In an oscilla- tory transient, the difference of stored energy of the previous and the after condition of the circuit, at a circuit change, oscillates between magnetic and dielectric energy. As there always must be some energy dissipation in the circuit, the oscillating energy of the transient must steadily decline, ...", "... m^plitude, only if a steady supply of oscillating energy occurs. Continual and cumulative oscillations thus involve a con- tinual energy supply to the oscillating system, therefore cannot be mere readjustments of circuit conditions by the dissipation of stored energy. If the continual energy supply is less than the energy dissipa- tion in the circuit, the oscillation dies out, that is, is transient, but A\\nth a lowered attenuation constant. This for instance is the case with the transient in those sections of a compo ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2162-2971", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "snippets": [ "LECTURE IV. SINGLE-ENERGY TRANSIENTS IN ALTERNATING- CURRENT CIRCUITS. 17. Whenever the conditions of an electric circuit are changed in such a manner as to require a change of stored energy, a transi- tion period appears, during which the stored energy adjusts itself from the condition existing before the change to the condition after the change. The currents in the circuit during the transition period can be considered as consisting of the ...", "LECTURE IV. SINGLE-ENERGY TRANSIENTS IN ALTERNATING- CURRENT CIRCUITS. 17. Whenever the conditions of an electric circuit are changed in such a manner as to require a change of stored energy, a transi- tion period appears, during which the stored energy adjusts itself from the condition existing before the change to the condition after the change. The currents in the circuit during the transition period can be considered as consisting of the superposition of the permanent current, corresponding to the co ...", "... by a concen- tric circle a, Fig. 18. This, however, applies only to the permanent condition. In the moment of start, all the three currents are zero, and their resultant magnetic field thus also zero, as shown above. Since the magnetic field represents stored energy and thus cannot be produced instantly, a transient must appear in the building up of the rotating field. This can be studied by considering separately SINGLE-ENERGY TRANSIENTS. 35 the permanent and the transient components of the three currents, a ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-06", "section_label": "Theory Section 6: Self-inductance of Continuous-current Circuits", "section_title": "Self-inductance of Continuous-current Circuits", "kind": "theory-section", "sequence": 6, "number": 6, "location": "lines 1785-2249", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-06/", "snippets": [ "... The effect at the time t of the e.m.f. of inductance in stop- ping the current is _ 2r + rif iei = io2 (r + n) c L ; thus the total energy of the generated e.m.f. >*» W = | z' Jo that is, the energy stored as magnetism in a circuit of current iQ and inductance L is 2 ' which is independent both of the resistance r of the circuit and the resistance n inserted in breaking the circuit. This energy has to be expended in ...", "... the rheostat? (3) If 500 volts are impressed upon the field of this alter- nator without insertion of resistance, how long will it take for the field to reach full strength? (4) With full field strength, what is the energy stored as magnetism? (1) The resistance of the alternator field is 33.2 ohms (Section 2, Example 2), the inductance 112 h. (Section 5, Example 1), the impressed e.m.f. is E = 230, the final value of current E io = — = 6. ...", "... ssing E = 500 volts upon a circuit of r = 33.2, L = 112, gives = 15.1 (1 - €-°-2960. i = 6.95, or full field strength, gives 6.95 = 15.1 (1 - e-°-2960. 1 - €-°-296 « = 0.46 and t = 2.08 seconds. (4) The stored energy is 6.952 X 112 ~ = 2720 watt-seconds or joules _ _ = 2000 foot-pounds. (1 joule = 0.736 foot-pounds.) Thus in case (3), where the field reaches full strength in 2.08 2000 seconds, the average power input is -c -^ ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-20", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit. 513", "section_title": "Power And Energy Of The Complex Circuit. 513", "kind": "chapter", "sequence": 20, "number": 7, "location": "lines 1228-1261", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-20/", "snippets": [ "CHAPTER VII. POWER AND ENERGY OF THE COMPLEX CIRCUIT. 513 50. Instantaneous power. Effective or mean power. Power transferred. 513 51. Instantaneous and effective value of energy stored in the magnetic field ; its motion along the circuit, and varia- tion with distance and with time. 513 52. The energy stored in the electrostatic field and its compo- nents. Transfer of energy between electrostatic and electromagnetic field. 517 53. ...", "... CUIT. 513 50. Instantaneous power. Effective or mean power. Power transferred. 513 51. Instantaneous and effective value of energy stored in the magnetic field ; its motion along the circuit, and varia- tion with distance and with time. 513 52. The energy stored in the electrostatic field and its compo- nents. Transfer of energy between electrostatic and electromagnetic field. 517 53. Energy stored in a circuit section by the total electric field, and power supplied to the circuit by it. 518 54. Power dissip ...", "... in the magnetic field ; its motion along the circuit, and varia- tion with distance and with time. 513 52. The energy stored in the electrostatic field and its compo- nents. Transfer of energy between electrostatic and electromagnetic field. 517 53. Energy stored in a circuit section by the total electric field, and power supplied to the circuit by it. 518 54. Power dissipated in the resistance and the conductance of a circuit section. 519 55. Relations between power supplied by the electric field of a circu ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "LECTURE VII. LINE OSCILLATIONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy surges between magnetic — and dielectric — , and a transient component, by which the total stored energy decreases. Considering only the periodic component, the maximum value of magnetic energy must equal the maximum value of dielectric '^'^e^gy- Li ...", "... CTURE VII. LINE OSCILLATIONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy surges between magnetic — and dielectric — , and a transient component, by which the total stored energy decreases. Considering only the periodic component, the maximum value of magnetic energy must equal the maximum value of dielectric '^'^e^gy- Li„^ Ce, 0 \"^^0 (1) where Iq = maximum value of transient current, 60 = maximum value of transient vo ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3956-4744", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "snippets": [ "LECTURE VII. LINE OSCILLATIONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy 7\" /j'2 f^ r/>2 surges between magnetic -^- and dielectric — , and a transient £i A component, by which the total stored energy decreases. Considering only the periodic component, the maximum mag- netic energy must equal the maximum dielectric ener ...", "... ONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy 7\" /j'2 f^ r/>2 surges between magnetic -^- and dielectric — , and a transient £i A component, by which the total stored energy decreases. Considering only the periodic component, the maximum mag- netic energy must equal the maximum dielectric energy, Lio2 _ Ceo2 \"2\" ~2~' where i0 = maximum transient current, e0 = maximum transient voltage. This gives the relation between eQ ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "... , is called fluorescence or phosphorescence. Fluorescence and Phosphorescence. Fluorescence is the production of radiation from the energy supplied to and absorbed by the fluorescent body, while phos- phorescence is the production of radiation from the energy stored in the phosphorescent body. This energy may be derived from internal changes in the body, as slow combustion, or may have been received by the body at some previous time — as by exposure to light a calcium sulphide screen absorbs the energy of incident r ...", "... , represent energy storage — the kinetic energy of the luminescent vibration, etc. — and when the energy supply to the body ceases, the radiation issuing from the body does not instantly cease, but continues, with gradually decreasing intensity, until the stored energy is dissipated : the body phos- 94 LUMINESCENCE. 95 phoresces. Inversely, fluorescent radiation probably does not appear instantly at full intensity, as energy has first to be stored. The persistence of the luminescence after the power supply has sto ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-43", "section_label": "Chapter 3: The Natural Period Of The Transmission Line", "section_title": "The Natural Period Of The Transmission Line", "kind": "chapter", "sequence": 43, "number": 3, "location": "lines 21721-23178", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "snippets": [ "... tep-down trans- formers, and load, a short circuit occurs in the line, the circuit comprising the load, the step-down transformers, and the lines from the step-down transformers to the short circuit is left closed upon itself without power supply, and its stored energy is, therefore, dissipated as a full-wave oscillation. Or, if in this system an excessive load, as the dropping out of step of a syn- chronous converter, causes the circuit to open at the generating station, the dissipation of the stored energy — in this c ...", "... ly, and its stored energy is, therefore, dissipated as a full-wave oscillation. Or, if in this system an excessive load, as the dropping out of step of a syn- chronous converter, causes the circuit to open at the generating station, the dissipation of the stored energy — in this case that of the excessive current in the system — occurs as a full-wave oscillation, if the line cuts off from the generating station on the low-tension side of the step-up transformers, and the oscillating circuit comprises the high-tension co ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-54", "section_label": "Chapter 5: Free Oscillations", "section_title": "Free Oscillations", "kind": "chapter", "sequence": 54, "number": 5, "location": "lines 31451-32708", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "snippets": [ "... rring in an electric circuit or part of the circuit to which neither electric energy is supplied by some outside source nor from which electric energy is abstracted. Free oscillations thus are the transient phenomena resulting from the dissipation of the energy stored in the electric field of the circuit, or inversely, the accumulation of the energy of the electric field; and their appearance therefore presupposes the possibility of energy storage in more than one form so as to allow 478 FREE OSCILLATIONS 479 an ...", "... constants Bn and yn, representing, respectively, the intensity and the phase of the nth harmonic. These pairs of integration constants are determined by the ter- minal conditions of time ; that is, they depend upon the amount and the distribution of the stored energy of the circuit at the starting moment of the oscillation, or, in other words, on the distribution of current and e.m.f. at t = 0. The e.m.f., e0, and the current, i0, at time t = 0, can be ex- pressed as an infinite series of trigonometric functions of t ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-05", "section_label": "Lecture 5: Single-Energy Tra.Nsient Of Ironclad Circuit", "section_title": "Single-Energy Tra.Nsient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3387-3720", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-05/", "snippets": [ "... SINGLE-ENERGY TRA.NSIENT OF IRONCLAD CIRCUIT. 22. Usually in electric circuits; current, voltage, the magnetic field and the dielectric field are proportional to each other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnetic materials, or if the dielectric field reaches densities beyond the dielectric strength of the carrier of the field, etc.; ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-05", "section_label": "Lecture 5: Single-Energy Transient Of Ironclad Circuit", "section_title": "Single-Energy Transient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2972-3286", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-05/", "snippets": [ "... SINGLE-ENERGY TRANSIENT OF IRONCLAD CIRCUIT. 22. Usually in electric circuits, current, voltage, the magnetic field and the dielectric field are proportional to each other, and the transient thus is a simple exponential, if resulting from one form of stored energy, as discussed in the preceding lectures. This, how- ever, is no longer the case if the magnetic field contains iron or other magnetic materials, or if the dielectric field reaches densities beyond the dielectric strength of the carrier of the field, etc. ; ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-02", "section_label": "Lecture 2: Conclusions From The Relativity Theory", "section_title": "Conclusions From The Relativity Theory", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 736-2388", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... t the frequency of the light wave, about 600 millions of millions of cycles, the wave length, about 50 micro cm., is an insignificant part of the extent of the field- — ^that is, of the distance to which the beam travels — and therefore virtually all the energy of the field is radiated, none returned to the radiator. Fig. 5. CONCLUSIONS FROM RELATIVITY THEORY 23 As the electromagnetic field represents energy storage in space, it cannot extend through space instantaneously, but must propagate through space at a finite ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-05", "section_label": "Lecture 5: Long Distance Transmission", "section_title": "Long Distance Transmission", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2562-3132", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-05/", "snippets": [ "... are of about the same magnitude, and the energy can therefore see- saw between the two forms and thereby produce oscillations and surges resulting in the production of high voltages, which are not liable to occur in circuits in which one of the forms of stored energy is small compared with the other. In distribution systems up to 2200 volts and even some- what higher, the electrostatic energy is still negligible and only the electromagnetic energy appreciable. In static machines the electrostatic energy is appreciab ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-32", "section_label": "Chapter 32: Transformation Of Polyphase Systems", "section_title": "Transformation Of Polyphase Systems", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 36062-36514", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-32/", "snippets": [ "... ced sys- tem will be transformed again into a balanced system, and an unbalanced system into an unbalanced system of the same bal- ance-factor, since the transformer is not able to store energy, and thereby to change the nature of the flow of energy. The energy stored as magnetism amounts in a well-designed trans- former only to a very small percentage of the total energy. This shows the futility of producing symmetrical balanced polyphase systems by transformation from the unbalanced single-phase system without additi ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-27", "section_label": "Chapter 27: Tbansfobmation Of Polyphase Systems", "section_title": "Tbansfobmation Of Polyphase Systems", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 26428-26583", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-27/", "snippets": [ "... tem will be transformed again in a balanced system, and an unbalanced system into an unbalanced sys- tem of the same balance factor, since the transformer is an apparatus not able to store energy, and thereby to change the nature of the flow of power. The energy stored as magnetism, amounts in a well-designed transformer only to a very small percentage of the total energy. This shows the futility of producing symmetrical balanced polyphase systems by transformation from the unbalanced single-phase system without additi ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-29", "section_label": "Chapter 29: Transformation Of Polyphase Systems", "section_title": "Transformation Of Polyphase Systems", "kind": "chapter", "sequence": 29, "number": 29, "location": "lines 24805-25135", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-29/", "snippets": [ "... tem will be transformed again in a balanced system, and an unbalanced system into an unbalanced sys- tem of the same balance factor, since the transformer is an apparatus not able to store energy, and thereby to change the nature of the flow of power. The energy stored as magnetism, amounts in a well-designed transformer only to a very small percentage of the total energy. This shows the futility of producing symmetrical balanced polyphase systems by transformation from the unbalanced single-phase system without additi ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-12", "section_label": "Chapter 14: Phase Conversion And Single-Phase Generation", "section_title": "Phase Conversion And Single-Phase Generation", "kind": "chapter", "sequence": 12, "number": 14, "location": "lines 17125-18412", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-12/", "snippets": [ "... ncreasing, and increases with decroaniBg kilovolt-ampere capacity. Furthermore, the use of mechanical momentum means moving machinery, requiring more or less attention, thus becomes less suitable, for smaller values of power. Hence, for smaller amounts of stored energy, inductance and capacity may become more economical than momentum, and for very small amounts of energy, the condenser may lie the cheapest device. The above figures thus give only the approxi- • \"Theorv and Calculation of Alterwi ting-current Phenomena, ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-10", "section_label": "Chapter 10: Instability Of Circuits : The Arc", "section_title": "Instability Of Circuits : The Arc", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 17632-21381", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-10/", "snippets": [ "... ELECTRIC CIRCUITS cumulative surges, hunting, etc. They may be considered as transients in which the attenuation constant is zero or negative. In the transient resulting from a change of circuit conditions, the energy which represents the difference of stored energy of the circuit before and after the change of circuit condition, is dissi- pated by the energy loss in the circuit. As energy losses always occur, the intensity of a true transient thus must always be a maximum at the beginning, and steadily decrease to z ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-11", "section_label": "Chapter 11: Instability Of Circuits: Induction And Syn Chronous Motors", "section_title": "Instability Of Circuits: Induction And Syn Chronous Motors", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 21382-22633", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-11/", "snippets": [ "... on- inductive as possible to give efficient damping. With the change of position, p, the current, and thus the ar- mature reaction, and with it the magnetic flux of the machine, changes. A flux change can not be brought about instantly, as it represents energy stored, and as a result the magnetic flux of the machine does not exactly correspond with the position, p, but lags behind it, and with it the synchronizing force, F, as shown in Fig. 104, lags more or less, depending on the design of the machine. The synchron ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-13", "section_label": "Chapter 13: Reactance Of Synchronous Machines", "section_title": "Reactance Of Synchronous Machines", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 23466-24022", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-13/", "snippets": [ "... for instance, when calculating efficiency and losses, the core loss of the machine does not correspond to eo, but corresponds to the actual or resultant magnetic flux. Fig. 112. Also, in deal- ing with transients involving the dissipation of the magnetic energy stored in the machine, the magnetic energy of the result- ant field, Fig. 112, comes into consideration, and not the — ^much REACTANCE OF SYNCHRONOUS MACHINES 237 larger — energy, which the fields corresponding to e© and Xo would have. Thus the short-circuit ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-24", "section_label": "Chapter 2: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 24, "number": 2, "location": "lines 1993-2658", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "snippets": [ "... ty C, give rise to transient phenomena, and the more the resist- 22 TRANSIENT PHENOMENA ance predominates, the less is therefore the severity and dura- tion of the transient term. When closing a circuit containing inductance or capacity or both, the energy stored in the inductance and the capacity has first to be supplied by the impressed e.m.f. before the circuit conditions can become stationary. That is, in the first moment after closing an electric circuit, or in general changing the circuit conditions, tne imp ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-27", "section_label": "Chapter 5: Resistance, Inductance, And Capacity In Series Condenser Charge And Discharge", "section_title": "Resistance, Inductance, And Capacity In Series Condenser Charge And Discharge", "kind": "chapter", "sequence": 27, "number": 5, "location": "lines 4072-5311", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "snippets": [ "... t the condenser at the moment t = 0. Inversely, since in a circuit containing inductance and capac- ity two electric quantities must be given at the moment of start of the phenomenon, the current and the condenser poten- tial — representing the values of energy stored at the moment t = 0 as electromagnetic and as electrostatic energy, respec- tively — the equations must lead to two integration constants, that is, to a differential equation of second order. Let i = i0 = current and et = e0 = potential difference at co ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-51", "section_label": "Chapter 2: Discussion Of General Equations", "section_title": "Discussion Of General Equations", "kind": "chapter", "sequence": 51, "number": 2, "location": "lines 28695-29315", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "snippets": [ "... ut the wave dies out with the increasing time t by £-(tt+s>< = s\"\"* e~st, that is, faster than the first wave. If the amplitude of the wave remained constant throughout the circuit — as would be the case in a free oscillation of the circuit, in which the stored energy of the circuit is dissipated, but no power supplied one way or the other — that is, if h = 0, from equation (56) s = 0; that is, both waves coincide and form one, which dies out with the time by the decrement e~ut. It thus follows: In general, two waves, ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... ontinuous current 27 polyphase or rotating field 192, 197 oscillation of cables and lines Ill, 117 Static, see Electrostatic. phenomena 13, 105 Stationary waves 439, 442 Steel, effective penetration of alternating current 378 INDEX 571 PAGE Stored energy of complex circuit 515 Stranded conductor, effective resistance of current distribution 370 Stray field and starting current of transformer 184 Suppression of pulsations of direct current by capacity and inductance. 134 Synchronous reactance and short ..." ] } ] }, { "id": "electric-field", "label": "Electric Field", "aliases": [ "electric field", "electrostatic field", "field of force", "field of forces" ], "total_occurrences": 212, "matching_section_count": 45, "matching_source_count": 11, "source_totals": [ { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 109, "section_count": 14 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 18, "section_count": 4 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 18, "section_count": 4 }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 14, "section_count": 3 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 13, "section_count": 3 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 12, "section_count": 4 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 12, "section_count": 4 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 7, "section_count": 4 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 6, "section_count": 3 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 2, "section_count": 1 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-48", "section_label": "Chapter 8: Velocity Of Propagation Of Electric Field", "section_title": "Velocity Of Propagation Of Electric Field", "kind": "chapter", "sequence": 48, "number": 8, "location": "lines 26095-27002", "status": "candidate", "occurrence_count": 37, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "snippets": [ "CHAPTER VIII. VELOCITY OF PROPAGATION OF ELECTRIC FIELD. 67. In the theoretical investigation of electric circuits the velocity of propagation of the electric field through space is usually not considered, but the electric field assumed as instan- taneous throughout space; that is, the electromagnetic com- p ...", "CHAPTER VIII. VELOCITY OF PROPAGATION OF ELECTRIC FIELD. 67. In the theoretical investigation of electric circuits the velocity of propagation of the electric field through space is usually not considered, but the electric field assumed as instan- taneous throughout space; that is, the electromagnetic com- ponent of the field is considered as in phase with the current, the electrostatic component as in phase with the ...", "CHAPTER VIII. VELOCITY OF PROPAGATION OF ELECTRIC FIELD. 67. In the theoretical investigation of electric circuits the velocity of propagation of the electric field through space is usually not considered, but the electric field assumed as instan- taneous throughout space; that is, the electromagnetic com- ponent of the field is considered as in phase with the current, the electrostatic component as in phase with the voltage. In reality, however, the electric field starts at the ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-23", "section_label": "Chapter 1: The Constants Of The Electric Circuit", "section_title": "The Constants Of The Electric Circuit", "kind": "chapter", "sequence": 23, "number": 1, "location": "lines 1317-1992", "status": "candidate", "occurrence_count": 29, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "snippets": [ "... ng to receiving circuit, and the power gradient therefore is characteristic of the direc- tion of the flow of energy.) In the space outside of the conductor, during the flow of energy through the circuit, a condition of stress exists which is called the electric field of the conductor. That is, the surrounding space is not uniform, but has different electric and magnetic properties in different directions. No power is required to maintain the electric field, but energy 3 4 TRANSIENT PHENOMENA is required to prod ...", "... the circuit, a condition of stress exists which is called the electric field of the conductor. That is, the surrounding space is not uniform, but has different electric and magnetic properties in different directions. No power is required to maintain the electric field, but energy 3 4 TRANSIENT PHENOMENA is required to produce the electric field, and this energy is returned, more or less completely, when the electric field dis- appears by the stoppage of the flow of energy. Thus, in starting the flow of electric ...", "... conductor. That is, the surrounding space is not uniform, but has different electric and magnetic properties in different directions. No power is required to maintain the electric field, but energy 3 4 TRANSIENT PHENOMENA is required to produce the electric field, and this energy is returned, more or less completely, when the electric field dis- appears by the stoppage of the flow of energy. Thus, in starting the flow of electric energy, before a perma- nent condition is reached, a finite time must elapse during ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-56", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit", "section_title": "Power And Energy Of The Complex Circuit", "kind": "chapter", "sequence": 56, "number": 7, "location": "lines 33528-34202", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "snippets": [ "... £ only but not of the distance ^, 1 2 (317) and the total energy of the electromagnetic field of circuit element dX at time t is Aw'rr 1 /7 \"~ = V £~2\"\"'{ (4(7+BI)) cos 2 9' + (^0-JSC) sin 2 qt\\, dX d^ dl dX dX 52. The energy stored in the electrostatic field of the conductor or by the capacity C is given by CV dw2 = — dl\\ 518 TRANSIENT PHENOMENA or, substituting (310), and substituting in (319) the value of e from equation (290) gives the same expression as (311) except that the sign of the last two ...", "... ign of the last two terms is reversed ; that is, the total energy of the electro- static field of circuit element dX at time t is dw2 dwn dw' dw\" dw'\" ~df = ~df + ~dT + ~dA~ + ~dT' (32°^ and adding (318) and (320) gives the total stored energy of the electric field of the conductor, dw dw, dw2 cydw^ dw' and integrated over a complete period of time this gives « 2^ = dw\" dw\"' The last two terms, — and — , thus represent the energy which is transferred, or pulsates, between the electromagnetic and the electros ...", "... ic field of the conductor, dw dw, dw2 cydw^ dw' and integrated over a complete period of time this gives « 2^ = dw\" dw\"' The last two terms, — and — , thus represent the energy which is transferred, or pulsates, between the electromagnetic and the electrostatic field of the circuit; and the term — repre- sents the alternating (or rather oscillating) component of stored energy. 53. The energy stored by the electric field in a circuit section ^, between A, and A2, is given by integrating - - between A2 and AI} U/A ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... 65 sin gfl; E = 8732 1>-^ (cos qX + 0.040 sin gj). 544 TRANSIENT PHENOMENA (6) Three-half wave: 541.94°. & = 20,920; UQ = 105.6; 7 = if-** (cos qX- 29.6 sin gd); jE/ = 10,460 v~Wo< (cos g>l + 0.033 sin qX). APPENDIX VELOCITY FUNCTIONS OF THE ELECTRIC FIELD IN the study of the propagation of the electric field through space (wireless telegraphy and telephony), a number of new functions appear (Section III, Chapter VIII). . By the following equations these functions are defined, and related to the \" Sine-I ...", "... 44 TRANSIENT PHENOMENA (6) Three-half wave: 541.94°. & = 20,920; UQ = 105.6; 7 = if-** (cos qX- 29.6 sin gd); jE/ = 10,460 v~Wo< (cos g>l + 0.033 sin qX). APPENDIX VELOCITY FUNCTIONS OF THE ELECTRIC FIELD IN the study of the propagation of the electric field through space (wireless telegraphy and telephony), a number of new functions appear (Section III, Chapter VIII). . By the following equations these functions are defined, and related to the \" Sine-Integral\" Si x, the \" Cosine-Integral\" Ci x, and the \" E ...", "... and inductance, equations 48 and velocity of propagation 400, 401 distributed series 348 energy of complex circuit 517 in mutual inductive circuit 161 of electric circuit 112 range in electric circuit 13 representing electrostatic component of electric field 5 shunting direct-current circuit 133 specific, numerical values 11 suppressing pulsations in direct-current circuit 134 Cast iron, effective penetration of alternating current 378 Cathode of arcs 249 Charge of condenser 51 of magnetic field 27 ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1003-1658", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-02/", "snippets": [ "LECTURE II. THE ELECTRIC FIELD. 7. Let, in Fig. 7, a generator G transmit electric power over line A into a receiving circuit M. While power flows through the conductors A, power is con- sumed in these conductors by JV[ conversion into heat, repre- sented by ^2r. This, however, F ...", "... , power is con- sumed in these conductors by JV[ conversion into heat, repre- sented by ^2r. This, however, Fig. 7. is not all, but in the space surrounding the conductor cer- tain phenomena occur: magnetic and electrostatic forces appear. Fig. 8. — Electric Field of Conductor. The conductor is surrounded by a magnetic field, or a magnetic flux, which is measured by the number of lines of magnetic force $. With a single conductor, the lines of magnetic force are concentric circles, as shown in Fig. 8. By the retu ...", "... rounded by a magnetic field, or a magnetic flux, which is measured by the number of lines of magnetic force $. With a single conductor, the lines of magnetic force are concentric circles, as shown in Fig. 8. By the return conductor, the circles 10 THE ELECTRIC FIELD. 11 are crowded together between the conductors, and the magnetic field consists of eccentric circles surrounding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from th ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 883-1530", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "snippets": [ "LECTURE II. THE ELECTRIC FIELD. 7. Let, in Fig. 7, a generator G transmit electric power over line A into a receiving circuit L. While power flows through the conductors A, power is con- sumed in these conductors by conversion into heat, repre- sented by i?r. This, however, Fig ...", "... A, power is con- sumed in these conductors by conversion into heat, repre- sented by i?r. This, however, Fig. 7. is not all, but in the space surrounding the conductor cer- tain phenomena occur: magnetic and electrostatic forces appear. Fig. 8. — Electric Field of Conductor. The conductor is surrounded by a magnetic field, or a magnetic flux, which is measured by the number of lines of magnetic force . With a single conductor, the lines of magnetic force are concentric circles, as shown in Fig. 8. By the ret ...", "... unded by a magnetic field, or a magnetic flux, which is measured by the number of lines of magnetic force . With a single conductor, the lines of magnetic force are concentric circles, as shown in Fig. 8. By the return conductor, the circles 10 THE ELECTRIC FIELD. 11 are crowded together between the conductors, and the magnetic field consists of eccentric circles surrounding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "... ce between center and outside of wire; k = 3.2 X 10 ~6 and NR* = .46, hence when, N = 125 100 60 25 X = .061 .068 .088 .136 cm. thus the effect is noticeable even with relatively small iron wire. Mutual Inductance. 97. When an alternating magnetic field of force includes a secondary electric conductor, it induces therein an E.M.F. which produces a current, and thereby consumes energy if the circuit of the secondary conductor is closed. A particular case of such induced secondary currents are the eddy or Foucaul ...", "... gy component of inductance, con- densance has an energy component also, namely, dielectric hysteresis. In an alternating magnetic field, energy is con- sumed in hysteresis due to molecular friction, and similarly, energy is also consumed in an alternating electrostatic field in the dielectric medium, in what is called electrostatic or dielectric hysteresis. FOUCAULT OR EDDY CURRENTS. 145 While the laws of the loss of energy by magnetic hys- teresis are fairly well understood, and the magnitude of the effect known, the ph ...", "... tood, and the magnitude of the effect known, the phenomenon of dielectric hysteresis is still almost entirely unknown as concerns its laws and the magnitude of the effect. It is quite probable that the loss of power in the dielec- tric in an alternating electrostatic field consists of two dis- tinctly different components, of which the one is directly proportional to the frequency, — analogous to magnetic hysteresis, and thus a constant loss of energy per cycle, independent of the frequency ; while the other component is p ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-02", "section_label": "Lecture 2: Conclusions From The Relativity Theory", "section_title": "Conclusions From The Relativity Theory", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 736-2388", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... tion of matter thus had to be abandoned and mass became a manifestation of energy. The law of gravitation has been recast, and the force of gravitation has become an effect of inertial motion, like centrifugal force. The ether has been abandoned, and the field of force of Faraday and Maxwell has become the fundamental conception of physics. The laws of mechanics ^ have been changed, and time and space have been bound' together in the four-dimensional world space, the dimen- sions of which are neither space nor time, but ...", "... Therefore the principal value of the relativity theory thus far consists in the better conception of nature and its laws which it affords. Some of the most interesting illustra- tions of this will be discussed in the following pages. B. THE ETHER AND THE FIELD OF FORCE Newton's corpuscular theory of light explained radiation as a bombardment by minute particles projected at extremely high velocities, in much the same way as the alpha and the beta rays are explained today. This corpuscular theory was disproven by the p ...", "... magnet M (Fig. 2) and bring a piece of iron / near it. It is attracted, or moved; that is, a force is exerted on it. We bring a piece of copper near the magnet, and nothing happens. We say the space surrounding the magnet is a magnetic field. A field, or field of force, we define as \"a condition in space exerting a force on a body susceptible to this field.\" Thus, a piece of iron being magnetizable — that is, susceptible to a magnetic field^ — ^will be acted upon; a piece of copper, not being magnetizable, shows no acti ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-19", "section_label": "Theory Section 19: Fields of Force", "section_title": "Fields of Force", "kind": "theory-section", "sequence": 19, "number": 19, "location": "lines 7737-7990", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-19/", "snippets": [ "... urrent in the conductor, there are therefore in the spaces outside of the con- ductor — where the current does not flow — forces exerted, and FIELDS OF FORCE 113 this space then is not neutral space, but has become a field of force, and the cause of the field, in this case the electric current in the conductor, is its \"motive force.\" As in this case the actions exerted in the field of force are magnetic, the space surrounding a conductor traversed ...", "... this space then is not neutral space, but has become a field of force, and the cause of the field, in this case the electric current in the conductor, is its \"motive force.\" As in this case the actions exerted in the field of force are magnetic, the space surrounding a conductor traversed by a current is a field of magnetic force, and the current in the conductor is the magneto- motive force. In the space surrounding a ponderable mass, as our earth, ...", "... he magnetic field of a current as magnetomotive force, the intensity H of the magnetic field is measured by the force F which the field exerts on a magnetic mass or pole strength m: F = Hm; the intensity K of the di- electric field of a potential difference as electromotive force is measured by the force F exerted upon an electric pole strength e: F = Ke', the direction of the force represents the direction of the field of force. 90. This concepti ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... luded from use at this frequency by the exter- nal selfrinduction, which is several times larger than the resistance. We thus see that unequal current distribution is usually negligible in practice. Mutual Inductance, 97. When an alternating magnetic field of force includes a secondary electric conductor, it induces therein an E.M.F. which produces a current, and thereby consumes energy if the circuit of the secondary conductor is closed. A particular case of such induced secondary currents are the eddy or Foucaul ...", "... gy component of inductance, cori- densance has an energy component also, called dielectric hysteresis. In an alternating magnetic field, energy is con- sumed in hysteresis due to molecular friction, and similarly, energy is also consumed in an alternating electrostatic field in the dielectric medium, in what is called dielectric hys- teresis. i 99] FOUCAULT OR EDDY CURRENTS. 145 While the laws of the loss of energy by magnetic hys- teresis are fairly well understood, and the magnitude of the effect known, the phenomenon ...", "... tood, and the magnitude of the effect known, the phenomenon of dielectric hysteresis is still almost entirely unknown as concerns its laws and the magnitude of the effect. It is quite probable that the loss of power in the dielec- tric in an alternating electrostatic field consists of two dis- tinctly different components, of which the one is directly proportional to the frequency, — analogous to magnetic hysteresis, and thus a constant loss of energy per cycle, independent of the frequency ; while the other component is p ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "section_label": "Lecture 10: Continual And Cumulative Oscillations", "section_title": "Continual And Cumulative Oscillations", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... c., are required. D. Calculation of capacity. 49. The lines of dielectric force of the conductor A are straight radial lines, shown dotted in Fig. 72, and the dielectric equipoten- tial lines are concentric circles, shown drawn in Fig. 72. Fig. 72. — Electric Field of Conductor. li e = voltage between conductor A and return conductor B, and s the distance between the conductors, the potential difference between the equipotential line at the surface of A, and the equi- potential line which traverses B, must be e. ...", "... als the reciprocal of the external inductance Li times the velocity square of light. The external inductance Li would be the inductance of a conductor which had perfect con- ductivity, or zero losses of power. It is Vlc = velocity of propagation of the electric field, and this velocity is less than the velocity of light, due to the retardacion by the power dissipation in the conductor, and becomes equal to the velocity of light V if there is no power dissipation, and, in the latter case, L would be equal to Li, the ex ...", "... capacity, etc. More complete, this equation is CLi = '^, (40) v where k = specific capacity or permittivity, jjl = permeability of the medium. ROUND PARALLEL CONDUCTORS. 139 E. Conductor with ground return. 50. As seen in the preceding, in the electric field of conductor A and return conductor B, at distance s from each other, Fig. 9, the lines of magnetic force from conductor A to the center line CC are equal in number and in magnetic energy to the lines of mag- netic force which surround the conductor in Fi ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-10", "section_label": "Lecture 10: Inductance And Capacity Of Round Parallel Conductors", "section_title": "Inductance And Capacity Of Round Parallel Conductors", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6089-7274", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "snippets": [ "... c., are required. D. Calculation of capacity. 46. The lines of dielectric force of the conductor A are straight radial lines, shown dotted in Fig. 64, and the dielectric equipoten- tial lines are concentric circles, shown drawn in Fig. 64. Fig. 64. — Electric Field of Conductor. If e = voltage between conductor A and return conductor B, and s the distance between the conductors, the potential difference between the equipotential line at the surface of A, and the equi- potential line which traverses B, must be e. ...", "... ls the reciprocal of the external inductance LI times the velocity square of light. The external inductance LI would be the inductance of a conductor which had perfect con- ductivity, or zero losses of power. It is VLC = velocity of propagation of the electric field, and this velocity is less than the velocity of light, due to the retardation by the power dissipation in the conductor, and becomes equal to the velocity of light v if there is no power dissipation, and, in the latter case, L would be equal to LI, the ex ...", "... y, etc. More complete, this equation is CLt = ^, (40) where K = specific capacity or permittivity, /* = permeability of the medium. 130 ELECTRIC DISCHARGES, WAVES AND IMPULSES. E. Conductor with ground return. 47. As seen in the preceding, in the electric field of conductor A and return conductor B, at distance s from each other, Fig. 9, the lines of magnetic force from conductor A to the center line CC' are equal in number and in magnetic energy to the lines of mag- netic force which surround the conductor in F ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-03", "section_label": "Lecture 3: Gravitation And The Gravitational Fleld", "section_title": "Gravitation And The Gravitational Fleld", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2389-3594", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-03/", "snippets": [ "... eding lecture, the conception of the ether as the carrier of radiation had to be abandoned as incompatible with the theory of relativity; the conception of action at a distance is repugnant to our reasoning, and its place is taken by the conception of the field of force, or, more correctly, the energy field. The energy field is a storage of energy in space, character- ized by the property of exerting a force on any body susceptible to this energy — that is, a magnetic field on a magnetizable body, a gravitational field ...", "... IELD 47 where H is the magnetic field intensity and P the magnetic mass, the same quantity which in the days of action at a distance was called the magnetic pole strength, and which is related to the magnetic flux $ by: $ = AtP. The force exerted by an electric field on an electrified body is: F=KQ, (2) where K is the dielectric field intensity and Q the electric mass or electric quantity, also called electrostatic charge, measured in coulombs. The force exerted by a gravitational field is : F = gN, (3) where ...", "... he velocity v. The acceleration produced by the force thus is : a = F/M, (6) 48 RELATIVITY AND SPACE and, substituting in (6) the expressions of the force, in equations (1) to (4), we get: Force: Acceleration: Magnetic field F = HP a = HP/M ] Electric field F = KQ a = KQ/M Gravitational field F = gN a = gN/M Centrifugal field F = CR a = CR/M (7) The acceleration given to a body in a field thus is pro- portional to the field intensity and to the energy mass (magnetic mass, electric mass, etc.) and inv ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "... osite charges on the line wires. This electrostatic influence requires a current pro- portional to the e.m.f. and consisting of a power component, in phase with the e.m.f., and a reactive component, in quadrature thereto. The alternating electromagnetic field of force set up by the line current produces in some materials a loss of energy by magnetic hysteresis, or an expenditure of e.m.f. in phase with the current, which acts as an increase of resistance. This electromagnetic hysteretic loss may take place in the con- ...", "... f iron wires are used, and will then be very serious at high frequencies, such as those of telephone currents. The effect of eddy currents has already been referred to under \"mutual inductive reactance,\" of which it is a power component. The alternating electrostatic field of force expends energy in dielectrics by corona and dielectric hysteresis. In concentric cables, where the electrostatic gradient in the dielectric is com- paratively large, the dielectric losses may at high potentials consume appreciable amounts of ener ...", "... ent, which may be considered as the power component of the capacity current. Besides this, there is the increase of ohmic resistance due to unequal distribution of current, which, however, is usually not large enough to be noticeable. Furthermore, the electric field of the conductor progresses with a finite velocity, the velocity of light, hence lags behind 174 ALTERNATING-CURRENT PHENOMENA the flow of power in the conductor, and so also introduces power components, depending on current as well as on potential di ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... tions at right angles to each other : one direction is the direction of propagation, or of wave travel; the second is the direction of vibration; IG' 6' and the third is the direction per- pendicular to progression and to vibration. For instance, the electric field of a conductor carrying alternating current is a polarized wave: the direction parallel to the conductor is the direction of energy flow; the direction concentric to the con- ductor is the direction of the electromagnetic component, and the direction radi ...", "... tion parallel to the conductor is the direction of energy flow; the direction concentric to the con- ductor is the direction of the electromagnetic component, and the direction radial to the conductor is the direction of the electrostatic component of the electric field. Therefore, if light rays can be polarized, that is, made to ex- hibit different properties in two directions at right angles to each other and to the direction of wave travel, this would prove tke light wave to be a transversal vibration. This is actual ...", "... The electric waves used in wireless telegraphy range in wave lengths from 100 feet or less to 10,000 feet or more, corresponding to 107 to 105 cycles per sec. Still very much longer waves are the fields of alternating cur- rent circuits: the magnetic and electrostatic field of an alterna- ting current progresses as a wave of radiation from the conductor. But as the wave length is very great, due to the low frequency, — 3 X 1010 a 60-cycle alternating current gives a wave length of ^ = 500 X 10\" cm. or 3100 miles — the dis ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "... ine wires. This electrostatic influence re- quires the expenditure of a current proportional to the E.M.F., and consisting of an energy component, in phase with the E.M.F., and a wattless component, in quadrature thereto. The alternating electromagnetic field of force set up by the line current produces in some materials a loss of energy by magnetic hysteresis, or an expenditure of E.M'.F. in phase with the current, which acts as an increase of re- sistance. This electromagnetic hysteretic loss may take place in the c ...", "... per if iron wires are used, and will then be very serious at high frequencies, such as those of telephone currents. The effect of eddy currents has already been referred to under \"mutual inductance,\" of which it is an energy component. The alternating electrostatic field of force expends energy in dielectrics by what is called dielectric hysteresis. In concentric cables, where the electrostatic gradient in the dielectric is comparatively large, the dielectric hysteresis may at high potentials consume considerable amounts ...", "... illations produced by sudden changes of circuit conditions are complex waves of many harmonics, which in their relative magnitude depend upon the initial charge and its distribution — that is, in the case of the lightning dis- charge, upon the atmospheric electrostatic field of force. The fundamental frequency of the oscillating discharge of a transmission line is relatively low, and of not much higher magnitude than frequencies in commercial use in alternating current circuits. Obviously, the more nearly sinusoidal the dis ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-20", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit. 513", "section_title": "Power And Energy Of The Complex Circuit. 513", "kind": "chapter", "sequence": 20, "number": 7, "location": "lines 1228-1261", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-20/", "snippets": [ "... ntaneous power. Effective or mean power. Power transferred. 513 51. Instantaneous and effective value of energy stored in the magnetic field ; its motion along the circuit, and varia- tion with distance and with time. 513 52. The energy stored in the electrostatic field and its compo- nents. Transfer of energy between electrostatic and electromagnetic field. 517 53. Energy stored in a circuit section by the total electric field, and power supplied to the circuit by it. 518 54. Power dissipated in the resistance and ...", "... ircuit, and varia- tion with distance and with time. 513 52. The energy stored in the electrostatic field and its compo- nents. Transfer of energy between electrostatic and electromagnetic field. 517 53. Energy stored in a circuit section by the total electric field, and power supplied to the circuit by it. 518 54. Power dissipated in the resistance and the conductance of a circuit section. 519 55. Relations between power supplied by the electric field of a circuit section, power dissipated in it, and power tra ...", "... ld. 517 53. Energy stored in a circuit section by the total electric field, and power supplied to the circuit by it. 518 54. Power dissipated in the resistance and the conductance of a circuit section. 519 55. Relations between power supplied by the electric field of a circuit section, power dissipated in it, and power transferred to, or received by other sections. 520 56. Flow of energy, and resultant circuit decrement. 521 57. Numerical examples. 522" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... the line wires. This electrostatic influence requires the expenditure of a current proportional to the e.m.f. and consisting of a power component in phase with the e.m.f. and a reactive com- ponent in quadrature thereto. The alternating electromagnetic field of force set up by the line current produces in some materials a loss of power by mag- netic hysteresis, or an expenditure of e.m.f. in phase with the cur- rent, which acts as an increase of resistance. This electro- magnetic hysteresis loss may take place in the ...", "... roper if iron wires are used, and may then be very serious at high fre- quencies such as those of telephone currents. The effect of eddy currents has already been referred to under \" mutual inductance,\" of which if is a power component. The alternating electrostatic field of force expends power in dielectrics by what is called dielectric hysteresis. In concentric cables, where the electrostatic gradient in the dielectric is com- paratively large, the dielectric hysteresis may at high potentials consume considerable amounts ...", "... ncrease of ohmic resistance due to unequal distribution of current, which, however, is usually not large enough to be noticeable at low frequencies. Also, especially at very high frequency, energy is radiated into space, due to the finite velocity of the electric field, and can be represented by power components of current and of voltage respectively. 5. This gives, as the most general case and per unit length of line, LONG-DISTANCE TRANSMISSION LINE 283 E.m.fs. consumed in phase with the current, I, and = r/, rep ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "... — ^i) and with {t + ^i), will occur. The general form of the line oscillation thus is given by substi- tuting {t =F ^i) instead of t into the equations (11), where ^i is the time of propagation over the distance I. li V = velocity of propagation of the electric field, which in air, as with a transmission line, is approximately V = 3X W, (12) and in a medium of permeability fx and permittivity (specific capacity) k is v= y=-y (13) and we denote then and if we denote a = -, (14) h = at', (15) 2 tt/^i ...", "... gressively along the line I, so that at some distance Iq current and voltage are 360 degrees displaced from their values at the starting point, that is, are again in the same phase. This distance Zo is called the wave length, and is the distance which the electric field travels during one period to — -j. of the frequency of oscillation. As current and voltage vary in phase progressively along the line, the effect of inductance and of capacity, as represented by the inductance voltage and capacity current, varies progre ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3956-4744", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "snippets": [ "... — t\\) and with (t + ti), will occur. The general form of the line oscillation thus is given by substi- tuting (t T ti) instead of t into the equations (11), where t\\ is the time of propagation over the distance I. If v = velocity of propagation of the electric field, which in air, as with a transmission line, is approximately v = 3 X 1010, (12) and in a medium of permeability /z and permittivity (specific capacity) K is 3 X 1010 ( . v =5 - T=^> (13) VfUJ and we denote ;•; • .v •'.,. a-j, ffifil (14) th ...", "... gressively along the line Z, so that at some distance 1Q current and voltage are 360 degrees displaced from their values at the starting point, that is, are again in the same phase. This distance Z0 is called the wave length, and is the distance which the electric field travels during one period to = j of the frequency of oscillation. As current and voltage vary in phase progressively along the line, the effect of inductance and of capacity, as represented by the inductance voltage and capacity current, varies progress ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "... noisy spark of very high brilliancy, which traverses the space between the electrodes in an erratic zigzag path, not unlike in appearance to the mechanical fracture of a solid material; and, indeed, the spark is an electrostatic rupture of the gas. If the electrostatic field is fairly uniform, as between parallel plates, or between spheres of a diameter 1.5 or more times their distance, with gradual rising voltage, the spark occurs when the disruptive voltage is reached, without being preceded, at lower voltage, by LUMINESC ...", "... between spheres of a diameter 1.5 or more times their distance, with gradual rising voltage, the spark occurs when the disruptive voltage is reached, without being preceded, at lower voltage, by LUMINESCENCE. 101 any other phenomenon. If, however, the electrostatic field is not uniform, as, for instance, between needle points or small spheres or wires, with increasing voltage the disruptive strength of the gas is exceeded at those places where the field intensity is highest, as at the needle points, before the disruptive ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-107", "section_label": "Apparatus Section 1: Induction Machines: General", "section_title": "Induction Machines: General", "kind": "apparatus-section", "sequence": 107, "number": 1, "location": "lines 18949-19165", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-107/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-107/", "snippets": [ "... f one or several circuits. In consequence of the relative motion of the primary and secondary, the magnetic circuit of the induction motor must be arranged so that the secondary while revolving does not leave the magnetic field of force. That means, the magnetic field of force must be of constant intensity in all directions, or, in other words, the component of magnetic flux in any direction in space be of the same or approximately the same intensity bu ...", "... of the relative motion of the primary and secondary, the magnetic circuit of the induction motor must be arranged so that the secondary while revolving does not leave the magnetic field of force. That means, the magnetic field of force must be of constant intensity in all directions, or, in other words, the component of magnetic flux in any direction in space be of the same or approximately the same intensity but differing in phase. Such a magnetic fie ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "section_title": "Dibtbisnted Capacity, Inductance, Besistance, And", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "... ine wires. This electrostatic influence re- quires the expenditure of a current proportional to the E.M.F., and consisting of an energy component, in phase with the E.M.F., and a wattless component, in quadrature thereto. The alternating electromagnetic field of force set up by the line current produces in some materials a loss of energy by magnetic hysteresis, or an expenditure of E.M.F. in phase with the current, which acts as an increase of re- sistance. This electromagnetic hysteretic loss may take place in the co ...", "... per if iron wires are used, and will then be very serious at high frequencies, such as those of telephone currents. The effect of eddy currents has already been referred to under \"mutual inductance,\" of which it is an energy component. The alternating electrostatic field of force expends energy in dielectrics by what is called dielectric hysteresis. In concentric cables, where the electrostatic gradient in the dielectric is comparatively large, the dielectric hysteresis may at high potentials consume far greater amounts o ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-01", "section_label": "Chapter 1: Electric Conduction. Soled And Liquid", "section_title": "Electric Conduction. Soled And Liquid", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 959-3894", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-01/", "snippets": [ "... When electric power flows through a circuit, we find phe- nomena taking place outside of the conductor which directs the flow of power, and also inside thereof. The phenomena outside of the conductor are conditions of stress in space which are called the electric field, the two main components of the electric field being the electromagnetic component, characterized by the cir- cuit constant inductance, L, and the electrostatic component, characterized by the electric circuit constant capacity, C. Inside of the conductor ...", "... e find phe- nomena taking place outside of the conductor which directs the flow of power, and also inside thereof. The phenomena outside of the conductor are conditions of stress in space which are called the electric field, the two main components of the electric field being the electromagnetic component, characterized by the cir- cuit constant inductance, L, and the electrostatic component, characterized by the electric circuit constant capacity, C. Inside of the conductor we find a conversion of energy into heat; that ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-12", "section_label": "Chapter 8: Velocity Of Propagation Op Electric Field. 387", "section_title": "Velocity Of Propagation Op Electric Field. 387", "kind": "chapter", "sequence": 12, "number": 8, "location": "lines 972-1013", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-12/", "snippets": [ "CHAPTER VIII. VELOCITY OF PROPAGATION OP ELECTRIC FIELD. 387 67. Conditions, under which the velocity of propagation of the field is of industrial importance. 387 68. Equations of decrease of electric field with the dis- tance. 388 69. Effect of return conductor on distance decrement of field. 389 70 ...", "CHAPTER VIII. VELOCITY OF PROPAGATION OP ELECTRIC FIELD. 387 67. Conditions, under which the velocity of propagation of the field is of industrial importance. 387 68. Equations of decrease of electric field with the dis- tance. 388 69. Effect of return conductor on distance decrement of field. 389 70. Inductance of length I of infinitely long conductor with- out return conductor. 390 71. Equations of magnetic flux, effective resistance of radia- ti ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-41", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 41, "number": 1, "location": "lines 19260-19338", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "snippets": [ "... (c) The distribution of alternating magnetic flux in solid iron, or the screening effect of eddy currents produced in the iron, and the apparent decrease of permeability and increase of power consumption resulting therefrom. (d) The distribution of the electric field of a conductor through space, resulting from the finite velocity of propagation of the electric field, and the variation of self-inductance and mutual inductance and of capacity of a conductor without return, as function of the frequency, in its effect on ...", "... ents produced in the iron, and the apparent decrease of permeability and increase of power consumption resulting therefrom. (d) The distribution of the electric field of a conductor through space, resulting from the finite velocity of propagation of the electric field, and the variation of self-inductance and mutual inductance and of capacity of a conductor without return, as function of the frequency, in its effect on wireless telegraphy. (e) Conductors conveying very high frequency currents, as lightning discharges ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-49", "section_label": "Chapter 9: High-Frequency Conductors", "section_title": "High-Frequency Conductors", "kind": "chapter", "sequence": 49, "number": 9, "location": "lines 27003-27760", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "snippets": [ "... as are used in the connections and the discharge path of lightning arresters and surge protectors, the unequal current distribution in the conductor (Chapter VII) and the power and voltage consumed by electric radiation, due to the finite velocity of the electric field (Chapter VIII), require con- sideration. The true ohmic resistance in high frequency conductors is usually entirely negligible compared with the effective resistance resulting from the unequal current distribution, and still greater may be, at very high ...", "... ffective resistance of unequal current distribution, or thermal resistance of the conductor, is, approximately, (6) and the effective reactance of the internal flux is 10- ohms. (7) The effective resistance resulting from the finite velocity of the electric field, or radiation resistance, by assuming the conductor as a section of an infinitely long conductor without return con- ductor, from Chapter VIII, (25), is r2 = 2 l^flO-* « 1.97 IJ1Q-* ohms, (8) and the effective reactance of the external field of finite ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-50", "section_label": "Chapter 1: General Equations", "section_title": "General Equations", "kind": "chapter", "sequence": 50, "number": 1, "location": "lines 27761-28694", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "snippets": [ "... e.m.f. consumed in the circuit, that is, with an alternating current, the voltage, ir, in phase with the current. L = effective inductance, representing the energy storage i2L depending upon the current, - — , as electromagnetic component & of the electric field; or the voltage generated due to the change of the current, L — , that is, with an alternating current, the at reactive voltage consumed in the circuit - jxi, where x = 2 nfL and / = frequency. g = effective (shunted) conductance, representing the pow ...", "... nt of the current consumed in the circuit, that is, with an alternating voltage, the current, eg, in phase with the voltage. C = effective capacity, representing the energy storage e*C depending upon the voltage, — , as electrostatic component of the electric field; or the current consumed by a change of the de voltage, C — , that is, with an alternating voltage, the (leading) dt reactive current consumed in the circuit - jbe, where 6 = 2 and / = frequency. 417 418 TRANSIENT PHENOMENA In the investigation ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-54", "section_label": "Chapter 5: Free Oscillations", "section_title": "Free Oscillations", "kind": "chapter", "sequence": 54, "number": 5, "location": "lines 31451-32708", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "snippets": [ "... circuit or part of the circuit to which neither electric energy is supplied by some outside source nor from which electric energy is abstracted. Free oscillations thus are the transient phenomena resulting from the dissipation of the energy stored in the electric field of the circuit, or inversely, the accumulation of the energy of the electric field; and their appearance therefore presupposes the possibility of energy storage in more than one form so as to allow 478 FREE OSCILLATIONS 479 an interchange or surge o ...", "... outside source nor from which electric energy is abstracted. Free oscillations thus are the transient phenomena resulting from the dissipation of the energy stored in the electric field of the circuit, or inversely, the accumulation of the energy of the electric field; and their appearance therefore presupposes the possibility of energy storage in more than one form so as to allow 478 FREE OSCILLATIONS 479 an interchange or surge of energy between its different forms, electromagnetic and electrostatic energy. Free ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 557-1002", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-01/", "snippets": [ "... onsideration of the electric power NATURE AND ORIGIN OF TRANSIENTS. 3 in generator, line, and load does not represent the entire phenome- non. While electric power flows over the line A, there is a magnetic field surrounding the line conductors, and an electrostatic field issuing from the line conductors. The magnetic field and the electrostatic or \" dielectric \" field represent stored energy. Thus, during the permanent conditions of the flow of power through the circuit Fig. 3, there is electric energy stored in the space ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 460-882", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "snippets": [ "... nsideration of the electric power NATURE AND ORIGIN OF TRANSIENTS. 3 in generator, line, and load does not represent the entire phenome- non. While electric power flows over the line A , there is a magnetic field surrounding the line conductors, and an electrostatic field issuing from the line conductors. The magnetic field and the electrostatic or \"dielectric \" field represent stored energy. Thus, during the permanent conditions of the flow of power through the circuit Fig. 3, there is electric energy stored in the space ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-04", "section_label": "Lecture 4: The Characteristics Of Space A. The Geometry Of The Gravitational Field", "section_title": "The Characteristics Of Space A. The Geometry Of The Gravitational Field", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3595-6820", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-04/", "snippets": [ "... y, 13 Dielectric field, 18 intensity, 47 Differential metric space, 115 Dimensions of physical space, 97 Direction of curve, 82 Distance between two events, 32 measure of time, 33 E Earth as elliptic 2-space, 75 Einstein, law of gravitation, 11 Electric field, 47 quantity, 47 Electricity, constancy of speed, 4 Electromagnet, 20 Electromagnetic field, 21 wave, 17, 21 frequency, 22 Electron velocity, 8 Electrostatic charge, 47 field, 18 ElUptic geometry, 64, 72, 74 trigonometry, 77 Energy equivalent ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... except e maneti mri the magnetic materials RELATION OF BODIES TO RADIATION. 25 This relation between the constant of the electric circuit K and the constant of optics d was one of the first evidences of the identity of the meclium in which the electric field exists with the medium which carries the light waves. It is, however, only approximately correct, as the refractive index d varies with the frequency and is derived for the extremely high frequencies of light radiation, while K refers to stationary condit ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-01", "section_label": "Theory Section 1: Magnetism and Electric Current", "section_title": "Magnetism and Electric Current", "kind": "theory-section", "sequence": 1, "number": 1, "location": "lines 477-909", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-01/", "snippets": [ "... ELECTRIC CURRENT 1. A magnet pole attracting (or repelling) another magnet pole of equal strength at unit distance with unit force1 is called a unit magnet pole. The space surrounding a magnet pole is called a magnetic field of force, or magnetic field. The magnetic field at unit distance from a unit magnet pole is called a unit magnetic field, and is represented by one line of magnetic force (or shortly \"one line\") per square centimeter, and from a ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-39", "section_label": "Apparatus Section 1: Direct-current Commutating Machines: General", "section_title": "Direct-current Commutating Machines: General", "kind": "apparatus-section", "sequence": 39, "number": 1, "location": "lines 10430-10474", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-39/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-39/", "snippets": [ "... which the field is excited by an electric circuit shunted across the machine terminals, and thus receives a small branch current at full machine voltage, as shown diagrammatically in Fig. 77; series machines, in which the electric field circuit is connected in series with the armature, and thus receives the full machine cur- rent at low voltage (Fig. 78) ; and compound machines, excited by a combination of shunt and series field (Fig. 79). . In compound ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-13", "section_label": "Chapter 13: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 13484-14333", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-13/", "snippets": [ "... ween center and outside of wire, k = 3.2 X 10\"*^, and fR^ = 0.46; hence, when / =' 125 100 60 25 R= 0.061 0.068 0.088 0.136 cm.; thus the effect is noticeable even with relatively small iron wire. Mutual Induction 115. When an alternating magnetic field of force includes a secondary electric conductor, it generates therein an e.m.f. which produces a current, and thereby consumes energy if the circuit of the secondary conductor is closed. 148 ALTERNATING-CURRENT PHENOMENA Particular cases of such secondary cur ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "section_label": "Chapter 14: Dielectric Losses", "section_title": "Dielectric Losses", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "... as high as 40 to 60 per cent. The foremost such losses are: leakage, that is, ih loss of the current passing by conduction (as \"dynamic current\") through the resistance of the dielectric; corona, that is, losses due to a partial or local breakdown of the electrostatic field, and dielectric hysteresis or phenomena of similar nature. It is doubtful whether a true dielectric hysteresis, that is, a molecular dielectric friction, exists. A dielectric loss, propor- tional to the- frequency and to the 1.6*^' power of the dielectri ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-35", "section_label": "Chapter 35: Balanced Symmetrical Polyphase Systems", "section_title": "Balanced Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 35, "number": 35, "location": "lines 37453-37957", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-35/", "snippets": [ "... he capacity of the circuit, of which the inductance is L, then is the fundamental frequency of oscillation, or natural period, that is, the frequency which makes the length, I, of the line a quarter-wave length. Since the velocity of propagation of the electric field is the ve- ^ \"Theoretical Elements of Electrical Engineering.\" BALANCED SYMMETRICAL POLYPHASE SYSTEMS 451 locity of light, v, with a wave-length, 4 I, the number of waves per second, or frequency of oscillation of the line, is f - — and herefrom ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-10", "section_label": "Chapter 10: F", "section_title": "F", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 8269-10499", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "snippets": [ "... expended outside of the conductor in the iron, by a kind of molecular friction, which, when the energy is supplied electrically, appears as magnetic hysteresis, and is caused by the cyclic reversals of magnetic flux in the iron in the alternating magnetic field of force. To examine this phenomenon, first a circuit may be con- sidered, of very high inductance, but negligible true ohmic resistance ; that is, a circuit entirely surrounded by iron, as, for instance, the primary circuit of an alternating-current transformer ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-14", "section_label": "Chapter 14: The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "section_title": "The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14089-14918", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "snippets": [ "... ay from the primary. This mechanical effect is made use of in the indAiction motor, which represents a transformer whose secondary is mounted movably with re- gard to the primary in such a way that, while set in rota- tion, it still remains in the primary field of force. The condition that the secondary circuit, while moving with regard to the primary, does not leave the primary field of magnetic force, requires that this field is not undirec- tional, but that an active field exists in every direction. One way of produ ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-15", "section_label": "Chapter 15: The General Alternating-Current Transformer Or Frequency Converter", "section_title": "The General Alternating-Current Transformer Or Frequency Converter", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 12683-13648", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "snippets": [ "... way from the primary. This mechanical effect is made use of in the induction motor, which represents a transformer whose secondary is mounted movably with re- gard to the primary in such a way that, while set in rota- tion, it still remains in the primary field of force. The condition that the secondary circuit, while revolving with regard to the primary, does not leave the primary field of magnetic force, requires that this field is not undirectional, but that an active field exists in every direction. One way of produ ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-11", "section_label": "Chapter 12: Frequency Converter Or General Alternating Current Transformer", "section_title": "Frequency Converter Or General Alternating Current Transformer", "kind": "chapter", "sequence": 11, "number": 12, "location": "lines 14897-17124", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-11/", "snippets": [ "... force is made use of for doing the work: the induction motor represents an alternating-current transformer, in which the secondary is mounted niovably with regards to the primary, in such a manner that, while set in motion, it still remains in the primary field of force. This requires, i hat the induction motor field is not constant in one direction, but that a magnetic field exists in every direction, in other words that the magnetic field successively assumes all directions, as a so- called rotating field. The induct ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-22", "section_label": "Chapter 9: Inductive Discharges. 535", "section_title": "Inductive Discharges. 535", "kind": "chapter", "sequence": 22, "number": 9, "location": "lines 1286-1316", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-22/", "snippets": [ "... . Line open or grounded at end. Evaluation of frequency constant and resultant decrement. 538 67. The final equations, and their discussion. 540 68. Numerical example. Calculation of the first six har- monics. 542 APPENDIX: VELOCITY FUNCTIONS OF THE ELECTRIC FIELD. 545 SECTION I TRANSIENTS IN TIME TKANSIENTS IN TIME" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-43", "section_label": "Chapter 3: The Natural Period Of The Transmission Line", "section_title": "The Natural Period Of The Transmission Line", "kind": "chapter", "sequence": 43, "number": 3, "location": "lines 21721-23178", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "snippets": [ "... scillations produced by sudden changes of circuit conditions are complex waves of many harmonics, which in their relative magnitude depend upon the initial charge and its distribution — that is, in the case of the lightning discharge, upon the atmospheric electrostatic field of force. NATURAL PERIOD OF TRANSMISSION LINE 329 The fundamental frequency of the oscillating discharge of a transmission line is relatively low, and of not much higher mag- nitude than frequencies in commercial use in alternating-current circuits. ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-51", "section_label": "Chapter 2: Discussion Of General Equations", "section_title": "Discussion Of General Equations", "kind": "chapter", "sequence": 51, "number": 2, "location": "lines 28695-29315", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "snippets": [ "... or L C r -H g = L H- C, (89) or, in words, the power coefficients of the circuit are proportional to the energy storage coefficients, or the time constant of the electromagnetic field of the circuit, — , equals the time constant L of the electrostatic field of the circuit, -^ , then u = — = — = time constant of the circuit, (90) L C and from equation (54) R* = s2 + (f, h = VWs = as, k = VWq = aq, and from equation (52) = L . /L c/ m 0, (91) and / = 0; (92) DISCUSSION OF GENERAL E ..." ] } ] }, { "id": "current-transformer", "label": "Current transformer", "aliases": [ "Current transformer", "current-transformer" ], "total_occurrences": 189, "matching_section_count": 59, "matching_source_count": 12, "source_totals": [ { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 46, "section_count": 8 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 32, "section_count": 8 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 28, "section_count": 15 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 25, "section_count": 5 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 21, "section_count": 5 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 9, "section_count": 2 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 7, "section_count": 3 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 7, "section_count": 4 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 5, "section_count": 3 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 3, "section_count": 2 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 3, "section_count": 2 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 3, "section_count": 2 } ], "section_hits": [ { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-11", "section_label": "Chapter 12: Frequency Converter Or General Alternating Current Transformer", "section_title": "Frequency Converter Or General Alternating Current Transformer", "kind": "chapter", "sequence": 11, "number": 12, "location": "lines 14897-17124", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-11/", "snippets": [ "CHAPTER XII FREQUENCY CONVERTER OR GENERAL ALTERNATING- CURRENT TRANSFORMER 103. In general, an alternating-current transformer conafete of a magnetic circuit, interlinked with two electric circuits or sets of electric circuits, the primary circuit, in which power, sup- plied by the impressed voltage, is consumed, and the second ...", "CHAPTER XII FREQUENCY CONVERTER OR GENERAL ALTERNATING- CURRENT TRANSFORMER 103. In general, an alternating-current transformer conafete of a magnetic circuit, interlinked with two electric circuits or sets of electric circuits, the primary circuit, in which power, sup- plied by the impressed voltage, is consumed, and the secondary circuit, in which a corresponding amount of elect ...", "... his power finds its mechanical equivalent in a repulsive llirusi acting between primary and secondary conductors. Thus, if the secondary is not held rigidly, with regards to the primary, it will be repelled and move. This repulsion is used in the constant-current transformer for regulating the current for constancy independent of the load. In the induction motor, this mechanical force is made use of for doing the work: the induction motor represents an alternating-current transformer, in which the secondary is mounted niovabl ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-14", "section_label": "Chapter 14: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 11605-12682", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "snippets": [ "CHAPTER XIV. THE ALTERNATING-CURRENT TRANSFORMER. 126. The simplest alternating-current apparatus is the transformer. It consists of a magnetic circuit interlinked with two electric circuits, a primary and a secondary. The primary circuit is excited by an impressed E.M.F., while in the secondary circu ...", "... 0 -8 = 4.44 .Afo* 10 -'volts; hence, if the E.M.F., frequency, and number of turns are determined, the maximum magnetic flux is To produce the magnetism, $, of the transformer, a M.M.F. of 5 ampere-turns is required, which is determined ALTERNATING-CURRENT TRANSFORMER. 195 by the shape and the magnetic characteristic of the iron, in the manner discussed in Chapter X. For instance, in the closed magnet circuit transformer, the maximum magnetic induction is ($> = & /S, where S = the cross-section of magnetic circuit. ...", "... of M.M.Fs. ot a transformer is constructed thus : Fig. 94. Let, in Fig. 94, O® = the magnetic flux in intensity and phase (for convenience, as intensities, the effective values are used throughout), assuming its phase as the vertical; ALTERNATING-CURRENT TRANSFORMER. 197 that is, counting the time from the moment where the rising magnetism passes its zero value. Then the resultant M.M.F. is represented by the vector QS, leading O^ a»^ = EjOA, 22. Thus, in Figs. 18, 19, and 20, the diagram of an ^temating-current transformer is drawn for the same sec- 122] GRAPHIC REPRESENTATION. 31 •ondary E.M.F., E^^ and secondary current, /j, but with dif- ferent conditions of secondary displacement : -. — In Fig. 18, the secondary current, f^ , lags 60° behind the sec- ondary ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-15", "section_label": "Chapter 15: Induction Motob", "section_title": "Induction Motob", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 14919-17024", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "snippets": [ "CHAPTER XV. INDUCTION MOTOB. 140. A specialization of the general alternating-current transformer is the induction motor. It differs from the sta- tionary alternating-current transformer in so far as the two sets of electric circuits — the primary or excited, and the secondary or induced, circuits — are movable with regard to each other ; and that in ...", "CHAPTER XV. INDUCTION MOTOB. 140. A specialization of the general alternating-current transformer is the induction motor. It differs from the sta- tionary alternating-current transformer in so far as the two sets of electric circuits — the primary or excited, and the secondary or induced, circuits — are movable with regard to each other ; and that in general a number of primary and a number of secondary circuits are used, angularly displa ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "section_label": "Chapter 30: Quartbr-Fhase System", "section_title": "Quartbr-Fhase System", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... we have 2 rt 2 V r« C hence, by substitution, fc fc /■=jeK/ — dec a, Er=jer\\^ — dec a, 422 APPENDIX II. [§294 ii = — ^=^1^^ , r 1 N== r'C 4 7rZ the final equations of the oscillating discharge, in symbolic expression. Oscillating Current Transformer. 294. As an instance of the application of the symbolic method of analyzing the phenomena caused by oscillating currents, the transformation of such currents may be inves- tigated. If an oscillating current is produced in a circuit including the primary ...", "... ombined, — (ri-2a JTi) +/« (r-^2ax) =0, ri+p^r=2a(x,+/^x), Xci +P^x, = (1 + a\") (x, +p^x). Substituting for x^, x, x^^, x^, we have 1 a = -1 £ = ^'{1 +/''Zr,} dec o, 7 = pE( J I dec o, /i = E( K, dec a, the equations of the oscillating-current transformer, with E^ as parameter." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "... these values of El and 7: and also r = 0 = g, we have From these equations it follows that which values, together with the foregoing values of Ev Iv r, g, a, and /8, substituted in (14) reduce these equations to — j (i\\ +jiC) \\~r s^ ALTERNATING-CURRENT TRANSFORMER, 181 Then at x Hence also •£\"„ and 70 are both in quadrature ahead of .C^O5(NCOOOOi'— l i— 1 CO CO CO »H i— 1 • OQ '^ CO CO C ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-94", "section_label": "Apparatus Subsection 94: Synchronous Converters: Thbee-wire Converter", "section_title": "Synchronous Converters: Thbee-wire Converter", "kind": "apparatus-subsection", "sequence": 94, "number": null, "location": "lines 16727-16803", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-94/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-94/", "snippets": [ "... onnections of transformers can, however, be used on six-phase converters, and the connection shown in Fig. 152, which has two coils on each transformer, connected to different phases, on three-phase converters. D. ALTERNATING-CURRENT TRANSFORMER" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-96", "section_label": "Apparatus Section 2: Alternating-current Transformer: Excitation", "section_title": "Alternating-current Transformer: Excitation", "kind": "apparatus-section", "sequence": 96, "number": 2, "location": "lines 16912-17026", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-96/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-96/", "snippets": [ "... uced voltage: and as the induced voltage is practically equal to the impressed voltage 61, at constant impressed voltage, the core loss is practi- cally constant, and is often assumed as constant, that is, the ALTERNATING-CURRENT TRANSFORMER 281 core loss is a constant or no-load loss, and is supplied by the exciting current i0. (b) The i2r losses in the primary and secondary coils. These are load losses, increasing with the square of the load. (c ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-98", "section_label": "Apparatus Section 2: Alternating-current Transformer: Low T*r Loss Type,", "section_title": "Alternating-current Transformer: Low T*r Loss Type,", "kind": "apparatus-section", "sequence": 98, "number": 2, "location": "lines 17030-17323", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-98/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-98/", "snippets": [ "... ransformer is generally heavily loaded only for a short time during the day, partly loaded for a moderate time, and prac- tically unloaded for most of the time. Thus load curves of such a transformer would be: ALTERNATING-CURRENT TRANSFORMER 283 A. Lighting and power B. Lighting only 2 hours at IK load. 2 hours at IK load. 2 hours at % load. 2 hours at % load. 6 hours at Y2 load. 20 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-04", "section_label": "Chapter 4: Vector Representation", "section_title": "Vector Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2149-2759", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-04/", "snippets": [ "... ith a non-inductive load it will be lower than when feeding into a cir- cuit with leading current, as for instance, a synchronous motor circuit under the circumstances stated above. 23. As a further example, we may consider the diagram of an alternating-current transformer, feeding through its secondary circuit an inductive load. For simplicity, we may neglect here the magnetic hysteresis, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the mag ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-13", "section_label": "Chapter 13: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 13484-14333", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-13/", "snippets": [ "... phenomenon of mutual induction as not merely producing a power component and a wattless component of e.m.f. in the primary conductor, but to consider explicitly both the secondary and the primary circuit, as will be done in the chapter on the alternating-current transformer. Only in cases where the energy transferred into the secondary circuit constitutes a small part of the total primary energy, as in the discussion of the disturbance caused by one circuit upon a parallel circuit, may the effect on the primary circuit be c ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-18", "section_label": "Chapter 18: Polyphase Induction Motors", "section_title": "Polyphase Induction Motors", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17717-20445", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-18/", "snippets": [ "... ning OE with OIzo gives the primary terminal voltage represented by vector OEo, and the angle of primary lag, EoOG - 6*0. POLYPHASE INDUCTION MOTORS 215 160. Thus far the diagram is essentially the same as the diagram of the stationary alternating-current transformer. Re- garding dependence upon the slip of the motor, the locus of the different quantities for different values of the slip, s, is determined thus, Fig. 119. Let Ei = sE'. Assume in opposition to 0$, a point. A, such that OA -^ IiTi = El -^ Iisxi ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-10", "section_label": "Chapter 10: F", "section_title": "F", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 8269-10499", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "snippets": [ "... etic field of force. To examine this phenomenon, first a circuit may be con- sidered, of very high inductance, but negligible true ohmic resistance ; that is, a circuit entirely surrounded by iron, as, for instance, the primary circuit of an alternating-current transformer with open secondary circuit. The wave of current produces in the iron an alternating magnetic flux which induces in the electric circuit an E.M.F., — the counter E.M.F. of self-induction. If the ohmic resistance is negligible, the counter E.M.F. equals ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "section_title": "Fouoault Or Eddy 0Ubbent8", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... menon of mutual inductance as not merely producing an energy component and a wattless component of E.M.F. in the primary conductor, but to consider explicitly both the sec- ondary and the primary circuit, as will be done in the chapter on the alternating-current transformer. Only in cases where the energy transferred into the secondary circuit constitutes a small part of the total pri- mary energy, as in the discussion of the disturbance caused by one circuit upon a parallel circuit, may the effect on the primary circuit b ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "section_title": "Dibtbisnted Capacity, Inductance, Besistance, And", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "... .F. differ by Jth period. D,) Generator feeding into elosed circuit : Let X = be the center of cable ; then, -fi'x = — ^_x ; hence : if = at x = ; which equations are the same as in B, where the line is grounded at x = 0. § 116, 117] AL TERN A TING-CURRENT TRANSFORMER, 167" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-04", "section_label": "Chapter 4: Graphic Representation", "section_title": "Graphic Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 1743-2321", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "snippets": [ "... ad it will be lower than when feeding into 'E. Fig. 17. a circuit with leading current, as, for instance, a synchro- nous motor circuit under the circumstances stated above. 21. As a further example, we may consider the dia- gram of an alternating-current transformer, feeding through its secondary circuit an inductive load. For simplicity, we may neglect here the magnetic hysteresis, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the ma ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "section_label": "Chapter 10: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "... ating magnetic field. To examine this phenomenon, first a circuit may be con- sidered, of very high inductance, but negligible true ohmic resistance ; that is, a circuit entirely surrounded by iron, as, for instance, the primary circuit of an alternating-current transformer with open secondary circuit. The wave of current produces in the iron an alternating magnetic flux which induces in the electric circuit an E.M.F., — the counter E.M.F. of self-induction. If the ohmic re- sistance is negligible, that is, practically no E ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "... menon of mutual inductance as not merely producing an energy component and a wattless component of E.M.F. in the primary conductor, but to consider explicitly both the sec- ondary and the primary circuit, as will be done in the chapter on the alternating-current transformer. Only in cases where the energy transferred into the secondary circuit constitutes a small part of the total pri- mary energy, as in the discussion of the disturbance caused by one circuit upon a parallel circuit, may the effect on the primary circuit b ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-02", "section_label": "Chapter 2: Multiple Squirrel-Cage Induction Motor", "section_title": "Multiple Squirrel-Cage Induction Motor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3543-5554", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-02/", "snippets": [ "... the secondary of the first motor is connected to the primary of the second motor, the second machine operates as a motor with the voltage and frequency impressed upon it by the secondary of the first machine. The first machine acts as general alternating-current transformer or frequency converter (see Chapter XII), changing^ part of the primary impressed power into secondary electrical power for the supply of the second machine, and a part into mechanical work. The frequency of the secondary voltage of the first motor, and ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-04", "section_label": "Chapter 5: Single-Phase Induction Motor", "section_title": "Single-Phase Induction Motor", "kind": "chapter", "sequence": 4, "number": 5, "location": "lines 8555-10582", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-04/", "snippets": [ "... the consideration of the internal 102 ELECTRICAL APPARATUS reaction of the motor is eliminated by the comparison with the polyphase motor. In calculating the effective impedance of the motor at stand- still, we consider the same as an alternating-current transformer, and use the equivalent circuit of the transformer, as discussed in Chapter XVII of \"Theory and Calculation of Alternating- current Phenomena.\" That is, the induction motor is con- sidered as two impedances, Za and Z(, connected in series to the -PFL ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-18", "section_label": "Chapter 20: Single-Phase Commutator Motors", "section_title": "Single-Phase Commutator Motors", "kind": "chapter", "sequence": 18, "number": 20, "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "... ism of the alter- nating-current motor must be in phase with the armature cur- rent, or nearly so. This is inherently the case with the series type of motor, in which the same current traverses field coils and armature windings. Since in the alternating-current transformer the primary and secondary currents and the primary voltage and the secondary voltage are proportional to each other, the different circuits of the alternating-current commutator motor may be connected with each other directly (in shunt or in series, accor ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-06", "section_label": "Chapter 6: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 11051-12221", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-06/", "snippets": [ "... thus is exerted the force F -: = 28 tons 4 This is the average force, and the force varies with double frequency, between and 56 tons, and is thus a large force. 56. Substituting to = — in (54), gives as the short-circuit force of an alternating-current transformer, at maintained terminal voltage, Co, the value „ eo\" 10^ 810 eo« ,„. That is, the short-circuit stresses are inversely proportional to the leakage reactance of the transformer, and to the distance, Z, between the coils. In large transformers on syste ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-08", "section_label": "Chapter 8: Shaping Of Waves By Magnetic Saturation", "section_title": "Shaping Of Waves By Magnetic Saturation", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 12962-16963", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-08/", "snippets": [ "... us, magnetic saturation may in supposedly low-voltage cir- cuits produce dangerously high-voltage peaks. A transformer, at open secondary circuit, is a closed magnetic circuit reactance, and in a transformer connected in series into a circuit — such as a current transformer, etc. — at open secondary circuit unexpectedly high voltages may appear by magnetic saturation. 67. From the preceding, it follows that the relation of alternat- ing current to alternating voltage, that is, the reactance of a closed magnetic circuit, wi ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... =223 10 vc Its / / / / / / / / / / / 6 4 2 / / ( / , / 4.0 ^ t = 0.2 0.4 0.6 0.8 1.0 1.2 X 10'8Sec. Fig. 18. Oscillating-current generator condenser charge. (a) The Tesla transformer, that is, an oscillating-current transformer, has no iron, but a primary coil of very few turns (20) and a secondary coil of a larger number of turns (360), both immersed in oil. While the actual ohmic resistance of the discharge circuit is only 0.1 ohm, the load on the secondary of the Tesla trans ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-41", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 41, "number": 1, "location": "lines 19260-19338", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "snippets": [ "... or carrying alternating current, as the rail return of a single-phase railway, with the current density at the center or in general inside of the conductor, or the distribution of alternating magnetism inside of a solid iron, as a lamina of an alternating-current transformer, etc. In such transient phenom- ena in space, the electric quantities, which appear as functions of space or distance, are not the instantaneous values, as in the preceding chapters, but are alternating currents, e.m.fs., etc., characterized by intensity ..." ] } ] }, { "id": "damping", "label": "Damping", "aliases": [ "damped", "damping", "decrement", "logarithmic decrement" ], "total_occurrences": 175, "matching_section_count": 38, "matching_source_count": 10, "source_totals": [ { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 66, "section_count": 20 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 33, "section_count": 4 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 21, "section_count": 4 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 19, "section_count": 3 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 12, "section_count": 1 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 12, "section_count": 1 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 6, "section_count": 1 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 2, "section_count": 1 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 2, "section_count": 2 }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 2, "section_count": 1 } ], "section_hits": [ { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 16, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... even in comparison with the time of one alternating half-wave. Characteristic con- stants of the oscillating current are the period, T, or frequency, / = 7p, the first amplitude and the ratio of any two successive amplitudes, the latter being called the decrement of the wave. The oscillating current will thus be represented by the product of a periodic function, and a function decreasing in geometric proportion with the time. The latter is the exponential function, A^\"<\". 343 344 ELECTRIC CIRCUITS 182. ...", "... at of the oscillating wave, E = ec\"*** cos { — 0), is tan jS = — {tan (0 — ^) + «}• Hence, it is increased over that of the alternating sine wave by the constant, a. The ratio of the amplitudes of two consequent periods is A is called the numerical decrement of the oscillating wave, a the exponential decrement of the oscillating wave, a the angu- lar decrement of the oscillating wave. The oscillating wave can be represented by the equation, E = e€\"***'^«cos(« - 6). In the example represented by Figs. 130 a ...", "... is tan jS = — {tan (0 — ^) + «}• Hence, it is increased over that of the alternating sine wave by the constant, a. The ratio of the amplitudes of two consequent periods is A is called the numerical decrement of the oscillating wave, a the exponential decrement of the oscillating wave, a the angu- lar decrement of the oscillating wave. The oscillating wave can be represented by the equation, E = e€\"***'^«cos(« - 6). In the example represented by Figs. 130 and 131, we have A = 0.4, a = 0.1435, a = 8.2°. Impe ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-11", "section_label": "Chapter 11: Instability Of Circuits: Induction And Syn Chronous Motors", "section_title": "Instability Of Circuits: Induction And Syn Chronous Motors", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 21382-22633", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-11/", "snippets": [ "... n shows the oscillation of speed corresponding to the oscillation of position. The dotted curve, Wi, then shows the energy losses resulting from the oscillation of speed (hysteresis and eddies in the pole faces, currents in damper windings), that is, the damping power, assumed as proportional to the square of the speed. If there is no lag of the synchronizing force behind the position displacement, the synchronizing force, that is, the force which tends to bring the rotor back from a position behind or ahead of ...", "... n to the normal position, then is INSTABILITY OF CIRCUITS 211 derived by multiplying —p with v, and is shown dotted as Wj in Fig. 104. As seen, it has a double-frequency alternation with zero as average. The total resultant power or the resulting damping effect which restores stability, then, is the sum of the synchronizing power ifa and_ the damping power wi, and is shown by the dotted Fio. 104. curve v>. As seen, under the assumption or Pig. 104, in this case a rapid damping occurs. If the dampin ...", "... h v, and is shown dotted as Wj in Fig. 104. As seen, it has a double-frequency alternation with zero as average. The total resultant power or the resulting damping effect which restores stability, then, is the sum of the synchronizing power ifa and_ the damping power wi, and is shown by the dotted Fio. 104. curve v>. As seen, under the assumption or Pig. 104, in this case a rapid damping occurs. If the damping winding, which consumes a part of all the power, Wi, is inductive — and to a shght extent it alwa ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-55", "section_label": "Chapter 6: Transition Points And The Complex Circuit", "section_title": "Transition Points And The Complex Circuit", "kind": "chapter", "sequence": 55, "number": 6, "location": "lines 32709-33527", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "snippets": [ "... (269) it then follows that ul + sl = u2 + s2 = M3 + s3 = . . . = un + sn = w0, (276) where w17 w2, w3, etc., wn are the time constants of the individual sections of the complex circuit, ^ ( 7 + ^ )> an<^ uo may ^e callet^ 2 \\L LI the resultant time decrement of the complex circuit. 45. Equation (269), by canceling equal terms on both sides, then assumes the form A1e+'>*' cos [q (^- t) - «J - 5^— '*« cos [g (^, + 0 - &] = A2^+S2^ cos b (A - 0— «21 - ^2^\"S2Al cos [q (^ + t) - ft], and, resolved for cos <# an ...", "... UIT 507 46. The general equation of current and e.m.f. in a complex circuit thus also consists of two terms, the main wave A in equations (272), (273), and its reflected wave B. The factor e-(»+^ = e-^ jn equations (273) and (275) repre- sents the time decrement, or the decrease of the intensity of the wave with the time, and as such is the same throughout the entire circuit. In an isolated section, of time constant u, the time decrement, from Chapters III and V, is, however, e~ut; that is, with the decrement e~u ...", "... The factor e-(»+^ = e-^ jn equations (273) and (275) repre- sents the time decrement, or the decrease of the intensity of the wave with the time, and as such is the same throughout the entire circuit. In an isolated section, of time constant u, the time decrement, from Chapters III and V, is, however, e~ut; that is, with the decrement e~ut the wave dies out in the isolated sec- tion at the rate at which its stored energy is dissipated by the power lost in resistance and conductance. In a section of the circuit con ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "section_label": "Chapter 30: Quartbr-Fhase System", "section_title": "Quartbr-Fhase System", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... even in comparison with the time of one alternating half- wave. Characteristic constants of the oscillating current are the period T or frequency .■V= 1/7\", the first ampli- tude and the ratio of any two successive amplitudes, the latter being called the decrement of the wave. The oscil- lating current will thus be represented by the product of s^ s: \"-^^ A 7' S;~-- X\" Ji~ S.' ^i ..-:^-~-^--_ Z ^ _--\" \\.z-- \"■\"Sfcit ^' ..335 .g^.- a periodic function, and a function decreasing in geometri ...", "... of the oscillating wave E ^ re\"** cos (<^ — w) is tan ^3 = — {tan (<^ — u>) + a} . Hence, it is increased over that of the alternating sine wave by the constant a. The ratio of the amplitudes of two consequent periods is E, A is called the numerical decrement of the oscillating wave, a the exponential decrement of the oscillating wave, a the angular decrement of the oscillating wave. The oscillating wave can be represented by the equation In the instance represented by Figs. 181 and 182, we have A = .4, a = ...", "... n ^3 = — {tan (<^ — u>) + a} . Hence, it is increased over that of the alternating sine wave by the constant a. The ratio of the amplitudes of two consequent periods is E, A is called the numerical decrement of the oscillating wave, a the exponential decrement of the oscillating wave, a the angular decrement of the oscillating wave. The oscillating wave can be represented by the equation In the instance represented by Figs. 181 and 182, we have A = .4, a = .1435, a = 8.2°. Impcdarice and Admittance, 283. I ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-32", "section_label": "Chapter 32: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 25904-27405", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "snippets": [ "... even in comparison with the time of one alternating half- wave. Characteristic constants of the oscillating current are the period T or frequency N = 1/7\", the first ampli- tude and the ratio of any two successive amplitudes, the latter being called the decrement of the wave. The oscil- lating current will thus be represented by the product of V ^ ! I\"**' \\ ^ -. \\ / S r~~ -- __ 1 > \\ 180 / 3W \\ MO ^ ^-1 raT X — — TWO — J j»W8Q \\ / \\ . ___ ^. •^-i ...", "... at of the oscillating wave E = *?e~a* cos (<£ — to) is tan /3 = — {tan (<£ — w) + a} . Hence, it is increased over that of the alternating sine wave by the constant a. The ratio of the amplitudes of two consequent periods is A is called the numerical decrement of the oscillating wave, a the exponential decrement of the oscillating wave, a the angular decrement of the oscillating wave. The oscillating wave can be represented by the equation £ = ec-**™\" cos ($ — 5). In the instance represented by Figs. 181 and ...", "... tan /3 = — {tan (<£ — w) + a} . Hence, it is increased over that of the alternating sine wave by the constant a. The ratio of the amplitudes of two consequent periods is A is called the numerical decrement of the oscillating wave, a the exponential decrement of the oscillating wave, a the angular decrement of the oscillating wave. The oscillating wave can be represented by the equation £ = ec-**™\" cos ($ — 5). In the instance represented by Figs. 181 and 182> we have A = .4, a = .1435, a = 8.2°. Impedan ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-53", "section_label": "Chapter 4: Traveling Waves", "section_title": "Traveling Waves", "kind": "chapter", "sequence": 53, "number": 4, "location": "lines 30244-31450", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "snippets": [ "... een in Chapter III, especially in electric power cir- cuits, overhead or underground, the longest existing standing wave has a wave length which is so small compared with the critical wave length — where the frequency becomes zero — that the effect of the damping constant on the frequency and the wave length is negligible. The same obviously applies also to traveling waves, generally to a still greater extent, since the lengths of traveling waves are commonly only a small part of the length of the circuit. Usually ...", "... e obviously applies also to traveling waves, generally to a still greater extent, since the lengths of traveling waves are commonly only a small part of the length of the circuit. Usually, therefore, in the discussion of traveling waves, the effect of the damping constants on the fre- quency constant q and the wave length constant k can be neglected, that is, frequency and wave length assumed as inde- pendent of the energy loss in the circuit. Usually, therefore, the equations (74) and (75) can be applied in dea ...", "... ) which latter term is independent of the distance, but merely a function of the time tt when counting the time at any point of the line from the moment of the passage of the same phase of the wave. Since the coefficient in the exponent of the distance decrement £~uA contains only the circuit constant, but does not contain s and q or the other integration constants, resubstituting from equations (71) to (68), x = ai = i VLO, we have uX = u \\/LC I where I is measured in any desired length. 462 TRANSIE ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "... a circuit storing energy in the dielectric and magnetic field, current and voltage are given by the expression i = ioe-\"^ cos ((/> T CO — 7), ^ . . e = eoe~\"' sin ((^ =F co — 7), where T co — 7), ) where 0 is the time angle, co the distance angle, u the exponential decrement, or the \"power-dissipation constant,\" and i0 and eQ the maximunl current and voltage respectively. The power flow at any point of the circuit, that is, at any dis- tance angle co, and at any time t, that is, time angle <£, then is p = ei, = e0ioe~2ut ...", "... , as illustrated by B in Fig. 42. (c) The flow of power is increasing in the direction of propaga- tion, as illustrated by C in Fig. 42. Obviously, in all three cases the flow of power decreases, due to the energy dissipation by r and g, that is, by the decrement e~ut. Thus, in case (a) the flow of power along the circuit decreases at TRAVELING WAVES. 93 the rate e~ut, corresponding to the dissipation of the stored energy by e-\"', as indicated by A ' in Fig. 42; while in the case (6) the power flow decreases f ...", "... he current and voltage would decrease by the term e~w<, if the line element had only its own stored energy available, when receiving energy from the power flow the decrease of current and voltage would be slower, that is, by a term hence the exponential decrement u is decreased to (u — s), and s then is the exponential coefficient corresponding to the energy supply by the flow of power. Thus, while u is called the dissipation constant of the circuit, s may be called the power-transfer constant of the circuit. I ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... trodynamic generation. It becomes of importance, therefore, to investigate whether by the use of the condenser discharge the range of frequencies can be extended. Since the oscillating current approaches the effect of an alternating current only if the damping is small, that is, the resistance low, the condenser discharge can be used as high frequency generator only by making the circuit of as low resist- ance as possible. 67 68 TRANSIENT PHENOMENA This, however, means limited power. When generating oscil ...", "... ndred thousands of cycles. At frequencies between 500 and 2000 cycles, the use of iron in the reactive coil has to be restricted to an inner core, and at frequencies above this iron cannot be used, since hysteresis and eddy currents would cause excessive damping of the oscil- lation. The reactive coil then becomes larger in size. 47. Assuming 96 per cent efficiency of the reactive coil and 99 per cent of the condenser, gives since r = 0.05 x, r - 0.05 V x = 2 xfL, 1 and the energy of the dischar ...", "... \\^LC = 10 6* C volt-ampere-seconds; — T thus the power factor is cos 00 = 0.05. 72 . TRANSIENT PHENOMENA Since the energy stored in the capacity is WQ = ^ joules, the critical resistance is hence, r. - „ 0 7 = 0.025, *'4 and the decrement of the oscillation is A = 0.92, that is, the decay of the wave is very slow at no load. Assuming, however, as load an external effective resistance equal to three times the internal resistance, that is, an elec- trical efficiency of 75 per cent, gives ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... lectric, speed of propagation in 422 Closed circuit transmission line 306 Col al 392, 394 Commutation and rectification 222 as transient phenomenon 40 Commutator, rectifying 229 Complex circuit, of waves 498 power and energy 513 resultant time decrement 504 traveling wave 468 Compound wave at transition point 532 Condenser, also see Capacity. charge, inductive 18 noninductive 18 circuit of negligible inductance 55 equations 48 oscillation, effective value of voltage, current and power. ... 70 ...", "... g wave 468 Compound wave at transition point 532 Condenser, also see Capacity. charge, inductive 18 noninductive 18 circuit of negligible inductance 55 equations 48 oscillation, effective value of voltage, current and power. ... 70 efficiency, decrement and output 72 frequency 62 general equations 60 size and rating 69 starting on alternating voltage 94 voltage in inductive circuit 49 Conductance, shunted, effective 12 Conductors at high frequency 403 Constant-current mercury arc rectifier 25 ...", "... nd discharge 53 resistance of condenser oscillation 66 start of condenser on alternating voltage 95 Current density, in alternating-current conductor 372 effective, of oscillating-current generator 81 transformation at transition point of wave 529 Damping of condenser oscillation 66, 72 Decay of continuous current in inductive circuit 17 of wave of condenser oscillation 72 Decrement of condenser oscillation 65, 72 resultant time, of complex circuit 504 Destructive voltages in cables and transmission ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-16", "section_label": "Chapter 18: Surging Of Synchronous Motors", "section_title": "Surging Of Synchronous Motors", "kind": "chapter", "sequence": 16, "number": 18, "location": "lines 20975-21712", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-16/", "snippets": [ "... variation of the phase relation between e and to, and correspond- ing variation of speed and current occurs, of an amplitude and period depending upon the circuit conditions and the mechanical momentum. If the amplitude of this pulsation has a positive decrement, that is, is decreasing, the motor assumes after a while a constant position of e regarding ea, that is, its speed becomes uniform. If, however, the decrement of Hie pulsation is negative, an infinitely small pulsation will continuously increase in amplit ...", "... cuit conditions and the mechanical momentum. If the amplitude of this pulsation has a positive decrement, that is, is decreasing, the motor assumes after a while a constant position of e regarding ea, that is, its speed becomes uniform. If, however, the decrement of Hie pulsation is negative, an infinitely small pulsation will continuously increase in amplitude, until the motor is thrown out of step, or the decrement becomes zero, by the power consumed by forces opposing the pulsation, as anti-surging devices, or ...", "... while a constant position of e regarding ea, that is, its speed becomes uniform. If, however, the decrement of Hie pulsation is negative, an infinitely small pulsation will continuously increase in amplitude, until the motor is thrown out of step, or the decrement becomes zero, by the power consumed by forces opposing the pulsation, as anti-surging devices, or by the periodic pulsation of the syn- chronous reactance, etc. If the decrement is zero, a pulsation 288 SURGING OF SYNCHRONOUS MOTORS 289 started once ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 6125-6803", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-09/", "snippets": [ "... in velocity measure) Xi, X2, X3 . . . , this entire circuit, when left to itself, gradually dissipates its stored energy by a transient. As function of the time, this transient must decrease at the same rate Uq throughout the entire circuit. Thus the time decrement of all the sections must be Every section, however, has a power-dissipation constant, Ui, U2, U3 . . . , which represents the rate at which the stored energy of the section would be dissipated by the losses of power in the section, t , t , t ... But ...", "... the rate at which the stored energy of the section would be dissipated by the losses of power in the section, t , t , t ... But since as part of the whole circuit each section must die down at the same rate e~\"o', in addition to its power-dissipation decrement e\"\"'^, e~\"2< , . . ^ each section must still have a second time decrement, e~^\"o~\"i^V' e~^\"''~\"2)< . . . This latter does not represent power dissipation, and thus represents power transfer. That is, §1 = Wo \"~ Ui, S2 = Uo — II2, (1) It thus follows ...", "... the losses of power in the section, t , t , t ... But since as part of the whole circuit each section must die down at the same rate e~\"o', in addition to its power-dissipation decrement e\"\"'^, e~\"2< , . . ^ each section must still have a second time decrement, e~^\"o~\"i^V' e~^\"''~\"2)< . . . This latter does not represent power dissipation, and thus represents power transfer. That is, §1 = Wo \"~ Ui, S2 = Uo — II2, (1) It thus follows that in a compound circuit, if Uo is the average exponential time decreme ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 5521-6088", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "snippets": [ "... in velocity measure) Xi, X2, X3 . . . , this entire circuit, when left to itself, gradually dissipates its stored energy by a transient. As function of the time, this transient must decrease at the same rate u0 throughout the entire circuit. Thus the time decrement of all the sections must be 6-**. Every section, however, has a power-dissipation constant, u\\t Uz, u3 . . . , which represents the rate at which the stored energy of the section would be dissipated by the losses of power in the section, €-\"»', €-«*' ...", "... which the stored energy of the section would be dissipated by the losses of power in the section, €-\"»', €-«*', €-\"*' . . . But since as part of the whole circuit each section must die down at the same rate e~Uot, in addition to its power-dissipation decrement e~Ul*, e~\"2' . . . , each section must still have a second time decrement, €-(«*-*J*, e-(u0-u,)t t t t This latter does not represent power dissipation, and thus represents power transfer. That is, 51 = U0 — Ui, 52 = UQ — Uz, (1) It thus follows tha ...", "... of power in the section, €-\"»', €-«*', €-\"*' . . . But since as part of the whole circuit each section must die down at the same rate e~Uot, in addition to its power-dissipation decrement e~Ul*, e~\"2' . . . , each section must still have a second time decrement, €-(«*-*J*, e-(u0-u,)t t t t This latter does not represent power dissipation, and thus represents power transfer. That is, 51 = U0 — Ui, 52 = UQ — Uz, (1) It thus follows that in a compound circuit, if u0 is the average exponential time decrement o ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-27", "section_label": "Chapter 5: Resistance, Inductance, And Capacity In Series Condenser Charge And Discharge", "section_title": "Resistance, Inductance, And Capacity In Series Condenser Charge And Discharge", "kind": "chapter", "sequence": 27, "number": 5, "location": "lines 4072-5311", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "snippets": [ "... and by (48) and (55) : CONDENSER CHARGE AND DISCHARGE 65 43. Due to the factor e ' , successive half waves of oscilla- tion decrease the more in amplitude, the greater the resistance r. The ratio of the amplitude of successive half waves, or the decrement of the oscillation, is A = e 2L \\ where tl = duration of one half wave or one half cycle, = -— . 2/ A a.o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Fig. 15. Decrement of Oscillation. Hence, from (50), and Denoting the critical resistance ...", "... he resistance r. The ratio of the amplitude of successive half waves, or the decrement of the oscillation, is A = e 2L \\ where tl = duration of one half wave or one half cycle, = -— . 2/ A a.o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Fig. 15. Decrement of Oscillation. Hence, from (50), and Denoting the critical resistance as 2 _ 4L r> :: c' we have or, A «e -s -^-i (60) (61) (62) 66 TRANSIENT PHENOMENA that is, the decrement of the oscillating wave, or the decay ...", "... 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Fig. 15. Decrement of Oscillation. Hence, from (50), and Denoting the critical resistance as 2 _ 4L r> :: c' we have or, A «e -s -^-i (60) (61) (62) 66 TRANSIENT PHENOMENA that is, the decrement of the oscillating wave, or the decay of the oscillation, is a function only of the ratio of the resistance of the circuit to its critical resistance, that is, the minimum resistance which makes the phenomenon non-oscillatory. In Fig. 15 are shown the nu ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2485-3386", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-04/", "snippets": [ "... e transient pulsation of armature reaction appears with reduced amplitude in the field current, and this reduction is the greater, the poorer the mutual inductance, that is, the more distant the field winding is from the armature wind- ing. In Fig. 22(7 a damping of 20 per cent is assumed, which corresponds to fairly good mutual inductance between field and armature, as met in turboalternators. If the field-exciting circuit contains inductance outside of the alternator field, as is always the case to a slight ext ...", "... ature reaction. The transient of the rotating field, of duration T = .1 sec, is constructed as in paragraph 18, and for its instan- taneous values the percentage deviation of the resultant field from its permanent value is calculated. Assuming 20 per cent damping in the reaction on the field excitation, the instantaneous values of the slow field transient (that is, of the current (^ ~ z'o), since I'o is the permanent component) then are increased or de- creased by 80 per cent of the percentage variation of the tran ...", "... from an initial value, which is m times the final value, on the field transient. Assume then that the mutual induction between field and armature is such that 60 per cent of the pulsation of armature reaction appears in the field current. Forty per cent damping for the double-frequency reaction would about correspond to the 20 per cent damping assumed for the transient full-frequency pulsa- tion of the polyphase machine. The transient field current thus pulsates by 60 per cent around the slow field transient, as ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2162-2971", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "snippets": [ "... e transient pulsation of armature reaction appears with reduced amplitude in the field current, and this reduction is the greater, the poorer the mutual inductance, that is, the more distant the field winding is from the armature wind- ing. In Fig. 22(7 a damping of 20 per cent is assumed, which corresponds to fairly good mutual inductance between field and armature, as met in turboalternators. If the field-exciting circuit contains inductance outside of the alternator field, as is always the case to a slight ext ...", "... ure reaction. The transient of the rotating field, of duration T = .1 sec., is constructed as in paragraph 18, and for its instan- taneous values the percentage deviation of the resultant field from its permanent value .is calculated. Assuming 20 per cent damping in the reaction on the field excitation, the instantaneous values of the slow field transient (that is, of the current (i — i'0), since i0 is the permanent component) then are increased or de- creased by 80 per cent of the percentage variation of the trans ...", "... from an initial value, which is m times the final value, on the field transient. Assume then that the mutual induction between field and armature is such that 60 per cent of the pulsation of armature reaction appears in the field current. Forty per cent damping for the double-frequency reaction would about correspond to the 20 per cent damping assumed for the transient full-frequency pulsa- tion of the polyphase machine. The transient field current thus pulsates by 60 per cent around the slow field transient, as ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-51", "section_label": "Chapter 2: Discussion Of General Equations", "section_title": "Discussion Of General Equations", "kind": "chapter", "sequence": 51, "number": 2, "location": "lines 28695-29315", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "snippets": [ "... e oscillation of the circuit, in which the stored energy of the circuit is dissipated, but no power supplied one way or the other — that is, if h = 0, from equation (56) s = 0; that is, both waves coincide and form one, which dies out with the time by the decrement e~ut. It thus follows: In general, two waves, with their reflected waves, traverse the circuit, of which the one, i\", e\", increases in amplitude in the direction of propagation, but dies out corre- spondingly more rapidly in time, that is, faster than a ...", "... 2 + i4 = e~utf2 (t + A);J DISCUSSION OF GENERAL EQUATIONS 437 hence, for constant (t - X) on the main waves, and for constant (t + X) on the reflected waves, we have and (78) that is, during its passage along the circuit the wave decreases by the decrement e~ut, or at a constant rate, independent of frequency, wave length, etc., and depending merely on the circuit constants r, L, g, C. The decrement of the traveling wave in the direction of its motion is and therefore is independent of the character of th ...", "... eflected waves, we have and (78) that is, during its passage along the circuit the wave decreases by the decrement e~ut, or at a constant rate, independent of frequency, wave length, etc., and depending merely on the circuit constants r, L, g, C. The decrement of the traveling wave in the direction of its motion is and therefore is independent of the character of the wave, for instance its frequency, etc. 11. The physical meaning of the two waves i' and e' can best be appreciated by observing the effect of ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-56", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit", "section_title": "Power And Energy Of The Complex Circuit", "kind": "chapter", "sequence": 56, "number": 7, "location": "lines 33528-34202", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-56/", "snippets": [ "... being the distance coordinate of the circuit section in any measure, as miles, turns, etc., and r, L, g, C the circuit constants per unit length of I, a- = VIC, u = -(-=• + — ) = time constant of circuit section, 2 YL/ C ' UQ= u + s = resultant time decrement of complex circuit, s = u0 - u = energy transfer constant of circuit section. 613 514 TRANSIENT PHENOMENA The instantaneous value of power at any point X of the circuit at any time t is p = ei [A cos q(X-t) + B sin q (X - t)]2 [C cos q (X + 0 + ...", "... power at any time and any point of the circuit is the difference between the instantaneous power of the main wave and that of the reflected wave. The effective power at any point of the circuit gradually decreases in any section with the resultant time decrement of the total circuit, £-2uotf and varies gradually or exponentially with the distance A, the one wave increasing, the other decreasing, so that at one point of the circuit or circuit section the effective power is zero ; which point of the circuit is a po ...", "... is approximately the case. In this case, as the total power transferred between the sections must be zero, thus: hence, substituting (341), 2X-V = °> (346) and, since O fit , ^ /)/ *» — ^o »# w0A = 5)1^'; (347) that is, the resultant circuit decrement multiplied by the total length of the circuit equals the sum of the time constants of the sections multiplied with the respective length of the section, or, if ?!, ?2 • • • ?i = length of the circuit section, as fraction of the total circuit length A, K ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-03-record", "section_label": "Report Record 4: Record of Four Troubles", "section_title": "Record of Four Troubles", "kind": "report-record", "sequence": 4, "number": 4, "location": "PDF pages 16-27, lines 1139-2164", "status": "pdf-text-extracted-candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-03-record/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-03-record/", "snippets": [ "... machine reverses, and the ma- chines thus oscillate against each other, while the interchange current between the machines fluctuates between a maximum value at maximum phase difference, and zero or a minimum value when machines are in phase. If there were no damping effects, this oscillation would con- tinue with constant amplitude. Due to the damping effects exerted mainly by the lag of the field flux behind the resultant field excitation (the armature reaction component of the synchronous impedance), the amplitude of t ...", "... change current between the machines fluctuates between a maximum value at maximum phase difference, and zero or a minimum value when machines are in phase. If there were no damping effects, this oscillation would con- tinue with constant amplitude. Due to the damping effects exerted mainly by the lag of the field flux behind the resultant field excitation (the armature reaction component of the synchronous impedance), the amplitude of the oscillation steadily diminishes, until the oscillation disappears. That is, the inte ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "section_label": "Lecture 10: Continual And Cumulative Oscillations", "section_title": "Continual And Cumulative Oscillations", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... discharge over the lightning arrester. The only effective protection seems to be a continuous dissipa- tion of the oscillating energy by a resistance closing the oscillat- ing circuit. In general, a moderate capacity would be connected in series with such damping resistance, and would be chosen so as to allow the high frequency to pass practically unobstructed, while practically stopping the passage of the machine frequency, and the waste of power, incident thereto. 2. A continual oscillation involves an energy t ...", "... imentally produced in Hues and high-potential transformer windings. The continual oscillations in transmission lines usually seem to be recurrent oscillations, as in Figs. 59 and 60, while in high-potential trans- former windings, due to their much lesser damping, continuous oscillations seem to be more common, as in Fig. 46. Our knowl- edge of these phenomena is however still extremely incomplete. LECTUEE XI, INDUCTANCE AND CAPACITY OF ROUND PARALLEL CONDUCTORS. A. Inductance and capacity. 46. As inductan ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-84", "section_label": "Apparatus Section 5: Synchronous Converters: Armature Reaction", "section_title": "Synchronous Converters: Armature Reaction", "kind": "apparatus-section", "sequence": 84, "number": 5, "location": "lines 15161-15475", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-84/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-84/", "snippets": [ "... ce it is in quadrature with the field excitation, tends to shift the magnetic flux rapidly across the field poles, and thereby tends to cause sparking and power losses. This oscillating reaction is, however, reduced by the damping effect of the mag- netic field structure. It is somewhat less in the two-circuit single-phase converter. Since in consequence hereof the commutation of the single- phase converter is not as good as that of the polyphase co ...", "... three-phase converter, and quadruple frequency in a four- phase converter. The amplitude of this oscillation in a polyphase converter is small, arid its influence upon the magnetic field is usually neg- ligible, due to the damping effect of the field spools, which act like a short-circuited winding for an oscillation of magnetism. A polyphase converter on unbalanced circuit can be con- sidered as a combination of a balanced polyphase and a single- p ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-19", "section_label": "Chapter 6: Transition Points And The Complex Circuit. 498", "section_title": "Transition Points And The Complex Circuit. 498", "kind": "chapter", "sequence": 19, "number": 6, "location": "lines 1187-1227", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-19/", "snippets": [ "... 1. Transformation of general equations, to velocity unit of distance. 499 42. Discussion. 501 43. Relations between constants, at transition point. 502 xxiv CONTENTS. PAGE 44. The general equations of the complex circuit, and the resultant time decrement % 503 45. Equations between integration constants of adjoining sections. 504 46. The energy transfer constant of the circuit section, and the transfer of power between the sections. 507 47. The final form of the general equations of the complex ci ...", "... er of power between the sections. 507 47. The final form of the general equations of the complex circuit, . 508 48. Full-wave, half-wave, quarter-wave oscillation, and gen- eral high-frequency oscillation. 509 49. Determination of the resultant time decrement of the cir- cuit. 510" ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-06", "section_label": "Lecture 6: Higher Harmonics Of The Generator Wave", "section_title": "Higher Harmonics Of The Generator Wave", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3133-3507", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-06/", "snippets": [ "... of the grounded phase. The use of a resistance in the generator neutral is very desirable also, since it eliminates the danger of a high frequency oscillation between line and ground through the generator reactance in the path of the third harmonic, by damping the oscillation in the resistance. For this reason, the resistance should be non-inductive. To ground the gener- ator neutral through a reactance is very dangerous since it intensifies the danger of a resonance voltage rise. In grounding the generator ne ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... rom the photometric consideration, as 10,000 K. W. seconds, the duration of the discharge would be: 10V5 X 10* = 2 x 10\"* sec, or two-millionths of a second. The discharge probably is oscillatory. In view of the high resistance of the discharge path, the damping effect must be very great, that is, a very large part or nearly all the energy LIGHTNING AND LIGHTNING PROTECTION 269 is expended in the first half-wave ; that is, the discharge consists of only one or very few half- waves. With a duration of the disc ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-04", "section_label": "Chapter 4: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 6942-9061", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-04/", "snippets": [ "... uce high losses. Such, for instance, is the case in induction machines, if the stator and rotor teeth are not proportioned so as to maintain uniform reluctance, or in alterna- tors or direct-current machines, in which the pole faces are slotted to receive damping windings, or compensating windings, etc., if the proportion of armature and pole-piece slots is not carefully designed. 46. The hysteresis loss in an unsymmetrical cycle, between limits Si and B2, that is, with the amplitude of magnetic variation B = 2 ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-10", "section_label": "Chapter 10: Instability Of Circuits : The Arc", "section_title": "Instability Of Circuits : The Arc", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 17632-21381", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-10/", "snippets": [ "... umulative oscillation of some arc in the 200 ELECTRIC CIRCUITS system, and building up to high stationary waves, have frequently been observed. The \"arcing ground\" as recurrent single impulses, the \"arcing ground oscillation'' as more or less rapidly damped recurrent oscillations in transmission lines — of frequencies from a few hun- dred to a few thousand cycles — ^and the \"stationary oscillations\" causing destruction in high-potential transformer windings, at frequencies of 10,000 to 100,000 cycles, thus a ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-07", "section_label": "Chapter 3: The Natural Period Of The Transmission Line. 320", "section_title": "The Natural Period Of The Transmission Line. 320", "kind": "chapter", "sequence": 7, "number": 3, "location": "lines 836-874", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-07/", "snippets": [ "... t both ends : Half-wave oscillation. 333 35. The even harmonics of the half-wave oscillation. 334 36. Circuit open at both ends. 335 37. Circuit closed upon itself: Full-wave oscillation. 336 38. Wave shape and frequency of oscillation. 338 39. Time decrement of oscillation, and energy transfer be- tween sections of complex oscillating circuit. 339 xx CONTENTS. PAGE" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-10", "section_label": "Chapter 6: Alternating Magnetic Flux Distribution. 355", "section_title": "Alternating Magnetic Flux Distribution. 355", "kind": "chapter", "sequence": 10, "number": 6, "location": "lines 904-937", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-10/", "snippets": [ "... es of 60, 1000 and 10,000 cycles per second. 362 55. Depth of penetration of alternating magnetic flux in different metals. 363 56. Wave length, attenuation, and velocity of penetration. 365 57. Apparent permeability, as function of frequency, and damping. 366 58. Numerical example and discussion. 367" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-12", "section_label": "Chapter 8: Velocity Of Propagation Op Electric Field. 387", "section_title": "Velocity Of Propagation Op Electric Field. 387", "kind": "chapter", "sequence": 12, "number": 8, "location": "lines 972-1013", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-12/", "snippets": [ "... PROPAGATION OP ELECTRIC FIELD. 387 67. Conditions, under which the velocity of propagation of the field is of industrial importance. 387 68. Equations of decrease of electric field with the dis- tance. 388 69. Effect of return conductor on distance decrement of field. 389 70. Inductance of length I of infinitely long conductor with- out return conductor. 390 71. Equations of magnetic flux, effective resistance of radia- tion, inductance and impedance. 391 72. Evaluation of functions sil al and col al. ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-15", "section_label": "Chapter 2: Discussion Of General Equations. 431", "section_title": "Discussion Of General Equations. 431", "kind": "chapter", "sequence": 15, "number": 2, "location": "lines 1063-1086", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-15/", "snippets": [ "... two component waves and their reflected waves. Attenuation in time and in space. 431 8. Period, wave length, time and distance attenuation constants. 433 9. Simplification of equations at high frequency, and the velocity unit of distance. 434 10. Decrement of traveling wave. 436 11. Physical meaning of the two component waves. 437 12. Stationary or standing wave. Trigonometric arid logarith- mic waves. 438 13. Propagation constant of wave. 440" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-20", "section_label": "Chapter 7: Power And Energy Of The Complex Circuit. 513", "section_title": "Power And Energy Of The Complex Circuit. 513", "kind": "chapter", "sequence": 20, "number": 7, "location": "lines 1228-1261", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-20/", "snippets": [ "... the conductance of a circuit section. 519 55. Relations between power supplied by the electric field of a circuit section, power dissipated in it, and power transferred to, or received by other sections. 520 56. Flow of energy, and resultant circuit decrement. 521 57. Numerical examples. 522" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-22", "section_label": "Chapter 9: Inductive Discharges. 535", "section_title": "Inductive Discharges. 535", "kind": "chapter", "sequence": 22, "number": 9, "location": "lines 1286-1316", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-22/", "snippets": [ "... ng into distributed circuit. Combination of generating station and transmission line. 535 65. Equations of inductance, and change of constants at transition point. 536 66. Line open or grounded at end. Evaluation of frequency constant and resultant decrement. 538 67. The final equations, and their discussion. 540 68. Numerical example. Calculation of the first six har- monics. 542 APPENDIX: VELOCITY FUNCTIONS OF THE ELECTRIC FIELD. 545 SECTION I TRANSIENTS IN TIME TKANSIENTS IN TIME" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-30", "section_label": "Chapter 8: Low Frequency Surges In High Potential Systems", "section_title": "Low Frequency Surges In High Potential Systems", "kind": "chapter", "sequence": 30, "number": 8, "location": "lines 7826-9227", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "snippets": [ "... m.f. wave, at which the oscillation begins, while the third term, inf , e/\", represents the component of oscillation which depends upon the instantaneous values of current and e.m.f. respectively, at the moment at which the oscillation begins, s c is the decrement of the oscillation. 66. The frequency of oscillation is where / is the impressed frequency. That is, the frequency of oscillation equals the impressed frequency times the square root of the ratio of condensive reactance and inductive reactance of the c ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-40", "section_label": "Chapter 4: Arc Rectification", "section_title": "Arc Rectification", "kind": "chapter", "sequence": 40, "number": 4, "location": "lines 17755-19259", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "snippets": [ "... — at constant L, as resulting dt from a decrease of the angle of overlap by delayed starting of the arc, caused by a defective rectifier, however increases the amplitude of this oscillation, and if the electrostatic capacity is high, and therefore the damping out of the oscillation slow, the Fig. 77. E.m.f. between rectifier anodes. oscillation may reach considerable values, as shown in oscillo- gram, Fig. 77, of the potential difference db. In such cases, if the second half wave of the oscillation reaches ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-46", "section_label": "Chapter 6: Alternating Magnetic Flux Distribution", "section_title": "Alternating Magnetic Flux Distribution", "kind": "chapter", "sequence": 46, "number": 6, "location": "lines 23948-24980", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "snippets": [ "... iron ; and the effect of iron in increasing the magnetic flux disappears only at 400 million cycles, and beyond this frequency iron lowers the magnetic flux. However, even at these frequencies, the presence of iron still exerts a great effect in the rapid damping of the oscillations by the lag of the mean magnetic flux by 45 degrees. Obviously, in large solid pieces of iron, the permeability // falls below that of air even at far lower frequencies. Where the penetration of the magnetic flux lp is small com- par ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-52", "section_label": "Chapter 3: Standing Waves", "section_title": "Standing Waves", "kind": "chapter", "sequence": 52, "number": 3, "location": "lines 29316-30243", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "snippets": [ "... ength lWo is relatively short, so that in long submarine cables standing waves may appear which are not oscillatory in time but die out gradually, that is, are shown by the equation of case B. In such cables, due to their relatively high resist- ance, the damping effect is very great; u = 1500, and standing waves, therefore, rapidly die out. In the investigation of the submarine cable, the complete equations must therefore be used, and q cannot always be assumed as large compared with m and u, except when dealing ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-54", "section_label": "Chapter 5: Free Oscillations", "section_title": "Free Oscillations", "kind": "chapter", "sequence": 54, "number": 5, "location": "lines 31451-32708", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "snippets": [ "... t (237) = 2 Z0 v LC in a half-wave oscillation, J and MV £~w< = e ~ .-^T. (246) ^0 is the wave length, and thus — the frequency, of the funda- mental wave, with the velocity of propagation as distance unit. It is interesting to note that the time decrement of the free oscillation, e~ut, is the same for all frequencies and wave lengths, FREE OSCILLATIONS 491 and that the relative intensity of the different harmonic compo- nents of the oscillation, and thereby the wave shape of the oscillation, remains un ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-57", "section_label": "Chapter 8: Reflection And Refraction At Transition Point", "section_title": "Reflection And Refraction At Transition Point", "kind": "chapter", "sequence": 57, "number": 8, "location": "lines 34203-34896", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-57/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-57/", "snippets": [ "... sec tion of a complex circuit, from equations (290), is - £-sA [C cos q 0* + 0 + D sin q (A + 0]} e = C£-Uot {e+8* [A cos g (J - 0 + # sin g (A - 0] where A = is the same 192 RADIATION, LIGHT, AND ILLUMINATION. FIG. 64. FIG. 65. FIG. 66. LIGHT FLUX AND DISTRIBUTION. 193 as with the ...", "... UMINATION. FIG. 64. FIG. 65. FIG. 66. LIGHT FLUX AND DISTRIBUTION. 193 as with the plane circular radiator (2), the same equations apply. (4) Rounded Circular Surface. Such, for instance, is approximately the incandescent carbon tip of the arc-lamp electrodes, when using carbons of sufficiently small size, so that the entire tip becomes heated. Assuming, in Fig. 66, the radiator as a segment of a sphere, and let 2 aj = the angle subtending this segment, rl the radius of this sphere. For all direc ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-09", "section_label": "Lecture 9: Measurement Of Light And Radiation", "section_title": "Measurement Of Light And Radiation", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 8511-9388", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-09/", "snippets": [ "... In such cases, frequently lights of intermediary color are used to reduce the differences in each observation. Thus the carbon filament lamp is compared with the tungsten lamp, the MEASUREMENT OF LIGHT AND RADIATION. 173 tungsten lamp with the carbon arc lamp, and the latter with the mercury arc lamp. Hereby the uncertainty of each obser- vation is reduced by the reduced color difference. In the final result, however, the comparison of the carbon incandescent- lamp standard and the mercury arc lamp no advantag ...", "... mediary color are used to reduce the differences in each observation. Thus the carbon filament lamp is compared with the tungsten lamp, the MEASUREMENT OF LIGHT AND RADIATION. 173 tungsten lamp with the carbon arc lamp, and the latter with the mercury arc lamp. Hereby the uncertainty of each obser- vation is reduced by the reduced color difference. In the final result, however, the comparison of the carbon incandescent- lamp standard and the mercury arc lamp no advantage is gained, because the errors of the suc ...", "... the carbon arc lamp, and the latter with the mercury arc lamp. Hereby the uncertainty of each obser- vation is reduced by the reduced color difference. In the final result, however, the comparison of the carbon incandescent- lamp standard and the mercury arc lamp no advantage is gained, because the errors of the successive measurements add. Especially is this the case with the constant errors, that is, errors due to the specific color effect, and in consequence thereof the inaccuracy of the final result is not muc ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-40", "section_label": "Chapter 4: Arc Rectification", "section_title": "Arc Rectification", "kind": "chapter", "sequence": 40, "number": 4, "location": "lines 17755-19259", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "snippets": [ "... ridge. This can be done by bringing the terminals into contact and so starting the current, and then by gradually withdrawing the terminals derive the energy of the arc flame by means of the current, from the electric circuit, as is done in practically all arc lamps. Or by increasing the voltage across the gap between the terminals so high that the electrostatic stress in the gap repre- sents sufficient energy to establish a path for the current, i.e., by jumping an electrostatic spark across the gap, this spark is fo ...", "... o cathode; ea = counter e.m.f. Fig. 64. Constant-current of rectifying arc, which is constant; Z0 = mercury arc rectifier. r0 — jx0 = impedance of reactive coil in rectified circuit (\" direct-current re- active coil\"); Z2 = r2 ~ JX2 = impedance of load or arc-lamp circuit; e/ = counter e.m.f. in rectified circuit, which is con- ARC RECTIFICATION 257 stant (equal to the sum of the counter e.m.fs. of the arcs in the lamp circuit) ; #0 = angle of overlap of the two rectifying arcs, or overlap of the currents it an ...", "... ), (19), (20) gives the equations of the rectified current i0, iQ', and of the anode currents i^ and i2 = i0 — iv determined by the constants of the system, Z, Zv e0, and by the impressed e.m.f., e. In the constant-current mercury-arc rectifier system of arc lighting, e, the secondary generated voltage of the constant- current transformer, varies with the load, by the regulation of the transformer, and the rectified current, iQ, i0', is required to remain constant, or rather its average value. Let then be given as co ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-05", "section_label": "Lecture 5: Temperature Radiation", "section_title": "Temperature Radiation", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3946-5076", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-05/", "snippets": [ "... he highest attainable temperature, the boiling point of carbon, the efficiency is much lower, probably below 10 per cent and this would be the highest efficiency attainable by normal temperature radiation. It is utilized for light production in the carbon arc lamp. The carbon arc flame gives practically no light, but all the light comes from the incandescent tips of the carbon electrodes, mainly the positive, which are at the boiling point of carbon and thus give the most efficient temperature radiation. Obviousl ...", "... flame gives practically no light, but all the light comes from the incandescent tips of the carbon electrodes, mainly the positive, which are at the boiling point of carbon and thus give the most efficient temperature radiation. Obviously, in the carbon arc lamp a very large part of the energy is wasted by heat conduction through the carbons, heat convection by air currents, etc., and the total efficiency of the carbon arc lamp, that is, the ratio of the power of the visible radiation to the total electric power ...", "... bon and thus give the most efficient temperature radiation. Obviously, in the carbon arc lamp a very large part of the energy is wasted by heat conduction through the carbons, heat convection by air currents, etc., and the total efficiency of the carbon arc lamp, that is, the ratio of the power of the visible radiation to the total electric power input into the lamp, thus is much lower than the radiation efficiency, that is, the ratio of the power of the visible to the total radiation. Thus the efficiency of the ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "... iciently large not to get too hot, does not con- sume; only the negative terminal of the arc consumes in feeding the arc flame, that is, supplying the vapor conductor, but the positive is inherently non-consuming, and may be made a perma- nent part of the arc-lamp mechanism. On the contrary, if the positive is made so large that its temperature remains very much below the arc temperature, condensation of the arc vapor occurs at it, and it builds up, that is, increases in size. Consumption of the positive terminal i ...", "... range. Carbon, which is most generally used for arc terminals, is one of the most inefficient materials : the carbon arc gives very little light, and that of a disagreeable violet color; it is practi- cally non-luminous, and the light given by the carbon arc lamp is essentially incandescent light, temperature radiation of the incandescent tip of the positive carbon. The fairly high effi- ciency of the carbon arc lamp is due to the very high tempera- ture of the black body radiator, which gives the light. LUMINE ...", "... f a disagreeable violet color; it is practi- cally non-luminous, and the light given by the carbon arc lamp is essentially incandescent light, temperature radiation of the incandescent tip of the positive carbon. The fairly high effi- ciency of the carbon arc lamp is due to the very high tempera- ture of the black body radiator, which gives the light. LUMINESCENCE. 123 The materials which give the highest efficiencies of light production by their spectrum in the arc stream arcs mercury, calcium and titanium. ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-12", "section_label": "Lecture 12: Illumination And Illuminating Engineering", "section_title": "Illumination And Illuminating Engineering", "kind": "lecture", "sequence": 12, "number": 12, "location": "lines 16485-17445", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-12/", "snippets": [ "... dirt or age, thus are made more distinct by using an illuminant defi- cient in the long waves of light, as the mercury lamp, while in- versely they are decreased by using a reddish-yellow illuminant, as the incandescent lamp or the candle. Thus the white arc lamp and still more so the bluish-green mercury lamp shows blemishes and slight color differences of age and dirt harsh and exaggerated, while the yellow light softens them and makes them disappear; and while, for a ballroom, the yellow light is thus preferred ...", "... atigue caused by it, reducing the effective illumination at the minimum point between the lamps. Most objectionable in this respect is the open direct current car- bon arc and those types of lamps giving a downward distribution, but even with the enclosed arc lamp the distribution of light on the street surface is still far from uniform, and the intensity too high near the lamp, and in this respect improvements are desirable. 121. The greatest defects of the present street illumination, which frequently makes it ...", "... idway point between lamps is under a greater angle against the horizontal ; thus a more downward dis- tribution of the light flux permissible. For the largest part of American street lighting, however, this does not apply. 122. In the early days of using arc lamps for American city lighting, lighting towers were frequently used, and such tower lighting has still survived in some cities. One or a number of arc lamps are installed on a high tower and were supposed from there, like artificial suns, to spread their lig ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-21", "section_label": "Apparatus Introduction 21: Introduction", "section_title": "Introduction", "kind": "apparatus-introduction", "sequence": 21, "number": null, "location": "lines 8292-8517", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-21/", "snippets": [ "... tus is unsatisfactory, since it includes in the same class apparatus of entirely different character, as the induction motor and the alternating-current generator, or the constant-potential commutating machine and the rectifying arc light machine. Thus the following classification, based on the characteristic features of the apparatus, as adopted by the A. I. E. E. Standard- izing Committee, is used in the following discussion. It refers only to the apparatu ...", "... ive half waves of an alternating single-phase or polyphase circuit in the same direction into the receiving circuit. The most impor- 124 ELEMENTS OF ELECTRICAL ENGINEERING tant class of such apparatus were the open-coil arc light ma- chines. They have been practically superseded by the mercury arc rectifier. (4) Induction machines are generally used as motors, poly- phase or single-phase. In this case they run at practically constant speed, ...", "... and the elec- trolytic cell; the transformation between electrical and heat energy by the thermopile and the electric heater or electric fur- nace; the transformation between electrical and light energy by the incandescent and arc lamps. In the following will be given a general discussion of the charac- teristics of the most frequently used and therefore most impor- tant classes of apparatus. A further discussion and calculation of these apparatus is given ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-21", "section_label": "Chapter 23: Review", "section_title": "Review", "kind": "chapter", "sequence": 21, "number": 23, "location": "lines 32138-32819", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-21/", "snippets": [ "... 141-144. A quarter-phase constant- current alternator with rectifying commutators. Thomson-Houston Arc Machine. — 141-144. A three-phase F-connected constant-current alternator with rectifying commu- tator. The development of alternating-current series arc lighting by constant-current transformers greatly reduced the importance of the arc machine, and when in the magnetite lamp arc lighting returned to direct current, the development of the mercury-arc rectifier superseded the arc machine. Asynchronous Motor. — Na ...", "... ree-phase F-connected constant-current alternator with rectifying commu- tator. The development of alternating-current series arc lighting by constant-current transformers greatly reduced the importance of the arc machine, and when in the magnetite lamp arc lighting returned to direct current, the development of the mercury-arc rectifier superseded the arc machine. Asynchronous Motor. — Name used for all those types of alternating-current (single-phase or polyphase) motors or motor couples, which approach a definite ...", "... oremost objection to the mechanical rectifier is, that the power which can be rectified without injurious inductive spark- ing, is limited, especially in single-phase rectifiers, but for small amounts of power, as for battery charging and constant-current arc lighting they are useful. However, even there the arc recti- fier is usually preferable. The brush arc machine and the Thomson Houston arc machine were polyphase alternators with rectifying commutators. Regulating Pole Converter. — Variable-ratio converter. Split ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... g the meaning of the numerical value, as regards its accuracy. This is not always realized, and especially in the reduction of common fractions to decimals an unjustified laxness exists which impairs the reliability of the results. For instance, if in an arc lamp the arc length, for which the mechanism is adjusted, is stated to be 0.8125 inch, such a statement is ridiculous, as no arc lamp mechanism can control for one-tenth as great an accuracy as implied in this numerical value: the value is an unjustified trans ...", "... ommon fractions to decimals an unjustified laxness exists which impairs the reliability of the results. For instance, if in an arc lamp the arc length, for which the mechanism is adjusted, is stated to be 0.8125 inch, such a statement is ridiculous, as no arc lamp mechanism can control for one-tenth as great an accuracy as implied in this numerical value: the value is an unjustified translation from 13/16 inch. The principle thus should be adhered to, that all calcula- tions are carried out for one decimal more th ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-01", "section_label": "Lecture 1: General Review", "section_title": "General Review", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 154-565", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-01/", "snippets": [ "... c system, only the two standard frequencies, 25 and 60 cycles, come into considera- tion. b. Constant current, either alternating or direct, that is, a current of constant amperage, varying in voltage with the load, is mostly used for street lighting by arc lamps; for all other purposes, constant poteatial is employed. 1 2 GENERAL LECTURES c. For long distance transmission, the highest permis- sible voltage is used ; for primary distribution by alternating current, 2200 volts, that is, voltages between 2000 an ...", "... 550 to 600 volts. I. General Distribution eor Lighting and Power. In general distribution for lighting and power, direct current and 60 cycles alternating current are available. 25 cycles alternating current is not well suited, since it does not permit arc lighting, and for incandescent lighting it is just at the limit , where under some conditions and with some genera- tor waves, flickering shows, while with others it does not show appreciably. The distribution voltage is determined by the limitation of the incan ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... we are close to the limit of temperature which even tungsten can stand, and to show you light of high frequency or short wave length I use a different apparatus in which a more direct conversion of electric energy into radiation takes place, — the mercury arc lamp. Here the light is bluish green, containing only the highest frequencies of visible radiation, violet, blue and green, but practically none of the lower frequencies of visible radiation, red or orange. FIG. 11. In the tungsten lamp at high brilliancy ...", "... are thus called \" ultra-red rays,\" or \" infra-red rays/' as they are outside of and below the red end of the range of visible radiation. To produce powerful ultra-violet rays, I use a condenser dis- charge between iron terminals, a so-called ultra-violet arc lamp. Three iron spheres, 7 in Fig. 11, of about f in. diameter, are mounted on an insulator B. The middle sphere is fixed, the NATURE AND DIFFERENT FORMS OF RADIATION. 13 outer ones adjustable and set for about ^ in. gap. This lamp is connected across a h ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-13", "section_label": "Chapter 15: Synchronous Rectifier", "section_title": "Synchronous Rectifier", "kind": "chapter", "sequence": 13, "number": 15, "location": "lines 18413-19373", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-13/", "snippets": [ "... s. As mechanical rectifiers, mainly single-phase, they have found a limited use for small powers since a long time, and during the last years arc rectifiers have found extended use for small and moderate powers, for storage-battery charging and for series arc lighting by constant direct current. For large powers, however, the rectifier does not appear applicable, but the synchronous converter takes its place. The two most important types of direct-current arc-light ma- chines, however, have in reality been mechanical r ...", "... powers, for storage-battery charging and for series arc lighting by constant direct current. For large powers, however, the rectifier does not appear applicable, but the synchronous converter takes its place. The two most important types of direct-current arc-light ma- chines, however, have in reality been mechanical rectifiers, and for compounding alternators, and for starting synchronous motors, rectifying commutators have been used to a considerable extent. Let, in Fig. 72, e be the alternating voltage wave of ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-10", "section_label": "Chapter 10: Instability Of Circuits : The Arc", "section_title": "Instability Of Circuits : The Arc", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 17632-21381", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-10/", "snippets": [ "... electric circuits, they either remained imunderstood or the theo- retical study was limited to the specific phenomenon, as in the case of lightning, dropping out of step of induction motors, hunt- ing of synchronous machines, etc., or, as in the design of arc lamps and arc-lighting machinery, the opinion prevailed that theoretical calculations are impossible and only design by trying, based on practical experience, feasible. The first class of imstable phenomena, which was systemat- ically investigated, were the t ...", "... its, they either remained imunderstood or the theo- retical study was limited to the specific phenomenon, as in the case of lightning, dropping out of step of induction motors, hunt- ing of synchronous machines, etc., or, as in the design of arc lamps and arc-lighting machinery, the opinion prevailed that theoretical calculations are impossible and only design by trying, based on practical experience, feasible. The first class of imstable phenomena, which was systemat- ically investigated, were the transients, and eve ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-14", "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "section_title": "Constant-Potential Constant-Current Trans Formation", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "... nstant alternating voltage, or inversely, constitutes a good application of the terms \"impedance,\" admittance,\" etc., and offers a large number of problems or examples for the symbolic method of dealing with alternating-current phenomena. Even outside of arc lighting, such combinations of inductance and capacity which t«nd toward constant-voltage constant-cur- rent transformation are of considerable importance as a poffsiblo source of danger to the system. In a constant-current circuit, the load is taken off by short- ...", "... that is, contains, in addition to the resistance, r, an inductive reactance, x, and if this reactance is proportional to the resistance, X = kr, as is commonly the case in arc circuits, due to the inductive reactance of the regulating mechanism of the arc lamp (the effective resistance, r, and the inductive reactance, a:, in this case are both proportional to the number of lamps, hence pro- portional to each other), it is: total impedance: Z = r +j (xo + x) = r +j (xo + kr) ; or the absolute value is z = V ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-15", "section_label": "Chapter 15: Constant-Voltage Series Operation", "section_title": "Constant-Voltage Series Operation", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 27996-29301", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-15/", "snippets": [ "... tion of each device. In such a case, series connection of the devices is the most eco- nomical arrangement, and therefore conmionly used. Such for instance is the case in lighting the streets of a city, etc. Most of the street lighting has been done by arc lamps operated on constant-current circuits, and as the imiversal electric power supply today is at constant voltage, transformation from constant voltage to constant current thus is of importance, and has been discussed in Chapter XIV. The constant-current s ...", "... ant voltage, transformation from constant voltage to constant current thus is of importance, and has been discussed in Chapter XIV. The constant-current system thus is used in this case: (o) Because by series connection of the consuming devices, as the arc lamps in street lighting, it permits the use of a suflBciently high voltage to make the distribution economical. (6) The dropping volt-ampere characteristic of the arc makes it unstable on constant voltage, as further discussed in Chapters II and X, and a cons ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-04", "section_label": "Lecture 4: Load Factor And Cost Of Power", "section_title": "Load Factor And Cost Of Power", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 1527-2561", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-04/", "snippets": [ "... n are partly fixed cost A, partly proportional cost B, — economy of operation requires therefore a shifting of as large a part thereof over into class B, by shutting down smaller substations during periods of light load, etc. Incandescent lamp renewals, arc lamp trimming, etc., are essentially proportional costs, B. The reserve capacity of a plant, the steam reserve main- tained at the receiving end of a transmission line, the difference in cost between a duplicate pole line and a single pole line with two circ ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-11", "section_label": "Lecture 11: Lightning Protection", "section_title": "Lightning Protection", "kind": "lecture", "sequence": 11, "number": 11, "location": "lines 4931-5294", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-11/", "snippets": [ "... large extent, but is beginning to be superseded by the aluminum cell. The multi-gap, being based on the non-arcing or rectifying prop- erty of the metal cylinders which exists only with alternating current, is not suitable for direct current circuits. In arc light circuits, that is, constant current circuits, horn gap arresters with series resistance are generally used, especially on direct current arc circuits, in which the multi-gap is not permissible. In such circuits of limited current, and very high inductance ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-16", "section_label": "Lecture 16: The Incandescent Lamp", "section_title": "The Incandescent Lamp", "kind": "lecture", "sequence": 16, "number": 16, "location": "lines 9687-9919", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-16/", "snippets": [ "... ell on constant potential as on con- stant current. As electric distribution systems are always constant potential, most incandescent lamps are operated on constant potential ; and only for outdoor lighting, that is, for street lighting in cases where the arc lamp is too large and too expensive a unit of light for the requirements, incandescent lamps are used on a constant, direct or alternating current cir- cuit; they are then usually built for the standard arc circuits, and thus for low voltage. For general con ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-04", "section_label": "Lecture 4: Chemical And Physical Effects Of Radiation", "section_title": "Chemical And Physical Effects Of Radiation", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3639-3945", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-04/", "snippets": [ "... hot iron in the mercury light, especially through a red glass, while in the light of the incandescent lamp it loses all its brilliancy. This solution of rhodamine 6 G in alcohol, fluoresces a glaring orange in the mercury light, in the light of a carbon arc lamp (or in daylight) it fluoresces green and less brilliant. Thus you see that the color of the fluorescent light is not always the same, but depends to some extent on the frequency of radiation which causes the fluorescence. Here I have a sheet of paper co ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-07", "section_label": "Lecture 7: Flames As Illuminants", "section_title": "Flames As Illuminants", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 6609-7140", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-07/", "snippets": [ "... AS ILLUMINANTS. 56. Two main classes of illuminants exist: those producing radiation by the conversion of the chemical energy of com- bustion— the flames — and those deriving the energy of radia- tion from electric energy — the incandescent lamp and the arc lamp, and other less frequently used electric illuminants. Flames. To produce light from the chemical energy of combustion, almost exclusively hydrocarbon flames are used, as the gas flame, the candle, the oil lamp, the gasolene and kerosene lamp, etc.; tha ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-74", "section_label": "Apparatus Subsection 74: Direct-current Commutating Machines: C. Commutating Machines", "section_title": "Direct-current Commutating Machines: C. Commutating Machines", "kind": "apparatus-subsection", "sequence": 74, "number": null, "location": "lines 12660-12763", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-74/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-74/", "snippets": [ "... maximum current value even overturns the curve as shown in F. Curves E and F correspond to a very great shift of brushes, and an armature demagnetizing effect of the same magnitude as the field excitation, as realized in arc-light machines, in which the last part of the curve is used to secure inherent regulation for constant current. The resistance characteristic, that is, the dependence of the current and of the terminal voltage of the series gen ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-21", "section_label": "Chapter 21: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 22302-23970", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-21/", "snippets": [ "... f. vary in inverse proportion, as between 130 and 200 amp. in Fig. 132. The modern alternators are generally more or less machines of the first class; the old alternators, as built by Jablockkoff, Gramme, etc., were machines of the second class, used for arc lighting, where constant-current regulation is an advantage. Very high-power steam-turbine alternators are now again built with fairly high reactance, for reasons of safety. Obviously, large external reactances cause the same regula- ALTERNATING-CURRENT GENERA ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-16", "section_label": "Chapter 16: Aiitebnatingh-Current Osnebator", "section_title": "Aiitebnatingh-Current Osnebator", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 17025-18828", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-16/", "snippets": [ "... e near short circuit. The modern alternators are generally more or less ma- § 167] ALTERNATING-CURRENT GENERATOR. 24T chines of the first class ; the old alternators, as built by Jablockkoff, Gramme, etc., were machines of the second class, used for arc lighting, where constant-current regula- tion is an advantage. Obviously, large external reactances cause the same reg- ulation for constant current independently of the resistance^ r, as a large internal reactance, jTq. On non-inductive circuit, if 1 = E ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-17", "section_label": "Chapter 17: Alternating-Current Generator", "section_title": "Alternating-Current Generator", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16362-17596", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-17/", "snippets": [ "... and 200 amperes in Fig. 129. The modern alternators are generally more or less ma- 310 ALTERNATING-CURRENT PHENOMENA. chines of the first class ; the old alternators, as built by Jablockkoff, Gramme, etc., were machines of the second class, used for arc lighting, where constant-current regula- tion is an advantage. Obviously, large external reactances cause the same reg- ulation for constant current independently of the resistance, r, as a large internal reactance, .r0. On non-inductive circuit, if theoutpu ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-14", "section_label": "Chapter 16: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 14, "number": 16, "location": "lines 19374-20293", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-14/", "snippets": [ "... ion or overexcitation) are often used for the same purpose. Machines having more or less the characteristics of the reac- tion machine have been used to a considerable extent in the very early days, for generating constant alternating current for series arc lighting by Jablochkoff candles, in the 70's and early 80's. Structurally, the reaction machine is similar to the inductor machine, but the essential difference is, that the former operates by making and breaking the magnetic circuit, that is, periodically chang ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-02", "section_label": "Chapter 2: Electric Conduction. Gas And Vapor", "section_title": "Electric Conduction. Gas And Vapor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3895-5444", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-02/", "snippets": [ "... e, to give better proportions. The boiling points of some materials are approximately indicated on the curves. It is essential for the electrical engineer to thoroughly undeiv stand the nature of the arc, not only because of its use as illumi- nant, in arc lighting, but more still because accidental arcs are the foremost cause of instability and troubles from dangerous transients in electric circuits. \\ .^ s \\ ( m \\ \\ \\ \\ \\ \\ ™ V \\ '^ \\ s ^ ^ V ^ '., ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-06", "section_label": "Chapter 6: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 11051-12221", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-06/", "snippets": [ "... nservation of energy, will be illustrated by some examples, and the general equations then given. 2. The Constant-current Electromagnet 62. Such magnets are most direct-current electromagnets, and also the series operating magnets of constant-current arc lamps on alternating-current circuits. Let io = current, which is constant dming the motion of the armatm'e of the electromagnet, from its initial position 1, to its final position 2,1 = the length of this motion, or the stroke of the electromagnet, in centime ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-07", "section_label": "Chapter 7: Shaping Of Waves : General", "section_title": "Shaping Of Waves : General", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 12222-12961", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-07/", "snippets": [ "... city in the secondary 124 ELECTRIC CIRCUITS circuit, and elimination by delta connection, has been discussed in Chapter XXV of \"Theory and Calculation of Alternating- current Phenomena.\" In the flickering of incandescent lamps, and the steadiness of arc lamps at low frequencies, a difference exists between the flat- top wave of current with steep zero, and the peaked wave with flat zero, the latter showing appreciable flickering already at a somewhat higher frequency, as is to be expected. In general, where s ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-31", "section_label": "Chapter 9: Divided Circuit", "section_title": "Divided Circuit", "kind": "chapter", "sequence": 31, "number": 9, "location": "lines 9228-10474", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "snippets": [ "... e change of current il takes care of the increased friction of rest in setting the operating mechanism in motion, and gives a quicker reaction than a mechanism operated directly by the main current. This arrangement has been proposed for the operation of arc lamps of high arc voltage from constant potential circuits. The operating magnet, being in the circuit iv more or less anticipates the change of arc resistance by temporarily over- reaching. 77. The temporary increase of the voltage, e, across the branch circ ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-39", "section_label": "Chapter 3: Mechanical Rectification", "section_title": "Mechanical Rectification", "kind": "chapter", "sequence": 39, "number": 3, "location": "lines 15963-17754", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-39/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-39/", "snippets": [ "... ned, leaving the circuits in series in opposite direction. Special cases hereof are: 1. If r = r0 = 0, that is, during rectification both circuits are short circuited. Such short-circuit rectification is feasible only in limited-current circuits, as on arc lighting machines, or in * If the circuit is reversed at the moment when the alternating current passes zero, due to self-inductance of the rectified circuit its current differs from zero, and an arc still appears at the rectifier. 229 230 TRANSIENT PHENOMENA ..." ] } ] }, { "id": "spectrum", "label": "Spectrum", "aliases": [ "Spectrum", "spectra", "spectral", "spectrum" ], "total_occurrences": 162, "matching_section_count": 13, "matching_source_count": 4, "source_totals": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 125, "section_count": 9 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 31, "section_count": 1 }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 5, "section_count": 2 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 51, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "LECTURE II. RELATION OF BODIES TO RADIATION. 9. For convenience, the total range of known radiations can be divided into two classes, the electric waves and the light waves, which are separated from each other by the blank space in the middle of the spectrum of radiation (Fig. 14). Under light waves we here include also the invisible ultra-red radiation and the ultra-violet radiation and the non-refrangible radiations, as X-rays, etc., separated from the latter by the second blank space of the radiation spect ...", "... ctrum of radiation (Fig. 14). Under light waves we here include also the invisible ultra-red radiation and the ultra-violet radiation and the non-refrangible radiations, as X-rays, etc., separated from the latter by the second blank space of the radiation spectrum. In the following, mainly the light waves, that is, the second or high frequency range of radiation, will be discussed. The elec- tric waves are usually of importance only in their relation to the radiator or oscillator which produces them, or to the rec ...", "... 6. more than the lower frequencies, thus showing that the velocity of propagation decreases with an increase of frequency, that is, a decrease of wave length. This gives a means of resolving a mixed radiation into its com- ponent waves, that is, into a spectrum, by refraction. A narrow beam of light B (Fig. 16) is passed through a prism P of transparent material, and the component frequencies then appear on the screen A (or are seen by the eye) side by side, the red R to the left, the violet V to the right, in ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 33, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "... aining mercury, flashes of light are seen in the darkness. This, however, is not real phosphorescence but due to electrostatic flashes of frictional electricity. The light given by fluorescence and phosphorescence of solids or liquids, gives a continuous spectrum, that is, is a mixture of all frequencies, just as is the case with temperature radiation; it differs, however, from temperature radiation by the distribu- tion of the energy in the spectrum, which is more or less charac- teristic of the luminescent body, ...", "... nce and phosphorescence of solids or liquids, gives a continuous spectrum, that is, is a mixture of all frequencies, just as is the case with temperature radiation; it differs, however, from temperature radiation by the distribu- tion of the energy in the spectrum, which is more or less charac- teristic of the luminescent body, and to some extent, also, of the method of exciting the luminescence. Thus crystalline calcium tungstate, W04Ca, fluoresces white in the X-ray, light blue with ultra-violet light; the anilin ...", "... bunsen flame. I dip a platinum wire into a solution of lithium chloride, LiCl, and then hold it into the lower edge of the flame: the flame colors a bright red, and through the spectroscope you see a bright deep red line and a less bright orange line, the spectrum of Li. After a little while, the color- ing disappears by the LiCl evaporating from the wire, and the flame again becomes non-luminous. I repeat the same experi- ment, but dip the platinum wire into sodium chloride, NaCl, solution, and you see the flame c ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 31, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... which no incandescent lamp can hope -to approach. In the carbon arc, practically all the light comes from the incandescent tips of the carbons, very little from the arc flame. Then by using materials, which in the arc flame give an intense- ly luminous spectrum, the efficiency of \\the arc lamp has been vastly improved. So far only three materials have been found, which in luminous arcs give efficiences vastly superior to incandescence : mercury, calcium (lime), and titanium. All (three even in moderate sized u ...", "... bon had to be eliminated altogether as electrode material, and its place was taken by magnetite, while titanium compounds give the high efficiency. This lead to the long 226 GENERAL LECTURES burning luminous arc of the white color of the titanium-iron spectrum as represented by the magnetite arc, the metallic oxide arc, and other types still in development. In all these long burning luminous arcs, some efficiency had to be sacrificed in developing sufficiently small units for general illumination. While the su ...", "... her frequency; that is, if the atoms are left to vibrate freely as under the influence of an electric current in the arc, then we get radiations of the frequency inherent to the atom. The general tendency then is toward the violet or short wave end of the spectrum. If we assume that the mass of the silver atom is such as to give a rate of vibration in the range of the violet and ultraviolet, it is easy to understand that radiation of this frequency splits up the silver salt by increasing the vibration of the atom b ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-03", "section_label": "Lecture 3: Physiological Effects Of Radiation", "section_title": "Physiological Effects Of Radiation", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2366-3638", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-03/", "snippets": [ "... e reproduction. 21. The sensitivity of the eye to radiation obviously changes with the frequency, as it is zero in the ultra-red, and in the ultra- violet — where the radiation is not visible — and thus gradually increases from zero at the red end of the spectrum to a maximum somewhere near the middle of the spectrum and then decreases again to zero at the violet end of the spectrum; that is, the physi- PHYSIOLOGICAL EFFECTS OF RADIATION. 41 ological effect produced by the same radiation power — as one wat ...", "... ation obviously changes with the frequency, as it is zero in the ultra-red, and in the ultra- violet — where the radiation is not visible — and thus gradually increases from zero at the red end of the spectrum to a maximum somewhere near the middle of the spectrum and then decreases again to zero at the violet end of the spectrum; that is, the physi- PHYSIOLOGICAL EFFECTS OF RADIATION. 41 ological effect produced by the same radiation power — as one watt of radiating power — is a maximum near the middle of t ...", "... tra-red, and in the ultra- violet — where the radiation is not visible — and thus gradually increases from zero at the red end of the spectrum to a maximum somewhere near the middle of the spectrum and then decreases again to zero at the violet end of the spectrum; that is, the physi- PHYSIOLOGICAL EFFECTS OF RADIATION. 41 ological effect produced by the same radiation power — as one watt of radiating power — is a maximum near the middle of the visible spectrum and decreases to zero at the two ends, about as ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-05", "section_label": "Lecture 5: Temperature Radiation", "section_title": "Temperature Radiation", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3946-5076", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-05/", "snippets": [ "... thus changes from red to orange, yellow, yellowish white and then white, the latter at that temperature where all the visible radiations are present in the same propor- tion as in daylight. With still further increase of temperature, the violet end of the spectrum would increase faster than the red end and the light thus shift to bluish white, blue and violet. The invisibility of the radiation of low temperature is not due to low intensity. I have here an incandescent lamp at normal brilliancy. If I decrease the p ...", "... of black body radiation; that is, its radiation for some frequencies would be a greater part of black body radiation. The radiation of such a body is called \"colored body radiation.\" In colored body radiation the distribution of intensities throughout the spectrum, that is, for different frequencies, thus differs from that of the black or grey body at the same temperature, that is, colored radiation is not normal radiation and thus also does not follow the temperature law equation (1). For instance, if in Fig. 29, ...", "... ght, far brighter than the platinum wire immersed in the same flame. The dis- tribution of intensity of this radiation differs from that corre- sponding to any temperature, and the percentage of visible radiation, especially from the center of the visible spectrum (greenish yellow) , is abnormally large. This, therefore, is a colored radiator, giving a higher radiation efficiency than the normal temperature radiation. A radiation which does not follow the temperature law of normal radiation as regard to the distr ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-07", "section_label": "Lecture 7: Flames As Illuminants", "section_title": "Flames As Illuminants", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 6609-7140", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-07/", "snippets": [ "... res, — and this is the case in the flame, — chemical luminescence of the flame gases must be expected in the hydro- carbon flame. It does occur, but does not contribute anything 134 RADIATION, LIGHT, AND ILLUMINATION. to the light production, since the spectra of hydrogen and of carbon (or CO and CH4) are practically non-luminous. The luminescence of the hydrocarbon flame therefore can be observed only with those hydrocarbons which are sufficiently poor in car- bon as not to deposit free carbon, as methane, alc ...", "... s produced by the combustion: alumina, zinc oxide, etc. Superimposed upon the temperature radiation of the incan- descent radiator of those flames is the radiation of chemical luminescence. Since, however, magnesium, zinc, aluminum, give fairly luminous spectra, in these flames the chemical lumi- nescence contributes a considerable part of the light, and where the luminescent light, that is, the metal spectrum, is of a marked color — as green with zinc — the flame of the burning metal also is colored. Hence burn ...", "... the radiation of chemical luminescence. Since, however, magnesium, zinc, aluminum, give fairly luminous spectra, in these flames the chemical lumi- nescence contributes a considerable part of the light, and where the luminescent light, that is, the metal spectrum, is of a marked color — as green with zinc — the flame of the burning metal also is colored. Hence burning zinc gives a greenish-yellow flame, burning calcium an orange -yellow flame, etc. FLAMES AS ILLUMINANTS. 135 Obviously, where during the combust ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-09", "section_label": "Lecture 9: Measurement Of Light And Radiation", "section_title": "Measurement Of Light And Radiation", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 8511-9388", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-09/", "snippets": [ "... per- ature rise produced by the energy of the incident beam of radia- tion is observed. Probably the most sensitive method of measuring even very small amounts of radiation is the bolometer. The beam of the radiation (or after dissolving the beam into a spectrum, the wave length of which the power is to be measured) impinges upon a narrow and thin strip of metal, as platinum, and thereby raises its temperature by conversion of the radiation energy into heat. A rise of temperature, however, produces a rise of ele ...", "... uld base the physiological effect, under speci- fied conditions of temperature, on the unit of power, or the watt, as unit of light. Its disadvantage is the difficulty of measuring the power of the total visible radiation, since at the ends of the visible spectrum the power is high and the physio- logical effect low, and a small error in the limits of the spectrum would make a considerable error in the result. More satisfactory, therefore, appears the derivation of a primary standard of light by combining three pr ...", "... or the watt, as unit of light. Its disadvantage is the difficulty of measuring the power of the total visible radiation, since at the ends of the visible spectrum the power is high and the physio- logical effect low, and a small error in the limits of the spectrum would make a considerable error in the result. More satisfactory, therefore, appears the derivation of a primary standard of light by combining three primary colors of light in definite power proportions. Thus, choosing three lines of the mercury spectr ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-04", "section_label": "Lecture 4: Chemical And Physical Effects Of Radiation", "section_title": "Chemical And Physical Effects Of Radiation", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3639-3945", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-04/", "snippets": [ "... obable by the relation which exists between the active frequency range and the weight of the atom or molecule which responds to the radiation. Thus, while the fairly heavy silver atom (atomic weight 108) responds to rays near the violet end of the visible spectrum, the much lighter oxygen atom (atomic weight 16) responds only to much higher frequencies, to those of the physiologically most destructive rays, about one to two octaves beyond the visible spectrum. These very short radiations energetically produce ozone ...", "... 108) responds to rays near the violet end of the visible spectrum, the much lighter oxygen atom (atomic weight 16) responds only to much higher frequencies, to those of the physiologically most destructive rays, about one to two octaves beyond the visible spectrum. These very short radiations energetically produce ozone 03,from oxygen 02, probably by dissociating oxygen molecules 02,into free atoms, and these free atoms then join existing molecules: 0 + 02 = 03, thus forming ozone. Possibly their destructive physio ...", "... paper or cardboard colored red by rhodamine does not fluoresce, but if a small quantity of rhoda- mine is added to some transparent varnish and the paper colored red by a heavy layer of this varnish it fluoresces brightly red. To show you the fluorescent spectrum, I have here a mercury lamp surrounded by a very diluted solution of rhodamine 6 G, and some rhodamine R, contained between two concentric glass cylinders. As you see, through the spectroscope a broad band appears in the red and the green light has faded ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-03", "section_label": "Lecture 3: Gravitation And The Gravitational Fleld", "section_title": "Gravitation And The Gravitational Fleld", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2389-3594", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-03/", "snippets": [ "... radius would be: R^ = 1.08 X 10\" cm. R = S& X 10>2 cm. = 225,000,000 miles. 68 RELATIVITY AND SPACE electrical constants of the hydrogen atom and showing us the exact rate of its vibration in the spectroscope by the wave length or frequency of its spectrum lines. Thus in a strong gravitational field the frequency of luminous vibrations of the atoms should be found slowed down; in other words, the spectrum lines should be shifted towards the red end of the spectrum. The amount of this shift is so small that ...", "... showing us the exact rate of its vibration in the spectroscope by the wave length or frequency of its spectrum lines. Thus in a strong gravitational field the frequency of luminous vibrations of the atoms should be found slowed down; in other words, the spectrum lines should be shifted towards the red end of the spectrum. The amount of this shift is so small that it has not yet been possible to prove its existence beyond doubt, but there seems to be some evidence of it.", "... ope by the wave length or frequency of its spectrum lines. Thus in a strong gravitational field the frequency of luminous vibrations of the atoms should be found slowed down; in other words, the spectrum lines should be shifted towards the red end of the spectrum. The amount of this shift is so small that it has not yet been possible to prove its existence beyond doubt, but there seems to be some evidence of it." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-04", "section_label": "Lecture 4: The Characteristics Of Space A. The Geometry Of The Gravitational Field", "section_title": "The Characteristics Of Space A. The Geometry Of The Gravitational Field", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3595-6820", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-04/", "snippets": [ "... ce of radial acceleration, 55 as inertia of accelerated system, 53 laws of, 9, 11, 50 and metric axiom, 110 Gravitational field, 18, 21, 47 and deflection of light, 55, 59 as space curvature, 121 its geometry, 69 intensity, 47 shifting of spectrum lines, 68 Gravitational force as centrifugal force of imaginary velocity, 55 and inertia, 53 Gravitational mass, 47 H in projective Harmonic relation geometry, 108 as non-metric, 110 Hertz, 17, 21 Hyperbolic geometry, 64, 72, 74 Hypersurfa ...", "... e perceptions as primary, 23 Simultaneousness of events, 28 Singular points and lines in space, 90 Six-dimensional physical space, 97 Space, bending of, 88 characteristic, 69 curved, visional appearance, 116 general, 95 mathematical and physical, 92 Spectrum lines, shift in gravitational field, 68 Speed, length and time, 8 (See velocity). Sphere as element of four-dimen- sional space, 99 Spherical or elhptic geometry, 74 trigonometry as plane trigonom- etry of elliptic 2-space, 77 Spindle as elliptic 2 ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... known forms of radia- tion are arranged by their frequency and wave length, and also given in octaves, choosing as zero1 point the middle c of the piano, or a frequency of 128 cycles per sec. UNIVERSITY OF NAT IFFERENT FORMS OF RADIATION. 17 SPECTRUM OF RADIATION. Zero point chosen at c = 128 cycles per second. Speed of radiation S = 3 X lu10 cm. Cycles. Wave Length in Air (or Vacuum). Octave: Q^/ £. Alternating current 1> field: 15 20,000 km. = 12,500 mi. 25 12.000 km. = 7, 500 ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-12", "section_label": "Lecture 12: Illumination And Illuminating Engineering", "section_title": "Illumination And Illuminating Engineering", "kind": "lecture", "sequence": 12, "number": 12, "location": "lines 16485-17445", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-12/", "snippets": [ "... differences increased and made more distinct, or decreased and thus obliterated. For instance, the color resulting from age and dirt is usually the color of carbon and of iron, yellowish brown or reddish brown, that is, colors at the long wave end of the spectrum. Spots and blemishes due to dirt or age, thus are made more distinct by using an illuminant defi- cient in the long waves of light, as the mercury lamp, while in- versely they are decreased by using a reddish-yellow illuminant, as the incandescent lamp or ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-02", "section_label": "Chapter 2: Electric Conduction. Gas And Vapor", "section_title": "Electric Conduction. Gas And Vapor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3895-5444", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-02/", "snippets": [ "... ed into three distinct types: spark conduction, arc conduction, and true electronic conduction. In spark conduction, the gas or vapor which fills the space be- tween the electrodes is the conductor. The light given by the gaseous conductor thus shows the spectrum of the gas or vapor which fills the space, but the material of the electrodes is imma- terial, that is, affects neither the light nor the electric behavior of the gaseous conductor, except indirectly, in so far as the section of the conductor at the termi ..." ] } ] }, { "id": "symbolic-method", "label": "Symbolic Method", "aliases": [ "symbolic", "symbolic expression", "symbolic method", "symbolic representation" ], "total_occurrences": 160, "matching_section_count": 44, "matching_source_count": 8, "source_totals": [ { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 48, "section_count": 12 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 46, "section_count": 12 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 24, "section_count": 7 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 22, "section_count": 5 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 14, "section_count": 4 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 2, "section_count": 1 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 2, "section_count": 2 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 2, "section_count": 1 } ], "section_hits": [ { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-17", "section_label": "Theory Section 17: Impedance and Admittance", "section_title": "Impedance and Admittance", "kind": "theory-section", "sequence": 17, "number": 17, "location": "lines 6814-7380", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-17/", "snippets": [ "... d in ohms: reactance x. The e.m.f. consumed by reactance x is in quadrature with the current, that consumed by resistance r in phase with the current. Reactance and resistance combined give the impedance, + x2; or, in symbolic or vector representation, Z = r + jx. In general in an alternating-current circuit of current i, the e.m.f. e can be resolved in two components, a power component ei in phase with the current, and a wattless or reactiv ...", "... t is called the effective resistance. The quantity 62 _ reactive e.m.f., or e.m.f. in quadrature with the current _ i current is called the effective reactance of the circuit. And the quantity 21 = Vr!2 + x2 or, in symbolic representation, Zi = ri + jxi is the impedance of the circuit. If power is consumed in the circuit only by the ohmic resist- ance r, and counter e.m.f. produced only by self-inductance, the effective resistance TI is the true or oh ...", "... nce, Ohm's law can be expressed in alternating- current circuits in the form • = - e m y / 9 T ~ 9; ^ ' Zi vVi2 + Xi2 or, e = izi = i V^i2 + Zi2; (2) or, «! = Vri8 + a;ia = p (3) or, in symbolic or vector representation, or, E = IZl = /(n+jxi); (5) 7^7 or, Zi = ri + jzi = j- (6) In this latter form Ohm's law expresses not only the intensity but also the phase relation of the quantities; thus ei = iri ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "section_label": "Chapter 30: Quartbr-Fhase System", "section_title": "Quartbr-Fhase System", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... .4, a = .1435, a = 8.2°. Impcdarice and Admittance, 283. In complex imaginary quantities, the alternating wave /* '»\\ s = £\" cos (<^ — cu) is represented by the symbol E — e (cos ci +y sin w) = c^ -\\- je^ . By an extension of the meaning of this symbolic ex- pression, the oscillating wave E=^et~^^ cos (<^ — w) can be expressed by the symbol E = e (cos a> +y sin ui) dec a = {e^ +jc^ dec a, where a = tan a is the exponential decrement, a the angular decrement, t~^^** the numerical decrement. 414 APPEN ...", "... . The electromotive force consumed by the inductance L of the circuit, 77 r d I o A- r if f d I Ex = /' — = 2 TT A Z = .V . lit i/ ii Hence Ej, = — xit\"*'^ {sin ( — w) + ^ cos ( — w)} = -— — - -- sin ( — (u + «)• cos tt Thus, in symbolic expression, ^x = — {— sin (w — a) +ycos (w — a)} dec a COS a = — xi {a -\\- J) (cos « + y sin w) dec a ; that is, E^ = — X I{a +j) dec a. Hence the apparent reactance of the oscillating current circuit is, in symbolic expression, X == X (a +y) dec a. Hence ...", "... > — (u + «)• cos tt Thus, in symbolic expression, ^x = — {— sin (w — a) +ycos (w — a)} dec a COS a = — xi {a -\\- J) (cos « + y sin w) dec a ; that is, E^ = — X I{a +j) dec a. Hence the apparent reactance of the oscillating current circuit is, in symbolic expression, X == X (a +y) dec a. Hence it contains an energy component ax, and the impedance is Z ={r — X) dec a = {r — x (a +j)) dec a = {r—ax —jx) dec a. Capacity, 285. Let r = resistance, C= capacity, and x^ = 1/ 2 «• C = capacity reactance. In a circuit ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-32", "section_label": "Chapter 32: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 25904-27405", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "snippets": [ "... have A = .4, a = .1435, a = 8.2°. Impedance and Admittance. 312. In complex imaginary quantities, the alternating wave * = e cos (* - ffl) is represented by the symbol E = e (cos w -\\-j sin w) = cos ( — w) can be expressed by the symbol E = e (cos w -\\-j sin w) dec a = (e± -\\-j'e^) dec a, where a = tan a is the exponential decrement, a the angular decrement, e~27ra the numerical decrement. 50 ...", "... stance r of the circuit ^ The electromotive force consumed by the inductance L of the circuit, Ef**L—~*iNI&t = *—. dt d<$> d<$> Hence Ex = — xif.~a^> (sin ( — fy -\\- a cos (<£ — w)} xi(.~a^ . ,. „ , N = sin (^> — w -f- a). COS a Thus, in symbolic expression, £x = - °^—{— sin (w — a) +/ cos (w — a)} dec a COS a = — x i (a -f y ) (cos w + 7 sin a>) dec a ; that is, Ex = — x I (a +/') dec a . Hence the apparent reactance of the oscillating current circuit is, in symbolic expression, X = x (a +y') dec a ...", "... a). COS a Thus, in symbolic expression, £x = - °^—{— sin (w — a) +/ cos (w — a)} dec a COS a = — x i (a -f y ) (cos w + 7 sin a>) dec a ; that is, Ex = — x I (a +/') dec a . Hence the apparent reactance of the oscillating current circuit is, in symbolic expression, X = x (a +y') dec a. Hence it contains an energy component ax, and the impedance is Z = (r — X) dec a = {r — x (a +/')} dec a = (r — ax —jx) dec a. Capacity. 314. Let r = resistance, C = capacity, and xc = 1 /2-n-JVC = capacity reactance. In a ci ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-05", "section_label": "Chapter 5: Symbolic Method", "section_title": "Symbolic Method", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2760-3266", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-05/", "snippets": [ "CHAPTER V SYMBOLIC METHOD 25. The graphical method of representing alternating-current phenomena affords the best means for deriving a clear insight into the mutual relation of the different alternating sine waves entering into the problem. For numerical calculation, however, th ...", "... ram is shown in Fig. 21. Obviously, no exact numerical values can be taken from a parallelogram as flat as OFiFFo, and from the combination of vectors of the relative magnitudes 1 :6 :100. Hence the importance of the graphical method consists not 30 SYMBOLIC METHOD 31 so much in its usefulness for practical calculation as to aid in the simple understanding of the phenomena involved. 26. Sometimes we can calculate the numerical values trigo- nometrically by means of the diagram. Usually, however, this becomes too ...", "... present, j is nothing but a distinguishing index, and otherwise free for definition except that it is not an ordinary number. 29. A wave of equal intensity, and differing in phase from the wave, a -\\- jh, by 180°, or one-half period, is represented in SYMBOLIC METHOD 33 Fig. 24. polar coordinates by a vector of opposite direction, and denoted by the symbolic expression, — a — jb. Or, Multiplying the symbolic expression, a + jb, of a sine wave by — 1 means reversing the wave, or rotating it through 180°, or on ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-27", "section_label": "Chapter 27: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 33011-34776", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-27/", "snippets": [ "CHAPTER XXVII SYMBOLIC REPRESENTATION OF GENERAL ALTERNATING WAVES 259. The vector representation, A — a'^ -{- ja^'^ = a (cos d -\\- j sin 6) of the alternating wave, A = tto cos {(f) — 6) apphes to the sine wave only. The general alternating wave, however, contains an infinite series ...", "... roducts of different harmonics vanish, each term can be represented by a complex symbol, and the equations of the general wave then are the resultants of those of the individual harmonics. This can be represented symbolically by combining in one formula symbolic representations of different frequencies, thus, A = 22n-i(a„i+i„a„ii),^ 1 1 The index 2n — 1 in the S sign denotes that only the odd values of n are considered. If the wave contained even harmonics, the even vahies of n would also be considered, and th ...", "... al inductance, synchronous motion, etc.). Xc is that part of the reactance which is inversely propor- tional to the frequency (capacity, etc.). The impedance for the nth harmonic is + jn (nxr^ + a^o + -^ ) This term can be considered as the general symbolic expression of the impedance of a circuit of general wave-shape. Ohm's law, in symbolic expression, assumes for the general alternating wave the form 7 = ^or, S2n-i(t„i +j„^„ii) = Ssn-i E r -{- Jn [^nxm + Xo + — j = IZ or, 22n-i (e„i -\\-jner}^) = S2n-i l^r + ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "CHAPTER XXIV. SYMBOLIC REPRESENTATION OF GENERAL ALTERNATING WAVES. 253. The vector representation, A = a1 +y — 6), can be expressed by the symbol, JjJ = e(cos 6 — j sin 0) dec a = (ei — je2) dec a, where a = tan a is the exponential decrement, a the angular decrement, e\"^'** the numerical decrement. OSCILLATING ...", "... e then, the e.m.f. consumed by the resistance, r, of the circuit, Er = rl dec a. The e.m.f. consumed due to the inductance, L, of the circuit, n T dl rk TT dl dl Hence E^ = — a;i€-\"*{sin (0 — ^) + a cos (0 — ^)} = sm (0 — ^ + a). cos a Thus, in symbolic expression, jFx = I — sin {B — a) — j cos (^ — a) } dec a cos a / ^ \\ /I = — xtXa — j) (cos ^ — j sin ^) dec a; that is, jFx = — x7 (a — j) dec a. Hence the apparent reactance of the oscillating-current cir- cuit is, in symbolic expression, X = x{a — j) dec ...", "... . cos a Thus, in symbolic expression, jFx = I — sin {B — a) — j cos (^ — a) } dec a cos a / ^ \\ /I = — xtXa — j) (cos ^ — j sin ^) dec a; that is, jFx = — x7 (a — j) dec a. Hence the apparent reactance of the oscillating-current cir- cuit is, in symbolic expression, X = x{a — j) dec a. Hence it contains a power component, ax, and the impedance is Z = (r—X) dec a= {r—x{a—j)] dec a = {r —ax +jx) dec a. Capacity 186. Let r = resistance, C = capacity, and Xc = o~~7?t = con- ZtJkj densive reactance. In a circui ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-14", "section_label": "Theory Section 14: Rectangular Coordinates", "section_title": "Rectangular Coordinates", "kind": "theory-section", "sequence": 14, "number": 14, "location": "lines 5264-5831", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-14/", "snippets": [ "... ngle is the vertical compo- nent divided by the horizontal com- ponent, or the term with prefix j divided by the term without j. The total current intensity is obviously I = V> + i'2> (18) The capital letter I in the symbolic expression / = i + jif thus represents more than the / used in the preceding for total current, etc., and gives not only the intensity but also the phase. It is thus necessary to distinguish by the type of the latter the capit ...", "... e / used in the preceding for total current, etc., and gives not only the intensity but also the phase. It is thus necessary to distinguish by the type of the latter the capital letters denoting the resultant current in symbolic expres- sion (that is, giving intensity and phase) from the capital letters giving merely the intensity regardless of phase; that is, I = denotes a current of intensity / = and phase tan 0 = — . ^ RECTANGULAR COO ...", "... letters giving merely the intensity regardless of phase; that is, I = denotes a current of intensity / = and phase tan 0 = — . ^ RECTANGULAR COORDINATES 81 In the following, dotted italics wfll be used for the symbolic expressions and plain italics for the absolute values of alternating waves. In the same way z = \\/r2 + x2 is denoted in symbolic repre- sentation of its rectangular components by Z = r + jx. (91) When using the symbo ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-05", "section_label": "Chapter 5: Symbolic Method", "section_title": "Symbolic Method", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2322-2773", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-05/", "snippets": [ "CHAPTER V. SYMBOLIC METHOD. 23. The graphical method of representing alternating, current phenomena by polar coordinates of time affords the best means for deriving a clear insight into the mutual rela- tion of the different alternating sine waves entering into the problem. For n ...", "... for definition except that it is not an .ordinary number. 27. A wave of equal intensity, and differing in phase from the wave a + jb by 180°, or one-half period, is repre- sented in polar coordinates by a vector of opposite direction, and denoted by the symbolic expression, — a — jb. Or — Multiplying the symbolic expression, a + jb, of a sine wave by — 1 weans reversing' the wave, or rotating it through 180°, or one-half period. A wave of equal intensity, but lagging 90°, or one- quarter period, behind a -f jb, has (Fig. ...", "... ber. 27. A wave of equal intensity, and differing in phase from the wave a + jb by 180°, or one-half period, is repre- sented in polar coordinates by a vector of opposite direction, and denoted by the symbolic expression, — a — jb. Or — Multiplying the symbolic expression, a + jb, of a sine wave by — 1 weans reversing' the wave, or rotating it through 180°, or one-half period. A wave of equal intensity, but lagging 90°, or one- quarter period, behind a -f jb, has (Fig. 24) the horizontal SYMBOLIC METHOD. 37 component ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-12", "section_label": "Chapter 12: Power, And Double Frequency Quantities In General", "section_title": "Power, And Double Frequency Quantities In General", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 9381-9740", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "snippets": [ "... nt chosen as co-ordinate center) and their connection the dif- ference of potential in phase and intensity. Algebraically these vectors are represented by complex quantities. The impedance, admittance, etc., of the circuit is a complex quantity also, in symbolic denotation. Thus current, E.M.F., impedance, and admittance are related by multiplication and division of complex quantities similar as current, E.M.F., resistance, and conductance are related by Ohms law in direct current circuits. In direct current c ...", "... The real component will be distinguished by the index 1, the imaginary or wattless component by the index/. By introducing this symbolism, the power of an alternat- ing circuit can be represented in the same way as in the direct current circuit, as the symbolic product of current and E.M.F. Just as the symbolic expression of current and E.M.F. as complex quantity does not only give the mere intensity, but also the phase, £ = jfc == P tan = -j so the double frequency vector product P = [E /] denotes ...", "... x 1, the imaginary or wattless component by the index/. By introducing this symbolism, the power of an alternat- ing circuit can be represented in the same way as in the direct current circuit, as the symbolic product of current and E.M.F. Just as the symbolic expression of current and E.M.F. as complex quantity does not only give the mere intensity, but also the phase, £ = jfc == P tan = -j so the double frequency vector product P = [E /] denotes more than the mere power, by giving with its two compo- nents ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... characteristic of line and cable, 44 dielectric and dynamic, 159 factor of general wave, 383 Coefficient of eddy currents, 138 of hysteresis, 123 Combination of sine waves, 31 Compensation for lagging currents by condensance, 72 Condensance in symbolic expression, 36 Condenser as reactance and suscep- tance, 96 with distorted wave, 384 motor on distorted wave, 392 motor, single-phase induction, 249, 257 synchronous, 339 Conductance of circuit with induc- tive line, 84 direct current, 55 due to eddy curre ...", "... in line, 174 loss, 122 with distorted wave, 377 power current, 117 voltage, 123 Imaginary power, 186 Impedance, 2, 9 apparent, of transformer, 201 of induction motor, 211 in series with circuit, 69 series and parallel connections, 55, 59 in symbolic expression, 35 synchronous, of alternator, 277 Independent polyphase system, 397 Inductance, 3, 9 factor of general wave, 382 Induction generator, 237 machine as inductive reactance, 96 motor, 208 on distorted wave, 392 Inductive devices, starting single- ...", "... ape distortion, 358, 361 Iron wire and eddy currents, 140 unequal current distribution, 147 j as distinguishing index, 32 as imaginary unit, 33 Joule's law, 1, 5 Kirchhoff's laws, direct current, 1 in crank diagram, 22, 60 in polar diagram, 49 in symbolic expression, 34 Lag ill alternator, demagnetizing, 260 of current, 21 in synchronous motor, magnet- izing, 261 Laminated iron and eddy currents, 138 Lead in alternator, magnetizing, 260 of current, 21 by synchronous condenser, 339 in synchronous motor, dem ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-05", "section_label": "Chapter 5: Symbouc Mbthod", "section_title": "Symbouc Mbthod", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2744-3229", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "snippets": [ "... mined analytically by two numerical quanti- ties — the length, Of, or intensity ; and the amplitude, AO/, or phase is the horizontal component, ^ = /sin 0) is the vertical component of the sine wave. This representation of the sine wave by its rectangular ...", "... for definition except that it is not an ordinary number. 27. A wave of equal intensity, and differing in phase from the wave a + jb by 180°, or one-half period, is repre- sented in polar coordinates by a vector of opposite direction, and denoted by the symbolic expression, — a — jb. Or — Multiplying the algebraic exprcssiotiy a '\\-jby of a sine wave by —1 means reversing the wave, or rotating it through 180*^, or one-half period, A wave of equal intensity, but lagging 90*^, or one- quarter period, behind a + jb, has (Fi ...", "... e algebraic exprcssiotiy a '\\-jby of a sine wave by —1 means reversing the wave, or rotating it through 180*^, or one-half period, A wave of equal intensity, but lagging 90*^, or one- quarter period, behind a + jb, has (Fig. 24) the horizontal 128] SYMBOLIC METHOD, 8T component, — by and the vertical component, ^, and is rep- resented algebraically by the expression, ja — b. Multiplying, however, a + jb by 7, we get : — jii+rb\\ therefore, if we define the heretofore meaningless symbol, /, by the condition, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-16", "section_label": "Chapter 16: Power, And Double-Frequency Quantities In", "section_title": "Power, And Double-Frequency Quantities In", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 16077-16520", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-16/", "snippets": [ "... hosen as coordi- nate center), and their connection the difference of potential in phase and intensity. Algebraically these vectors are represented by complex quan- tities. The impedance, admittance, etc., of the circuit is a com- plex quantity also, in symbolic denotation. Thus current, voltage, impedance, and admittance are related by multiplication and division of complex quantities in the same way as current, voltage, resistance, and conductance are related by Ohm's law in direct-current circuits. In direc ...", "... The real component will be distinguished by the index 1; the imaginary or reactive component by the index, j. By introducing this symbolism, the power of an alternatmg circuit can be represented in the same way as in the direct-cur- rent circuit, as the symbolic product of current and voltage. Just as the symbolic expression of current and voltage as com- plex quantity does not only give the mere intensity, but also the phase, ^ =. gi +jeii ^ = \\e' + ell' tan 6 = —r, so the double-frequency vector product ...", "... 1; the imaginary or reactive component by the index, j. By introducing this symbolism, the power of an alternatmg circuit can be represented in the same way as in the direct-cur- rent circuit, as the symbolic product of current and voltage. Just as the symbolic expression of current and voltage as com- plex quantity does not only give the mere intensity, but also the phase, ^ =. gi +jeii ^ = \\e' + ell' tan 6 = —r, so the double-frequency vector product P = [EI] denotes more than the mere power, by giving with its two ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-07", "section_label": "Chapter 7: Polar Coordinates And Polar Diagrams", "section_title": "Polar Coordinates And Polar Diagrams", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 3619-4087", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-07/", "snippets": [ "... crank diagram discussed in Chapter IV. It may be called the time diagram or polar diagram, and is used to a considerable extent in the literature, thus must be familiar to the engineer, though in the following we shall in graphic representation and in the symbolic representation based thereon, use the crank diagram of Chapters IV and V. In the time diagram as well as in the crank diagram, instead of the maximum value of the wave, the effective value, or square root of mean square, may be used as the vector, which is more conven ...", "... d vice versa. Or, the one diagram is the image of the other and can 62 ALTERNATING-CURRENT PHENOMENA be transformed into it by reversing right and left, or top and bottom. So the crank diagram, Fig. 47, is the image of the polar diagram, Fig. 46. In symbolic representation, based upon the crank diagram, the impedance was denoted by Z = r -\\- jx, where x == inductive reactance. In the polar diagram, the impedance thus is denoted by: Z = r — jx since the latter is the mirror image of the crank diagram, that is, differs ...", "... e x == inductive reactance. In the polar diagram, the impedance thus is denoted by: Z = r — jx since the latter is the mirror image of the crank diagram, that is, differs from it symbolically by the interchange of + j and — j. A treatise written in the symbolic repre- sentation by the polar diagram, thus can be translated to the representation by the crank diagram, and inversely, by simply reversing the signs of all imaginary quantities, that is, considering the signs of all terms with j Fig. 47. changed. A ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-22", "section_label": "Chapter 22: Armature Reactions Of Alternators", "section_title": "Armature Reactions Of Alternators", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 23971-25134", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-22/", "snippets": [ "... ., OEi. The armature resistance, r, consumes an e.m.f., OEi, in phase with the current, which subtracts vectorially from the actual generated e.m.f., and thus gives the terminal voltage, OE. 194. Analytically, these reactions are best calculated by the symbolic method. ARMATURE REACTIONS OF ALTERNATORS 275 Let the impressed m.in.f., or field-excitation, Fo, be chosen as the imaginary axis, hence represented by ^ Fo = + jfo (1) Let / = u — ji2 = armature current. (2) The m.m.f. of the armature then is Fi =nl ...", "... o) + (Pm'i. (5) The e.m.f. generated by the magnetic flux $ in the armature is 62 = 2 7r/ncI>10-8, (6) where / = frequency. Denoting 2 irfn 10 ~ ^ by a we have, (7) 62 = a $ (8) and since the generated e.m.f. is 90° behind the generating flux, in symbolic expression, E2= - ja^; (9) hence, substituting (5) in (9), E2 = a(P{fo - ni2) - jaiPnii, . (10) the virtual generated e.m.f. The e.m.f. consumed by the self-inductive reactance of the armature circuit is, E3 = jxl = jxii + xi2; (11) and therefore, the act ...", "... own, when starting the construc- tion of the diagram. That is, as usually, the graphical representation affords an insight into the inner relations of the phenomena, but not a method for their numerical cal- culations, and for the latter purpose, the symbolic method is required. Let Eo = nominal generated e.m.f., or e.m.f. corresponding to the field-excitation, Fo, on a straight line continuation of the magnetic characteristic from the actual value of the field onward Fig. 141. -as shown by Fig, 141. The ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-29", "section_label": "Chapter 29: Symmetrical Polyphase Systems", "section_title": "Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 29, "number": 29, "location": "lines 34929-35255", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-29/", "snippets": [ "... in(^ - -^y, ' . I ^ 2{n - l)x\\ The next e.m.f. is, again, ei = E sin (/3 - 2 x) = E sin /3. In the vector diagram the n e.m.fs. of the symmetrical n-phase system are represented by n equal vectors, following each other under equal angles. Since in symbolic writing rotation by - of a period, or angle 2 TT . ..... — , IS represented by multiplication with 27r , . . 27r COS h 7 sin — = e, n 71 the e.m.fs. of the symmetrical polyphase system are E; 27r . . . 2 ( 27r , . . 27r\\ (cos \\- J sin — = ...", "... rectangular space components of this m.m.f. are /T r- Zirl . [^ ZTn\\ = n L \\/2 COS sin 1/3 I n \\ n / and ft, f ■ 2 7ri h = }i Sin — - ,^^.27rt. /^ 2ti\\ = n i v2 sm sin \\B ) • n \\ n I Hence the m.m.f. of this coil can be expressed by the symbolic formula ,r A- • / 2 7rA / 2 7rt , . . 2 7rA /. = n/V2 sm (^ - --) ( cos— +jsm~-j- Thus the total or resultant m.m.f. of the n coils displaced under the n equal angles is /= Si/, = n7V2S^ sinf^-?^Vcos^\"+jsin^![!V 1 \\ \\ n l\\ n n ) or, expanded, £ ...", "... sin-^ = o ( 1 ~ cos ? sin n n n 2 \\ n n I = |(i-.\"): and, since 1 1 it is, nn'I\\/2 , . ^ f = 2 ^^^^ ^ ~ ^ ^^^ ^^ ' SYMMETRICAL POLYPHASE SYSTEMS 403 or, . nn'I , . . . / = — ^ (sin (8 - J cos /?) nF = --^ (sm 13 - j cos /3) ; the symbolic expression of the m.m.f. produced by the n circuits of the symmetrical n-phase system, when exciting n equal mag- netizing coils displaced in space under equal angles. The absolute value of this m.m.f. is _ nn'I _ nF _ nF^ax n Hence constant and equal — 7=: time ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-24", "section_label": "Chapter 24: Symmetbicaii Polyphase Ststems", "section_title": "Symmetbicaii Polyphase Ststems", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 25271-25604", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-24/", "snippets": [ "... n ( )8 — 2(n - l)ir ^) The next E.M.F. is again : ^i = /^ s\\n (P — 2 w) = £ sin /S. In the polar diagram the ;/ E.M.Fs. of the symmetrical «-phase system are represented by ;/ equal vectors, follow- ing each other under equal angles. Since in symbolic writing, rotation by 1/// of a period, or angle 2ir/;/, is represented by multiplication with: cos h J sm = c , the E.M.Fs. of the symmetrical polyphase system are: £• §236] SYMMETRICAL POLYPHASE SYSTEMS, 351 E I cos ^^ + J sin ^^ ) = ^ c ; \\ u ...", "... in/'i8-?^\\ The two rectangular components of this M.M.F. are: and fi' .. 2iri =// cos n = /i'/V2cos 2 7r/ // A\" ^. . 27r/ = // Sin -¥) // = ///V2sin?Ji'sin/')8-?^A Hence the M.M.F. of this coil can be expressed by the symbolic formula : /z = n'/^2sin(fi - ?^\\ /cos^+ysin^Y \\ ^ A '' « y Thus the total or resultant M.M.F. of the ;/ coils dis- placed under the n equal angles is : 1 1 \\ « /\\ '' « / or, expanded : /=;//V2 \\ sin/J^tfcos^ — +ysin?''-*cos?^^- cos P 2lL sm ...", "... [$237 . 27r/ 27r/ , . . o^tt/ j I ^ Aiiri . . 47r/\\ sm COS h / sin-* = ^ ( 1 — cos / sin \\ n n n 2\\ n n j and, since: as the sum of all the roots of Vl, it is, /= \"AI^ (sin p+J cos /3). or, /=!L^(sin)3+ycos/3) V2 = !^(sin)3 +ycos/3); the symbolic expression of the M.M.F. produced by the n circuits of the symmetrical //-phase system, when exciting n equal magnetizing coils displaced in space under equal angles. The absolute value of this M.M.F. is : V'2 V2 ^ Hence constant and equal h/V2 times the effec ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "... d from (29), V^ = (2^2f/)7r- <37') These substituted in (26) give, f- (38.) 4/7 (2£ + l)7rx /=(2TTi)-^cosL^H The oscillating discharge of a line can thus follow any of the forms given by making k — 0, 1, 2, 3 . . .in equation (38). Reduced from symbolic representation to absolute values 186 ALTERNATING-CURRENT PHENOMENA. by multiplying E with cos 2 * Nt and / with sin 2 TT A7/ and omitting j, and substituting A7\" from equation (34), we have, (2£+l)7rx — sin — JT— - — -cos 2/ where ^4 is an integration constan ...", "... n a transmission line leads to a space problem of which Figs. 34 and 35 are par- tial views. The single-phase line is represented by a double screw, the three-phase line by a triple screw, and the quarter- phase four-wire line by a quadruple screw. In the symbolic expression of the electric distribution in the transmission line, the real part of the symbolic equation represents a pro- jection on a plane passing through the axis of the screw, and the imaginary part a projection on a plane perpendicular to the first, and also p ...", "... single-phase line is represented by a double screw, the three-phase line by a triple screw, and the quarter- phase four-wire line by a quadruple screw. In the symbolic expression of the electric distribution in the transmission line, the real part of the symbolic equation represents a pro- jection on a plane passing through the axis of the screw, and the imaginary part a projection on a plane perpendicular to the first, and also passing through the axis of the screw. ALTERNATING-CURRENT TRANSFORMER. 193" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-26", "section_label": "Chapter 26: Symmetrical Polyphase Systems", "section_title": "Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 23781-24053", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-26/", "snippets": [ "... en = E sin ( ft - L V* ~ - \\ The next E.M.F. is again : ^ = E sin (ft — 2 TT) = E sin ft. In the polar diagram the n E.M.Fs. of the symmetrical 0-phase system are represented by n equal vectors, follow- ing each other under equal angles. Since in symbolic writing, rotation by l/« of a period, or angle 2ir/n, is represented by multiplication with : the E.M.Fs. of the symmetrical polyphase system are: SYMMETRICAL POLYPHASE SYSTEMS. 435 / 9 T- ? -rr E( cos — + / sin — = • ' n „ f 2 (n — 1) TT . ...", "... M.F. of one of the magnetizing coils. Then the instantaneous value of the M.M.F. of the coil acting in the direction 2 «•*'/» is : The two rectangular space components of this M.M.F. are ; and Hence the M.M.F. of this coil can be expressed by the symbolic formula : fi n \\ n Thus the total or resultant M.M.F. of the n coils dis- placed under the n equal angles is : or, expanded : n 438 ALTERNATING-CURRENT PHENOMENA. It is, however : cos'2 — + / sin — cos — = £ ( 1 + cos — +/ sin —] n n n ...", "... however : cos'2 — + / sin — cos — = £ ( 1 + cos — +/ sin —] n n n V w w / \\ / sin 2=1 cos ?Z£+ysin«2=£= ^Yl - cos i^'-ysin4^' « » • « z y « « _ ^ /I _ ,2A X 2(1-^ and, since: 5t<2< = 0, it is, /= nn'f^ (-sin ft _ y cos ft), or, the symbolic expression of the M.M.F. produced by the « circuits of the symmetrical «-phase system, when exciting n equal magnetizing coils displaced in space under equal angles. The absolute value of this M.M.F. is : nn' I n\"S n <5 V2 V2 2 Hence constant and equal w/V2 ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-14", "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "section_title": "Constant-Potential Constant-Current Trans Formation", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "... stigation of different methods of producing constant alternating current from constant alternating voltage, or inversely, constitutes a good application of the terms \"impedance,\" admittance,\" etc., and offers a large number of problems or examples for the symbolic method of dealing with alternating-current phenomena. Even outside of arc lighting, such combinations of inductance and capacity which t«nd toward constant-voltage constant-cur- rent transformation are of considerable importance as a poffsiblo source of danger ...", "... use of quadrature e.m.fs. taken from a second phase of the polyphase system, the secondary output, for the same amount of reactances, increased. These combinations afford very convenient and instructive examples for accustoming oneself to the use of the symbolic method in the solution of alternating-current problems. Only two typical cases, the T-connection and the monocyclic square will be more fully discussed. Fig. 119. A. T-Connection or Resonating Circuit 136. General. — A combination, in a constant-potential ...", "... nt of the constant-current .regulation, could thus be expected only with devices using capacity reactance. As example may be investigated the effect of the distortion of the impressed voltage wave on the T connection, and on the monocyclic square. The symbolic method of treating general alternating waves may be used, as discussed in Chapter XXVII, of \"Theory and Calculation of Alternating-current Phenomena,\" fifth edition, page 379. That is, the voltage wave is represented by 00 1 and the impedance by Z = r + jn ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 557-1002", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-01/", "snippets": [ "... nception of the \" effective values,\" and more completely by the introduction of the general number or complex quantity, which represents the periodic func- tion of time by a constant numerical value. In this feature lies the advantage and the power of the symbolic method of dealing with alternating-current phenomena, — the reduction of a periodic transient to a permanent or constant quantity. For this reason, wherever periodic transients occur, as in rectification, commuta- tion, etc., a considerable advantage is frequent ...", "... ansient to a permanent or constant quantity. For this reason, wherever periodic transients occur, as in rectification, commuta- tion, etc., a considerable advantage is frequently gained by their reduction to permanent phenomena, by the introduction of the symbolic expression of the equivalent sine wave. Hereby most of the periodic transients have been eliminated from consideration, and there remain mainly the nonperiodic transients, as occur at any change of circuit conditions. Since they are the phenomena of the readjustmen ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 460-882", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "snippets": [ "... nception of the \" effective values,\" and more completely by the introduction of the general number or complex quantity, which represents the periodic func- tion of time by a constant numerical value. In this feature lies the advantage and the power of the symbolic method of dealing with alternating-current phenomena, — the reduction of a periodic transient to a permanent or constant quantity. For this reason, wherever periodic transients occur, as in rectification, commuta- tion, etc., a considerable advantage is frequent ...", "... ansient to a permanent or constant quantity. For this reason, wherever periodic transients occur, as in rectification, commuta- tion, etc., a considerable advantage is frequently gained by their reduction to permanent phenomena, by the introduction of the symbolic expression of the equivalent sine wave. Hereby most of the periodic transients have been eliminated from consideration, and there remain mainly the nonperiodic transients, as occur at any change of circuit conditions. Since they are the phenomena of the readjustmen ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-17", "section_label": "Chapter 17: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16521-17716", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-17/", "snippets": [ "... = 0.01 ohm; Xi = 0.00025 ohm; Xq = 0.033 ohm; go = 0.001 mho; ri = 0.00008 ohm; 6o = 0.00173 mho; that is, about one-tenth as large as assumed. Thus the changes of the values of Eo, Ei, etc., under the different conditions will be very much smaller. Symbolic Method 149. In symbolic representation by complex quantities the transformer problem appears as follows: The exciting current, /oo, of the transformer depends upon the primary e.m.f., which dependence can be represented by an admittance, the \"primary admittan ...", "... hm; Xq = 0.033 ohm; go = 0.001 mho; ri = 0.00008 ohm; 6o = 0.00173 mho; that is, about one-tenth as large as assumed. Thus the changes of the values of Eo, Ei, etc., under the different conditions will be very much smaller. Symbolic Method 149. In symbolic representation by complex quantities the transformer problem appears as follows: The exciting current, /oo, of the transformer depends upon the primary e.m.f., which dependence can be represented by an admittance, the \"primary admittance,\" Fo = g^i — jbo, of the trans ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-24", "section_label": "Chapter 24: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 25682-29374", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-24/", "snippets": [ "... netic field, and so the intensity and phase of the current in its effect on the charac- teristic curves of the synchronous motor, can be carried out in the same manner as done for the alternating-current generator in Chapter XX. In the graphical and the symbolic investigations in Chapter XX, the current, I = ii — jiz, has been considered as the output current, and chosen of such phase as to differ less than 90° from the terminal voltage, E = ex -\\- je^, so representing power output. Choosing then the current ve ...", "... ronous motor. The graphical representation in Chapter XX so applies equally well to alternating-current generator as to synchronous motor, and the former corresponds to the case Z EOI < 90°, the latter to the case: Z EOI > 90°. In the same manner, in the symbolic representation of Chapter XX, choosing the current as 7 = — t'l + JH, or, in the final equation, where the current has been assumed as zero vector, 7 = — i, that is, reversing all the signs of the current, gives the equations of the synchronous motor. Choosing the sam ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-13", "section_label": "Chapter 13: Ths Alternating^Cnrrent Traxsfobmer", "section_title": "Ths Alternating^Cnrrent Traxsfobmer", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 12673-14088", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "snippets": [ "... s ; x^ = .00025 ohms ; g^ = .001 ohms ; do = .00173 ohms ; that is, about one-tenth as large as assumed. Thus the changes of the values of E^y E^, etc., under the different conditions will be very much smaller. A/. TERAA TINC-CVRRENT PHENOMKAA Symbolic Method. 124- In symbolic representation by complex quantities the transformer problem appears as follows : The exciting current, /„, of the transformer depends upon the primary K.M.K., which dcpendance can be rc|> resented by an admittance, the \" primary admi ...", "... g^ = .001 ohms ; do = .00173 ohms ; that is, about one-tenth as large as assumed. Thus the changes of the values of E^y E^, etc., under the different conditions will be very much smaller. A/. TERAA TINC-CVRRENT PHENOMKAA Symbolic Method. 124- In symbolic representation by complex quantities the transformer problem appears as follows : The exciting current, /„, of the transformer depends upon the primary K.M.K., which dcpendance can be rc|> resented by an admittance, the \" primary admittance,\" Y^=^ g^ ■\\- j b^, of the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-14", "section_label": "Chapter 14: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 11605-12682", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "snippets": [ "... #! = .00025 ohms ; g0 = .001 ohms ; b0 = .00173 ohms ; that is, about one-tenth as large as assumed. Thus the changes of the values of E0, Elt etc., under the different conditions will be very much smaller. 204 ALTERNATING-CURRENT PHENOMENA. Symbolic Method. 134. In symbolic representation by complex quantities the transformer problem appears as follows : The exciting current, 700, of the transformer depends upon the primary E.M.F., which dependance can be rep- resented by an admittance, the \" primary adm ...", "... .001 ohms ; b0 = .00173 ohms ; that is, about one-tenth as large as assumed. Thus the changes of the values of E0, Elt etc., under the different conditions will be very much smaller. 204 ALTERNATING-CURRENT PHENOMENA. Symbolic Method. 134. In symbolic representation by complex quantities the transformer problem appears as follows : The exciting current, 700, of the transformer depends upon the primary E.M.F., which dependance can be rep- resented by an admittance, the \" primary admittance,\" °f tne transformer. F ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-16", "section_label": "Theory Section 16: Phase Control of Transmission Lines", "section_title": "Phase Control of Transmission Lines", "kind": "theory-section", "sequence": 16, "number": 16, "location": "lines 6222-6813", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-16/", "snippets": [ "... cuit; that is, P — ei = transmitted power, and ii = reactive current produced in the system for controlling the voltage. i\\ shall be considered positive as lagging, negative as leading current. Then the total current, in symbolic representation, is / = i - jii; the line impedance is Z = r + jx, and thus the e.m.f. consumed by the line impedance is Ei = ZI = (r + jx) (i - jii) = ri + jrii + jxi - J2xii; and substituting f — — 1, Ei = (ri + ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-26", "section_label": "Apparatus Section 5: Synchronous Machines: Synchronous Reactance", "section_title": "Synchronous Machines: Synchronous Reactance", "kind": "apparatus-section", "sequence": 26, "number": 5, "location": "lines 9035-9169", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-26/", "snippets": [ "... ive load, 6 = 60 degrees lag or inductive load, and & — — 60 degrees or anti-inductive load. Resolving all e.m.fs. into components in phase and in quad- rature with the current, or into power and reactive components, in symbolic expression we have: 138 ELEMENTS OF ELECTRICAL ENGINEERING the terminal voltage E = E cos 6 + jE sin 6 ; the e.m.f. consumed by resistance, E\\ = ir; the e.m.f. consumed by synchronous reactance, E'0 = + jixQ, and the nominal ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-28", "section_label": "Apparatus Section 7: Synchronous Machines: Synchronous Motor", "section_title": "Synchronous Machines: Synchronous Motor", "kind": "apparatus-section", "sequence": 28, "number": 7, "location": "lines 9292-9398", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-28/", "snippets": [ "... diagram of synchronous motor. FIG. 63. — Vector diagram of synchronous motor. 0=0 ing and lower with lagging current in a synchronous motor, while the opposite is the case in an alternating-current generator. In symbolic representation, by resolving all e.m.fs. into power components in phase with the current and wattless components in quadrature with the current i, we have: the terminal voltage, E = E cos 6 + jE sin 6 = Ep + jEq; the e.m.f. consume ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-12", "section_label": "Chapter 12: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 10718-13483", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-12/", "snippets": [ "... enoting the absolute value of the impedance of the circuit, E J, by z — where z is determined by the magnetic characteristic of the iron and the shape of the magnetic and electric circuits — the impedance is represented, in phase and intensity, by the symbolic expression, Z — r -{- jx =^ z '&\\n a -\\- jz cos a; and the admittance by, 1 ^ g — JO = - Bin a — J- cos a = y sm a — jy cos a. The quantities z, r, x, and y, g, h are, however, not constants as in the case of the circuit without iron, but depend upon the inten ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "section_label": "Chapter 14: Dielectric Losses", "section_title": "Dielectric Losses", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "... ght- ning arrester. 121. As seen, in the dielectric circuit, that is, in insulators in which the current is essentially a displacement current, the relations between voltage, current, power, phase angle and power- factor can be represented by the same symbolic equations as the relations between voltage, current, power and power-factor in metallic conductors, in which the current flow is dynamic, by the introduction of the effective admittance of the dielectric circuit, or part of circuit: where g is the effec ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-20", "section_label": "Chapter 20: Single-Phase Induction Motors", "section_title": "Single-Phase Induction Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 21538-22301", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-20/", "snippets": [ "... wo impedances of different power-factor, as an inductive reactance and a resistance, or an inductive and a condensive reactance connected in series across the mains. The investigation of these starting-devices offers a very instructive application of the symbolic method of investiga- tion of alternating-current phenomena, and a study thereof is thus recommended to the reader.^ ' See paper on the Single-phase Induction Motor, A. I. E. E. Transactions, 1898. SINGLE-PHASE INDUCTION MOTORS 247 179. Occasionally, no spe ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-04", "section_label": "Chapter 4: Graphic Befrisxintation", "section_title": "Graphic Befrisxintation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 2122-2743", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-04/", "snippets": [ "... conclusion from the foregoing is that the transformer is not suitable for producing currents of displaced phase ; since primary and secondary current are, except at very light loads, very nearly in phase, or rather, in opposition,, to each other. i 23] SYMBOLIC METHOD. 88" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-10", "section_label": "Chapter 10: F", "section_title": "F", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 8269-10499", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "snippets": [ "... IIG AL TERNA TING-CURRENT PHENOMENA, [§ 80 circuit, -£\"//, by ir, — where z is determined by the mag- netic characteristic of the iron, and the shape of the magnetic and electric circuits, — the impedance is repre- sented, in phase and intensity, by the symbolic expression, Z =^ r ^ jx = ;? sin a — jz cos a ; and the admittance by, K = ^ + y ^ = - sin a + y - cos a = >» sin a + jy cos a. z z The quantities, xr, r, ;r, and y^ gy 6, are, however, not constants as in the case of the circuit without iron, but depend upo ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-18", "section_label": "Chapter 16: Il", "section_title": "Il", "kind": "chapter", "sequence": 18, "number": 16, "location": "lines 19346-21338", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-18/", "snippets": [ "... roduces mechanical, power ; that is, runs as a synchronous motor, so that the investigation of the synchronous motor is already contained essentially in the equations of parallel-running alternators. Since in the foregoing we have made use mostly of the symbolic method, we may in the following, as an instance of the graphical method, treat the action of the synchronous motor diagrammatically. Let an alternator of the E.M.F., E^, be connected as synchronous motor w^ith a supply circuit of E.M.F., E^y by a circuit of th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-04", "section_label": "Chapter 4: Graphic Representation", "section_title": "Graphic Representation", "kind": "chapter", "sequence": 4, "number": 4, "location": "lines 1743-2321", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-04/", "snippets": [ "... ry. A conclusion from the foregoing is that the transformer is not suitable for producing currents of displaced phase ; since primary and secondary current are, except at very light loads, very nearly in phase, or rather, in opposition, to each other. SYMBOLIC METHOD." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "section_label": "Chapter 10: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "... he 116 A L TERNA TING-CURRENT PHENOMENA . circuit, E 1 1, by s, — where s is determined by the mag- netic characteristic of the iron, and the shape of the magnetic and electric circuits, — the impedance is repre- sented, in phase and intensity, by the symbolic expression, Z = r — jx = z sin a — jz cos a ; and the admittance by, Y = g + j b = - sin a -j- j - cos a = y sin a -f- jy cos a. z z The quantities, z, r, x, and y, g, b, are, however, not constants as in the case of the circuit without iron, but depend upon ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-15", "section_label": "Chapter 15: The General Alternating-Current Transformer Or Frequency Converter", "section_title": "The General Alternating-Current Transformer Or Frequency Converter", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 12683-13648", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "snippets": [ "... ely be done, and assum- ing the primary impedance reduced to the secondary circuit as equal to the secondary impedance, Substituting this in the equations of the general trans- former, we get, £,= - «0 e\\ I + - fr fa + r) 146. The true power is, in symbolic representation (see Chapter XII.) : 228 ALTERNATING-CURRENT PHENOMENA. denoting, safe* -7F = W gives : Secondary output of the transformer Internal loss in secondary circuit, m -2 t s n\\ ^\\2 -Pi = 'i2 n = ( — — } V ** / Total secondary power, ** ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "section_label": "Chapter 16: Induction Motor", "section_title": "Induction Motor", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "... onnection of two impedances of different power factor, as an inductance and a resistance, or an in- ductance and a condensance connected in series across the mains. The investigation of these starting-devices offers a very instructive application of the symbolic method of investiga- tion of alternating-current phenomena, and a study thereof is thus recommended to the reader.* » See paper on the Single-phase Induction Motor, A.I.E.E. Transactions, 1898. 284 ALTERNATING-CURRENT PHENOMENA. 177. As a rule, no special m ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-19", "section_label": "Chapter 19: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 18053-19457", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "snippets": [ "... roduces mechanical, power ; that is, runs as a synchronous motor, so that the investigation of the synchronous motor is already contained essentially in the equations of parallel-running alternators. Since in the foregoing we have made use mostly of the symbolic method, we may in the following, as an instance of the graphical method, treat the action of the synchronous motor diagrammatically. Let an alternator of the E.M.F., E±, be connected as synchronous motor with a supply circuit of E.M.F., EQ, by a circuit of the ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-11", "section_label": "Chapter 12: Frequency Converter Or General Alternating Current Transformer", "section_title": "Frequency Converter Or General Alternating Current Transformer", "kind": "chapter", "sequence": 11, "number": 12, "location": "lines 14897-17124", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-11/", "snippets": [ "... Substituting this in the equations of the general transformer we get: #o = no6 { 1 + \\ \\t\\ (n + r) + sxx (xi + x)] - J 2 [srx (xi + x) - Xi (r! + r)] Zk $i = *\"-e \\[r (n + r) + «2x (xi + x)] - js[rxi -xri]}, Zk Zk 106. The true power is, in symbolic representation: P = WY, denoting: srti2e2 -. - = w Zk2 gives: Secondary output of the transformer: FREQUENCY CONVERTER 183 Internal loss in secondary circuit: Total secondary power: Pi + Pi1 = (-\"*) % (r + n) =sw(r + r,) ; Internal loss in primary ci ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-16", "section_label": "Chapter 18: Surging Of Synchronous Motors", "section_title": "Surging Of Synchronous Motors", "kind": "chapter", "sequence": 16, "number": 18, "location": "lines 20975-21712", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-16/", "snippets": [ "... otor, have the radius of gyration of 20 in., a weight of the revolving part of 6000 lb. The momentum then is Af„ = 850,000 joules. Deriving the angles, 0, corresponding to given values of output. P, and excitation, r, from the polar diagram, or from the symbolic SURGING OF SYNCHRONOUS MOTORS 293 representation, and substituting in (16), gives the frequency of oscillation : P = 0: e = 1600 volts; 0 = - 2°;/0 = 2.17 cycles, or 130 periods per minute. 2180 volts + 3° 2.50 cycles, or 150 periods per ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-08", "section_label": "Chapter 8: Shaping Of Waves By Magnetic Saturation", "section_title": "Shaping Of Waves By Magnetic Saturation", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 12962-16963", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-08/", "snippets": [ "... s 83 The equation of the peaked voltage in Fig. 62 then becomes e = eo {1.270 cos <^ + 1.242 cos 3* + 1.188 cos 5« + 1.114 cos7« + 1.018 cos 9^ + 0.906 cos 11* + 0.786 cos 13* + 0.668 cos 15* + 0.629 cos 170 + 0.400 cos 19* + 0.240 cos 21*}. Or, in symbolic writing, e = eo|1.270i + 1.242, + LISS^ + 1.114t + 1.018» + 0.906,, + 0.786ia + 0.658i6 + 0.529n + 0.400i» + 0.240,,) SHAPING OF WAVES BY MAGNETIC SATURATION 143 = 1.270 eo {li + 0.9783 + 0.953s H + 0.617,j + 0.517u + O.4I617 0.877, + 0.800a + 0.7 ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-12", "section_label": "Chapter 12: Reactance Of Induction Apparatus", "section_title": "Reactance Of Induction Apparatus", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 22634-23465", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-12/", "snippets": [ "... 17 H r- 0.25. thus are greatly exaggerated, to show the effect more plainly. Actually, the relations are usually of the magnitude, P -4- Po -5- Pi = 1 -^ 1000 -r- 1000 F -^ Fo -^ Fi = 1 -T- 20.6 -5- 20 $ -5- $'o -^ ^'i = 1 -^ 0.02 4- 0.02 113. In symbolic representation, denoting, f» = mutual magnetic flux. fJ = mutual induced voltage. f>o = resultant primary flux. f>'o = primary leakage flux. fJo = primary terminal voltage, /o = primary current. Zo = ro + jxo = primary self-inductive imped- ance, f 1 = resultant ..." ] } ] }, { "id": "complex-quantities", "label": "Complex Quantities", "aliases": [ "complex quantities", "complex quantity", "imaginary quantities", "imaginary quantity" ], "total_occurrences": 156, "matching_section_count": 48, "matching_source_count": 10, "source_totals": [ { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 41, "section_count": 9 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 41, "section_count": 10 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 31, "section_count": 10 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 16, "section_count": 7 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 12, "section_count": 2 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 5, "section_count": 2 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 4, "section_count": 3 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 2, "section_count": 2 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 2, "section_count": 1 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 2, "section_count": 2 } ], "section_hits": [ { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-05", "section_label": "Chapter 5: Symbolic Method", "section_title": "Symbolic Method", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2760-3266", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-05/", "snippets": [ "... eriod; that is, leading the wave by one-quarter period. Similarly — Multiplying by — j jneans lagging the wave by one-quarter period. Since j^ = - 1, it is j = v^^=n:; and j is the imaginary unit, and the sine wave is represented by a complex imaginary quantity or general number, a ^- jb. As the imaginary unit, j, has no numerical meaning in the system of ordinary numbers, this definition of j = V — 1 does not contradict its original introduction as a distinguishing index. For the Algebra of Complex Quantities ...", "... imaginary quantity or general number, a ^- jb. As the imaginary unit, j, has no numerical meaning in the system of ordinary numbers, this definition of j = V — 1 does not contradict its original introduction as a distinguishing index. For the Algebra of Complex Quantities see Appendix I. For a more complete discussion thereof see \" Engineering Mathematics.\" 30. In the vector diagram, the sine wave is represented in intensity as well as phase by one complex quantity, a + jb, 3 34 ALTERNATING-CURRENT PHENOMENA where ...", "... roduction as a distinguishing index. For the Algebra of Complex Quantities see Appendix I. For a more complete discussion thereof see \" Engineering Mathematics.\" 30. In the vector diagram, the sine wave is represented in intensity as well as phase by one complex quantity, a + jb, 3 34 ALTERNATING-CURRENT PHENOMENA where a is the horizontal and h the vertical component of the wave; the intensity is given by i = Va2 + 62, the phase by tan 6 = — a and a = i cos 6, b = i sin 6] hence the wave, a + jh, can ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-01", "section_label": "Chapter 1: The General Number", "section_title": "The General Number", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 915-3491", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-01/", "snippets": [ "... rature with each other can be expressed by the plus si^n, and the result of combination thereby expressed by OB^-BP = 3+2j. THE GENERAL NUMBER. 17 Such a combination of an ordinary number and a quadra- ture number is called a general number or a complex quantity. The quadrature number jh thus enormously extends the field of usefulness of algebra, by affording a numerical repre- sentation of two-dimensional systems, as the plane, by the general number a-\\-jh. They are especially useful and impor- tant in electri ...", "... ors in space. In the quaternion calculus methods have been devised to deal with space problems. The quaternion calculus, however, has not yet found an engineering appHcation comparable with that of the general number, or, as it is frequently called, the complex quantity. The reason is that the quaternion is not an algebraic quantity, and the laws of algebra do not uniformly apply to it. 17. With the rectangular coordinate system in the plane. Fig. 11, the X axis may represent the ordinary numbers, the y axis the quadra ...", "... ich is obviously wrong. For this reason all the mechanisms devised for vector analysis in space have proven more difficult in their application, and have not yet been used to any great extent in engineering practice. B. ALGEBRA OF THE GENERAL NUMBER, OR COMPLEX QUANTITY. Rectangular and Polar Coordinates. i8. The general number, or complex quantity, a+jb, is the most general expression to which the laws of algebra apply. It therefore can be handled in the same manner and under the same rules as the ordinary number of ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-05", "section_label": "Chapter 5: Symbouc Mbthod", "section_title": "Symbouc Mbthod", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2744-3229", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "snippets": [ "... ing the wave through one-quarter period. Fig. 24, Similarly, — Multiplying by — / means advancing the wave through -one-quarter period. since y^ = ~ 1, y = V— 1 ; that is, — j is the imaginary unity and the sine wave is represented by a complex imaginary quantity ^ a -\\- jb. As the imaginary unit j has no numerical meaning in the system of ordinary numbers, this definition ofy = V— 1 does not contradict its original introduction as a distinguish- ing index. For a more exact definition of this complex imaginary q ...", "... ry quantity ^ a -\\- jb. As the imaginary unit j has no numerical meaning in the system of ordinary numbers, this definition ofy = V— 1 does not contradict its original introduction as a distinguish- ing index. For a more exact definition of this complex imaginary quantity, reference may be made to the text books of mathematics. 28. In the polar diagram of time, the sine wave is represented in intensity as well as phase by one complex quantity — , .^ a +jb, 38 AL TERXA TING-CUKKENT PHENOMENA. [§ 29 where a is the ...", "... ion as a distinguish- ing index. For a more exact definition of this complex imaginary quantity, reference may be made to the text books of mathematics. 28. In the polar diagram of time, the sine wave is represented in intensity as well as phase by one complex quantity — , .^ a +jb, 38 AL TERXA TING-CUKKENT PHENOMENA. [§ 29 where a is the horizontal and b the vertical component of the wave ; the intensity is given by — the phase by and /= V^^a^/,^, tan o) = - , a a -= t cos o), ^ = /■ sin a> ; he ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "section_label": "Chapter 30: Quartbr-Fhase System", "section_title": "Quartbr-Fhase System", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... ual distribution of load, but are liable to become un- balanced at unequal distribution of load ; the three-wire quarter-phase system is unbalanced in voltage and phase, even at equal distribution of load. APPENDICES APPENDIX I. ALGEBRA OF COMPLEX IMAGINARY QUANTITIES. INTRODUCTION. 267. The system of numbers, of which the science of algebra treats, finds its ultimate origin in experience. Directly derived from experience, however, are only the absolute integral numbers ; fractions, for instance, are not directly d ...", "... ction under any circumstances, the system of abso- lute numbers has to be expanded by the introduction of the negative number: — a = (— 1) X a, where (— 1) is the negative unit. Thereby the system of numbers is subdivided in the 270,271] COMPLEX IMAGINARY QUANTITIES. 403 positive and negative numbers, and the operation of sub- traction possible for all values of subtrahend and minuend. or (-l)x (-1) = 1; that is, the negative unit is defined by : (- 1)^ = 1- 270. The reverse operation of multiplication introdu ...", "... ns under all conditions, 2d. Permanence of the laws of calculation, the expansion of the system of numbers has become neces- sary, into Positive and negative numbers. Integral numbers and fractions. Rational and irrational numbers. S 274] COMPLEX IMAGINARY QUANTITIES, 405 Real and imaginary numbers and complex imagmary numbers. ^ Therewith closes the field of algebra, and all the alge- braic operations and their reverse operations can be carried out irrespective of the values of terms entering the opera- tion. T ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-05", "section_label": "Chapter 5: Symbolic Method", "section_title": "Symbolic Method", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 2322-2773", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-05/", "snippets": [ "... ing the wave through one-quarter period. Fig. 24. Similarly, — Multiplying by — j means advancing the wave through one-quarter period. since y'2 = — 1, j = V— 1 ; that is, — j is the imaginary unit, and the sine wave is represented by a complex imaginary quantity, a -+- jb. As the imaginary unit j has no numerical meaning in the system of ordinary numbers, this definition of/ = V— 1 does not contradict its original introduction as a distinguish- ing index. For a more exact definition of this complex imaginary qu ...", "... ary quantity, a -+- jb. As the imaginary unit j has no numerical meaning in the system of ordinary numbers, this definition of/ = V— 1 does not contradict its original introduction as a distinguish- ing index. For a more exact definition of this complex imaginary quantity, reference may be made to the text books of mathematics. 28. In the polar diagram of time, the sine wave is represented in intensity as well as phase by one complex quantity — 38 ALTERNATING-CURRENT PHENOMENA. where a is the horizontal and b the ver ...", "... tion as a distinguish- ing index. For a more exact definition of this complex imaginary quantity, reference may be made to the text books of mathematics. 28. In the polar diagram of time, the sine wave is represented in intensity as well as phase by one complex quantity — 38 ALTERNATING-CURRENT PHENOMENA. where a is the horizontal and b the vertical component of the wave ; the intensity is given by — the phase by — tan -*• As the reciprocal of the complex quantity, Z = r —jx, the admittance is a complex quantity also, or Y = g+jb; 54 ALTERNATING-CURRENT PHENOMENA. it consists of the component g, which represents the co- efficient of current in phase with the E.M.F., or energy current, gEt in the equation of Ohm ...", "... es where Ohm's law is expressed in the form, -I- It is preferable, then, to introduce the reciprocal of impedance, which may be called the admittance of the circuit, or >-*• As the reciprocal of the complex quantity, Z = r —jx, the admittance is a complex quantity also, or Y = g+jb; 54 ALTERNATING-CURRENT PHENOMENA. it consists of the component g, which represents the co- efficient of current in phase with the E.M.F., or energy current, gEt in the equation of Ohm's law, — and the component b, which represents ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... (8) By equation (1), E ld' Y~dl' and substituting herein equation (8) gives E -A,™ + A*-\" , (9) 286 TRANSIENT PHENOMENA or, substituting (7), E =\\/A1e+vl+A,e-vi . (10) The integration constants A1 and A2 in (8), (9), (10), in general, are complex quantities. The coefficient of the exponent, F, as square root of the product of two complex quantities, also is a complex quantity, therefore may be written V = a - jp, (11) and substituting for F, Z and Y gives (a - j/?)2 = (r - jx) (g - jb), or (a2 - /?2) ...", "... A*-\" , (9) 286 TRANSIENT PHENOMENA or, substituting (7), E =\\/A1e+vl+A,e-vi . (10) The integration constants A1 and A2 in (8), (9), (10), in general, are complex quantities. The coefficient of the exponent, F, as square root of the product of two complex quantities, also is a complex quantity, therefore may be written V = a - jp, (11) and substituting for F, Z and Y gives (a - j/?)2 = (r - jx) (g - jb), or (a2 - /?2) - 2 jap = (rg - xb) - j (rb + gx), and this resolves into the two separate equations a2 — ...", "... ENOMENA or, substituting (7), E =\\/A1e+vl+A,e-vi . (10) The integration constants A1 and A2 in (8), (9), (10), in general, are complex quantities. The coefficient of the exponent, F, as square root of the product of two complex quantities, also is a complex quantity, therefore may be written V = a - jp, (11) and substituting for F, Z and Y gives (a - j/?)2 = (r - jx) (g - jb), or (a2 - /?2) - 2 jap = (rg - xb) - j (rb + gx), and this resolves into the two separate equations a2 — ft2 = rg — xb ) 2 aQ = rb + ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-08", "section_label": "Chapter 8: Admittance, Conductance, Susceptance", "section_title": "Admittance, Conductance, Susceptance", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 4088-4673", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-08/", "snippets": [ "... e produced by the same e.m.f., such as in cases where Ohm's law is expressed in the form, / = I . Z It is preferable, then, to introduce the reciprocal of impe- dance, which may be called the admittance of the circuit, or Z As the reciprocal of the complex quantity, Z = r -{- jx, the admittance is a complex quantity also, or Y = g — jh; it con- sists of the component, g, which respresents the coefficient of current in phase with the e.m.f., or the power or active com- ponent, gE, of the current, in the equation of O ...", "... e Ohm's law is expressed in the form, / = I . Z It is preferable, then, to introduce the reciprocal of impe- dance, which may be called the admittance of the circuit, or Z As the reciprocal of the complex quantity, Z = r -{- jx, the admittance is a complex quantity also, or Y = g — jh; it con- sists of the component, g, which respresents the coefficient of current in phase with the e.m.f., or the power or active com- ponent, gE, of the current, in the equation of Ohm's law, I =YE ={g- jh)E, and the component, h, ...", "... CE 59 The joint impedance of a number of series-connected impedances is equal to the sum of the individual impedances; the joint admit- tance of a number of parallel-connected admittances is equal to the sum of the individual admittances, if expressed in complex quantities. In diagrammatic representation, combination by the parallelogram law takes the place of addition of the complex quantities. 52. Experimentally, impedances and admittances are most conveniently determined by establishing an alternating current in the ci ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-18", "section_label": "Chapter 18: Polyphase Induction Motors", "section_title": "Polyphase Induction Motors", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17717-20445", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-18/", "snippets": [ "... ective e.m.f. generated by the magnetic field per primary circuit. Counting the time from the moment where the rising mag- netic flux of mutual induction, (flux interlinked with both electric circuits, primary and secondary), passes through zero, in complex quantities, the magnetic flux is denoted by $ = - i$, and the primary generated e.m.f., E = - e; where e = \\/2 xn/$ 10~* may be considered as the \"active e.m.f. of the motor,\" or \"counter e.m.f.\" Since the secondary frequency is sf, the secondary induced e.m ...", "... 4 7r/(ri2 + s^x,^) In the foregoing, we found ^0 = e jl +s|- +Zor j' POLYPHASE INDUCTION MOTORS 219 or, approximately, Eo = e{l +s|-\"}; or, EqZi e = sZo + Zx' expanded, „ ri -\\-jsxi e = Eo (ri+ sro) -i- js(xi + XqY or, eliminating imaginary quantities, = '^°^k ri^ + s^Xi\"^ Substituting this value in the equations of torque and of power, they become, torque, ^ ^ qpiTiEph . ^ ~ 4 tt/ { (ri + snY + s^ix^ + XoY}' power, p ^ PiVrEoMl - S) (ri -\\- sroY -{- s'^{xi-\\-Xoy Maximum Torque 163. ...", "... i + ro] + Xi{X], + Xo]) + 6(roXi - XorO' 224 ALTERNATING-CURRENT PHENOMENA Neglecting the exciting current, g = 0 = b, these equations assume the form, J (ri + ro) - j (xi + xo) Eq (ri + ro)2 + {xi + Xo)\" . (ri + ro) + j {xi + Xq) ' or, ehminating imaginary quantities, V(ri + nY + (xi + x,Y z ' and , . Xi + Xq tan do ; ri + ro That means, that in starting the induction motor without additional resistance in the armature circuit — in which case Xi + Xo is large compared with ri + ro, and the total impe- dance ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-13", "section_label": "Chapter 13: Ths Alternating^Cnrrent Traxsfobmer", "section_title": "Ths Alternating^Cnrrent Traxsfobmer", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 12673-14088", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "snippets": [ "... 73 ohms ; that is, about one-tenth as large as assumed. Thus the changes of the values of E^y E^, etc., under the different conditions will be very much smaller. A/. TERAA TINC-CVRRENT PHENOMKAA Symbolic Method. 124- In symbolic representation by complex quantities the transformer problem appears as follows : The exciting current, /„, of the transformer depends upon the primary K.M.K., which dcpendance can be rc|> resented by an admittance, the \" primary admittance,\" Y^=^ g^ ■\\- j b^, of the transformer. rig. 9 ...", "... 189 and, 2r. R = pd. 2x, = <\\d, Rgo h ~~d' lib. d' Substituting these values we get, as the equations of the transformer on non-inductive load, Ratio of E.M.Fs. : I = - . { 1 + j or, eliminating imaginary quantities, Ratio of currents : /._ 1 li . (h+yg) , (P-yq)(t.+yg) ) /i « ( ^ ^ ^ 2 ) or, eliminating imaginary quantities. ^Mi I h ph + qg+g« t a\\ ^ d^ 2d* S 190 AL TERNA TING-CURRENT PHENOMENA. L§ 1 29 Total apparent primary impedance : or, eliminating ...", "... as the equations of the transformer on non-inductive load, Ratio of E.M.Fs. : I = - . { 1 + j or, eliminating imaginary quantities, Ratio of currents : /._ 1 li . (h+yg) , (P-yq)(t.+yg) ) /i « ( ^ ^ ^ 2 ) or, eliminating imaginary quantities. ^Mi I h ph + qg+g« t a\\ ^ d^ 2d* S 190 AL TERNA TING-CURRENT PHENOMENA. L§ 1 29 Total apparent primary impedance : or, eliminating imaginary quantities, ^t 2 ^Ii//«) .fji + .p-hj Angle of lag in primary circuit : tan u>o = 1 + ^p ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-15", "section_label": "Chapter 15: Induction Motob", "section_title": "Induction Motob", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 14919-17024", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-15/", "snippets": [ "... = effective E.M.F. induced by the mag- netic field per primary circuit. Counting the time from the moment where the rising magnetic flux of mutual induction * (flux interlinked with both electric circuits, primary and secondary) passes through zero, in complex quantities, the magnetic flux is denoted by and the primary induced E.M.F., j5 = — ^; where e = V2 TTfiN^ 10~* may be considered as the \" Active E.M.F. of the motor.\" Since the secondary frequency is s Ny the secondary induced E.M.F. (reduced to primary syst ...", "... N MOTOR. 219 and the total power of the motor, At the linear speed, V = — — (1 - s) a at unit radius the torque is dp r, e^ s T = ^irN(r^^-^x^ In the foregoing, we found or, approximately, expanded, . = ^. __^^^Z^^__ ; or, eliminating imaginary quantities : Substituting this value in the equations of torque and of power, it is, d pr^E^s torque: r ^^^^^^^^ ^^y^^,^^^^ ^y^\\ power : P = — -^ — - ^ , \\. — ^2 • Maximum Torque, 148. The torque of the induction motor is a maximum for that value of slip ...", "... - xr^) tan 01, (''i + r) +g{r, [ri + r'] + x^ [.Vi + x'\\) + b (rxy - xr^) Neglecting the exciting current, ^ = = ^, these equa- tions assume the form : J ^ (n + ^) +J(^i + ^ ) jj; ^ r^o . (ri + ry+(x, + xy ' {r, + r)^j(x, + x)' or, eliminating imaginary quantities, ^(n + ry+(x, + xy ^' and tan w^ = — ; — . n + r § 152] INDUCTION MOTOR, 226 That means, that in starting the induction motor without additional resistance in the armature circuit, — in which case oTj + ;r is large compared with r^ + r, and the t ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-12", "section_label": "Chapter 12: Power, And Double Frequency Quantities In General", "section_title": "Power, And Double Frequency Quantities In General", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 9381-9740", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "snippets": [ "... ints, these points representing the abso- lute values of potential (with regard to any reference point chosen as co-ordinate center) and their connection the dif- ference of potential in phase and intensity. Algebraically these vectors are represented by complex quantities. The impedance, admittance, etc., of the circuit is a complex quantity also, in symbolic denotation. Thus current, E.M.F., impedance, and admittance are related by multiplication and division of complex quantities similar as current, E.M.F., resistance, ...", "... egard to any reference point chosen as co-ordinate center) and their connection the dif- ference of potential in phase and intensity. Algebraically these vectors are represented by complex quantities. The impedance, admittance, etc., of the circuit is a complex quantity also, in symbolic denotation. Thus current, E.M.F., impedance, and admittance are related by multiplication and division of complex quantities similar as current, E.M.F., resistance, and conductance are related by Ohms law in direct current circuits. I ...", "... aically these vectors are represented by complex quantities. The impedance, admittance, etc., of the circuit is a complex quantity also, in symbolic denotation. Thus current, E.M.F., impedance, and admittance are related by multiplication and division of complex quantities similar as current, E.M.F., resistance, and conductance are related by Ohms law in direct current circuits. In direct current circuits, power is the product of cur- rent into E.M.F. In alternating current circuits, if The product, P0 = EI= (Ml - *\"/ ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-14", "section_label": "Chapter 14: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 11605-12682", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "snippets": [ "... ms ; that is, about one-tenth as large as assumed. Thus the changes of the values of E0, Elt etc., under the different conditions will be very much smaller. 204 ALTERNATING-CURRENT PHENOMENA. Symbolic Method. 134. In symbolic representation by complex quantities the transformer problem appears as follows : The exciting current, 700, of the transformer depends upon the primary E.M.F., which dependance can be rep- resented by an admittance, the \" primary admittance,\" °f tne transformer. Fig. 105. The resista ...", "... he load of the transformer, as fraction of full load, we have ALTERNATING-CURRENT TRANSFORMER. 215 and, **.-«. a Substituting these values we get, as the equations of the transformer on non-inductive load, Ratio of E.M.Fs. : or, eliminating imaginary quantities, H\"-\"^) Ratio of currents : + (h +> d 2 f . ^ or, eliminating imaginary quantities, 1 f a \\ i i h i 216 ALTERNATING-CURRENT PHENOMENA. Total apparent primary impedance : Z, = or, eliminating imaginary quantities, Angle of ...", "... 15 and, **.-«. a Substituting these values we get, as the equations of the transformer on non-inductive load, Ratio of E.M.Fs. : or, eliminating imaginary quantities, H\"-\"^) Ratio of currents : + (h +> d 2 f . ^ or, eliminating imaginary quantities, 1 f a \\ i i h i 216 ALTERNATING-CURRENT PHENOMENA. Total apparent primary impedance : Z, = or, eliminating imaginary quantities, Angle of lag in primary circuit : That is, An alternate-current transformer, feeding into a non-induc- ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "section_label": "Chapter 16: Induction Motor", "section_title": "Induction Motor", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "... = effective E.M.F. induced by the mag- netic field per primary circuit. Counting the time from the moment where the rising magnetic flux of mutual induction & (flux interlinked with both electric circuits, primary and secondary) passes through zero, in complex quantities, the magnetic flux is denoted by and the primary induced E.M.F., 240 ALTERNATING-CURRENT PHENOMENA. where e= V2irrt7V10-8 maybe considered as the \"Active E.M.F. of the motor,\" or \" Counter E.M.F.\" Since the secondary frequency is s N, the seco ...", "... hence, since the imaginary part has no meaning as power, and the total power of the motor, At the linear speed, at unit radius the torque is In the foregoing, we found £0 = e\\ 1 + j|? + Z, Y or, approximately, or, expanded, or, eliminating imaginary quantities, 250 ALTERNATING-CURRENT PHENOMENA. Substituting this value in the equations of torque and of power, they become, torque, T = Maximum Torque. 159. The torque of the induction motor is a maximum for that value of slip s, where qpi r^ Eg s or, ...", "... 1 010,io1 . - 8 and, displacement of phase, or angle of lag, fi + r0] + *! [Jfx 4- Jf0]) - jf (r0 ^ - *0 rt) „ _ 1 W° r0) INDUCTION MOTOR. 255 Neglecting the exciting current, g = 0 = b, these equa- tions assume the form, or, eliminating imaginary quantities, and tan w0 = + 'o That means, that in starting the induction motor without additional resistance in the armature circuit, — in which case ^ + x0 is large compared with t\\ •+• r0, and the total impe- dance, z, small, — the motor takes excessive an ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... lar decrement of the oscillating wave. The oscillating wave can be represented by the equation, E = e€\"***'^«cos(« - 6). In the example represented by Figs. 130 and 131, we have A = 0.4, a = 0.1435, a = 8.2°. Impedance and Admittance 184. In complex imaginary quantities, the alternating wave, z = e cos (0 — 6)^ is represented by the symbol, fl = e(cos d — j sin ^) = ei — je2» By an extension of the meaning of this symbolic expression, the oscillating wave, JS? = tt\"*** cos { — 6), can be expressed by the symbol, ...", "... 349 where X — tan d = 1 + a' r — ax — a 1 +a' Xe substituting ^ + 6 f or B, and e = isa we have B = ee-*^ cos (0 — ^), / = - 1-^ cos (0-^-5) . f COS 5 , . -V , sin 5 . / . .v = ee-\"^ J COS { — B) -\\ sin (0 — B) hence in complex quantities, ^ = e(cos ^ — j sin B) dec a, , r, f cos 5 . sin 5 1 J I = e\\ — J — — dec a; or, substituting, I = E r — ax — a 1 +a' x, (^ - r?-^.) +('• - «^ - rTT*=^«)* x — Xe -J 1 + a 2 (^-m\"») +(''-''^-rf^^') dec a. 189. ...", "... (cos ^ — j sin B) dec a, , r, f cos 5 . sin 5 1 J I = e\\ — J — — dec a; or, substituting, I = E r — ax — a 1 +a' x, (^ - r?-^.) +('• - «^ - rTT*=^«)* x — Xe -J 1 + a 2 (^-m\"») +(''-''^-rf^^') dec a. 189. Thus in complex quantities, for oscillating currents, we have: conductance, a r — ax — g = 1 +a' X, (^-rf^)+(''-\"^-rTT^^')\" susceptance. X — X, b = 1 + a2 (^-i^2)+(^-«^-rf^2^0 1> .admittance, in absolute values. y = Vff* + 6* = V (* - rf^^ ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-14", "section_label": "Chapter 14: The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "section_title": "The Osni!Raij Aiitebnatina-Cubbent Tbakbfobmsb", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14089-14918", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-14/", "snippets": [ "... ^^^ + ^\"^\"^ (\"■' \"•'•''\"^ I • z, = <7 1+ — ^ ^0 —7-^0 tfTi — y^^i + (^0 -JXo)(go +J^o) /Returning now to the general alternating-current trans- former, we have, by substituting (n + r)« -t- ^ (x, + xy = V, and separating the real and imaginary quantities, £,= -noe\\ h + -^^(ro(r, + r)-^sxo(x, + x)) 1136] ALTERNATING'CURRENT TRANSFORMER. 201 + (^0^0 +^o^o) + y -/-iC-f '•o(-^i +^)-^o(n + r)) V\\77. + (^0^0 - ^o--^o^o)1 I • Neglecting the exciting current, or rather considering it as a separate ...", "... secondary impedance, y, = 0, ^, = ^11. a* Substituting this in the equations of the general trans- former, we get, ^0= - ''o^ I 1 + -^ [n (^1 + '•) + J^i (^1 + x)\\ + ^ [-f ''i (-^1 + •^) - ^1 (n + '•)]}• ^k 136. If -£■ = « + y)3 = KM.F., in complex quantities, and I ^=^ c '■\\- J d =^ current in complex quantities, the power is, P^\\E, I \\^ EI cos {E, I) ^ac+ pd. 202 AL TERNA TING-CURRENT PHENOMENA. [% 1 37 Making use of this, and denoting, gives: Secondary output of the transformer Internal loss i ...", "... ting this in the equations of the general trans- former, we get, ^0= - ''o^ I 1 + -^ [n (^1 + '•) + J^i (^1 + x)\\ + ^ [-f ''i (-^1 + •^) - ^1 (n + '•)]}• ^k 136. If -£■ = « + y)3 = KM.F., in complex quantities, and I ^=^ c '■\\- J d =^ current in complex quantities, the power is, P^\\E, I \\^ EI cos {E, I) ^ac+ pd. 202 AL TERNA TING-CURRENT PHENOMENA. [% 1 37 Making use of this, and denoting, gives: Secondary output of the transformer Internal loss in secondary circuit, Total secondary power, P, + P^ = ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-19", "section_label": "Chapter 19: Commutatob Motobs", "section_title": "Commutatob Motobs", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 21339-22387", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-19/", "snippets": [ "... X = cos X = 1 / V2, it is, sub- stituted : ^1= - V2fl-«*{iV^cos)3+^isin)3}10-» or, since * = ; ^1 = — ^ { cos )3 + ^ sin )3 } ; where * = A = ratio _^P??d_ . N frequency or the effective value of secondary induced E.M.F., 197. Introducing now complex quantities, and counting the time from the zero value of rising magnetism, the mag- netism is represented by the primary induced E.M.P\\, E =^ — e\\ the secondary induced E.M.F. : hence, if V2 Zi = /*! — j Xx = secondary impedance reduced to primary circu ...", "... -'i — — : — f primary exciting current, 298 AL TERN A TING-CURRENT PHENOMENA. [ § 198 hence, total primary current, Primary impressed E.M.F., or Neglecting in -C© ^^e last term, as of higher order, xSq — ^ ■^ -*- \"1 _- : ( » or, eliminating imaginary quantities, ^ ^ ^ V(^ + nV^ + kxf + (x + x^V2 - krf ^ 198. The power consumed by the primary counter E.M.F., r, that is, transferred into the secondary circuit, is or, eliminating the imaginary quantities. 7^' = n + '^-''^i V2 n' + -^'i The power consu ...", "... gher order, xSq — ^ ■^ -*- \"1 _- : ( » or, eliminating imaginary quantities, ^ ^ ^ V(^ + nV^ + kxf + (x + x^V2 - krf ^ 198. The power consumed by the primary counter E.M.F., r, that is, transferred into the secondary circuit, is or, eliminating the imaginary quantities. 7^' = n + '^-''^i V2 n' + -^'i The power consumed by the secondary resistance is 2 n^ + ^/^ ' Hence, the difference, or the mechanical power at the motor shaft — §1981 COMMUTATOR MOTORS. 299 and, substituting for e, J, ..■(>-|(y ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-41", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 41, "number": 1, "location": "lines 19260-19338", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "snippets": [ "... ime, and the analytical method of dealing with such phenomena therefore introduces two independent variables, time t and distance I, that is, the electric quantities are periodic functions of time and transient functions of space. The introduction of the complex quantities, as representing the alternating wave by a constant algebraic number, eliminates 277 278 TRANSIENT PHENOMENA the time t as variable, so that, in the denotation by complex quantities, the transient phenomena in space are functions of one independent ...", "... s of time and transient functions of space. The introduction of the complex quantities, as representing the alternating wave by a constant algebraic number, eliminates 277 278 TRANSIENT PHENOMENA the time t as variable, so that, in the denotation by complex quantities, the transient phenomena in space are functions of one independent variable only, distance Z, and thus lead to the same equations as the previously discussed phenomena, with the difference, however, that here, in dealing with space phenom- ena, the depend ...", "... ctions of one independent variable only, distance Z, and thus lead to the same equations as the previously discussed phenomena, with the difference, however, that here, in dealing with space phenom- ena, the dependent variables, current, e.m.f., etc., are complex quantities, while in the previous discussion they appeared as instantaneous values, that is, real quantities. Otherwise the method of treatment and the general form of the equations are the same as with transient functions of time. 2. Some of the cases in which tr ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-50", "section_label": "Chapter 1: General Equations", "section_title": "General Equations", "kind": "chapter", "sequence": 50, "number": 1, "location": "lines 27761-28694", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "snippets": [ "... t variables, time t and space or distance /; that is, these phenomena are transient in time and in space. The difficulty met in studying such phenomena is that they are not alternating functions of time, and therefore can no longer be represented by the complex quantity. It is possible, however, to derive from the constants of the circuit, r, L, g, C, and without any assumption whatever regard- ing current, voltage, etc., general equations of the electric cir- cuits, and to derive some results and conclusions from such ...", "... rcuit — connecting point of one circuit with another one. As illustration, some of these cases will be discussed below. The quantities i and e must always be real; but since an and bn appear in the exponent of the exponential function, an and bn may be complex quantities, in which case the integration constants An must be such complex quantities that by com- bining the different exponential terms of the same index n, that is, corresponding to the different pairs of a and b derived from the same equation (10), the imaginar ...", "... some of these cases will be discussed below. The quantities i and e must always be real; but since an and bn appear in the exponent of the exponential function, an and bn may be complex quantities, in which case the integration constants An must be such complex quantities that by com- bining the different exponential terms of the same index n, that is, corresponding to the different pairs of a and b derived from the same equation (10), the imaginary terms in An and bnL - r An cancel. an In the exponential function ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-108", "section_label": "Apparatus Section 2: Induction Machines: Polyphase Induction Motor", "section_title": "Induction Machines: Polyphase Induction Motor", "kind": "apparatus-section", "sequence": 108, "number": 2, "location": "lines 19166-20427", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-108/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-108/", "snippets": [ "... Q is /oZo, the counter-generated e.m.f. is e, hence, the primary terminal voltage is EQ = e + IQZQ = e[l + (bi — j&2) (r0 + jx0)] .= e (ci — jc2), where Ci = 1 + robi + Xobz and c2 = r062 — Xobi. Eliminating complex quantities, we have EQ = e Vci2 + c22, hence, the counter-generated e.m.f. of motor, e = — == , where EQ = impressed e.m.f., absolute value. Substituting this value in the equations of /i, /oo, /o, etc , gives the complex ex ...", "... ated e.m.f. of motor, e = — == , where EQ = impressed e.m.f., absolute value. Substituting this value in the equations of /i, /oo, /o, etc , gives the complex expressions of currents and e.m.fs., and elimi- nating the imaginary quantities we have the primary current, /o = e V&i2 + 622, etc. INDUCTION MACHINES 313 The torque of the polyphase induction motor (or any other motor or generator) is proportional to the product of the mutual magnetic flux and ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-09", "section_label": "Chapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "section_title": "Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 4674-6992", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-09/", "snippets": [ "... s of alternating- current circuits, when expressed in their complex form, E = ZI, or, 7 = YE, and \"EE = 0 in a closed circuit, S/ = 0 at a distributing point, where E, I, Z, Y, are the expressions of e.m.f., current, impe- dance, and admittance in complex quantities — these values representing not only the intensity, but also the phase, of the alternating wave — we can now — by application of these laws, and in the same manner as with continuous-current circuits, keeping in mind, however, that E, I, Z, Y, are complex ...", "... alternating current from constant alternating potential, or inversely, constitutes a good illustration of the application of the terms \"impedance,\" \"reactance,\" etc., and offers a large number of problems or examples for the application of the method of complex quantities. A numl)er of such are given in \"Theory and Calculation of Electric Circuits.\"" ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-22", "section_label": "Chapter 22: Armature Reactions Of Alternators", "section_title": "Armature Reactions Of Alternators", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 23971-25134", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-22/", "snippets": [ "... n this case the syn- chronous reactance, Xo, has two different values, .t'o and x\"o, corresponding respectively to the two main axes of the magnetic structure, in line and in quadrature with the field-poles. 199. In the equation (46), E, Eo, V and 7\" are complex quantities, and I\" is in phase with Eo, I' is in quadrature behind Eo, and so behind I\": hence, I' can be represented by /' = - jtr\\ (47) ARMATURE REACTIONS OF ALTERNATORS 285 where t = ratio of numerical values of /\" and /', that is r t = jr, = isin d (4 ...", "... 59) 286 ALTERNA TING-C URRENT PHENOMENA substituting (57) in (56) and transposing, eoVrH'-(ei']-je2){l-jt)-i{(r-\\-jx\"o)-jt(r-\\-jx'o)} = 0, (60) or, expanded, {eoVl + t^-ei-te2-i{r-htx'o))-\\-j{tei-e2 + i(tr-x'\\)} =0. (61) As the left side is a complex quantity, and equals zero, the real part as well as the imaginary part must be zero, and equation (61) so resolves into the two equations Co VT+I\" - e, - ^62 - 4 (r + tx'o) = 0, tei — ei -\\- i {tr — x'\\) = 0. From equation (63) follows t 62 + X\"oi ei + ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... hase at equal distribution of load, but are liable to become unbalanced at unequal distribution of load; the three-wire, quarter-phase system is unbalanced in voltage and phase, even at equal dis- tribution of load. 30 APPENDIX ALGEBRA OF COMPLEX IMAGINARY QUANTITIES (\"See Engineering Mathematics\") INTRODUCTION 312. The system of numbers, of which the science of algebra treats, finds its ultimate origin in experience. Directly derived from experience, however, are only the absolute integral numbers; fractions, for ...", "... ther extension of the system of numbers is necessary or possible, and the most general number is a + jb, where a and 6 can be integers or fractions, positive or negative, rational or irrational. Any attempt to extend the system of numbers beyond the complex quantity, leads to numbers, in which the factors of a product are not interchangeable, in which one factor of a product 470 ALTERNATING-CURRENT PHENOMENA may be zero without the product being zero, etc., and which thus cannot be treated by the usual methods of ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-08", "section_label": "Chapter 8: Capacity", "section_title": "Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3872-6370", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "snippets": [ "... ernating-current circuits, or, as expressed in their com- plexform. ^ _^ ' „_ E -= ZJ^ or, / = \\Ey and S-f = in a closed circuit, 5/ = at a distributing point, where J?, /, Z^ V, are the expressions of E.M.F*., current, impedance, and admittance in complex quantities, — these laws representing not only the intensity, but also the phase, of the alternating wave, — we can now — by application of these laws, and in the same manner as with continuous- current circuits, keeping in mind, however, that E, /, Z, V, are compl ...", "... ities, — these laws representing not only the intensity, but also the phase, of the alternating wave, — we can now — by application of these laws, and in the same manner as with continuous- current circuits, keeping in mind, however, that E, /, Z, V, are complex quantities — calculate alternating-current cir- cuits and networks of circuits containing resistance, induc- tance, and capacity in any combination, without meeting with greater difficulties than when dealing with continuous- current circuits. It is obviously not ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-08", "section_label": "Chapter 8: Circuits Containing Resistance, Inductance, And Capacity", "section_title": "Circuits Containing Resistance, Inductance, And Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3577-5333", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "snippets": [ "... aws of alternating-current circuits, when expressed in their com- plex form, E = ZS, or, / = YE, and *%E = 0 in a closed circuit, S/ = 0 at a distributing point, where E, I, Z, Y, are the expressions of E.M.F., current, impedance, and admittance in complex quantities, — these values representing not only the intensity, but also the phase, of the alternating wave, — we can now — by application of these laws, and in the same manner as with continuous- current circuits, keeping in mind, however, that E, I, Z, Y, are com ...", "... ies, — these values representing not only the intensity, but also the phase, of the alternating wave, — we can now — by application of these laws, and in the same manner as with continuous- current circuits, keeping in mind, however, that E, I, Z, Y, are complex quantities — calculate alternating-current cir- cuits and networks of circuits containing resistance, induc- tance, and capacity in any combination, without meeting with greater difficulties than when dealing with continuous- current circuits. It is obviously not ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-20", "section_label": "Chapter 20: Commutator Motors", "section_title": "Commutator Motors", "kind": "chapter", "sequence": 20, "number": 20, "location": "lines 19458-20501", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-20/", "snippets": [ "... in cycles per second, and k = N^/ N speed we have frequency thus, gl = — 2-TrnJV® {sin X cos /? + k cos X sin B\\ 10~8, or, since $ = — — — — , et = e V2 {sin X cos /3 + k cos X sin fi\\. 360 ALTERNATING-CURRENT PHENOMENA. 218. Introducing now complex quantities, and counting the time from the zero value of rising magnetism, the mag- netism is represented by /4>, the primary induced E.M.F., E = — e, the secondary induced E.M.F., £1 = — e {sin X +j\"k cos X|; hence, if Zl = r1—jx1= secondary impedance reduced to ...", "... e - _ - , primary exciting current, I0 = eY= e (g +jb}, hence, total primary current, Primary impressed E.M.F., E0= — E + IZ\\ = e 1 + (sinX Neglecting in E0 the last term, as of higher order, £0 = e j 1 + sin X +jk cos X ^ ^4^ j ; or, eliminating imaginary quantities, e V(?i + r sin X -f- kx cos X)2 + (x^ + x sin X — kr cos X)2 The power consumed by the component of primary counter E.M.F., whose flux is interlinked with the secondary e sin X, is, f = [e sin X /]' = ^inXfosuiX-^cosX) , r\\ + x\\ the power consumed ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-05", "section_label": "Chapter 6: Induction-Motor Regulation And Stability", "section_title": "Induction-Motor Regulation And Stability", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 10583-12397", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-05/", "snippets": [ "... formers, at constant supply voltage at the transformer primaries. 3. With constant voltage at the generator terminals, and about 8 per cent, resistance, 40 per cent, reactance voltage in line and transformers between generator and motor. This gives, in complex quantities, the impedance between the motor terminals and the constant voltage supply: 1. Z - 0.04 + 0.08 j, 2. Z = 0.04 + 0.3 j\", 3. Z = 0.16 + 0.8,/. It is assumed that the constant supply voltage is such u hi give 1 10 volts at the motor terminals at FulHoa ...", "... istics at constant termi- nal voltage, eBl as follows: At slip, I, and constant terminal voltage, ea, the current in the motor is i0, its power-factor p = cos 8. The effective or equiva- lent impedance of the motor at this slip then is z\" = .-, and, in complex quantities, Z* = .\" (cos 0 + i Bin 0), and the total irn- pedance, including that of transformers and line, thus is: Zx = Z° + Z = (?\" cos 6 + r) + j(* sin 0 + xj , or, in absolute values: tlm .J(pcos0 4-r)'+ (^sin0+j and, at the supply voltage, e ,, the current ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-53", "section_label": "Chapter 4: Traveling Waves", "section_title": "Traveling Waves", "kind": "chapter", "sequence": 53, "number": 4, "location": "lines 30244-31450", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "snippets": [ "... - ; -(C/C3 + c2(73Osin(^-^)}]. (177) In these equations of current i and e.m.f. e the first term represents the usual equations of the distribution of alternating current and voltage in a long-distance transmission line, and can by the substitution of complex quantities be reduced to a form given in Section III. The second term is a transient term of the same frequency; that is, in a long-distance transmission line or other circuit of distributed r, L, gt C, when carrying alternating current under an alternating impres ...", "... kl) } (178) and /> . * fit \\ ( f+ '§* * /> (i \\ r*r\\cy ( nl 1/*7\\ /*/» '/^ ^l_ /> /• f\\ 01 T~I /'/v/ 7^7\\ (. t/fl — c i I O- vy .| ' O^vy -. / l^\\_/o \\tyt/ IV v J V^i ^ i ~1~ ^•|^-/ -i / olll I Ul> — fi/L ) I (179) are reduced to their usual form- in complex quantities by resolv- ing the trigonometric function into functions of single angles, qt and kl, then dropping cos qt, and replacing sin qt by the imagi- nary unit j. This gives i0 = s~hl { (Cl cos kl — Of sin kl) cos qt' + (C/ cos kl + Cj sin A;Z) sin ^} — e+h ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 557-1002", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-01/", "snippets": [ "... inuous-current phenomena, until methods were devised to treat the periodic transients of the alternating-current circuit as permanent phenomena, by the conception of the \" effective values,\" and more completely by the introduction of the general number or complex quantity, which represents the periodic func- tion of time by a constant numerical value. In this feature lies the advantage and the power of the symbolic method of dealing with alternating-current phenomena, — the reduction of a periodic transient to a permanent ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "... (18) separately gives i = ioe+^'^ cos (0 — co — 71) — ^o'e~^^ (0 + co — 72), e = eoe+^^ cos (0 — co — 71) + ^o'e-^^ (0 + co — 72), (19) and these are the equations of the alternating-current transmission line, and reduce, by the substitution of the complex quantity for the function of the time angle 0, to the standard form given in \"Transient Phenomena,\" Section III. 36. Obviously, traveling waves and standing waves may occur simultaneously in the same circuit, and usually do so, just as in alternating-current cir ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 460-882", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "snippets": [ "... inuous-current phenomena, until methods were devised to treat the periodic transients of the alternating-current circuit as permanent phenomena, by the conception of the \" effective values,\" and more completely by the introduction of the general number or complex quantity, which represents the periodic func- tion of time by a constant numerical value. In this feature lies the advantage and the power of the symbolic method of dealing with alternating-current phenomena, — the reduction of a periodic transient to a permanent ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 4745-5520", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "snippets": [ "... lternating currents and voltages. Writing the two waves in (18) separately gives cos (0 - co - 70 - i'0'e-sX e = e0e+sx cos (0 - co - and these are the equations of the alternating-current transmission line, and reduce, by the substitution of the complex quantity for the function of the time angle , to the standard form given in \"Transient Phenomena,\" Section III. 36. Obviously, traveling waves and standing waves may occur simultaneously in the same circuit, and usually do so, just as in alternating-current c ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... +jX2] \\ (4) y=yi+jy2, J and likewise are the coefficients ooo, aoi • • . cinn'. 265 266 ENGINEERING MATHEMATICS. If all the coefficients a are real, and x is real, the corre- sponding n values of y are either real, or pairs of conjugate complex imaginary quantities: 2/1 +^2/2 and y\\ — jy2. 171. For 71 = 1, the implicit function (1), solved for y, gives the rational function, aoo+aoiX + ao2y^ + . . . , . and if in this function (5) the denominator contains no x, the integer function, y = ai)+aix+a2X^-\\ . . .-\\- ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-07", "section_label": "Chapter 7: Polar Coordinates And Polar Diagrams", "section_title": "Polar Coordinates And Polar Diagrams", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 3619-4087", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-07/", "snippets": [ "... ffers from it symbolically by the interchange of + j and — j. A treatise written in the symbolic repre- sentation by the polar diagram, thus can be translated to the representation by the crank diagram, and inversely, by simply reversing the signs of all imaginary quantities, that is, considering the signs of all terms with j Fig. 47. changed. A graphical representation in the polar dia- gram can be considered as a graphic representation in the crank diagram, with clockwise or right-handed rotation, and inversely. Thus, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-16", "section_label": "Chapter 16: Power, And Double-Frequency Quantities In", "section_title": "Power, And Double-Frequency Quantities In", "kind": "chapter", "sequence": 16, "number": 16, "location": "lines 16077-16520", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-16/", "snippets": [ "... ly these vectors are represented by complex quan- tities. The impedance, admittance, etc., of the circuit is a com- plex quantity also, in symbolic denotation. Thus current, voltage, impedance, and admittance are related by multiplication and division of complex quantities in the same way as current, voltage, resistance, and conductance are related by Ohm's law in direct-current circuits. In direct-current circuits, power is the product of current into voltage. In alternating-current circuits, if the product, is not th ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-17", "section_label": "Chapter 17: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16521-17716", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-17/", "snippets": [ "... 0.001 mho; ri = 0.00008 ohm; 6o = 0.00173 mho; that is, about one-tenth as large as assumed. Thus the changes of the values of Eo, Ei, etc., under the different conditions will be very much smaller. Symbolic Method 149. In symbolic representation by complex quantities the transformer problem appears as follows: The exciting current, /oo, of the transformer depends upon the primary e.m.f., which dependence can be represented by an admittance, the \"primary admittance,\" Fo = g^i — jbo, of the transformer. The resistan ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-27", "section_label": "Chapter 27: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 33011-34776", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-27/", "snippets": [ "... 1I7 1 M=f''-7 ^7 1 J where ^\" = ^ EI ' consists of a series of inductance factors, q„, of the individual harmonics. As a rule, if g^ = S2n-ig(„2^ 1 p' + 9' < 1, for the general alternating wave, that is, q differs from qo = Vl - p'. The complex quantity, V = S. = ^-^ JiiL±MIl ^ Pa EI EI _ J 1 Ji2n-i (en'' + e„ii') 22 n- 1 (^•„l' + ^•„ll') \\ 1 1 = P -\\- 22n-lj„g„^ 1 takes in the circuit of the general alternating wave the same position as power-factor and inductance factor with the sine wave. ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-09", "section_label": "Chapter 9: Kbsistanci: And Kbactance Of Transmission Iine8", "section_title": "Kbsistanci: And Kbactance Of Transmission Iine8", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 6371-8268", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "snippets": [ "... with the E.M.F. at the generator terminals. Hence the condition of maximum output at given loss, or of maximum efficiency, is — tan a)<, = 0. The current is — multiplying numerator and denominator by (1 + r^g + x^b) + j(x^g — ^'o^), to eliminate the imaginary quantity from the denominator, we have — ({giX + rog + Xob) - b(x,g - rob)} +\\ J=£ \\ J {^ iX + ^og + x ^b) +g {xpg - r^ b)} ) ^ (1 + rog + Xoby + (xog^r.by The current, /^, is in plvise with the E.M.F., E^, if its quadrature component — that is, the imaginary ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-15", "section_label": "Chapter 15: The General Alternating-Current Transformer Or Frequency Converter", "section_title": "The General Alternating-Current Transformer Or Frequency Converter", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 12683-13648", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-15/", "snippets": [ "... = _ s «0 f ] -T, . . 1 «•(>-!— y**o r j«,^ A = — —5 \"^ : — ~ + (ro — y^o)(^b +/ «2^i — JSXi Returning now to the general alternating-current trans^ former, we have, by substituting (ri + r? + ^2 (*i + *)2 = **f, and separating the real and imaginary quantities, -±- (r0 (r, + r)+sx9(Xl + x)) 22 ALTERNATING-CURRENT TRANSFORMER, 227 Neglecting the exciting current, or rather considering it as a separate and independent shunt circuit outside of the transformer, as can approximately be done, and assum- ing t ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "... ION OF ALTERNATING WAVES. 4] > The term, /#. El = 2/n~17 where, consists of a series of inductance factors qn of the individual harmonics. As a rule, if + Xt\"b ta,X'( + SX\",)| - j|K\",6 - St'b (c„X', + SX\",i + S!\"c.(SX'. - e„X\",)]]; (HI) ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-14", "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "section_title": "Constant-Potential Constant-Current Trans Formation", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "... o- transformer. 286 ELECTRIC CIRCUITS D. Problems 149. In the following problems referring to constant-potential to constant-current transformation by reactances, it is recom- mended: (a) To derive the equation of all the currents and e.m.fs., in complex quantities as well as in absolute terms, while neglecting the loss of power in the reactances. (6) To determine the volt-amperes in the different parts of the circuit, as load, reactances, etc., and therefrom derive the apparatus economy, to find its maximum value, ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-27", "section_label": "Chapter 5: Resistance, Inductance, And Capacity In Series Condenser Charge And Discharge", "section_title": "Resistance, Inductance, And Capacity In Series Condenser Charge And Discharge", "kind": "chapter", "sequence": 27, "number": 5, "location": "lines 4072-5311", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "snippets": [ "... ms. V C In this case, and i = 10,000 t£~looot e, = 1000 {!-(! + 10000 £\"1000'}. 39. In the trigonometric or oscillating case, The term under the square root (10) is negative, that is, the square root, s, is imaginary, and al and a2 are complex imaginary quantities, so that the equations (11) and (12) appear in imagi- nary form. They obviously can be reduced to real terms, CONDENSER CHARGE AND DISCHARGE 59 since the phenomenon is real. Since an exponential function with imaginary exponents is a trigonometric ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-43", "section_label": "Chapter 3: The Natural Period Of The Transmission Line", "section_title": "The Natural Period Of The Transmission Line", "kind": "chapter", "sequence": 43, "number": 3, "location": "lines 21721-23178", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "snippets": [ "... ee oscillation, thus are represented by their effective values (13) and (14). 30. Substituting in equations (4), Cl = <>i + jcv (16) gives I = (cl + jc2) cos ftl and (17) NATURAL PERIOD OF TRANSMISSION LINE 325 By the definition of the complex quantity as vector represen- tation of an alternating wave the cosine component of the wave is represented by the real, the sine component by the imaginary term; that is, a wave of the form ct cos 2 nft + c2sin 2 nft is represented by cl + jc2J and inversely, the ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-46", "section_label": "Chapter 6: Alternating Magnetic Flux Distribution", "section_title": "Alternating Magnetic Flux Distribution", "kind": "chapter", "sequence": 46, "number": 6, "location": "lines 23948-24980", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "snippets": [ "... the center of the lamination is due to the magnetic flux in the space from I to 1Q. Thus the e.m.fs. at the two sides of the zone dl differ from each other by the e.m.f. generated by the magnetic flux ($>dl in this zone. Considering now (B, E, and I as complex quantities, the e.m.f. dE, that is, the difference between the e.m.fs. at the two sides of the zone dl, is in quadrature ahead of ($>dl, and thus denoted by dE = - j 2 TT/CB 10-8 dl, (6) where / = the frequency of alternating magnetism. This gives the second diff ..." ] } ] }, { "id": "wave-propagation", "label": "Wave Propagation", "aliases": [ "standing wave", "traveling wave", "travelling wave", "wave front", "wave propagation" ], "total_occurrences": 156, "matching_section_count": 18, "matching_source_count": 6, "source_totals": [ { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 80, "section_count": 10 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 32, "section_count": 2 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 31, "section_count": 2 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 8, "section_count": 1 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 4, "section_count": 2 }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-53", "section_label": "Chapter 4: Traveling Waves", "section_title": "Traveling Waves", "kind": "chapter", "sequence": 53, "number": 4, "location": "lines 30244-31450", "status": "candidate", "occurrence_count": 33, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "snippets": [ "CHAPTER IV. TRAVELING WAVES. 20. As seen in Chapter III, especially in electric power cir- cuits, overhead or underground, the longest existing standing wave has a wave length which is so small compared with the critical wave length — where the frequency becomes zero — that the effect of the damping constant on the frequency and the wave length is negligible. The same obviously applies also to traveling waves, ...", "... the fre- quency constant q and the wave length constant k can be neglected, that is, frequency and wave length assumed as inde- pendent of the energy loss in the circuit. Usually, therefore, the equations (74) and (75) can be applied in dealing with the traveling wave. In these equations the distance traveled by the wave per second is used as unit length by the substitution /I = [C3 cos q(t- X)+ C3' sin q (t - /I)] - <•-* ('+A) [C4 cos g (t + ;) + C/ sin q (t + ^)] } (141) and — v/I-- [Cj cos g ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "... y dis- tance angle co, and at any time t, that is, time angle 0, then is p = ei, = eo^e~2\"* cos (0 =F co — 7) sin (0 =F co — 7), = ^6-^«'sin2(0Ta>-7), (2) and the average power flow is Po = avg p, (3) = 0. Hence, in a stationary oscillation, or standing wave of a uni- form circuit, the average flow of power, po, is zero, and no power flows along the circuit, but there is a surge of power, of double frequency. That is, power flows first one way, during one-quarter cycle, and then in the opposite direction, dur ...", "... ^o [1 + cos 2 ( =F CO -7)], (5) and the average flow of power is po = avg p, (6) Such a wave thus consists of a combination of a steady flow of power along the circuit, jpo, and a pulsation or surge, pi, of the same nature as that of the standing wave (2) : pi =^%-2\"*cos2((/)Tco-7). (7) Such a flow of power along the circuit is called a traveling wave. It occurs very frequently. For instance, it may be caused if by a lightning stroke, etc., a quantity of dielectric energy is impressed Fig. 39 ...", "... ve thus consists of a combination of a steady flow of power along the circuit, jpo, and a pulsation or surge, pi, of the same nature as that of the standing wave (2) : pi =^%-2\"*cos2((/)Tco-7). (7) Such a flow of power along the circuit is called a traveling wave. It occurs very frequently. For instance, it may be caused if by a lightning stroke, etc., a quantity of dielectric energy is impressed Fig. 39. — Starting of Impulse, or Traveling Wave. upon a part of the circuit, as shown by curve A in Fig. 39, or i ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 4745-5520", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "snippets": [ "... tance angle co, and at any time t, that is, time angle <£, then is p = ei, = e0ioe~2ut cos ( T co — 7) sin (0 =F co — 7), = ^|V2«=Fco-7), (2) and the average power flow is Po = avg p, (3) = 0. Hence, in a stationary oscillation, or standing wave of a uni- form circuit, the average flow of power, p0, is zero, and no power flows along the circuit, but there is a surge of power, of double frequency. That is, power flows first one way, during one-quarter cycle, and then in the opposite direction, dur ...", "... = = eQiQe-2ut cos2 co - 7), and the average flow of power is p0 = avg p, (5) (6) Such a wave thus consists of a combination of a steady flow of power along the circuit, p0) and a pulsation or surge, pi, of the same nature as that of the standing wave (2) : Such a flow of power along the circuit is called a traveling wave. It occurs very frequently. For instance, it may be caused if by a lightning stroke, etc., a quantity of dielectric energy is impressed A • Fig. 39. — Starting of Impulse, or Tr ...", "... p0 = avg p, (5) (6) Such a wave thus consists of a combination of a steady flow of power along the circuit, p0) and a pulsation or surge, pi, of the same nature as that of the standing wave (2) : Such a flow of power along the circuit is called a traveling wave. It occurs very frequently. For instance, it may be caused if by a lightning stroke, etc., a quantity of dielectric energy is impressed A • Fig. 39. — Starting of Impulse, or Traveling Wave. upon a part of the circuit, as shown by curve A in Fig. 39 ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-52", "section_label": "Chapter 3: Standing Waves", "section_title": "Standing Waves", "kind": "chapter", "sequence": 52, "number": 3, "location": "lines 29316-30243", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "snippets": [ "CHAPTER III. STANDING WAVES. 14. If the propagation constant of the wave vanishes, h = 0, the wave becomes a stationary or standing wave, and the equa- tions of the standing wave are thus derived from the general equations (50) to (61), by substituting therein h = 0, which gives R2 = V(k2 - LCm2)2; (97) hence, if k2 > LCm2, R2 = tf- LCm2; and if /c2 < LCm2, R2 = LCm2'- tf. There ...", "CHAPTER III. STANDING WAVES. 14. If the propagation constant of the wave vanishes, h = 0, the wave becomes a stationary or standing wave, and the equa- tions of the standing wave are thus derived from the general equations (50) to (61), by substituting therein h = 0, which gives R2 = V(k2 - LCm2)2; (97) hence, if k2 > LCm2, R2 = tf- LCm2; and if /c2 < LCm2, R2 = LCm2'- tf. Therefore, two different cases exist, depending ...", "... - [B2 cos (qt + kl) + B2' sin (qt + kl)]} (105) and L C = k f-qBJ cos (qt-kl)-(mB, + qB,'} sin (qt-kl)] + [(mB2'-qB3) cos (qt + Jd)-(mB2 + qBJ) sin (qt + kl)]}. (106) Equations (105) and (106) represent a stationary electrical oscil- lation or standing wave on the circuit. B. Long waves, k2 < LCm2] (107) 444 hence, and TRANSIENT PHENOMENA R22 = LCm2 - k2, s = (108) (109) or approximately, for very small values of &, 1 r herefrom then follows (HO) ci = c2 = 0, and ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... nner, thus giving rise (to very different wave shapes of the impulses. So some impulses may rise very rapidly, with •A. I. E. E. Transact. March, 1907: \"Lightning Phenomena in Electric Circuits.\" LIGHTNING AND LIGHTNING PROTECTION 273 extremely steep wave front, and slowly die down. Others may rise slowly, then suddenly fall and reverse, or a series of oscillations may occur in the impulse, etc. If the lightning flash is parallel with the line, simultaneous impulses of different directions may be produced, corre ...", "... interference between the reflected waves, the incoming waves and the waves passing over the reactances, and so give rise to systems of standing waves or oscillations, similarly as an ocean wave rolling on to a sloping beach breaks up into surf. Where a traveling wave is reflected, the combination of the reflected wave and the incoming wave produces a standing wave or oscillation, that is, a wave in which the voltage maxi- ma and the zero points or nodes have fixed positions on the line. By superposition of the wave ...", "... ces, and so give rise to systems of standing waves or oscillations, similarly as an ocean wave rolling on to a sloping beach breaks up into surf. Where a traveling wave is reflected, the combination of the reflected wave and the incoming wave produces a standing wave or oscillation, that is, a wave in which the voltage maxi- ma and the zero points or nodes have fixed positions on the line. By superposition of the wave maxima of incoming and reflected wave, the standing wave rises to a maximum double 274 GENERAL LE ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... 2 + nno 07 c 1 75 + .008 487 1 80 j»fe 79 X sil|s=(-l) + 1 2~2 INDEX PAGE Acceleration constant of traveling wave 466 Air blast, action in oscillating-current generator 75 pressure required in oscillating-current generator 75 Alternating-current circuit and transient term of fundamental frequency 473 distribution in conductor 369 transformer operating oscillati ...", "... ator 75 pressure required in oscillating-current generator 75 Alternating-current circuit and transient term of fundamental frequency 473 distribution in conductor 369 transformer operating oscillating-current generator 87 transmission, equations of traveling wave 477 wave as traveling wave without attenuation 472 Alternator control by periodic transient term of field excitation 223 Aluminum cell rectifier 222 effective penetration of alternating current 378 Amplitude of traveling wave 465 of wave 438 Arc ...", "... n oscillating-current generator 75 Alternating-current circuit and transient term of fundamental frequency 473 distribution in conductor 369 transformer operating oscillating-current generator 87 transmission, equations of traveling wave 477 wave as traveling wave without attenuation 472 Alternator control by periodic transient term of field excitation 223 Aluminum cell rectifier 222 effective penetration of alternating current 378 Amplitude of traveling wave 465 of wave 438 Arc, and spark 249 continuity ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 5521-6088", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "snippets": [ "LECTURE IX. OSCILLATIONS OF THE COMPOUND CIRCUIT. 38. The most interesting and most important application of the traveling wave is that of the stationary oscillation of a com- pound circuit, as industrial circuits are never uniform, but consist of sections of different characteristics, as the generating system, transformer, line, load, etc. Oscillograms of such circuits have been ...", "... section must have a second exponential time decrement, S = UQ — U, (2) which represents power transfer from the section to other sections, or, if s is negative, power received from other sections. The oscil- lation of every individual section thus is a traveling wave, with a power-transfer constant s. As UQ is the average dissipation constant, that is, an average of the power-dissipation constants u of all the sections, and s = UQ — u the power-transfer constant, some of the s must be positive, some negative. In a ...", "... er than the average power dissipation of the entire circuit, u0 = 800; and the line thus receives power only at the rate —s= 100, that is, receives only one-ninth of its power from the transformer; the other eight-ninths come from its stored energy. The traveling wave passing along the circuit section thus increases or decreases in its power at the rate e+2*x; that is, in the line: p = pie~200X, the energy of the wave decreases slowly; in the transformer: p = 7?2C+1400X, the energy of the wave increases rapidly; ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-17", "section_label": "Chapter 4: Traveling Waves. 457", "section_title": "Traveling Waves. 457", "kind": "chapter", "sequence": 17, "number": 4, "location": "lines 1112-1147", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-17/", "snippets": [ "CHAPTER IV. TRAVELING WAVES. 457 20. Different forms of the equations of the traveling wave. 457 CONTENTS. xxiii PAGE 21. Component waves and single traveling wave. Attenua- tion. 459 22. Effect of inductance, as loading, and leakage, on attenu- ation. Numerical example of telephone circuit. 462 23. Traveling sine wave and traveling c ...", "CHAPTER IV. TRAVELING WAVES. 457 20. Different forms of the equations of the traveling wave. 457 CONTENTS. xxiii PAGE 21. Component waves and single traveling wave. Attenua- tion. 459 22. Effect of inductance, as loading, and leakage, on attenu- ation. Numerical example of telephone circuit. 462 23. Traveling sine wave and traveling cosine wave. Ampli- tude and wave front. 464 24. Discussion of traveling wav ...", "... E 21. Component waves and single traveling wave. Attenua- tion. 459 22. Effect of inductance, as loading, and leakage, on attenu- ation. Numerical example of telephone circuit. 462 23. Traveling sine wave and traveling cosine wave. Ampli- tude and wave front. 464 24. Discussion of traveling wave as function of distance, and of time. 466 25. Numerical example, and its discussion. 469 26. The alternating-current long-distance line equations as special case of a traveling wave. 471 27. Reduction of the g ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-54", "section_label": "Chapter 5: Free Oscillations", "section_title": "Free Oscillations", "kind": "chapter", "sequence": 54, "number": 5, "location": "lines 31451-32708", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "snippets": [ "... for Z = 0, thus: and if i = 0 for I = 0, thus: h = 0, sin kl0 = 0 kl — nn. (208) 0 and cos kl0 = 0, (2 n + 1) TT (209) From equations (206) to (209) it thus follows that h = 0, that is, the free oscillation of a uniform circuit is a standing wave. Also (2 n (210) if e = 0 at one, i = 0 at the other end of the circuit, and kl, - nn (211) if either e = 0 at both ends of the circuit or i = 0 at both ends of the circuit. 32. From (210) it follows that or an odd multiple thereof; that is ...", "... t — r) and e= -2AV/|e-\" sin kl sin (qt — f) . (219) With the lower sign, or for i = 0 at I = 0, this gives i = 2 As~w' sin &/ sin ($ - 7-) and e = — 2 A\\f -e- \"* cosklcos (qt - (220) 33. While the free oscillation of a circuit is a standing wave, the general standing wave, as represented by equations (139) and (140), with four integration constants Av A,', Av A2', is not necessarily a free oscillation. To be a free oscillation, the power ei, that is, either e or i, must be zero at two points of ...", "... \" sin kl sin (qt — f) . (219) With the lower sign, or for i = 0 at I = 0, this gives i = 2 As~w' sin &/ sin ($ - 7-) and e = — 2 A\\f -e- \"* cosklcos (qt - (220) 33. While the free oscillation of a circuit is a standing wave, the general standing wave, as represented by equations (139) and (140), with four integration constants Av A,', Av A2', is not necessarily a free oscillation. To be a free oscillation, the power ei, that is, either e or i, must be zero at two points of the circuit, the ends of th ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-09", "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "section_title": "Oscillations Of The Compound Circuit", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 6125-6803", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-09/", "snippets": [ "... section must have a second exponential time decrement, s = Uq — u, (2) which represents power transfer from the section to other sections, or, if s is negative, power received from other sections. The oscil- lation of every individual section thus is a traveling wave, with a power-transfer constant s. As Uo is the average dissipation constant, that is, an average of the power-dissipation constants u of all the sections, and s = uq — u the power-transfer constant, some of the s must be positive, some negative. In a ...", "... r than the average power dissipation of the entire circuit, Uo = 800 ; and the line thus receives power only at the rate —s= 100, that is, receives only one-ninth of its power from the transformer; the other eight-ninths come from its stored energy. The traveling wave passing along the circuit section thus increases or decreases in its power at the rate e^^^^; that is, in the line: p = 79ie\"2oox^ the energy of the wave decreases slowly; in the transformer: p = p2€+^''°°^, the energy of the wave increases rapidly; ...", "... n velocity measure, Xo is constant and equal to the period Tq through- out all the sections of the circuit, the product of maximum voltage and of maximum current, eoio, thus must be constant throughout the entire circuit. The same applies to an ordinary traveling wave or impulse. Since it is the same energy which moves along the circuit at a constant rate, the energy contents for equal sections of the circuit must be the same except for the factor e~ ^ ut^ j^y which the energy decreases with the time, and thus with the ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-51", "section_label": "Chapter 2: Discussion Of General Equations", "section_title": "Discussion Of General Equations", "kind": "chapter", "sequence": 51, "number": 2, "location": "lines 28695-29315", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "snippets": [ "... e have and (78) that is, during its passage along the circuit the wave decreases by the decrement e~ut, or at a constant rate, independent of frequency, wave length, etc., and depending merely on the circuit constants r, L, g, C. The decrement of the traveling wave in the direction of its motion is and therefore is independent of the character of the wave, for instance its frequency, etc. 11. The physical meaning of the two waves i' and e' can best be appreciated by observing the effect of the wave when travers- ...", "... envelope. 438 TRANSIENT PHENOMENA The combination of two waves thus represents the passage of a wave across a given point, the amplitude rising during the arrival and decreasing again after the passage of the wave. Fig. 98. Amplitude of electric traveling wave. 12. If h and so also s equal zero, i' , er and i\" ', e\" coincide in equations (74) and (75), and Cl and C3 thus can be combined into one constant Bv C2 and C4 into one constant J52, thus : C3 = Bv Ct - Bv Cs' = Bt', (82) and (74), (75) then as ...", "... ther words, the oscillation is of uniform intensity throughout the circuit, dying out uniformly with the time from an initial maximum value; however, the wave does not travel along the DISCUSSION OF GENERAL EQUATIONS 439 circuit, but is a stationary or standing wave. It is an oscillatory discharge of a circuit containing a distributed r, L, g, C, and therefore is analogous to the oscillating condenser discharge through an inductive circuit, except that, due to the distributed capacity, the phase changes along the cir ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... in the present instance. Let then Sl = speed of propagation in medium A, S2 = speed of propagation in medium W. Then, while the center of the beam moves the distance EC, the back edge, in the denser medium, a moves only the distance DI = -^EC, and the wave front of the »i back half of the beam thus changes to CI while that of the front half of the beam, which is still in the medium A, remains GC. Then, while the front edge of the beam moves from G to H, the center and the whole back half of the beam moves in t ...", "... of the front half of the beam, which is still in the medium A, remains GC. Then, while the front edge of the beam moves from G to H, the center and the whole back half of the beam moves in the denser o medium TF, only the distance CK = — 2 GH, and the wave front «i of the beam, in the medium TF, now is EL. That is, due to the difference in velocity in the two media A and W, the wave front of the beam, and thereby its direction of propagation, is changed RELATION OF BODIES TO RADIATION. 23 when traversing t ...", "... , the center and the whole back half of the beam moves in the denser o medium TF, only the distance CK = — 2 GH, and the wave front «i of the beam, in the medium TF, now is EL. That is, due to the difference in velocity in the two media A and W, the wave front of the beam, and thereby its direction of propagation, is changed RELATION OF BODIES TO RADIATION. 23 when traversing the boundary between the two media, and the beam EC continues its motion in the direction CM. Let then o^ = angle of incidence, that ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-15", "section_label": "Chapter 2: Discussion Of General Equations. 431", "section_title": "Discussion Of General Equations. 431", "kind": "chapter", "sequence": 15, "number": 2, "location": "lines 1063-1086", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-15/", "snippets": [ "... t waves and their reflected waves. Attenuation in time and in space. 431 8. Period, wave length, time and distance attenuation constants. 433 9. Simplification of equations at high frequency, and the velocity unit of distance. 434 10. Decrement of traveling wave. 436 11. Physical meaning of the two component waves. 437 12. Stationary or standing wave. Trigonometric arid logarith- mic waves. 438 13. Propagation constant of wave. 440", "... ngth, time and distance attenuation constants. 433 9. Simplification of equations at high frequency, and the velocity unit of distance. 434 10. Decrement of traveling wave. 436 11. Physical meaning of the two component waves. 437 12. Stationary or standing wave. Trigonometric arid logarith- mic waves. 438 13. Propagation constant of wave. 440" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-18", "section_label": "Chapter 5: Free Oscillations. 478", "section_title": "Free Oscillations. 478", "kind": "chapter", "sequence": 18, "number": 5, "location": "lines 1148-1186", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-18/", "snippets": [ "CHAPTER V. FREE OSCILLATIONS. 478 28. Types of waves: standing waves, traveling waves, alter- nating-current waves. 478 29. Conditions and types of free oscillations. 478 30. Terminal conditions. 480 31. Free oscillation as standing wave. 481 32. Quarter-wave and half-wave oscillation, and their equa- tions. 482 33. Conditions under which a standing wave is a free oscilla- tion, and the power nodes of the free oscillation. 485 34. Wave length, and angular measure of distance. 487 ...", "... ating-current waves. 478 29. Conditions and types of free oscillations. 478 30. Terminal conditions. 480 31. Free oscillation as standing wave. 481 32. Quarter-wave and half-wave oscillation, and their equa- tions. 482 33. Conditions under which a standing wave is a free oscilla- tion, and the power nodes of the free oscillation. 485 34. Wave length, and angular measure of distance. 487 35. Equations of quarter-wave and half-wave oscillation. 489 36. Terminal conditions. Distribution of current and voltage ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-55", "section_label": "Chapter 6: Transition Points And The Complex Circuit", "section_title": "Transition Points And The Complex Circuit", "kind": "chapter", "sequence": 55, "number": 6, "location": "lines 32709-33527", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "snippets": [ "... t s of the circuit, therefore, may be called energy transfer constant, and positive s means transfer of energy from the section to the rest of the circuit, and negative s means reception of energy from other sections. This explains the vanishing of s in a standing wave of a uniform circuit, due to the absence of energy transfer, and the presence of s in the equations of the traveling wave, due to the transfer of energy along the circuit, and in the general equations of alternating-current circuits. It immediately follo ...", "... ection to the rest of the circuit, and negative s means reception of energy from other sections. This explains the vanishing of s in a standing wave of a uniform circuit, due to the absence of energy transfer, and the presence of s in the equations of the traveling wave, due to the transfer of energy along the circuit, and in the general equations of alternating-current circuits. It immediately follows herefrom that in a complex circuit some of the s of the different sections must always be positive, some negative. 5 ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-02", "section_label": "Lecture 2: Conclusions From The Relativity Theory", "section_title": "Conclusions From The Relativity Theory", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 736-2388", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... troducing now the local time ^ = t ± \\, the complex expression of the two variables I and t simplifies into an expression of a single variable only, the \"local\" time t?; that is, the time counted at every point from the moment as stai-ting point where the wave front reaches this point, in other words, the local time on the moving wave. CONCLUSIONS FROM RELATIVITY THEORY 35 The transformation equations between train and track then become: X' = w = V X w c or: X + ~IV c V IV X c w' + x' c ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... ery great, due to the low frequency, — 3 X 1010 a 60-cycle alternating current gives a wave length of ^ = 500 X 10\" cm. or 3100 miles — the distance to which the field of the circuit extends is an insignificant fraction only of the wave length, and the wave propagation of the field thus is usually not considered. Electric waves of higher frequencies than used in wireless telegraphy are the Herzian waves, produced by electric oscilla- tors, that is, a moderately long straight conductor cut in the middle by a gap and te ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-16", "section_label": "Chapter 3: Standing Waves. 442", "section_title": "Standing Waves. 442", "kind": "chapter", "sequence": 16, "number": 3, "location": "lines 1087-1111", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-16/", "snippets": [ "CHAPTER III. STANDING WAVES. 442 14. Oscillatory, critical and gradual standing wave. 442 15. The wave length which divides the gradual from the oscillatory wave. 446 16. High-power high-potential overhead transmission line. Character of waves. Numerical example. General equations. 449 17. High-potential underground power cable. Ch ..." ] } ] }, { "id": "synchronous-machines", "label": "Synchronous machines", "aliases": [ "Synchronous machines", "synchronous-machines" ], "total_occurrences": 141, "matching_section_count": 52, "matching_source_count": 10, "source_totals": [ { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 44, "section_count": 22 }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 34, "section_count": 3 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 18, "section_count": 5 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 16, "section_count": 8 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 10, "section_count": 3 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 7, "section_count": 3 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 4, "section_count": 2 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 3, "section_count": 2 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 3, "section_count": 2 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 2, "section_count": 2 } ], "section_hits": [ { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-03-record", "section_label": "Report Record 4: Record of Four Troubles", "section_title": "Record of Four Troubles", "kind": "report-record", "sequence": 4, "number": 4, "location": "PDF pages 16-27, lines 1139-2164", "status": "pdf-text-extracted-candidate", "occurrence_count": 22, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-03-record/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-03-record/", "snippets": [ "... are no power limiting reactors between Fisk B and North- west Station, and the six tie cables between these stations are of very low resistance, the Northwest Station was just as seriously affected as Fisk B, and indeed acted like a part of Fisk B. b) All the synchronous machines on Fisk Street B, and on North- west Station dropped out, and many synchronous machines on Fisk A and Quarry Street: 44 synchronous machines on Fisk B and 18 on Northwest are recorded as shut down. Of 26 machines on Fisk A, 12 dropped out and 14 stayed in; of ...", "... ables between these stations are of very low resistance, the Northwest Station was just as seriously affected as Fisk B, and indeed acted like a part of Fisk B. b) All the synchronous machines on Fisk Street B, and on North- west Station dropped out, and many synchronous machines on Fisk A and Quarry Street: 44 synchronous machines on Fisk B and 18 on Northwest are recorded as shut down. Of 26 machines on Fisk A, 12 dropped out and 14 stayed in; of 8 machines on Quarry Street, 4 dropped out and 4 stayed in. [[END_PDF_PAGE:16]] [[PDF_ ...", "... ce, the Northwest Station was just as seriously affected as Fisk B, and indeed acted like a part of Fisk B. b) All the synchronous machines on Fisk Street B, and on North- west Station dropped out, and many synchronous machines on Fisk A and Quarry Street: 44 synchronous machines on Fisk B and 18 on Northwest are recorded as shut down. Of 26 machines on Fisk A, 12 dropped out and 14 stayed in; of 8 machines on Quarry Street, 4 dropped out and 4 stayed in. [[END_PDF_PAGE:16]] [[PDF_PAGE:17]] Report of Charles P. Steinmetz 11 c) Due to ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-13", "section_label": "Chapter 13: Reactance Of Synchronous Machines", "section_title": "Reactance Of Synchronous Machines", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 23466-24022", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-13/", "snippets": [ "CHAPTER XIII REACTANCE OF SYNCHRONOUS MACHINES 119. The synchronous machine — ^alternating-current generator, synchronous motor or synchronous condenser — consists of an armature containing one or more electric circuits traversed by alternating currents and synchronously revolving relative to a uni ...", "... e fluxes in Figs. 110 and 111. As seen, in Fig. 112A, all the lines of magnetic forces are inter- linked with the field circuit, but there is no line of magnetic flux interlinked with the armature circuit only, that is, there is ap- 232 REACTANCE OF SYNCHRONOUS MACHINES 233 parently no self-inductive armature flux, and no true self-inducts ive reactance, x, and the self-inductive armature flux of Fig. Ill thus merely is a mathematical fiction, a theoretical component of the resultant flux, Fig. 112. The effect of the ar ...", "... ase is to increase the field flux and the flux entering the armature at one side of the pole, and decrease it on the other side of the pole, without changing the total field flux and the leakage flux of the field. Indirectly, a reduction of REACTANCE OF SYNCHRONOUS MACHINES 235 the field flux usually occurs, by magnetic saturation limiting the increase of flux at the strengthened pole comer; but this is a sec- ondary effect. Fio. 112. As seen, in 112A the armature current acts demagnetizing, in 112B distorting on the f ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-appendix-01-synchronous-operation", "section_label": "Mathematical Appendix 5: Appendix: Synchronous Operation", "section_title": "Appendix: Synchronous Operation", "kind": "mathematical-appendix", "sequence": 5, "number": 5, "location": "PDF pages 27-68, lines 2165-5013", "status": "pdf-text-extracted-candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "snippets": [ "... io = 3900 A. p = 8300KW. so =-82%. As seen, the calculated value of the terminal voltage of Quarry Street, 6600, agrees as closely with the observed value of 6800 V. as can be expected from such approximated calculations, especially when considering that some synchronous machines had been lost by Quarry Street in the substations, and the load thereby reduced, which would result hi an increase of voltage. As the total impedance of Fisk Street A is about 1.1, and it is connected to Quarry Street by x=1.75, the voltage of Fisk Street A s ...", "... ltage, which were greatest at the source of the trouble, Fisk Street A, and decreased towards the other end of the station chain, whether due to the hunting of the stations against each other, or due to excessive load of lagging current, caused by starting of synchronous machines, or due to some other cause. Assuming first, that the voltage drop and voltage fluctuations was due to the simultaneous starting of numerous synchronous machines. To estimate the effect thereof, in the following table are given, in columns (1) to (3), the rec ...", "... e stations against each other, or due to excessive load of lagging current, caused by starting of synchronous machines, or due to some other cause. Assuming first, that the voltage drop and voltage fluctuations was due to the simultaneous starting of numerous synchronous machines. To estimate the effect thereof, in the following table are given, in columns (1) to (3), the recorded voltages of the four stations: [[END_PDF_PAGE:60]] [[PDF_PAGE:61]] Report of Charles P. Steinmetz 55 The initial minimum and the final minimum towards the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-22", "section_label": "Apparatus Section 1: Synchronous Machines: General", "section_title": "Synchronous Machines: General", "kind": "apparatus-section", "sequence": 22, "number": 1, "location": "lines 8518-8657", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-22/", "snippets": [ "I. General 3. The most important class of alternating-current apparatus consists of the synchronous machines. They comprise the alternating-current generators, single-phase and polyphase, the synchronous motors, the phase compensators, the phase con- verters, the phase balancers, the synchronous boosters and the exciters of induction gen ...", "... e alternating-current generators, single-phase and polyphase, the synchronous motors, the phase compensators, the phase con- verters, the phase balancers, the synchronous boosters and the exciters of induction generators, that is, synchronous machines producing wattless lagging or leading currents, and the con- verters. Since the latter combine features of the commutating machines with those of the synchronous machines they will be considered separately. In the synchronous ...", "... ters and the exciters of induction generators, that is, synchronous machines producing wattless lagging or leading currents, and the con- verters. Since the latter combine features of the commutating machines with those of the synchronous machines they will be considered separately. In the synchronous machines the terminal voltage and the generated e.m.f. are in synchronism with, that is, of the same frequency as, the speed of rotation. These machines consist of an ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-02-discussion-of-recommendations", "section_label": "Report Section 3: Discussion of Recommendations", "section_title": "Discussion of Recommendations", "kind": "report-section", "sequence": 3, "number": 3, "location": "PDF pages 12-16, lines 721-1138", "status": "pdf-text-extracted-candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-02-discussion-of-recommendations/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-02-discussion-of-recommendations/", "snippets": [ "... ower be- tween the station sections. Thus if in a station section as Fisk Street A, which is connected by one power limiting reactor to the rest of the system, full load of 60,000 KW is suddenly thrown off as by a short circuit at the busbars dropping out the synchronous machines in the substations while full steam supply is still on, the synchronizing power coming over the power limiting reactor is insufficient to hold the station in step, and the station breaks synchronism and speeds up. Whether synchronous operation is preserved or ...", "... onizing power coming over the power limiting reactor is insufficient to hold the station in step, and the station breaks synchronism and speeds up. Whether synchronous operation is preserved or synchronism broken, depends on the relative speed, with which the synchronous machines in the substations drop out, the turbine governors shut off steam and the alternators speed up. The synchronous machines in the substations, carrying load on the direct current side and feeding back on the alter- nating side, probably would drop out very quic ...", "... synchronism and speeds up. Whether synchronous operation is preserved or synchronism broken, depends on the relative speed, with which the synchronous machines in the substations drop out, the turbine governors shut off steam and the alternators speed up. The synchronous machines in the substations, carrying load on the direct current side and feeding back on the alter- nating side, probably would drop out very quickly, while the turbine governors must take an appreciable time to reduce the steam supply, and the alternators speed up r ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-09", "section_label": "Lecture 9: Hunting Of Synchronous Machines", "section_title": "Hunting Of Synchronous Machines", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 4218-4594", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-09/", "snippets": [ "NINTH LECTURE HUNTING OF SYNCHRONOUS MACHINES C\"^ROSS currents can flow between alternators due to dif- ferences in voltage, that is, differences in excitation; ■—^ and due to differences in phase, that is, differences in position of their rotors. Cross currents due to differences in excitation a ...", "... itation. 2nd. If the speed of the engine varies during the rota- tion, rising and falling with the steam impulses, then the alternator speed and the frequency also pulsate with a speed equal to, or a multiple of the engine speed. If now two HUNTING OF SYNCHRONOUS MACHINES 117 such alternators happen to be thrown together so that the moment of maximum frequency of one coincides with the moment of minimum frequency of the other, the two machines cannot run in perfect phase with each other, but pulsate, alter- natingly gett ...", "... alternator gets too much steam and its governor must cut off, but then cuts off too much, the same way as the first alternator did before; so the two governors hunt against each other by alternatingly admitting too much and too little steam. HUNTING OF SYNCHRONOUS MACHINES 119 In this case the frequency of hunting does not depend on the engine speed and does not vary much with the field exci- tation, but the hunting is usually much less at heavy load than at light load. The reason is that at load, when the engfines take m ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-21", "section_label": "Apparatus Introduction 21: Introduction", "section_title": "Introduction", "kind": "apparatus-introduction", "sequence": 21, "number": null, "location": "lines 8292-8517", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-21/", "snippets": [ "... and between electric and mechanical power. 1st. Commutating machines, consisting of a magnetic field and a closed-coil armature, connected with a multi-segmental commutator. 121 122 ELEMENTS OF ELECTRICAL ENGINEERING 2d. Synchronous machines, consisting of a undirectional mag- netic field and an armature revolving relatively to the mag- netic field at a velocity synchronous with the frequency of the alternating-current circuit connected thereto. . 3d. Rectifying ap ...", "... ly where high starting torque efficiency is required. They usually are of single-phase type. (2) While in commutating machines the magnetic field is, INTRODUCTION 123 almost always stationary and the armature rotating, synchronous machines were built with stationary field and revolving armature, or with stationary armature and revolving field, or as inductor machines with stationary armature and stationary field winding but revolving magnetic circuit. Generally n ...", "... rnating-current generators; as motors a very important class of apparatus, the synchronous motors, which are usually preferred for large powers, especially where frequent starting and considerable starting torque are not needed. Synchronous machines may be used as compensators or synchronous condensers, to produce wattless current, leading by over-excitation, lagging by under-excitation, or may be used as phase converters by operat- ing a polyphase synchronous motor by on ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-35", "section_label": "Chapter 35: Balanced Symmetrical Polyphase Systems", "section_title": "Balanced Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 35, "number": 35, "location": "lines 37453-37957", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-35/", "snippets": [ "... voltage, eo = 52,100 X \\/3 = 90,000 volts; voltage drop in line, = 11.1 per cent. 305. Balanced polyphase systems thus can be calculated as single-phase systems, and this has been done in man}^ preceding chapters, as in those on the induction machines, synchronous machines, etc., that is, apparatus which is usually operated on polyphase circuits. BALANCED SYMMETRICAL POLYPHASE SYSTEMS 453 Only in dealing with those phenomena which are resultants of all the phases of the polyphase system, in the resolution of the polypha ...", "... lue of the constant has to be used, which corresponds to the resultant effect. This, for instance, is the case in calcu- lating the magnetic field of the induction machine — which is energized by the combination of all phases — or the armature reaction of synchronous machines, etc. For instance, in the induction machine, from the generated e.m.f., e — in Chapter XVIII — the magnetic flux of the machine is calculated, and from the magnetic flux and the dimensions of the magnetic circuit: length and section of air-gap, and leng ...", "... rent per phase required to produce the resulting m.m.f,, Fo, therefore, is 1 = > nm hence, for a three-phase system, 1 = 5 ' 6 n and for a quarter-phase system, with two coils in quadrature, n V2 In the investigation of the armature reaction of synchronous machines. Chapter XXII, the armature reaction of an 7«-phase machine is, by §271, Worn/ . 454 ALTERNATING-CURRENT PHENOMENA where m = number of phases, no = number of turns per phase, effective, that is, allow- ing for the spread of turns over an arc of t ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-06", "section_label": "Lecture 6: Higher Harmonics Of The Generator Wave", "section_title": "Higher Harmonics Of The Generator Wave", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3133-3507", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-06/", "snippets": [ "... ccur between the line capacity and the circuit inductance. The origin and existence of higher harmonics therefore bears investigation in transformers, transmlission lines and cable systems. ORIGIN OF HIGHER HARMONICS Higher harmonics may originate in synchronous machines, as generators, synchronous motors and converters, and in transformers. These two classes of higher harmonics are very different. The former have constant potential character; the latter, con- stant current character; their cure and prevention there- f ...", "... coming from a transformer is eliminated by short circuit Short circuiting a generator harmonic, however, gives large 8o GENERAL LECTURES short circuit currents, due to the constant potential character, and is therefore dangerous. HIGHER HARMONICS OF SYNCHRONOUS MACHINES In synchronous machines, as alternating current genera- tors, the higher harmonics are : At No Load I St. The distribution of magnetism in the air gap depends on the shape of the field poles; it is not a sine wave; neither is the e. m. f . induced by ...", "... is eliminated by short circuit Short circuiting a generator harmonic, however, gives large 8o GENERAL LECTURES short circuit currents, due to the constant potential character, and is therefore dangerous. HIGHER HARMONICS OF SYNCHRONOUS MACHINES In synchronous machines, as alternating current genera- tors, the higher harmonics are : At No Load I St. The distribution of magnetism in the air gap depends on the shape of the field poles; it is not a sine wave; neither is the e. m. f . induced by it in an armature a sine ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-30", "section_label": "Apparatus Section 9: Synchronous Machines: Magnetic Characteristic or Saturation Curve", "section_title": "Synchronous Machines: Magnetic Characteristic or Saturation Curve", "kind": "apparatus-section", "sequence": 30, "number": 9, "location": "lines 9554-9650", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-30/", "snippets": [ "... r knee, and a saturated part beyond the knee. Gener- ally the change from the unsaturated to the over-saturated por- tion of the curve is more gradual; thus the knee is less pronounced in the magnetic characteristic of the synchronous machines, since the different parts of the magnetic circuit approach saturation successively. The dependence of the terminal voltage upon the field excita- tion, at constant full-load current through the amature into a 148 ELEMENT ...", "... factor, assuming E = 1000, I = 100 as full-load values. In the preceding the characteristic curves of synchronous ma- chines were discussed under the assumption that the saturation curve is a straight line ; that is, the synchronous machines working below saturation. 21. The effect of saturation on the characteristic curves of synchronous machines is as follows: The compounding curve is impaired by saturation; that is, a greater change of field excita- tion is ...", "... ynchronous ma- chines were discussed under the assumption that the saturation curve is a straight line ; that is, the synchronous machines working below saturation. 21. The effect of saturation on the characteristic curves of synchronous machines is as follows: The compounding curve is impaired by saturation; that is, a greater change of field excita- tion is required with changes of load. Under load the magnetic density in the armature corresponds to the true gene ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... tems, calculating the discharge capacity of lightning arres- ters, etc., the magnitude of the quantity is often sufficient. In 254 ^ ENGINEERING MATHEMATICS. calculating the critical speed of turbine alternators, or the natural period of oscillation of synchronous machines, the same applies, since it is of importance only to see that these speeds are sufficiently^ remote from the normal operating speed to give no trouble in operation. (b) Approximate calculation, requiring an accuracy of one or a few per cent only; a larg ...", "... onstant and an exact calculation of the motion of the pendulum by elliptic functions becomes necessary. In electrical engineering, one has frequently to deal w^ith oscillations similar to those of the pendulum, for instance, in the hunting or surging of synchronous machines. In general, the frequency of oscillation is assumed as constant, but where, as in cumulative hunting of synchronous machines, the amplitude of the swing reaches large values, an appreciable change of the period must be expected, and where the hunting is ...", "... ering, one has frequently to deal w^ith oscillations similar to those of the pendulum, for instance, in the hunting or surging of synchronous machines. In general, the frequency of oscillation is assumed as constant, but where, as in cumulative hunting of synchronous machines, the amplitude of the swing reaches large values, an appreciable change of the period must be expected, and where the hunting is a resonance effect with some other periodic motion, as the engine rotation, the change of frequency with increase of amplitud ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-29", "section_label": "Apparatus Section 8: Synchronous Machines: Characteristic Curves of Synchronous Motor", "section_title": "Synchronous Machines: Characteristic Curves of Synchronous Motor", "kind": "apparatus-section", "sequence": 29, "number": 8, "location": "lines 9399-9553", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-29/", "snippets": [ "... current I and power-factor p. As iron loss is assumed 3000 watts, as friction 2000 watts. Such curves are called load characteristics of the synchronous motor. 18. In Fig. 68 are shown, with constant power output = PO, SYNCHRONOUS MACHINES 145 i (Ep — ir), and the same constants, r = 0.1, XQ = 5, E = 1000, and with the nominal counter-generated voltage E0, that is, field excitation FQ, as abscissas, the values of current / for the four conditions, ...", "... will, and the syn- chronous motor thus offers the simplest means of producing out of phase or wattless currents for controlling the voltage in trans- mission lines, compensating for wattless currents of induction motors, etc. Synchronous machines used merely for supplying wattless currents, that is, synchronous motors or generators running light, with over-excited or under-excited field, are called synchronous condensers. They are used as exciters for induc- tion generat ...", "... ynchronous motors or generators running light, with over-excited or under-excited field, are called synchronous condensers. They are used as exciters for induc- tion generators, as compensators for the reactive lagging currents SYNCHRONOUS MACHINES 147 of induction motors, for voltage control of transmission lines, etc. Sometimes they are called \"rotary condensers\" or \"dynamic condensers\" when used only for producing lead- ing currents." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-38", "section_label": "Apparatus Section 17: Synchronous Machines: Short-circuit Currents of Alternators", "section_title": "Synchronous Machines: Short-circuit Currents of Alternators", "kind": "apparatus-section", "sequence": 38, "number": 17, "location": "lines 10190-10429", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-38/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-38/", "snippets": [ "... time — occasionally several seconds — elapses before the armature reaction becomes effective. At short circuit, the magnetic field flux is greatly reduced by the demagnetizing action of the armature current, and the gen- SYNCHRONOUS MACHINES 161 erated e.m.f. thereby reduced from the nominal value EQ to the virtual value Ez; the latter is consumed by the armature self- inductive impedance z, or self-inductive reactance, which is practically the same in most c ...", "... rrent has somewhat decreased. 33. In single-phase machines, and in polyphase machines in case of a short circuit on one phase only, the armature reaction is pulsating, and the field current in the first moment after the SYNCHRONOUS MACHINES 163 short circuit therefore pulsates, with double frequency, and remains pulsating even after the permanent condition has been reached. The double frequency pulsation of the field current in case of a single-phase short c ...", "... three-phase turbo- alternator. double frequency pulsation symmetrical, if the circuit is closed at the moment when the short-circuit current should be zero. 34. As illustration is shown, in Fig. 74, the oscillogram of SYNCHRONOUS MACHINES 165 one phase of the three-phase short circuit of a three-phase turbo- alternator, giving the unsymmetrical start of the armature currents and the full frequency pulsation of the field current. In Fig. 75 is shown a sing ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-14", "section_label": "Chapter 16: Reaction Machines", "section_title": "Reaction Machines", "kind": "chapter", "sequence": 14, "number": 16, "location": "lines 19374-20293", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-14/", "snippets": [ "CHAPTER XVI REACTION MACHINES 147. In the usual treatment of synchronous machines and induction machines, the assumption is made that the reactance, x, of the machine is a constant. While this is more or less approximately the case in many alternators, in others, especially in machines of large armature reaction, the reactance, x, is ...", "... his is constant in intensity and direc- tion, in the single-phase machine constant in direction, hut pul- sating in intensity, and the intensity pulsation can be reduced by a short-circuit winding around the field structure, as more fully discussed under \"Synchronous Machines.\" Thus a machine as shown diagram mat ically in Fig. 124, with a polyphase (three-phase) current impressed on the rotating armature, A, and no winding on the field poles, starts, runs up to synchronous and does considerable work as synchronous motor, an ...", "... reactance has to be represented by X = k + jx, where h is what has been called the \"effective hysteretic resistance.\" A similar phenomenon takes place in alternators of variable reactance, or, what is the same, variable magnetic reluctance. Operation of synchronous machines without field excitation is most conveniently treated by resolving the synchronous reactance, 3\"u, in its two components, the armature reaction and the true armature reactance, and once more resolving the armature reaction into a magnetizing and a distort ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-22", "section_label": "Chapter 24: Conclusion", "section_title": "Conclusion", "kind": "chapter", "sequence": 22, "number": 24, "location": "lines 32820-33531", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-22/", "snippets": [ "... -used types of apparatus have been discussed in the preceding, and a comprehensive list of them is given in Chapter XXIII, together with their definitions and short characterization. While electric machines are generally divided into induction machines, synchronous machines and commutating machines, this classification becomes difficult in considering all known apparatus, as many of them fall in two or even all three classes, or are intermediate, or their inclusion in one class depends on the particular definition of this cl ...", "... each other, and of which one may be called the primary cir- cuit, the other the secondary circuit. The magnetic field of the induction machine inherently must be an alternating field (usually a polyphase rotating field) excited by alternating currents. Synchronous machines are machines in which the frequency of rotation has a fixed and rigid relation to the frequency of the supply voltage. Usually the frequency of rotation is the same as the frequency of the. supply voltage: in the standard synchronous machine, with direc ...", "... motor on common rheostat, 159 Synchronous exciter of induction motor, 72 frequency converter, 191 induction generator, 191, 194 induction generator with low frequency exciter, 199, 203 induction motor, 166 as reaction machine, 264 480 INDEX Synchronous machines, surging, 288 motor, concatenation with in- duction motor, 54, 71 phase balancer, 228 phase converter, 227 rectifier, 234 U Unipolar induction, 452 machines, 400 motor meter, 458 Tandem control, see Concatenation. Temperature starting device o ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-11", "section_label": "Chapter 11: Instability Of Circuits: Induction And Syn Chronous Motors", "section_title": "Instability Of Circuits: Induction And Syn Chronous Motors", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 21382-22633", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-11/", "snippets": [ "... d to speed and electric supply, is rare. It has been observed, especially in single-phase motors, in cases of considerable oversaturation of the magnetic circuit. Oscillatory instability, however, is typical of the synchronous machine, and the hunting of synchronous machines has probably been the first serious problem of cimiulative oscillations in electric circuits, and for a long time has limited the industrial use of syn- chronous machines, in its different forms: (a) Difficulty and failure of alternating-current generato ...", "... ulty and failure of alternating-current generators to operate in parallel. (6) Hunting of synchronous converters. (c) Hunting of synchronous motors. While considerable theoretical work has been done, practically all theoretical study of the hunting of synchronous machines has been limited to the calculation of the frequency of the transi- ent oscillation of the synchronous machine, at a change of load, frequency or voltage, at synchronizing, etc. However, this transient oscillation is harmless, and becomes dangerous only i ...", "... e study of hunt- ing thus is the determination of the cause, which converts the transient oscillation into a cumulative one, that is, the determina- tion of the source of the energy, and the mechanism of its trans- fer to the oscillating system. To design synchronous machines, so as to have no or very little tendency to hunting, obviously re- INSTABILITY OF CIRCUITS 209 quires a knowledge of those characteristics of design which are instrumental in the energy transfer to the oscillating system, and thereby cause hunting, s ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "section_label": "Lecture 10: Continual And Cumulative Oscillations", "section_title": "Continual And Cumulative Oscillations", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... nstrumental in the energy supply to other systems of continual oscillation. Thus, for instance, the hysteresis cycle between synchronizing force and position displacement supplies the energy of the con- tinual or cumulative oscillation, called hunting, in synchronous machines, as alternators, synchronous motors and converters. The mechanism, by which the hysteresis cycle supplies the energy of continual oscillations, has been investigated in the case of the hunting of synchronous machines,* but is still practically un- known i ...", "... lative oscillation, called hunting, in synchronous machines, as alternators, synchronous motors and converters. The mechanism, by which the hysteresis cycle supplies the energy of continual oscillations, has been investigated in the case of the hunting of synchronous machines,* but is still practically un- known in the case of continual oscillations between magnetic and dielectric energy in electric circuits. Recurrent oscillations, as in Fig. 59, must be or very soon be- come continual, that is, the successive wave trains ar ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-24", "section_label": "Apparatus Section 3: Synchronous Machines: Armature Reaction", "section_title": "Synchronous Machines: Armature Reaction", "kind": "apparatus-section", "sequence": 24, "number": 3, "location": "lines 8741-8906", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-24/", "snippets": [ "... a synchronous motor with the magnetic attractions and repulsions between field and armature). In this case the armature current neither magnetizes nor demag- netizes the field as a whole, but magnetizes the one side, demag- SYNCHRONOUS MACHINES 131 netizes the other side of each field pole, and thus merely distorts the magnetic field. 9. If the armature current lags behind the nominal generated e.m.f., it reaches its maximum in a position where the armature ...", "... t revolving synchronously with regard to the armature, that is, stationary with regard to the field. These values of armature reaction correspond strictly only to the case where all conductors of the same phase are massed SYNCHRONOUS MACHINES 133 together in one slot. If the conductors of each phase are dis- tributed over a greater part of the armature surface, the values of armature reaction have to be multiplied by the average cosine of the total angle of ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-27", "section_label": "Apparatus Section 6: Synchronous Machines: Characteristic Curves of Alternating-current Generator", "section_title": "Synchronous Machines: Characteristic Curves of Alternating-current Generator", "kind": "apparatus-section", "sequence": 27, "number": 6, "location": "lines 9170-9291", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-27/", "snippets": [ "... abscissas and for the three conditions, 1. Non-inductive load, p = 1, q = 0. 2. Inductive load of 0 = 60 degrees lag, p = 0.5, q = 0.866. 3. Anti-inductive load of — 6 = 60 degrees lead, p = 0.5, q = -0.866. SYNCHRONOUS MACHINES 139 The values r = 0.1, XQ = 5, E = 1000, are assumed. These curves are called the compounding curves of the synchronous generator. In Fig. 60 are shown, at constant nominal generated e.m.f. EQ, that is, at constan ...", "... tation, which is 2.25 times full-load current; and the maximum output, 124 kw., at full non-induct- ive load excitation, which is 1.24 times rated output, at 775 volts and 160 amp. It depends upon the point on the field SYNCHRONOUS MACHINES 141 characteristic at which the alternator works, whether it tends to regulate for, that is, maintains, constant voltage, or constant current, or constant power, approximately. z L 7 \\ H 20 40 60 80 10 ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-32", "section_label": "Apparatus Section 11: Synchronous Machines: Unbalancing of Polyphase Synchronous Machines", "section_title": "Synchronous Machines: Unbalancing of Polyphase Synchronous Machines", "kind": "apparatus-section", "sequence": 32, "number": 11, "location": "lines 9719-9748", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-32/", "snippets": [ "XI. Unbalancing of Polyphase Synchronous Machines 23. The preceding discussion applies to polyphase as well as single-phase machines. In polyphase machines the nominal generated e.m.fs. or nominal counter-generated e.m.fs. are neces- sarily the same in all phases (or bear a ...", "... lyphase machines the nominal generated e.m.fs. or nominal counter-generated e.m.fs. are neces- sarily the same in all phases (or bear a constant relation to each other). Thus in a polyphase generator, if the current or the SYNCHRONOUS MACHINES 151 phase relation of the current is different in the different branches, the terminal voltage must become different also, more or less. This is called the unbalancing of the polyphase generator. It is due to different lo ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-36", "section_label": "Apparatus Section 15: Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "section_title": "Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "kind": "apparatus-section", "sequence": 36, "number": 15, "location": "lines 9918-10123", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-36/", "snippets": [ "... the cross current is 31.2 per cent, of full-load current. If the short-circuit current is 6 times full-load current, the cross current is 93.6 per cent, of full-load current or practically equal to full-load current. Thus SYNCHRONOUS MACHINES 157 the smaller the armature reaction, or the better the regulation, the larger are the pulsating cross currents between the alternators, due to the inequality of the rate of rotation of the prime movers. Hence for satisf ...", "... y as in direct-current machines, when operating in parallel, to connect all the series fields in paral- lel by equalizers of negligible resistance, for the same reason — to insure proper division of current between machines. SYNCHRONOUS MACHINES 159" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-37", "section_label": "Apparatus Section 16: Synchronous Machines: Higher Frequency Cross Currents Between Synchronous Machines", "section_title": "Synchronous Machines: Higher Frequency Cross Currents Between Synchronous Machines", "kind": "apparatus-section", "sequence": 37, "number": 16, "location": "lines 10124-10189", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-37/", "snippets": [ "XVI. Higher Frequency Cross Currents between Synchronous Machines 30. If several synchronous machines of different wave shapes are connected into the same circuit, cross currents exist between the machines of frequencies which are odd multiples of the circuit frequency, that is, higher ha ...", "XVI. Higher Frequency Cross Currents between Synchronous Machines 30. If several synchronous machines of different wave shapes are connected into the same circuit, cross currents exist between the machines of frequencies which are odd multiples of the circuit frequency, that is, higher harmonics thereof. The machines may be ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-81", "section_label": "Apparatus Section 1: Synchronous Converters: General", "section_title": "Synchronous Converters: General", "kind": "apparatus-section", "sequence": 81, "number": 1, "location": "lines 13189-13795", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-81/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-81/", "snippets": [ "... field, and connected to a segmental commutator as well as to collector rings. Structurally it thus differs from a direct- current machine by the addition of the collector rings, from certain (now very little used) forms of synchronous machines by the addition of the segmental commutator. In consequence hereof, regarding types of armature windings and of field windings, etc., the same rule applies to the converter as to all commutating machines, except that in th ...", "... .m.f. usually approximates a sine wave, due to the multi-tooth distributed winding. Thus, in the following, only those features will be discussed in which the synchronous converter differs from the commu- tating machines and synchronous machines treated in the preceding chapters. Fig. 122 represents diagrammatically the commutator of a direct-current machine with the armature coils A connected to adjacent commutator bars. The brushes are BiB2, and the field poles Fi ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-06", "section_label": "Chapter 7: Higher Harmonics In Induction Motors", "section_title": "Higher Harmonics In Induction Motors", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 12398-13955", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-06/", "snippets": [ "... ICS 149 and its return, 1', 2', 3', covers another third of the circumference of two poles, in the lower layer of the armature winding, 180° away from 1, 2, 3. However, this type of true three-phase wind- ing is practically never used in induction or synchronous machines, but the type of winding is used, which is shown as S, in Fig. 57 C. This is in reality a six-phase winding: each of the three e Uddt N i; 2' 2o r 2' ■ 2' 1o 3' 2'a I KCffl N 2o 1 mm a r 2' ''^«a ...", "... is shown under <& to the right. The pitch of a turn of the winding is indicated under F. Fig. 58 shows: Full-pitch quarter-phase winding: Q — 0. Full-pitch six-phase winding: S — 0. This is the three-phase winding almost always used in induction and synchronous machines. Full-pitch three-phase winding: T — 0. This is the true three-phase winding, as used in closed-circuit armatures, as synchronous converters, but of little importance in induction and synchronous motors. %> % and J^-pitch quarter-phase windings: Q - ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-15", "section_label": "Chapter 17: Inductor Machines", "section_title": "Inductor Machines", "kind": "chapter", "sequence": 15, "number": 17, "location": "lines 20294-20974", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-15/", "snippets": [ "CHAPTER XVII INDUCTOR MACHINES Inductor Alternators, Etc. 156. Synchronous machines may be built with stationary field and revolving armature, as shown diagrammatically in Fig. 134, or with revolving field and stationary armature, Fig. 135, or with stationary field and stationary armature, but revolving magnetic circuit. The revolving- ...", "... e-half the number of poles. An inductor with p projections thus gives twice as many cycles per revolution, thus as syn- chronous motor would run at half the speed of a standard syn- chronous machine of p poles. As the result hereof, in starting polyphase synchronous machines by impressing polyphase voltage on the armature and using the hysteresis and the induced currents in the field poles, for producing the torque of starting and acceleration, there frequently appears at half synchronism a tendency to drop into step with the ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-16", "section_label": "Chapter 18: Surging Of Synchronous Motors", "section_title": "Surging Of Synchronous Motors", "kind": "chapter", "sequence": 16, "number": 18, "location": "lines 20975-21712", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-16/", "snippets": [ "... omentum is M0 = 1,360,000 joules, hence, at no-load: P = 0, e = 1600 volts ;/0 = 1.72 cycles, or 103 periods per minute. 1.98 cycles, or 119 periods per minute. 1.23 cycles, or 134 periods per minute. 169. In the preceding discussion of the surging of synchronous machines, the assumption has been made that the mechanical power consumed by the load is constant, and that no damping or anti-surging devices were used. The mechanical power consumed by the load varies, however, more or less with the speed, approximately proport ...", "... 6i2, g = y/a - bS, 8 = £€ + Mcos(00 + 6). (34) That is, the motor oscillates, with constantly increasing am- plitude, until it drops out of step. This is the typical case of cumulative surging by electro-mechanical resonance. The problem of surging of synchronous machines, and its elimination, thus resolves into the investigation of the coefficient: 8x/Jlf0 (35) while the frequency of surging, where such exists, is given by: f _ jfeeo sin (a - 0) (c2 + pP0 - /i2)2 (Wi Case (4), steady drifting out of step, has o ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-18", "section_label": "Chapter 20: Single-Phase Commutator Motors", "section_title": "Single-Phase Commutator Motors", "kind": "chapter", "sequence": 18, "number": 20, "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "... for single-phase railroading, and as con- stant-speed motors or adjustable-speed motors, where efficient acceleration under heavy torque is necessary. As generators, they would be of advantage for the generation of very low fre- quency, since in this case synchronous machines are uneconom- ical, due to their very low speed, resultant from the low frequency. The direction of rotation of a direct-current motor, whether shunt or series motor, remains the same at a reversal of the im- pressed e.m.f., as in this case the current i ...", "... producing the equivalent of a leading current. Therefore, the alternating-current commutator is one of the important methods of compensating for lagging: currents. Other methods are the use of electrostatic or electro- lytic condensers and of overexcited synchronous machines. Based on this principle, a number of designs of induction motors and other apparatus have been developed, using Qm commutator for neutralizing the lagging magnetizing current and the lag caused by self-inductance, and thereby produdng unity power-facto ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-10", "section_label": "Chapter 10: Instability Of Circuits : The Arc", "section_title": "Instability Of Circuits : The Arc", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 17632-21381", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-10/", "snippets": [ "... made themselves felt as disturbances or troubles in electric circuits, they either remained imunderstood or the theo- retical study was limited to the specific phenomenon, as in the case of lightning, dropping out of step of induction motors, hunt- ing of synchronous machines, etc., or, as in the design of arc lamps and arc-lighting machinery, the opinion prevailed that theoretical calculations are impossible and only design by trying, based on practical experience, feasible. The first class of imstable phenomena, which was s ...", "... that the phenomenon of a permanent or cumulative line surge involves an energy supply or energy transformation of a fre- quency equal to that of the oscillation. Possibly the oldest and best-known instance of such cumulative oscillation is the hunting of synchronous machines. Cumulative oscillations between electromagnetic and electro- static energy have been observed by their destructive effects in high- voltage electric circuits on transformers and other apparatus, and have been, in a number of instances where their freque ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... on by wave screens, 157 Heusler alloys, magnetic properties, 81 High harmonics in alternator, 120 excessive in wave distortion by magnetic saturation, 140 by slot pitch, 120 temperature insulators^ 26 Homogeneous magnetic materials, 55 Hunting of synchronous machines, 166, 208 Hysteresis, 56 loss and wave shape, 112 Impedance and admittance with oscillating currents, 346 of hne in regulation of series circuits, 306 Induced current in leaky cable armor, 336 Inductance, 1 and capacity shunting circuit, 18 ...", "... ent regulation, 246, 281 of line in regulation of series circuit, 306 with oscillating currents, 347 self inductive and mutual in- ductive, of alternator arma- ture, 239 shunt in series circuit, 298 regulating series circuit by saturation, 302 of synchronous machines, 232 total, of transformer, 224 of transformer, measurement, 227 and short-circuit stress, 100 as wave screen, 153 Reactive power of system, total and resultant, 317 Recovery of induction motor after overload, 204 Rectification by arc, 32 by ele ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... operation of apparatus which require approximate constancy of voltage but do not operate on constant current — as most synchronous apparatus — becomes difficult. Hence, at the end of very long transmission lines the voltage regulation becomes poor, and synchronous machines tend to instability and have to be provided with powerful steadying devices, giving induction motor features, and with a line approaching quarter-wave length, voltage regulation at the receiving end ceases. In this case the constant potential-constant c ...", "... -current input, the output voltage would drop off, from no load to full load, by about 8 per cent. This, with a line of 15 per cent resistance drop, is a far closer voltage regulation than can be produced by constant potential supply, except by the use of synchronous machines for phase control." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 557-1002", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-01/", "snippets": [ "... ic stored energy. This for instance is the case in the charge or discharge of a condenser through an inductive circuit. If energy can be stored in more than two different forms, still more complex phenomena may occur, as for instance in the hunt- ing of synchronous machines at the end of long transmission lines, where energy can be stored as magnetic energy in the line and apparatus, as dielectric energy in the line, and as mechanical energy in the m_omentum of the motor. 6. The study and calculation of the permanent phenom ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-01", "section_label": "Lecture 1: Nature And Origin Of Transients", "section_title": "Nature And Origin Of Transients", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 460-882", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "snippets": [ "... ic stored energy. This for instance is the case in the charge or discharge of a condenser through an inductive circuit. If energy can be stored in more than two different forms, still more complex phenomena may occur, as for instance in the hunt- ing of synchronous machines at the end of long transmission lines, where energy can be stored as magnetic energy in the line and apparatus, as dielectric energy in the line, and as mechanical energy in the momentum of the motor. 6. The study and calculation of the permanent phenome ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2162-2971", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "snippets": [ "... ng the transi- tion period can reach, is limited to less than double the final value, as is obvious from the construction of the 'field, Fig. 19. It is evident herefrom, however, that in apparatus containing rotating fields, as induction motors, polyphase synchronous machines, etc., the resultant field may under transient conditions reach nearly double value, and if then it reaches far above magnetic saturation, excessive momentary currents may appear, similar as in starting transformers of high magnetic density. In polyphase ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-05", "section_label": "Chapter 6: Empirical Curves", "section_title": "Empirical Curves", "kind": "chapter", "sequence": 5, "number": 6, "location": "lines 16483-21988", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-05/", "snippets": [ "... the thirteenth harmonics. This method of determining two similar harmonics, with a little practice, becomes very convenient and useful, and may 248 ENGINEERING MATHEMATICS. frequently be used visually also, in determining the frequency of hunting of synchronous machines, etc. In the phenomenon of hunting, frequently two periods are superimposed, forced frequency, resulting from the speed of generator, etc., and the natural frequency of the machine. Counting the number of impulses, /, per minute, and the number of nodes, ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-08", "section_label": "Lecture 8: Generation", "section_title": "Generation", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 3781-4217", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-08/", "snippets": [ "... eriority of the steam turbine in efficiency, while marked at rated load, is still far greater at partial load, light load and overload. b. Smaller size, weight and space occupied. c. Uniform rate of rotation, therefore decreased liability of hunting of synchronous machines, and decreased necessity of heavy foundations to withstand reciprocating strains. d. Greater reliability of operation and far less attend- ance required. The steam turbine reaps a far greater benefit in economy than the steam engine from superheat of t ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-23", "section_label": "Apparatus Section 2: Synchronous Machines: Electromotive Forces", "section_title": "Synchronous Machines: Electromotive Forces", "kind": "apparatus-section", "sequence": 23, "number": 2, "location": "lines 8658-8740", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-23/", "snippets": [ "... , r = effective resistance. The virtual generated e.m.f. E2 is the e.m.f. which would be generated by the flux produced by the field poles, or flux corre- sponding to the resultant m.m.f., that is, the resultant of the SYNCHRONOUS MACHINES 129 m.m.fs. of field excitation and of armature reaction. Since the magnetic flux produced by the armature, or flux of armature self-inductance, combines with the field flux to the resultant flux, the flux produced by the ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-25", "section_label": "Apparatus Section 4: Synchronous Machines: Self-inductance", "section_title": "Synchronous Machines: Self-inductance", "kind": "apparatus-section", "sequence": 25, "number": 4, "location": "lines 8907-9034", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-25/", "snippets": [ "... gle EOI = 0. _The e.m.f. consumed by resistance is OE \\ = Ir in phase with 01. The e-m-i^ consumed by reactance is OEfz — Ix, 90 degrees ahead of 01. The real generated e.m.f. is found by combining OE and OE\\ to SYNCHRONOUS MACHINES 135 The virtual generated e.m.f. is OEi and OE'Z combined to = E2. The m.m.f. required to produce -this e.m.f. Ez is OF = F, Fa I E, FIG. 52. — Diagram of generator e.m.fs. and m.m.fs. for non-reactive l ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-26", "section_label": "Apparatus Section 5: Synchronous Machines: Synchronous Reactance", "section_title": "Synchronous Machines: Synchronous Reactance", "kind": "apparatus-section", "sequence": 26, "number": 5, "location": "lines 9035-9169", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-26/", "snippets": [ "... phases uniformly loaded, as \" poly- phase synchronous reactance.\" The resultant armature reac- tion of all phases of the polyphase machine is higher than that with the same current in one phase only, and so also the self- SYNCHRONOUS MACHINES 137 inductive flux, as resultant flux of several phases, and thus rep- resents a higher synchronous reactance. Let r = effective resistance, XQ = synchronous reactance of armature, as discussed in Section II. Let E = ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-28", "section_label": "Apparatus Section 7: Synchronous Machines: Synchronous Motor", "section_title": "Synchronous Machines: Synchronous Motor", "kind": "apparatus-section", "sequence": 28, "number": 7, "location": "lines 9292-9398", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-28/", "snippets": [ "... e.m.f. consumed by synchronous reactance, E'Q = + jix0. Thus the e.m.f. consumed by the nominal counter-generated e.m.f. is Eo = E - E'i - E'Q = (E cos 0 - ir) + j (E sin 6 - ixQ) = (Ep - ir) + j(Eq - ixQ); SYNCHRONOUS MACHINES 143 or, in absolute values, V(Ecos e - ir)2 + (Esin 6 - ix0)* = V(Ep- ij hence, E = i (rp + xQq) ± \\/EQ2 — i2 (x0p — rq)z. The power consumed by the synchronous motor is P = iEp; that is, the current tim ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-33", "section_label": "Apparatus Section 12: Synchronous Machines: Starting of Synchronous Motors", "section_title": "Synchronous Machines: Starting of Synchronous Motors", "kind": "apparatus-section", "sequence": 33, "number": 12, "location": "lines 9749-9820", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-33/", "snippets": [ "... the induction motor principle. Such squirrel-cage winding should have fairly high resistance to start well from rest, but low resistance to give powerful syn- chronizing, that is, to pull its load promptly into synchronism. SYNCHRONOUS MACHINES 153" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-35", "section_label": "Apparatus Section 14: Synchronous Machines: Division of Load in Parallel Operation", "section_title": "Synchronous Machines: Division of Load in Parallel Operation", "kind": "apparatus-section", "sequence": 35, "number": 14, "location": "lines 9879-9917", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-35/", "snippets": [ "... is not the same, the load is not divided proportionally between the alternators, but the alternator connected to the prime mover of closer speed regula- tion takes more than its share of the load under heavy loads, and SYNCHRONOUS MACHINES 155 less under light loads. Thus, too close speed regulation of prime movers is not desirable in parallel operation of alternators." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-39", "section_label": "Apparatus Section 1: Direct-current Commutating Machines: General", "section_title": "Direct-current Commutating Machines: General", "kind": "apparatus-section", "sequence": 39, "number": 1, "location": "lines 10430-10474", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-39/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-39/", "snippets": [ "... hanical power, and direct-current con- verters which transform electric power into a different form of electric power. Since the most important class of the latter are the synchronous converters, which combine features of the synchronous machines with those of the commutating machines, they shall be treated in a sepa- rate chapter. By the excitation of their mag- net fields, commutating machines are divided into magneto machines, in which the field consists of perm ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-45", "section_label": "Apparatus Subsection 45: Direct-current Commutating Machines: C. Commutating Machines 177", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 177", "kind": "apparatus-subsection", "sequence": 45, "number": null, "location": "lines 10737-10777", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-45/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-45/", "snippets": [ "... e side of the coil enters or leaves the field before the other. Therefore, in commutating machines it is seldom that a pitch is used that falls short of full pitch by more than one or two teeth, while in induction and synchronous machines occasionally as low a pitch as 50 per cent, is used, and two-thirds pitch is frequently employed. For special purposes, as in single-phase commutator motors fractional-pitch windings are sometimes used. 41. Series windings ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-59", "section_label": "Apparatus Section 8: Direct-current Commutating Machines: Armature Reaction", "section_title": "Direct-current Commutating Machines: Armature Reaction", "kind": "apparatus-section", "sequence": 59, "number": 8, "location": "lines 11616-11694", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-59/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-59/", "snippets": [ "... F ELECTRICAL ENGINEERING C -j- go 2 Fa with the average cos = — , and is thus — yu ^\" Fao 2 Fa 2 ni When comparing the armature reaction of commutating ma- chines with other types of machines, as synchronous machines 2 Fa etc., the resultant armature reaction Fao = - - has to be used. In discussing commutating machines proper, however, the value Fa = ni is usually considered as the armature reaction. 56. The armature reaction of ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-63", "section_label": "Apparatus Subsection 63: Direct-current Commutating Machines: C. Commutating Machines 197", "section_title": "Direct-current Commutating Machines: C. Commutating Machines 197", "kind": "apparatus-subsection", "sequence": 63, "number": null, "location": "lines 11795-11863", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-63/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-63/", "snippets": [ "... istic Curves 60. The field characteristic or regulation curve, that is, curve giving the terminal voltage as function of the current output at constant field excitation, is of less importance in commutating machines than in synchronous machines, since commutating machines are usually not operated with separate and constant excitation, and the use of the series field affords a convenient means of changing the field excitation proportionally to the load. The curve ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-65", "section_label": "Apparatus Section 13: Direct-current Commutating Machines: Commutation", "section_title": "Direct-current Commutating Machines: Commutation", "kind": "apparatus-section", "sequence": 65, "number": 13, "location": "lines 11905-11980", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-65/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-65/", "snippets": [ "... armature coil during commutation is eo = 2irfoLiot where io = current reversed, and the energy which has to be dissipated during commutation is i hence, E = — I ei sin -}- ^ 63 sin 3(0 — as) + -= e^ sin 5(0 — as) 1 2 - = 67 sin 7(0 - ay) — Q eg sin 9(0 - ag) — Tj-eii sin 11(0 - an) + ^^613 sin 13(0 — a^) H • • • } (6) SHAPING OF WAVES 119 Here the third harmonics do not cance ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... TS, 44. The charge and discharge of a condenser through an inductive circuit produces periodic currents of a frequency depending upon the circuit constants. The range of frequencies which can be produced by electro- dynamic machinery is rather limited: synchronous machines or ordinary alternators can give economically and in units of larger size frequencies from 10 to 125 cycles. Frequencies below 10 cycles are available by commutating machines with low frequency excitation. Above 125 cycles the difficulties rapidly increa ..." ] } ] }, { "id": "corporation", "label": "Corporation", "aliases": [ "Corporation", "corporation" ], "total_occurrences": 133, "matching_section_count": 12, "matching_source_count": 1, "source_totals": [ { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "occurrence_count": 133, "section_count": 12 } ], "section_hits": [ { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-17", "section_label": "Chapter 16: The Future Corporation", "section_title": "The Future Corporation", "kind": "chapter", "sequence": 17, "number": 16, "location": "lines 6975-7567", "status": "candidate", "occurrence_count": 53, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-17/", "snippets": [ "XVI THE FUTURE CORPORATION THE development of a national government by the industrial corporation presupposes that the social functions of the industrial cor- poration, which are now being developed, have been extended in all corporations and grown to ...", "XVI THE FUTURE CORPORATION THE development of a national government by the industrial corporation presupposes that the social functions of the industrial cor- poration, which are now being developed, have been extended in all corporations and grown to an activity equal in importance and scope, and directed by equally big ...", "... hich are now being developed, have been extended in all corporations and grown to an activity equal in importance and scope, and directed by equally big men, as the technical, administrative, and financial activities of the corporation. It would hardly be safe, even with the control exerted by an inhibitory tribunicial power, to intrust the entire constructive gov- ernment of our nation to the industrial cor- porations of to-day, with their very different ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-04", "section_label": "Chapter 3: The Individualistic Era: From Competition to Co-operation", "section_title": "The Individualistic Era: From Competition to Co-operation", "kind": "chapter", "sequence": 4, "number": 3, "location": "lines 874-1745", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-04/", "snippets": [ "... onsoli- dation is killing competition, and try to stop consolidation by breaking up the corporations, while in reality the death of competition as a beneficent industrial force is the cause of con- solidation, has led to the corporation as the only means of industrial production. Thus, not the \"trusts\" are killing competition, but the failure of competition is the cause of industrial consolidation, of the corporations. Thus, wherever outside forces did not ...", "... formation of a co-operative ar- rangement between the corporations dominating the industry, for self-preservation against the general destruction inevitable by unrestrained competition. Sometimes it was the formation of a single corporation controlling the entire industry; more frequently one large corpora- tion controlling a large part of the industry, and a number of smaller corporations, which, while financially and administratively independent, by tacit underst ...", "... e large corpora- tion controlling a large part of the industry, and a number of smaller corporations, which, while financially and administratively independent, by tacit understanding accepted the prices fixed by the dominating corporation. Usually, how- ever, with a number of large corporations in the field, the destructive competition was elimi- nated by agreements limiting production to that conforming with the demand, and agree- ing upon prices maintaining a ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-14", "section_label": "Chapter 13: Evolution: Industrial Government", "section_title": "Evolution: Industrial Government", "kind": "chapter", "sequence": 14, "number": 13, "location": "lines 5798-6232", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-14/", "snippets": [ "XIII evolution: industrial government HIE large industrial corporation is to-day by far the most efficient organization, in spite of the inefficiency forced upon it by the political Government. It is still very crude and imperfect in many respects, and especially it is still greatly deficient ...", "... ially it is still greatly deficient in the social relations within the organi- zation and toward the general public. If an efficient co-operative government is to be built up from the industrial corporations, the in- dustrial corporation must first become united within itself — that is, the indifference and an- tagonij?in within the corporation must be over- come, and the same co-operative feeling brought about between the shop force and the adminis- tration w ...", "... public. If an efficient co-operative government is to be built up from the industrial corporations, the in- dustrial corporation must first become united within itself — that is, the indifference and an- tagonij?in within the corporation must be over- come, and the same co-operative feeling brought about between the shop force and the adminis- tration which exists and always has existed in most corporations between the office force and the administration. Tha ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-11", "section_label": "Chapter 10: Public and Private Corporations", "section_title": "Public and Private Corporations", "kind": "chapter", "sequence": 11, "number": 10, "location": "lines 4716-5059", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-11/", "snippets": [ "... then apply, or adapt, the methods which have given satisfactory results, to the conditions where the results have been unsatisfactory. It is strange that in all the agitation for improving the ef- ficiency of the municipal corporation, in all the studies of commission government, municipal charters, etc., very little thought has been given to those forms of government which have proven satisfactory, efficient, and economical— the gov- ernments of the industr ...", "... municipal charters, etc., very little thought has been given to those forms of government which have proven satisfactory, efficient, and economical— the gov- ernments of the industrial corporations. The municipality is a public corporation, owned and governed by the citizens; the indus- trial corporation is a private corporation, owned and operated by the stockholders. In size and capitalization, many industrial corporations are far larger than the average munic ...", "... hose forms of government which have proven satisfactory, efficient, and economical— the gov- ernments of the industrial corporations. The municipality is a public corporation, owned and governed by the citizens; the indus- trial corporation is a private corporation, owned and operated by the stockholders. In size and capitalization, many industrial corporations are far larger than the average municipal corpora- tion; many smaller. Thus there is no essential diffe ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-10", "section_label": "Chapter 9: America in the Individualistic Era", "section_title": "America in the Individualistic Era", "kind": "chapter", "sequence": 10, "number": 9, "location": "lines 4268-4715", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-10/", "snippets": [ "... ization ap- proached the co-operative stage there was still a large class of small, individual producers in the West who felt their existence threatened by the rise of corporate industrial power, and were ready to fight the corporation by all means, po- litical and otherwise, in the vain attempt to avoid the inevitable, the extinction of the small producer before the higher efficiency of organ- ized corporate production. Add thereto the 123 AMERICA ...", "... er wishes to be the first in a small puddle than the second in the wide ocean; tempera- ments who prefer to be president of a ten- thousand-dollar business rather than assistant to the president of a hundred-million-dollar corporation. We must also consider that many of the organizers and corporation leaders are pronounced individualists, do not understand what they arc doing and whereto the path 124 AP^lEllICA IN THE INDIVIDUALISTIC ERA leads into ...", "... he wide ocean; tempera- ments who prefer to be president of a ten- thousand-dollar business rather than assistant to the president of a hundred-million-dollar corporation. We must also consider that many of the organizers and corporation leaders are pronounced individualists, do not understand what they arc doing and whereto the path 124 AP^lEllICA IN THE INDIVIDUALISTIC ERA leads into which economic laws forced them, and thus leadership in the transiti ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-18", "section_label": "Chapter 17: Conclusion", "section_title": "Conclusion", "kind": "chapter", "sequence": 18, "number": 17, "location": "lines 7568-8027", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-18/", "snippets": [ "... k out our own sal- vation, on new democratic lines, a problem far greater and more difficult. The most promising structural element of the future co-operative industrial organization, in our present nation, is the industrial corporation, and on this probably the structure of co-oper- ative industrial society will be built in our democratic nation. A positive, administrative, and executive in- dustrial government, i)rofessionally comi)etent, continuous and perman ...", "... orever, of Cain's answer, \"Am I my brother's keeper?\" Political legislation, or industrial organiza- tion, or a combination of both, may bring about this social reconstruction, and the rapidly in- creasing interest, within the corporation, in social activity, promises well in this direction. With this accomplished, and the enormous number of the emplo^'ees of the industrial cor- porations thereby attached to the interests of the corporations and ready for the ...", "... its defense — with this accomplished, quickly the political power would shift and the political government, instead of outlawing and fighting corporate success and business, would be brought into co-operation with the industrial corporation, and from thereon the progress toward democratic co-operative industrial or- ganization would be steady and rapid. Internationally the co-operative era would bring about material changes: with production controlled, first nationa ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-05", "section_label": "Chapter 4: The Individualistic Era: The Other Side", "section_title": "The Individualistic Era: The Other Side", "kind": "chapter", "sequence": 5, "number": 4, "location": "lines 1746-2408", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-05/", "snippets": [ "... ge, \"class consciousness\" has not become the slogan of a powerful polit- ical party, such as it did, for instance, in Ger- many, already a generation ago. ,_JWith the further development of industrial capitalism gradually the corporation took the place of the large individual employer, and the \"employer's class\" steadily dwindled down. First, individual personality still dominated the corporation: the \"Harriman\" roads, the \"Van- derbilt\" interests, etc. But wit ...", "... ith the further development of industrial capitalism gradually the corporation took the place of the large individual employer, and the \"employer's class\" steadily dwindled down. First, individual personality still dominated the corporation: the \"Harriman\" roads, the \"Van- derbilt\" interests, etc. But with the death of the men who organized the corporations, their management became impersonal, and so we find to-day, at least in those industries in which the d ...", "... nalism, un-American ideas, etc., can obscure the fact of the failure. This is the great problem modern industrial society has to face and to solve. It is the driving force back of the \"social activities\" which the modern corporation is beginning to recognize. The success of industrial capitalism is based on mass production by subdivision of labor. But with the increasing subdivision of work, the character of the work has changed, and with it the atti ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-15", "section_label": "Chapter 14: Evolution: Inhibitory Power", "section_title": "Evolution: Inhibitory Power", "kind": "chapter", "sequence": 15, "number": 14, "location": "lines 6233-6597", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-15/", "snippets": [ "XIV evolution: inhibitory power THE industrial corporation of to-day is or- ganized for effective constructive work; it has developed the characteristics necessary for economic efficiency — continuity of organization and at the same time flexibility to adapt itself in a high degree to ...", "... ears the natural and most logical step that the executive and administrative Gov- ernment of our nation in the co-operative era 177 AMERICA AND THE NEW EPOCH which we are now entering should evolve from the industrial corporation. Such organization is commensal — that is, every member of it gives and receives, and the maintenance and advance of the organization thus is to everybody's interest. It thus should form a stable and permanent form of soci ...", "... operative in- dustrial organization the industrial adminis- trative powers will more and more come into the foreground, the financial power become less dominating. Thus such industrial government based on the development of the corporation is not by itself entirely safe against abuse drifting in and destroying its efficiency and thereby endanger- ing its existence. Thus, there must be an inhibitory power out- side of the industrial government; a power not org ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-introduction-01", "section_label": "Introduction 1: Introduction", "section_title": "Introduction", "kind": "introduction", "sequence": 1, "number": null, "location": "lines 87-233", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/introduction-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/introduction-01/", "snippets": [ "... ery cent increase of wages appears so much out of the pockets of the owner — and of corporate production, and have realized, from my acquaintance with the inside workings of numerous large corpora- tions, that the industrial corporation is not the greedy monster of popular misconception, bent only on exploitation, and have most decidedly come to the conclusion that, even as crude and INTRODUCTION undeveloped as the industrial corporation of to-day still ...", "... at the industrial corporation is not the greedy monster of popular misconception, bent only on exploitation, and have most decidedly come to the conclusion that, even as crude and INTRODUCTION undeveloped as the industrial corporation of to-day still is in its social activities, if I were an unknown and unimportant employee I would far rather take my chances with the impersonal, huge industrial corporation than with the most well-meaning individual em- ...", "... and INTRODUCTION undeveloped as the industrial corporation of to-day still is in its social activities, if I were an unknown and unimportant employee I would far rather take my chances with the impersonal, huge industrial corporation than with the most well-meaning individual em- ployer. Charles P. Steinmetz. August, 1916. AMERICA AND THE NEW EPOCH AMERICA AND THE NEW EPOCH" ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-07", "section_label": "Chapter 6: Germany in the Individualistic Era", "section_title": "Germany in the Individualistic Era", "kind": "chapter", "sequence": 7, "number": 6, "location": "lines 2776-3206", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-07/", "snippets": [ "... that the antagonism of the masses against the corporations, which here in America paralyzes our rapid industrial progress and threatens to destroy our prosperity by in- terfering with the industries' most effective tool, the corporation, has never appeared in Ger- many, but consolidation has proceeded un- checked. The educational system was reorganized, and the university idea extended Into the industrial field, and a universal system of industrial edu- cati ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-09", "section_label": "Chapter 8: America in the Past", "section_title": "America in the Past", "kind": "chapter", "sequence": 9, "number": 8, "location": "lines 3741-4267", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-09/", "snippets": [ "... theater-director, a physician, a minister, a lawyer are placed in administrative charge of a municipality — all good men and true, but none of them by i)rofessional experience qualified to the administration of the municipal corporation of to-day — or where a barber is placed in charge of the city water- works, a saloon-keeper in the administration of tlie public works, no matter how cai)al)le, honest, and intelh'gent the men may be, the failure of any p ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-13", "section_label": "Chapter 12: Evolution: Political Government", "section_title": "Evolution: Political Government", "kind": "chapter", "sequence": 13, "number": 12, "location": "lines 5328-5797", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-13/", "snippets": [ "... been an established fact, has been the operating principle within all the more pro- gressive large industrial corporations, and all that is necessary is to extend methods of eco- nomic eflScicncy from the individual industrial corporation to the national organism as a whole. Thus there will be competition between water transportation and railway transportation, to decide which in each individual instance is more economical, considering quality of the trans- p ..." ] } ] }, { "id": "magnetic-permeability", "label": "Magnetic Permeability", "aliases": [ "Magnetic permeability", "magnetic permeability", "permeability" ], "total_occurrences": 120, "matching_section_count": 40, "matching_source_count": 12, "source_totals": [ { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 34, "section_count": 9 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 13, "section_count": 4 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 13, "section_count": 4 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 11, "section_count": 5 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 10, "section_count": 4 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 10, "section_count": 5 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 8, "section_count": 3 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 7, "section_count": 1 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 7, "section_count": 2 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 4, "section_count": 1 }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 2, "section_count": 1 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-46", "section_label": "Chapter 6: Alternating Magnetic Flux Distribution", "section_title": "Alternating Magnetic Flux Distribution", "kind": "chapter", "sequence": 46, "number": 6, "location": "lines 23948-24980", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-46/", "snippets": [ "CHAPTER VI. ALTERNATING MAGNETIC FLUX DISTRIBUTION. 48. As carrier of magnetic flux iron is used, as far as possible, since it has the highest permeability or magnetic conductivity. If the magnetic flux is alternating or otherwise changing rapidly, an e.m.f. is generated by the change of magnetic flux in the iron, and to avoid energy losses and demagnetization by the currents produced by these e.m.fs. the ir ...", "... nges of m.m.f. are built of thin wires or thin iron sheets, that is, are laminated. Since the generated e.m.fs. are proportional to the frequency of the alternating magnetism, the laminations must be finer the higher the frequency. To fully utilize the magnetic permeability of the iron, it there- fore has to be laminated so as to give, at the impressed frequency, practically uniform magnetic induction throughout its section, that is, negligible secondary currents. This, however, is no longer the case, even with the thinnest ...", "... decreases rapidly, and lags in phase, with increasing depth below the surface of the lamination, so that ultimately hardly any magnetic flux exists in the inside of the laminations, but practically only a surface layer carries magnetic flux. The apparent permeability of the iron thus decreases at very high frequency, and this has led to the opinion that at very high fre- quencies iron cannot follow a magnetic cycle. There is, however, no evidence of such a \" viscous hysteresis,\" but it is probable that iron follows ma ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... sen: 16 -1^ ^^ . ■ ■ — io- — 8- / / o c L/ ■ i2 / / o / X ^ } i \\ 1 0 1 2 1 t 1 5 1 i 2 »- i 1 i 28 3Q Fig. 51. Magnetization Curve. Example i. Determine that magnetic density (B, at which tlie permeability /it of a sample of iron is a maximum. The relation between magnetic field intensity 5C, magnetic density (35 and permeability jk cannot be expressed in a mathematical equation, and is therefore usually given in the form of an 1400 1200 ^ , -■ b. ...", "... 1 5 1 i 2 »- i 1 i 28 3Q Fig. 51. Magnetization Curve. Example i. Determine that magnetic density (B, at which tlie permeability /it of a sample of iron is a maximum. The relation between magnetic field intensity 5C, magnetic density (35 and permeability jk cannot be expressed in a mathematical equation, and is therefore usually given in the form of an 1400 1200 ^ , -■ b. ■V -\"ml ^ N \\ -800- -600- ^ X ■ s \\, / / \\ \\, / \\ £B ■ I \\ \\ i 1 > ( 5 i i ...", "... uation, and is therefore usually given in the form of an 1400 1200 ^ , -■ b. ■V -\"ml ^ N \\ -800- -600- ^ X ■ s \\, / / \\ \\, / \\ £B ■ I \\ \\ i 1 > ( 5 i i • ) 1 D 1 I 'Vt ^ 4 1 5 Fig. 52. Permeability Curve. empirical curve, relating (B and JC, as shown in Fig. 51. From this curve, corresponding values of (B and 3C are taken, and their ratio, that is, the permeability /^ =— , plotted against (B as abscissa. This is done in Fig. 52. Fig. 52 then show ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-01", "section_label": "Theory Section 1: Magnetism and Electric Current", "section_title": "Magnetism and Electric Current", "kind": "theory-section", "sequence": 1, "number": 1, "location": "lines 477-909", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-01/", "snippets": [ "... ghtly less in diamagnetic materials.) The ratio of the number of lines of force in a medium, to the number of lines of force which the same magnetizing force would produce in air (or rather in a vacuum), is called the permeability or magnetic conductivity /* of the medium. The number of lines of force per square centimeter in a mag- netic medium is called the magnetic induction B. The number of lines of force produced by the same magnetizing force ...", "... induction B and field intensity H are equal. As a r-ule, the magnetizing force in a magnetic circuit is changed by the introduction of the magnetic material, due to the change of distribution of the magnetic flux. The permeability of air = 1 and is constant. 6 ELEMENTS OF ELECTRICAL ENGINEERING . The permeability of iron and other magnetic materials varies with the magnetizing force between a little above 1 and values beyond 10,000 in soft ...", "... tic circuit is changed by the introduction of the magnetic material, due to the change of distribution of the magnetic flux. The permeability of air = 1 and is constant. 6 ELEMENTS OF ELECTRICAL ENGINEERING . The permeability of iron and other magnetic materials varies with the magnetizing force between a little above 1 and values beyond 10,000 in soft iron. The magnetizing force / in a medium of permeability /* pro- duces the field intensity ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-12", "section_label": "Chapter 12: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 10718-13483", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-12/", "snippets": [ "... ariable. In an ironclad electric circuit — that is, a circuit whose mag- netic field exists entirely within iron, such as the magnetic cir- cuit of a well-designed alternating-current transformer — (R is the reluctance of the iron circuit. Hence, if /* = permeability since Fk and and ^= $ F IF ^ ^ IH ^ m.m.f., $ = A(B = fiAH =^ magnetic flux, 10 Z . (R = 4:Tr/JiA substituting this value in the equation of the admittance, (R 10^ 130 ALTERNATING-CURRENT PHENOMENA we have . y'SwVfjiAf-fu.' ...", "... of the admittance, (R 10^ 130 ALTERNATING-CURRENT PHENOMENA we have . y'SwVfjiAf-fu.' where c = 110' 127 ZIO^ 8 x^n^A w^A Therefore, in an ironclad circuit, the absolute admittance, y, is inversely proportional to the frequency, f, to the permeability, n, to the cross-section. A, and to the square of the number of turns, n; and directly proportional to the length of the magnetic circuit, I. The conductance is _ K . 9 ~ fO.GJPO.i' and the admittance, fO.6^0 c hence, the angle of hystereti ...", "... we have 4/X77 sin oc = ^> which is independent of frequency, number of turns, and shape and size of the magnetic and electric circuit. Therefore, in an ironclad inductance, the angle of hysteretic ad- vance, a, depends upon the ynagnetic constants, permeability and coefficient of hysteresis, and upon the maximum magnetic induction, but is entirely independent of the frequency, of the shape and other conditions of the magnetic and electric circuit; and, therefore, all ironclad magnetic circuits constructed of the ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-05", "section_label": "Chapter 5: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 5, "number": 5, "location": "lines 9062-11050", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-05/", "snippets": [ "CHAPTER V MAGNETISM Magnetic Constants 47. With the exception of a few ferromagnetic substances, the magnetic permeability of all materials, conductors and dielectrics, gases, liquids and solids, is practically unity for all industrial purposes. Even liquid oxygen, which has the highest permea- bility, differs only by a fraction of a per cent, from non-magnetic materials. T ...", "... materials, conductors and dielectrics, gases, liquids and solids, is practically unity for all industrial purposes. Even liquid oxygen, which has the highest permea- bility, differs only by a fraction of a per cent, from non-magnetic materials. Thus the permeability of neodymium, which is one of the most paramagnetic metals, is /x = 1.003; the permeability of bismuth, which is very strongly diamagnetic, is /* = 1 — 0.00017 = 0.99983. The magnetic elements are iron, cobalt, nickel, manganese and chromium. It is intere ...", "... ll industrial purposes. Even liquid oxygen, which has the highest permea- bility, differs only by a fraction of a per cent, from non-magnetic materials. Thus the permeability of neodymium, which is one of the most paramagnetic metals, is /x = 1.003; the permeability of bismuth, which is very strongly diamagnetic, is /* = 1 — 0.00017 = 0.99983. The magnetic elements are iron, cobalt, nickel, manganese and chromium. It is interesting to note that they are in atomic weight adjoining each other, in the latter part of the ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-47", "section_label": "Chapter 7: Distribution Of Alternating-Current Density In Conductor", "section_title": "Distribution Of Alternating-Current Density In Conductor", "kind": "chapter", "sequence": 47, "number": 7, "location": "lines 24981-26094", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-47/", "snippets": [ "... t fully utilized, but the material in the interior of the conductor is more or less wasted. It is of importance, therefore, in alternating- current circuits, especially in dealing with very large currents, or with high frequency, or materials of very high permeability, as iron, to investigate this phenomenon. An approximate determination of this effect for the purpose of deciding whether the unequal current distribution is so small as to be negligible in its effect on the resistance of the conductor, 369 370 TRAN ...", "... , 40 per cent space between the strands, the mean conductivity is GO per cent of that of copper. If by the sub- division of an iron conductor into strands the reluctance of the magnetic circuit is increased tenfold, this represents a reduction of the mean permeability to one-tenth. Hence, if for the con- ductor material proper n = 1000, A = 105, and the conductor section is reduced by stranding to 60 per cent, the permeability to one-tenth, the mean values would be fjL0 = 100 and ^0 = 0.6 X 105, and the factor V7/T, ...", "... uctance of the magnetic circuit is increased tenfold, this represents a reduction of the mean permeability to one-tenth. Hence, if for the con- ductor material proper n = 1000, A = 105, and the conductor section is reduced by stranding to 60 per cent, the permeability to one-tenth, the mean values would be fjL0 = 100 and ^0 = 0.6 X 105, and the factor V7/T, in the equation of current distribution, is reduced from VT£ == 10,000 to VI^ = 2450, or to 24.5 per cent of its previous value. In this case, however, with iron ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-10", "section_label": "Chapter 10: F", "section_title": "F", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 8269-10499", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "snippets": [ "... , a circuit whose magnetic field exists entirely within iron, such as the mag- netic circuit of a well-designed alternating-current trans- J 82] EFFECTIVE RESISTANCE AND REACTANCE. 123 former, — (R is the reluctance of the iron circuit. Hence, if ;x = permeability, since — and $F^ = Z-F= :?^Z3C = M.M.F., * = 5CB = /A 5 JC = magnetic flux, and (R = ; ; 4 TT/XO substituting this value in the equation of the admittance, (R10« , Z10» z y = ;^ TTr» ^^ have where z = 2 7r«W Stt^z/V-STV^ ^ft' Z10» 127Z10« ...", "... TING-CURRENT PHENOMENA. [ § 83- which is independent of frequency, number of turns, and shape and size of the magnetic and electric circuit. Therefore^ in an ironclad inductance^ the angle of hysteretic advance^ a, dcpetids upon the magnetic constants^ permeability and coefficient of hysteresis^ atid upon the maximmn magnetic induction^ but is entirely independent of t/te frequency y of the sliape and other conditiotis of the magnetic and electric circuit ; andy therefore y all ironclad magnetic circuits constructed ...", "... angle of hysteretic advaftce. The angle of hysteretic advance^ o, in a closed circuit transformer, depends upon the quality of the iron, and upon the magftctic density only. The sine of the angle of hysteretic advatue equals Jf times the product of the permeability and coefficient of hysteresis, divided by the .^'* power of the magnetic density. 83. If the magnetic circuit is not entirely ironclad, and the magnetic structure contains air-gaps, the total re- luctance is the sum of the iron reluctance and of the air ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "section_label": "Chapter 10: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "... at is, a circuit whose magnetic field exists entirely within iron, such as the mag- netic circuit of a well-designed alternating-current trans- EFFECTIVE RESISTANCE AND REACl^ANCE. 123 former, — (R is the reluctance of the iron circuit. Hence, if p. = permeability, since — and g:A = jr/7=Zge = M.M.F., and we have 5— ; where „ L W 127Z10' TJierefore, in an ironclad circuit, the absolute admi ...", "... TERN A TING-CURRENT PHENOMENA. which is independent of frequency, number of turns, and shape and size of the magnetic and electric circuit. Therefore, in an ironclad inductance, tJie angle of Jiysteretic advance, a, depends upon the magnetic constants, permeability and coefficient of hysteresis, and tipon the maximum magnetic induction, but is entirely independent of the frequency, of the shape and other conditions of the magnetic and electric circuit ; and, therefore, all ironclad 'magnetic circuits constructed of ...", "... le of Jiysteretic advance. The angle of Jiysteretic advance, a, in a closed circuit transformer, depends tipon tJie quality of the iron, and upon the magnetic density only. The sine of tJie angle of Jiysteretic advance equals 4 times the product of the permeability and coefficient of hysteresis, divided by the .4th power of tJie magnetic density. 83. If the magnetic circuit is not entirely ironclad, and the magnetic structure contains air-gaps, the total re- luctance is the sum of the iron reluctance and of the air ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-05", "section_label": "Lecture 5: Single-Energy Tra.Nsient Of Ironclad Circuit", "section_title": "Single-Energy Tra.Nsient Of Ironclad Circuit", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3387-3720", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-05/", "snippets": [ "... t thus is the simple exponential discussed before. If the magnetic circuit is closed entirely by iron, the magnetic flux is not proportional to the current, and the inductance thus not constant, but varies over the entire range of currents, following the permeability curve of the iron. Furthermore, the transient due to a decrease of the stored magnetic energy differs in shape and in value from that due to an increase of magnetic energy, since the rising and decreasing magnetization curves differ, as shown by the hyste ...", "... ted in the form given by Kennelly: p = ^ = « + p = - = a + crOC; (2) that is, the reluctivity is a linear function of the field intensity. It gives a fair approximation for higher magnetic densities. This formula is based on the fairly rational assumption that the permeability of the iron is proportional to its remaining magnetiza- bility. That is, the magnetic-flux density (B consists of a compo- nent 3C, the field intensity, which is the flux density in space, and a component (B' = (B — 3C, which is the additional flux density ...", "... uently called the \" metallic-flux density.\" With increasing 3C, (B' reaches a finite limiting value, which in iron is about &x' = 20,000 lines per cm2. * At any density (B', the remaining magnetizability then is (B^' — (B', and, assuming the (metallic) permeability as proportional hereto, gives and, substituting gives a, = cftco'rc^ * See \"On the Law of Hysteresis,\" Part II, A.I.E.E. Transactions, 1892, page 621. 54 ELECTRIC DISCHARGES, WAVES AND IMPULSES. or, substituting 1_ 1 *** / t*« ,—fc / (/ • ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... n neglecting the energy losses in and by the con- ductor: S = -L= , (5) VLC where L is the inductance, C the capacity of the conductor per unit length (the length measured in the same measure as the speed S). The inductance L is proportional to the permeability /*, and the capacity C proportional to the dielectric constant, or specific capacity K of the medium surrounding the conductor, that is, the medium through which the electric wave propagates; that is, A V p* where A is a proportionality constant. Th ...", "... empty space, fj. = 1 and « = 1; hence, (8) where Sl is the speed of propagation in the medium of constants /^ and jcr Comparing equation (8) with (4) it follows : Vl = d*-, (9) that is, the square of the refractive index d equals the product of permeability JJL and dielectric constant K. Since for most media the permeability /JL = 1, for all except e maneti mri the magnetic materials RELATION OF BODIES TO RADIATION. 25 This relation between the constant of the electric circuit K and the constant ...", "... d of propagation in the medium of constants /^ and jcr Comparing equation (8) with (4) it follows : Vl = d*-, (9) that is, the square of the refractive index d equals the product of permeability JJL and dielectric constant K. Since for most media the permeability /JL = 1, for all except e maneti mri the magnetic materials RELATION OF BODIES TO RADIATION. 25 This relation between the constant of the electric circuit K and the constant of optics d was one of the first evidences of the identity of the mec ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-19", "section_label": "Theory Section 19: Fields of Force", "section_title": "Fields of Force", "kind": "theory-section", "sequence": 19, "number": 19, "location": "lines 7737-7990", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-19/", "snippets": [ "... ace also, and this space is not neutral and inert any more, but if we try to move a solid mass of metal rapidly through it, the motion is resisted, and heat produced in the metal by induced currents. Materials of high permeability, as iron filings, brought into this space arrange themselves in chains; a magnetic needle is moved and places itself in a definite direction. Due to the passage of the current in the conductor, there are therefore in the ...", "... 10,292). 91. In electrical engineering we have to deal with the electrical quantities: voltage, current, resistance, etc.; the magnetic quan- 116 ELEMENTS OF ELECTRICAL ENGINEERING titles: magnetic flux, field intensity, permeability, etc.; and the di- electric quantities: dielectric flux, field intensity, permittivity, etc. The electric current is the magnetomotive force F which produces the magnetic field, acting upon space. It is expressed in amperes, o ...", "... s determined by the unit of electric current; hence the factor 4 IT. The factor 10\"1 merely reduces from amperes to absolute unit. If then v is the magnetic conductivity of the material in the magnetic field, called its permeability, B = pH is the magnetic flux density, and the total magnetic flux <1> is given by the density B times the area or section of the flux. Or, passing directly from the magnetomotive force F to the F magnetic flux, by ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-23", "section_label": "Chapter 1: The Constants Of The Electric Circuit", "section_title": "The Constants Of The Electric Circuit", "kind": "chapter", "sequence": 23, "number": 1, "location": "lines 1317-1992", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "snippets": [ "... to the section and inversely proportional to the length of the magnetic circuit surrounding the conductor, and so can be represented by L = ^ (18) where /* is a constant of the material filling the space surround- ing the conductor, which is called the magnetic permeability. As in general neither section nor length is constant in differ- ent parts of the magnetic circuit surrounding an electric con- 10 TRANSIENT PHENOMENA ductor, the magnetic circuit has as a rule to be calculated piecemeal, or by integration over the s ...", "... ection nor length is constant in differ- ent parts of the magnetic circuit surrounding an electric con- 10 TRANSIENT PHENOMENA ductor, the magnetic circuit has as a rule to be calculated piecemeal, or by integration over the space occupied by it. The permeability, /*, is constant and equals unity or very closely fj. = 1 for all substances, with the exception of a few materials which are called the magnetic materials, as iron, cobalt, nickel, etc., in which it is very much higher, reaching sometimes and under certa ...", "... e exception of a few materials which are called the magnetic materials, as iron, cobalt, nickel, etc., in which it is very much higher, reaching sometimes and under certain conditions in iron values as high as fjL = 6000. In these magnetic materials the permeability /* is not con- stant but varies with the magnetic flux density, or number of lines of magnetic force per unit section, (B, decreasing rapidly for high values of (B. In such materials the use of the term /* is therefore incon- venient, and the inductance ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 883-1530", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "snippets": [ "... ampere turns per cm. in empty space. The magnetic density, in lines of magnetic force per cm2, pro- duced by the field intensity 3C in any material is & = /z3C, (15) where ju is a constant of the material, a \" magnetic conductivity,\" and is called the permeability. ^ = 1 or very nearly so for most materials, with the exception of very few, the so-called magnetic materials: iron, cobalt, nickel, oxygen, and some alloys and oxides of iron, manganese, and chromium. If then A is the section of the magnetic circuit, th ...", "... r/10-1 lines of magnetic force per cm2. Dielectric-field intensity: K = - — - lines of dielectric force 4 Try2 per cm2. Magnetic density: (B = M5C lines of magnetic force per cm2. Dielectric density: D = nK lines of dielectric force per cm2. Permeability: /* Permittivity or specific capacity: K Magnetic flux: $ = A($> lines of magnetic force. Dielectric flux: ^ = AD lines of dielectric force. v = 3 X 10 10 = velocity of light. The powers of 10, which appear in some expressions, are reduc- tion fa ...", "... -j = yG am- A. perespercm2. Magnetizing force: Dielectric gradient: Electric gradient: F / = j ampere turns per G = j volts per cm. G =j volts per cm. cm. Magnetic-field intensity: Dielectric-field inten- sity: OC = AT/. j^ \"\" . Permeability: Permittivity or specific Conductivity: capacity: *-|- K_D y = ~ mho — cm. Cr Reluctivity: (Elastivity ?): Resistivity: p = & 1 . K* 1 G , p = - = -?ohm — cm. y I Specific magnetic energy: Specific dielectric energy: Specific ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-03", "section_label": "Chapter 3: Magnetism", "section_title": "Magnetism", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 5445-6941", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-03/", "snippets": [ "... ides, \"leaks\" or \"strays.\" (c) In the electric circuit, current and e.m.f . are proportional, in most cases; that is, the resistance is constant, and the circuit therefore can be calculated theoretically. In the magnetic circuit, in the materials of high permeability, which are the most important carriers of the magoietic flux, the relation between flux, m.m.f. and energy is merely empirical, the \"reluctance\" or mag- netic resistance is not constant, but varies with the flux density, the previous history, etc. In the ...", "... . = 1 (2) and rearranging, where The frequency at the wave length lWo is zer ...", "... s unit length, r = 0.41 ohm per mile. The inductance of a conductor is given by = I (2 loge lf 10~9, in henrys, (131) where I = the length of conductor, in cm.; lr = the radius of conductor; ld = the distance from return conductor, and /* = the permeability of conductor material. For copper, fi = 1. As one mile equals 1.61 X 105 cm., substituting this, and reducing the natural logarithm to the common logarithm, by the factor 2.3026, gives L = f 0.7415 log ^ + 0.0805\\ in mh. per mile. (132) , For lr = 0.1 ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "... t =F ^i) instead of t into the equations (11), where ^i is the time of propagation over the distance I. li V = velocity of propagation of the electric field, which in air, as with a transmission line, is approximately V = 3X W, (12) and in a medium of permeability fx and permittivity (specific capacity) k is v= y=-y (13) and we denote then and if we denote a = -, (14) h = at', (15) 2 tt/^i = CO = 2 Trfal, (16) we get, substituting t T k for t and 0 =F co for (/> into the equation (11), the equatio ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "section_label": "Lecture 10: Continual And Cumulative Oscillations", "section_title": "Continual And Cumulative Oscillations", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... e capacities in complex systems of circuits from the inductances, or inversely, to determine the inductance of cables from the measured capacity, etc. More complete, this equation is CLi = '^, (40) v where k = specific capacity or permittivity, jjl = permeability of the medium. ROUND PARALLEL CONDUCTORS. 139 E. Conductor with ground return. 50. As seen in the preceding, in the electric field of conductor A and return conductor B, at distance s from each other, Fig. 9, the lines of magnetic force from conduct ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3956-4744", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "snippets": [ "... ti) instead of t into the equations (11), where t\\ is the time of propagation over the distance I. If v = velocity of propagation of the electric field, which in air, as with a transmission line, is approximately v = 3 X 1010, (12) and in a medium of permeability /z and permittivity (specific capacity) K is 3 X 1010 ( . v =5 - T=^> (13) VfUJ and we denote ;•; • .v •'.,. a-j, ffifil (14) then ti = al; (15) and if we denote co = 27rM (16) we get, substituting t =F t\\ for Z and 0 =F co for $ into t ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-10", "section_label": "Lecture 10: Inductance And Capacity Of Round Parallel Conductors", "section_title": "Inductance And Capacity Of Round Parallel Conductors", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6089-7274", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "snippets": [ "... lculate capacities in complex systems of circuits from the inductances, or inversely, to determine the inductance of cables from the measured capacity, etc. More complete, this equation is CLt = ^, (40) where K = specific capacity or permittivity, /* = permeability of the medium. 130 ELECTRIC DISCHARGES, WAVES AND IMPULSES. E. Conductor with ground return. 47. As seen in the preceding, in the electric field of conductor A and return conductor B, at distance s from each other, Fig. 9, the lines of magnetic forc ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-20", "section_label": "Theory Section 20: Nomenclature", "section_title": "Nomenclature", "kind": "theory-section", "sequence": 20, "number": 20, "location": "lines 7991-8291", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-20/", "snippets": [ "... agnetic flux Mho-centimeter Line; kiloline; megaline Electrical Magnetic £....... H Magnetic density Magnetic field inten- Lines per cm.2; kilo- lines per cm.2 Lines per cm 2 Magnetic Magnetic /* • • sity Permeability (magnetic Magnetic / conductivity) Magnetic gradient Ampere-turns per centi- Electrical F Magnetizing force Magnetomotive force meter. Ampere-turns Electrical R Reluctance (magnetic Electrical L M S .. . ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-33", "section_label": "Apparatus Section 12: Synchronous Machines: Starting of Synchronous Motors", "section_title": "Synchronous Machines: Starting of Synchronous Motors", "kind": "apparatus-section", "sequence": 33, "number": 12, "location": "lines 9749-9820", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-33/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-33/", "snippets": [ "... revolve in the opposite direction B). Lamination of the field poles reduces the starting torque caused by eddy currents in the field poles, but increases that caused by remanent magnetism or hysteresis, due to the higher permeability of the field poles. Thus the torque per volt-ampere input is approximately the same in either case, but with laminated i FIG. 72. — Magnetic circuit of a polyphase synchronous motor. poles the impressed voltage required ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-13", "section_label": "Chapter 13: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 13484-14333", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-13/", "snippets": [ "... e resistance. We thus see that un- equal current distribution is usually negligible in practice. The above calculation was made under the assumption that the conductor consists of unmagnetic material. If this is not the case, but the conductor of iron of permeability Ai, then d^ = — ^ ; and thus ultimately, k = \\/2 tr'^ftxR'^ 10~^, and k /^- JixRnO-' n^u V ■ . r • • . — = v2 TT- . thus, tor instance, tor iron wire at p = P P 10 X 10~^, fjL — 500, it is, permitting 5 per cent, difference be- tween center and out ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-25", "section_label": "Chapter 25: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 29375-32539", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-25/", "snippets": [ "... and synchronous motion. Since in an iron-clad magnetic circuit the magnetism is not propor- tional to the m.m.f., the wave of magnetism and thus the wave of e.m.f. will differ from the wave of current. As far as this distortion is due to the variation of permeability, the distortion is symmetrical and the wave of generated e.m.f. represents no power. The distortion caused by hysteresis, or the lag of the magnetism behind the m.m.f., causes an unsymmetrical distor- tion of the wave which makes the wave of generated e.m ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-35", "section_label": "Chapter 35: Balanced Symmetrical Polyphase Systems", "section_title": "Balanced Symmetrical Polyphase Systems", "kind": "chapter", "sequence": 35, "number": 35, "location": "lines 37453-37957", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-35/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-35/", "snippets": [ "... = 26 + 44johms. Choosing the voltage at the receiving end as zero vector, e = 46,100 volts, at 90 per cent, power-factor and therefore 43.6 per cent, induc- tance factor, the current is represented by 7 = 80 (0.9 - 0.436 j) =72-35 j. ^ Or. ii fi = permeability, k = dielectric constant of the medium sur- rounding the conductor, it is hence, V [^ I = \\W or. C = (4) 452 ALTERNATING-CURRENT PHENOMENA This gives: Voltage at receiver circuit, e = 46,100 volts; current in receiver circuit, Z = 72 — ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-21", "section_label": "Chapter 21: Dibtobtiox Of Wavs-Shafe And Its Causes", "section_title": "Dibtobtiox Of Wavs-Shafe And Its Causes", "kind": "chapter", "sequence": 21, "number": 21, "location": "lines 23274-24559", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-21/", "snippets": [ "... and synchronous motion. Since in an ironclad magnetic circuit the magnetism is not proportional to the M.M.F., the wave of magnetism and thus the wave of E.M.F. will differ from the wave of cur- rent. As far as this distortion is due to the variation of permeability, the distortion is symmetrical and the wave of induced E.M.F. represents no power. The distortion caused by hysteresis, or the lag of the magnetism behind the M.M.F., causes an unsymmetrical distortion of the wave which makes the wave of induced E.M.F. di ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "section_label": "Chapter 11: Foucault Or Eddy Currents", "section_title": "Foucault Or Eddy Currents", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "... resistance. We thus see that unequal current distribution is usually negligible in practice. The above calculation was made under the assumption that the conductor consists of unmagnetic material. If this is not the case, but the con- ductor of iron of permeability p., then ; d$ = pffx / (&x and thus ultimately ; k = V2 wW/^10 ~\" and ; k / P = V2 ** NpR* 10— '//»• Thus, for instance, for iron wire at /> = 10xlO-6, ft = 500 it is, permitting 5% difference between center and outside of wire; k = 3.2 X 10 ~6 and NR* = ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-22", "section_label": "Chapter 22: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 22, "number": 22, "location": "lines 21190-21982", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-22/", "snippets": [ "... and synchronous motion. Since in an ironclad magnetic circuit the magnetism is not proportional to the M.M.F., the wave of magnetism and thus the wave of E.M.F. will differ from the wave of cur- rent. As far as this distortion is due to the variation of permeability, the distortion is symmetrical and the wave of induced E.M.F. 'represents no power. The distortion caused by hysteresis, or the lag of the magnetism behind the M.M.F., causes an unsymmetrical distortion of the wave which makes the wave of induced E.M.F. d ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-20", "section_label": "Chapter 22: Unipolar Machines", "section_title": "Unipolar Machines", "kind": "chapter", "sequence": 20, "number": 22, "location": "lines 31716-32137", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-20/", "snippets": [ "... conductor, and 2500 amp. per square inch, this gives 100,000 ampere- turns m.m.f. of armature reaction, which probablyis sufficient to magnetic- ally saturate the iron in the pole faces, in the direction of the arrow in Fig. 224. At the greatly lowered permeability at saturation, with constant field excita- tion the voltage of the machine greatly drops, or, to maintain constant voltage, f,0 220. — Multi-con- a considerable increase of field excita- ductor unipolar machine .... -it wit\" compensating pole turn unde ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-08", "section_label": "Chapter 8: Shaping Of Waves By Magnetic Saturation", "section_title": "Shaping Of Waves By Magnetic Saturation", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 12962-16963", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-08/", "snippets": [ "... tion, or constant, since it depends on the rate of change of magnetism with current near the zero value, where there is no saturation, and dH the ratio -tj thus (approximately) constant. Or, in other words, if below saturation, in the range where the magnetic permeability is a maximum, the current, f, produces the magnetic flux, $, and thereby induces the voltage, e', the reactance is x' = i (14) This is the maximum reactance, below saturation, of the mag- netic circuit, and can be calculated from the dimensions and the ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-10", "section_label": "Chapter 6: Alternating Magnetic Flux Distribution. 355", "section_title": "Alternating Magnetic Flux Distribution. 355", "kind": "chapter", "sequence": 10, "number": 6, "location": "lines 904-937", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-10/", "snippets": [ "... n. 361 54. Numerical example, with frequencies of 60, 1000 and 10,000 cycles per second. 362 55. Depth of penetration of alternating magnetic flux in different metals. 363 56. Wave length, attenuation, and velocity of penetration. 365 57. Apparent permeability, as function of frequency, and damping. 366 58. Numerical example and discussion. 367" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-41", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 41, "number": 1, "location": "lines 19260-19338", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "snippets": [ "... nd the increase of effective resistance and decrease of effective inductance resulting therefrom. (c) The distribution of alternating magnetic flux in solid iron, or the screening effect of eddy currents produced in the iron, and the apparent decrease of permeability and increase of power consumption resulting therefrom. (d) The distribution of the electric field of a conductor through space, resulting from the finite velocity of propagation of the electric field, and the variation of self-inductance and mutual indu ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-50", "section_label": "Chapter 1: General Equations", "section_title": "General Equations", "kind": "chapter", "sequence": 50, "number": 1, "location": "lines 27761-28694", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "snippets": [ "... he speed — *., or, in other words, (15) is the speed of propagation of the electric phenomenon in the cir- cuit. (If no energy losses occur, r = 0, g = 0, in a straight con- ductor in a medium of unit magnetic and dielectric constant, that is, unit permeability and unit inductive capacity, S is the velocity of light.) 4. Since (11) is a quadratic equation, several pairs or corre- sponding values of a and b exist, which, in the most general case, are complex imaginary. The terms with conjugate complex imaginary ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... nating current in conductor 376, 378 magnetic flux in iron 361, 363, 365 Period of recurrence 218 wave . . 433 568 INDEX PAGE Periodic transient terms 22, 218 Permanent term of alternating-current circuit 91 values of electric quantities 16 Permeability 9 apparent,, of iron for alternating currents 355, 367 Phase difference in transmission line 296 of wave and transient term 45, 91 Physical meaning of transient term 103 Polyphase alternator short circuit 202, 204 m.m.f ., resultant 192 rectific ..." ] } ] }, { "id": "resonance", "label": "Resonance", "aliases": [ "resonance", "resonant" ], "total_occurrences": 120, "matching_section_count": 52, "matching_source_count": 12, "source_totals": [ { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 21, "section_count": 11 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 20, "section_count": 6 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 19, "section_count": 10 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 15, "section_count": 4 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 13, "section_count": 7 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 8, "section_count": 1 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 8, "section_count": 3 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 7, "section_count": 3 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 3, "section_count": 2 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 3, "section_count": 2 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 2, "section_count": 2 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-04", "section_label": "Lecture 4: Chemical And Physical Effects Of Radiation", "section_title": "Chemical And Physical Effects Of Radiation", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3639-3945", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-04/", "snippets": [ "... heat when it ceases to be radiation. Thus all radiations are chemical rays, that is, produce chemical action, if they strike a body which is responsive to them. The chemical action of radiation is specific to its frequency and seems to be some kind of a resonance effect. We may picture to ourselves that the frequency of vibration of a silver atom is that of violet or ultra-violet light, and therefore, when struck by a wave of this frequency, is set in vibration by resonance, just as a tuning fork is set in vibrati ...", "... frequency and seems to be some kind of a resonance effect. We may picture to ourselves that the frequency of vibration of a silver atom is that of violet or ultra-violet light, and therefore, when struck by a wave of this frequency, is set in vibration by resonance, just as a tuning fork is set in vibration by a sound wave of the frequency with which it can vibrate, and if the vibration of the silver atom, in response to the frequency of radiation, becomes sufficiently intense, it breaks away from the atom with whic ...", "... breaks away from the atom with which it is chemically 64 RADIATION, LIGHT, AND ILLUMINATION. combined in the compound, the silver bromide, etc., and this compound thus splits up, dissociates. The phenomenon, how- ever, must be more complex, as a simple resonance vibration would be especially pronounced at one definite frequency, the frequency of complete resonance, and rapidly decrease for higher and for lower frequencies. The chemical action of radiation on silver compounds, however, does not show such a respons ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-06", "section_label": "Lecture 6: Higher Harmonics Of The Generator Wave", "section_title": "Higher Harmonics Of The Generator Wave", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3133-3507", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-06/", "snippets": [ "SIXTH LECTURE HIGHER HARMONICS OF THE GENERATOR WAVE mHE open circuit reactance of the transformer is the only reactance high enough to give resonance with the line capacity at fundamental frequency. All other reactances are too low for this. Since, however, the inductive reactance increases and the capacity reactance decreases proportionally to the frequency, the two reactances come nearer together fo ...", "... reases and the capacity reactance decreases proportionally to the frequency, the two reactances come nearer together for higher frequency; that is, for the higher harmonics of the generator wave, and for some of the higher harmonics of the generator wave resonance rise of voltage so may occur between the line capacity and the circuit inductance. The origin and existence of higher harmonics therefore bears investigation in transformers, transmlission lines and cable systems. ORIGIN OF HIGHER HARMONICS Higher ha ...", "... t is, the e. m. f. wave is very low for a large part of the cycle and then rises to a very high peak, as shown by Fig. 23 ; and the maximum e. m. f . may exceed that of a sine wave by 50% and more, thus giving high insulation stress and the possibility of resonance voltages. EFFECTS OF HIGHER HARMONICS In a three-phase system the three phases are 120° apart, and their third harmonics are 3 x 120° = 360° apart, that is, in phase with each, and for the third harmonic the three-phase system therefore is a single-pha ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... convert their energy into other forms of energy, if the energy is only great enough, we get a high temperature, and thus a high chemical action, merely by the effect of temperature. But we may also get a chemical effect by what probably is some kind of a resonance phenomenon. The particles of a body, atoms or molecules, must have some rate of vibration of their own. If, then, a ray of radiation impinges upon them which is of a frequency of the same magnitude as the inherent rate of vibration of the atom, by resonan ...", "... sonance phenomenon. The particles of a body, atoms or molecules, must have some rate of vibration of their own. If, then, a ray of radiation impinges upon them which is of a frequency of the same magnitude as the inherent rate of vibration of the atom, by resonance this vibration of the atom must rapidly increase in intensity until the atom breaks away from the others, or the molecule breaks up, that is, the chemical combination is split up. The inherent frequency of oscillation of the atom seems to be of about of ...", "... f we assume that the mass of the silver atom is such as to give a rate of vibration in the range of the violet and ultraviolet, it is easy to understand that radiation of this frequency splits up the silver salt by increasing the vibration of the atom by resonance, and that shorter or longer waves have no effect, or much less effect. So it may be a mere incident that those chemical compounds on which we observe the chemical action of radiation just happen to be sensitive to the violet end of the spectrum. It is ind ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-26", "section_label": "Chapter 26: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 26, "number": 26, "location": "lines 32540-33010", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-26/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-26/", "snippets": [ "... rrent and of potential EFFECTS OF HIGHER HARMONICS 373 difference in the non-inductive part of the circuit more pro- nounced— intensifies the harmonics. Self-induction and capacity in series may cause an increase of voltage due to complete or partial resonance with higher har- monics, and a discrepancy between volt-amperes and watts, without corresponding phase displacement, as will be shown hereafter. 253. In long-distance transmission over lines of noticeable inductive and condensive reactance, rise of volt ...", "... ng-distance transmission over lines of noticeable inductive and condensive reactance, rise of voltage due to reso- nance may occur with higher harmonics, as waves of higher fre- quency, while the fundamental wave is usually of too low a frequency to cause resonance. An approximate estimate of the possible rise by resonance with various harmonics can be obtained by the investigation of a numerical example. Let in a long-distance line, fed by step-up transformers at 60 cycles. The resistance drop in the transformei ...", "... and condensive reactance, rise of voltage due to reso- nance may occur with higher harmonics, as waves of higher fre- quency, while the fundamental wave is usually of too low a frequency to cause resonance. An approximate estimate of the possible rise by resonance with various harmonics can be obtained by the investigation of a numerical example. Let in a long-distance line, fed by step-up transformers at 60 cycles. The resistance drop in the transformei'S at full-load = 1 per cent. The reactance voltage in the t ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-14", "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "section_title": "Constant-Potential Constant-Current Trans Formation", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "... 268 ELECTRIC CIRCUITS That is, if in a constant-potential circuit, of impressed e.m.f ., 60, an inductive reactance, Xo, and a condensive reactance, Xe, are connected in series with each other, and if Xe = Xo, (35) that is, the two reactances are in resonance condition with each other, any circuit shunting the capacity reactance is a constant- current circuit, and regardless of the impedance of this circuit, Z = r + jXf the current in the circuit is t = — . Xo 133. Such a combination of two equal reactanc ...", "... the more the higher the inductive reactance of the receiving circuit, and the constant secondary current, i, is 90° ahead of the constant primary e.m.f., €o. In general, it follows that, if equal inductive and condensive reactances, Xo = Xc, that is, in resonance conditions, are con- nected in series across a constant-potential circuit of impressed r=2»a -vC^: B IV e.m.f., eo, any circuit connected to the common point between the reactances is a constant-current circuit, and carries the current, i = — ...", "... c square will be more fully discussed. Fig. 119. A. T-Connection or Resonating Circuit 136. General. — A combination, in a constant-potential circuit, of an inductive and a condensive reactance in series with each 262 ELECTRIC CIRCUITS other in resonance condition, that is, with the condensive react- ance equal to the inductive reactance, gives constant current in a circuit shunting the capacity. This circuit thus can be called the \"secondary circuit'* of the constant potential constant- current transform ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... hen once started, even with zero impressed e.m.f., such alternating currents traverse the lines for some time, gradually decreasing in intensity by the energy consumption in the conductor, and so fading out. The condition of this phenomenon of electrical resonance thus is that alternating impulses occur at time intervals equal to the time required for the impulse to travel the length of the line and back; that is, the time of one half wave of impressed e.m.f. is the time required by light to travel twice the length ...", "... quired by light to travel twice the length of the line, or the time of one complete period is the time light requires to travel four times the length of the line; in other words, the number of periods, or frequency of the impressed alternating e.m.fs., in resonance condition, is the velocity of light divided by four times the length of the line; or, in free oscillation or resonance condition, the length of the line is one quarter wave length. 279 280 TRANSIENT PHENOMENA If then I = length of line, S = speed of ...", "... o travel four times the length of the line; in other words, the number of periods, or frequency of the impressed alternating e.m.fs., in resonance condition, is the velocity of light divided by four times the length of the line; or, in free oscillation or resonance condition, the length of the line is one quarter wave length. 279 280 TRANSIENT PHENOMENA If then I = length of line, S = speed of light, the frequency of oscillations or natural period of the line is — '• \"4? or, with I given in miles, hence S ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-22", "section_label": "Chapter 20: Ri", "section_title": "Ri", "kind": "chapter", "sequence": 22, "number": 20, "location": "lines 24560-25119", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-22/", "snippets": [ "... makes the higher harmonics of current and of poten- tial difference in the non-inductive part of the circuit more pronounced — intensifies the harmonics. Self-induction and capacity in series may cause an in- crease of voltage due to complete or partial resonance. 225. In long-distance transmission over lines of notice- able inductance and capacity, rise of voltage due to reso- nance may under circumstances be expected with higher harmonics, as waves of higher frequency, while the funda- mental wave is usually o ...", "... ission over lines of notice- able inductance and capacity, rise of voltage due to reso- nance may under circumstances be expected with higher harmonics, as waves of higher frequency, while the funda- mental wave is usually of too low a frequency to cause resonance. An approximate estimate of the possible rise by reso- nance with various harmonics can be obtained by the inves- tigation of a numerical instance. Let in a long-distance line, fed by step-up transformers : The resistance drop in the transformers at fu ...", "... by 276 per cent, the septuple harmonic by 118 per cent, while the still higher harmonics are reduced. The maximum possible rise will take place for : '^^ =0, or, k = 5.77. That is, at a frequency : N = 346. and is : a = 14.4. That is, complete resonance will appear at a frequency between quintuple and septuple harmonic, and would raise the voltage at this particular frequency 14.4 fold. If the voltage shall not exceed the impressed voltage by more than 100 per cent, even at coincidence of the maximum o ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-23", "section_label": "Chapter 23: Effects Of Higher Harmonics", "section_title": "Effects Of Higher Harmonics", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 21983-22448", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-23/", "snippets": [ "... makes the higher harmonics of current and of poten- tial difference in the non-inductive part of the circuit more pronounced — intensifies the harmonics. Self-induction and capacity in series may cause an in- crease of voltage due to complete or partial resonance with higher harmonics, and a discrepancy between volt-amperes and watts, without corresponding phase displacement, as will be shown hereafter. 246. In long-distance transmission over lines of notice- able inductance and capacity, rise of voltage due to ...", "... 246. In long-distance transmission over lines of notice- able inductance and capacity, rise of voltage due to reso- nance may occur with higher harmonics, as waves of higher frequency, while the fundamental wave is usually of too low a frequency to cause resonance. An approximate estimate of the possible rise by reso- nance with various harmonics can be obtained by the inves- tigation of a numerical instance. Let in a long-distance line, fed by step-up transformers at 60 cycles, The resistance drop in the transf ...", "... harmonic by 276 per cent, the septuple harmonic by 118 per cent, while the still higher harmonics are reduced. The maximum possible rise will take place for : = 0, or, 2,- 1 = 5.77 That is, at a frequency : N = 346, and a = 14.4. That is, complete resonance will appear at a frequency between quintuple and septuple harmonic, and would raise the voltage at this particular frequency 14.4 fold. If the voltage shall not exceed the impressed voltage by more than 100 per cent, even at coincidence of the maximum o ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-10", "section_label": "Chapter 10: Instability Of Circuits : The Arc", "section_title": "Instability Of Circuits : The Arc", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 17632-21381", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-10/", "snippets": [ "... ry simultaneously or in phase, current and voltage in the condenser branch circuit also must be in phase with each other, that is, the Fig. 87. frequency of the oscillation in Fig. 87 is that at which capacity, C, and inductance, L, balance, or is the resonance frequency. If circuit. A, in Fig. 87 is an arc circuit, and the resistance, r, in the shunt circuit small, instability again results, in the same man- ner as discussed before. 93. Another way of looking at the phenomena resulting from a condenser, C, s ...", "... Ci = Co — e, thus is in phase with the alternating current, ii, that is, capacity, C, and inductance, L, neutralize. Thus, the only pulsation of current and voltage, which could occur in a circuit, A, shimted by capacity and inductance, is that of the resonance frequency of capacity and inductance. Suppose the circuit. A, is a dead resistance. The voltage pulsa- tion produced by a current pulsation, i, in this circuit then would be in the same direction as i, that is, would be as shown in dotted line by e' in F ...", "... ent, ij, as shown in Fig. 89 in dotted line. That is, it would require a supply of power to maintain such pulsation. Thus, with a dead resistance as circuit. A, or in general with A as a circuit of rising volt-ampere characteristic, the maintenance of a resonance pulsation of current and voltage between A and C, at constant current, /, requires a supply of alternating-current power in the condenser circuit, and without such power supply the pulsation could not exist, hence, if started, would rapidly die out, as os ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-09", "section_label": "Chapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "section_title": "Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 4674-6992", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-09/", "snippets": [ "... very much faster than in a non-inductive circuit. Series inductive reactance in a condenser circuit, and series condensive reactance in an inductive circuit, cause a rise of potential. This rise is a maximum for a:o = ± 0.8, or Xq = — X (the condition of resonance), and the e.m.f, reaches the value £■ = 167 volts, or E = Eq— This rise of potential by series reactance continues up to Xo = + 1.6, or, Xo = — 2x, where E = 100 volts again; and for Xq > 1.6 the voltage drops again. At rro = ± 0.8, x = + 0.8, the tot ...", "... uit is r — j {x + Xo) = r = 0.6, x -{- Xo = 0, and tan do = 0; that 4 Eo Ex / E ^^ r Er 0 Fig. 55. Fig. 56. Fig. 57. is, the current and e.m.f. in the supply circuit are in phase with each other, or the circuit is in electrical resonance. Since a synchronous motor in the condition of efficient work- ing acts as a condensive reactance, we get the remarkable result that, in synchronous motor circuits, choking coils, or reactive coils, can be used for raising |he voltage. In Figs. 55 to 5 ...", "... of . consumer circuit Fig. 60. ,7 .6 .5 .4 .3 .2 .1 .0 LEADING CURRENT CIRCUITS CONTAINING RESISTANCE G9 The rise of voltage due to the balance of Xo and a; is a maxi- mum for a;o = + 1.0, a: = — 1.0, and r = 0, where £ = c» ; that is, absolute resonance takes place. Obviously, this condi- tion cannot be completely reached in practice. It is interesting to note, from Fig. 60, that the largest part of the drop of potential due to inductive reactance, and rise to condensive reactance — or conversely — take ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-08", "section_label": "Chapter 8: Circuits Containing Resistance, Inductance, And Capacity", "section_title": "Circuits Containing Resistance, Inductance, And Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3577-5333", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-08/", "snippets": [ "... non-inductive circuit. RESISTANCE, INDUCTANCE, CAPACITY. 65 Series inductance in a condenser circuit, and series con- densance in an inductive circuit, cause a rise of potential. This rise is a maximum for x0 = i .8, or, x0 = — x (the condition of resonance), and the E.M.F. reaches the value, E = 167 volts, or, E = E0z] r. This rise of potential by series reactance continues up to x0 = il.6, or, x0 = — %x, Fig. 42. where E = 100 volts again ; and for x0 > 1.6 the voltage drops again. At x0 = ± -8, x = ...", "... tage drops again. At x0 = ± -8, x = =f .8, the total impedance of the circuit is r — j (x -f x0} = r = .6, x + x0 = 0, and tan S>0 = 0 ; that is, the current and E.M.F. in the supply circuit are in phase with each other, or the circuit is in electrical resonance. \\ Fig. 43. Since a synchronous motor in the condition of efficient working acts as a condensance, we get the remarkable result that, in synchronous motor circuits, choking coils, or reactive coils, can be used for raising the voltage. In Figs. 4 ...", "... ariation of Voltage at Constant Series Reactance with Phase Angle of Receiver Circuit. Fig. 46. Variation of Voltage at Constant Series Reactance with Reactance of Receiver Circuit. 68 AL TERN A TING-CURRENT PHENOMENA. E = oo ; that is, absolute resonance takes place. Obvi- ously, this condition cannot be completely reached in practice. It is interesting to note, from Fig. 47, that the largest part of the drop of potential due to inductance, and rise to condensance — or conversely — takes place between r ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-03", "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "section_title": "Induction Motor With Secondary Excitation", "kind": "chapter", "sequence": 3, "number": 4, "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "... ds toward zero when approaching synchronism, 86 ELECTRICAL APPARATUS and peculiar speed characteristics result herefrom in such a motor. At a certain slip, s, the condenser current just balances all the reactive lagging currents of the induction motor, resonance may thus be said to exist, and a very large current flows into the motor, and correspondingly large power is produced. Above this \"resonance speed,\" however, the current and thus the power rapidly fall off, and so also below the resonance speed. It must ...", "... t a certain slip, s, the condenser current just balances all the reactive lagging currents of the induction motor, resonance may thus be said to exist, and a very large current flows into the motor, and correspondingly large power is produced. Above this \"resonance speed,\" however, the current and thus the power rapidly fall off, and so also below the resonance speed. It must be realized, however, that the frequency of the sec- ondary is the frequency of slip, and is very low at speed, thus a very great condenser c ...", "... induction motor, resonance may thus be said to exist, and a very large current flows into the motor, and correspondingly large power is produced. Above this \"resonance speed,\" however, the current and thus the power rapidly fall off, and so also below the resonance speed. It must be realized, however, that the frequency of the sec- ondary is the frequency of slip, and is very low at speed, thus a very great condenser capacity is required, far greater than would be sufficient for compensation by shunting the condens ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-09", "section_label": "Chapter 9: Wave Screens. Even Harmonics", "section_title": "Wave Screens. Even Harmonics", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 16964-17631", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-09/", "snippets": [ "... the alternating voltage, and the inductance, L, so high as to practically open-circuit the alternating voltage, the separation — of combi- nation — ^is practically complete, and independent of the frequency of the alternating wave. Wave screens based on resonance for a definite frequency by series connection of capacity and inductance, can be used to sepa- rate the ciurent of this frequency from a complex current or voltage wave, such as those given in Figs. 56 to 63, and thus can be used for separation of comp ...", "... = 2 TfCi' 1 6 ir/C 1 10 t/Cb' 1 2 vfnCn (39) Qii Lnf ggi Fig. 76. where / = frequency of the fundamental wave. Then, through any of the branch circuits Cn, L^ only the nth harmonic, in, can pass to an appreciable extent. Such resonant wave screen, however, has the serious disadvan- tage to require very high constancy of /, since the resonance condi- tion between C» and Ln depends on the square of /, 79. Even harmonics are produced in a closed magnetic circuit by the superposition of a ...", "... ncy of the fundamental wave. Then, through any of the branch circuits Cn, L^ only the nth harmonic, in, can pass to an appreciable extent. Such resonant wave screen, however, has the serious disadvan- tage to require very high constancy of /, since the resonance condi- tion between C» and Ln depends on the square of /, 79. Even harmonics are produced in a closed magnetic circuit by the superposition of a continuous current upon the alternating wave. With an alternating sine wave impressed upon an iron magnetic ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... oscillating discharge is Z = 0, that is, 1 o / ^ ^ 1^ T \\r^C 2aL 2L If r = 0, that is, in a circuit without resistance, we have a = 0, / = /=^j that is, the currents are alternating with no decre- 2 \"n\"^ LC ment, and the frequency is that of resonance. If ^ty-^-t < 0, that is, r > 2-1/7^, a and / become imaginary; that is, the discharge ceases to be oscillatory. An electrical discharge assumes an oscillating nature only, if r < ^xlp- In the case r = 2 -yj^ we have a = 00 , / = 0; that is, the curren ...", "... lator, constant current, 251 Reluctivity, 43 curve, 46 Remanent magnetism, 43 Resistance, 1 effective, of leaky conductor, 333 of line in series circuits, 306 negative effective, of arc, 191 Resistivity, magnitude of different conductors, 42 Resonance of transformer with har- monics of magnetic bridged gap, 151 Resonant wave screens, 157 Resonating circuit, constant current regulation, 256, 261, 282, 290 as wave screen, 154 Resultant flux of alternator, 232 Rising magnetic characteristic, 51 ...", "... ism, 43 Resistance, 1 effective, of leaky conductor, 333 of line in series circuits, 306 negative effective, of arc, 191 Resistivity, magnitude of different conductors, 42 Resonance of transformer with har- monics of magnetic bridged gap, 151 Resonant wave screens, 157 Resonating circuit, constant current regulation, 256, 261, 282, 290 as wave screen, 154 Resultant flux of alternator, 232 Rising magnetic characteristic, 51 S Saturation coefficient, magnetic, 44 magnetic, 77 equation of wa ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "section_label": "Lecture 10: Continual And Cumulative Oscillations", "section_title": "Continual And Cumulative Oscillations", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... l arcing ground oscillation in Figs. 44 and 45, page 98. In Fig. 44, the beginning of the disturbance, apparently a harmonic of the generator wave builds up by the energy supply through a beginning arc, and then builds down again, by being slightly out of resonance with a multiple of the natural frequency of the circuit. In Fig. 45, the arc has completely developed, and one of the harmonics of the generator wave appears as a steady continuous oscillation. Continual and cumulative oscillations naturally are the most ...", "... gy of the oscillation which gives its destructiveness thus is not limited to the small amount of the stored magnetic and dielectric energy of the system, but is supplied continuously from the engine or turbine power. 3. The continual oscillation is not a resonance phenomenon which depends on the frequency of the exciting disturbance just coinciding with one of the natural frequencies of the oscillating system, and which thus can occur only very rarely. The dis- CONTINUAL AND CUMULATIVE OSCILLATIONS 127 turbance ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... n general, the frequency of oscillation is assumed as constant, but where, as in cumulative hunting of synchronous machines, the amplitude of the swing reaches large values, an appreciable change of the period must be expected, and where the hunting is a resonance effect with some other periodic motion, as the engine rotation, the change of frequency with increase of amplitude of the oscillation breaks the complete resonance and thereby tends to limit the amplitude of the swing. 177. As example of the application ...", "... ge values, an appreciable change of the period must be expected, and where the hunting is a resonance effect with some other periodic motion, as the engine rotation, the change of frequency with increase of amplitude of the oscillation breaks the complete resonance and thereby tends to limit the amplitude of the swing. 177. As example of the application of elliptic integrals, may be considered the determination of the length of the arc of an ellipse. Let the ellipse of equation 5-^4=1' (31) be represented in ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-09", "section_label": "Lecture 9: Hunting Of Synchronous Machines", "section_title": "Hunting Of Synchronous Machines", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 4218-4594", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-09/", "snippets": [ "... or synchronous motors, it is frequently reduced by mak- ing the field excitation unequal, or putting a flywheel on one converter, or belting some other machine to it, or running an induction motor in the same station or in any other way break- ing up the resonance. 122 GENERAL LECTURES 2nd. Several converters hunting against each other in the same substation are frequently steadied by connecting the collector rings with each other, that is, by equalizer connec- tions between converter and transformer or regulat ...", "... governors, copper bridges on the alternators will cure it. 3rd. If the hunting has the speed of the engine, it may be reduced by increasing the flywheel or decreasing it, by running an induction motor in the station, or in any other way breaking up the resonance. HUNTING OF vSYNCHRONOUS MACHINES 123 In general, systems having all kinds of loads, different sizes of generators, motors and converters, induction motors and synchronous motors mixed, etc., are very little liable to hunting. Hunting is most liable t ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-24", "section_label": "Chapter 24: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 25682-29374", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-24/", "snippets": [ "... pedance, z = v r^ + x^, into a non-inductive circuit. Equation (34) is identical with the equation giving the maximum voltage, Ci, at current, i, which can be produced by shunting the receiving circuit with a condenser; that is, the condition of \"complete resonance\" of the line, z = V r^ + x^, with current, i. Hence, referring to equation (35), Ci = Co^is the maximum resonance voltage of the line reached when closed by a con- denser of reactance, — x. SYNCHRONOUS MOTOR 323 223. D. Maximum Displacement of Phase ...", "... m voltage, Ci, at current, i, which can be produced by shunting the receiving circuit with a condenser; that is, the condition of \"complete resonance\" of the line, z = V r^ + x^, with current, i. Hence, referring to equation (35), Ci = Co^is the maximum resonance voltage of the line reached when closed by a con- denser of reactance, — x. SYNCHRONOUS MOTOR 323 223. D. Maximum Displacement of Phase. (eo, i) = maximum. At a given power, p, the input is, Po = P + i'^r = Cot cos (eo, i) ] (38) hence, „_ / -x P ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-27", "section_label": "Chapter 27: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 27, "number": 27, "location": "lines 33011-34776", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-27/", "snippets": [ "... r the true capacity. With reactance, x, but no additional resistance, r, in series, the apparent capacity, C, rises from 4.2 times the true capacity at a; = 0, to a maximum of 5.03 times the true capacity, or C ~ 100. G mf. at a; = 0.28, the condition of resonance of the fifth harmonic, then decreases to a minimum of 27 mf., or 35 per cent, in excess of the true capacity, rises again to 60.2 mf., or 3.01 times the true capacity at a: = 9.67, the condition of resonance with the third harmonic, and finally decreases, ...", "... r C ~ 100. G mf. at a; = 0.28, the condition of resonance of the fifth harmonic, then decreases to a minimum of 27 mf., or 35 per cent, in excess of the true capacity, rises again to 60.2 mf., or 3.01 times the true capacity at a: = 9.67, the condition of resonance with the third harmonic, and finally decreases, reaching 20 mf., or the true capacity at re = 132, or an inductive reactance equal to the condensive reactance. GENERAL ALTERNATING WAVES 389 It thus follows that the true capacity of a condenser cannot ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-32", "section_label": "Chapter 32: Transformation Of Polyphase Systems", "section_title": "Transformation Of Polyphase Systems", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 36062-36514", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-32/", "snippets": [ "... connection of step-up transformers is frequently used in long-distance transmissions, to allow grounding of the high-potential neutral. Under certain conditions — which there- fore have to be guarded against — it is liable to induce excessive voltages by resonance with the line capacity. J_I_i P^^lIM nm Fig. 210. The reverse thereof, or the Y-delta connection, is undesirable on unbalanced load, since it gives what has been called a \"float- ing neutral;\" the three primary Y voltages do not remain even a ...", "... ly distorted even at moderate inequality of load, and the system thus loses all ability to maintain constant voltage at unequal distribution of load, that is, becomes inoperative. In high-potential systems in this case excessive voltages may be induced by resonance with the line capacity. For instance, if only one phase of the secondary triangle is 426 ALTERNATING-CURRENT PHENOMENA loaded, the other two unloaded, the primary current of the loaded phase must return over the other two transformers, which, at open ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-08", "section_label": "Chapter 8: Capacity", "section_title": "Capacity", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 3872-6370", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-08/", "snippets": [ "... ive circuit. 846] RESISTANCE, INDUCTANCE, CAPACITY. 65 Series inductance in a condenser circuit, and series con- densance in an inductive circuit, cause a rise of potential. This rise is a maximum for jr^ = i .8, or, ;r^ = — x (the condition of resonance), and the E.M.F. reaches the value, E = 167 volts, or, E = E^zj r. This rise of potential by series reactance continues up to ;r^ = ± 1.6, or, ;r = — 2;r, Rg, 42, where J? = 100 volts again ; and for x^> 1.6 the voltage drops again. At ;r^ = ± .8, ; ...", "... ^^ _-— __jj^ii- __ ---' LjiisiS, — — __ ^ ' r\"^ jj^_ — Li— - .\"-I tis c=|s.yai«p.J ' r. ., -s .. -5 L, -, ..Lw. ^ 4(L foriatroB o/ yoltagt at Conianl Serl. AL TKKA'A TIXG-Cl'KKENT PlIEXOMKA (§48 ^ = 00; that is, absolute resonance takes place. Obvi- ously, this condition cannot be completely reached in practice. It is interesting to note, from Fig. 4T, that the largest part of the drop of potential due to inductance, and rise to condensance — or conversely — takes place between r ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-09", "section_label": "Chapter 9: Kbsistanci: And Kbactance Of Transmission Iine8", "section_title": "Kbsistanci: And Kbactance Of Transmission Iine8", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 6371-8268", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "snippets": [ "... mpossible, since neither r^ nor g can be negative. The next possible value is ^ = 0, — a wattless circuit. Substituting this value, we get, and by substituting, in db ' zo^ ^ + ^0 = 0; that is, the sum of the susceptances = 0, or the condition of resonance is present. Substituting, we have 102 AL TERNA Tlh'G-CUKKENT PHENOMENA. \\% 71 The current in this case is, or the same as if the Hne resistance were short-circuited without any inductance. This is the condition of perfect resonance, with current ...", "... condition of resonance is present. Substituting, we have 102 AL TERNA Tlh'G-CUKKENT PHENOMENA. \\% 71 The current in this case is, or the same as if the Hne resistance were short-circuited without any inductance. This is the condition of perfect resonance, with current and E.M.F. in phase. s \\ *(sy; \\ \\ \\ \\ s \\, ks \\ \\ \"^\"^ 'Sn'Sn^Mt'iVa S\"., \"\"ISE'.S'S^'.'t\"-\" ■kmVt™ / - \"^ ^ - / J m ■^ s. m '•i K 1^' '%' 1 / ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-09", "section_label": "Chapter 9: Resistance And Reactance Of Transmission Lines", "section_title": "Resistance And Reactance Of Transmission Lines", "kind": "chapter", "sequence": 9, "number": 9, "location": "lines 5334-6956", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "snippets": [ "... is impossible, since neither r0 nor g can be negative. The next possible value is g — 0, — a wattless circuit. Substituting this value, we get, and by substituting, in , b + b0 = 0 ; that is, the sum of the susceptances = 0, or the condition of resonance is present. Substituting, *=-*-£, we have 102 AL TERNA TING-CURRENT PHENOMENA. The current in this case is, or the same as if the line resistance were short-circuited without any inductance. This is the condition of perfect resonance, with curr ...", "... dition of resonance is present. Substituting, *=-*-£, we have 102 AL TERNA TING-CURRENT PHENOMENA. The current in this case is, or the same as if the line resistance were short-circuited without any inductance. This is the condition of perfect resonance, with current and E.M.F. in phase. \\ s \\ \\ VOLT ^ \\ \\ \\ \\ 1SOO 1700 1COO 1500 -1400 \\ \\ \\\\ \\ \\ CONSTANT IMPRESSED E. M. F. Eo^lOOO \" LINE IMPEDANCE Z0=2.5- € 1 MAXIMUM OUTPUT BY COMPENSATION II MAXIMUM EFFICIENCY BY ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-19", "section_label": "Chapter 19: Synchronous Motor", "section_title": "Synchronous Motor", "kind": "chapter", "sequence": 19, "number": 19, "location": "lines 18053-19457", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-19/", "snippets": [ "... dance, z = vV2 + jr2 into a non-inductive circuit. Equation (34) is identical with the equation giving the maximum voltage, e± , at current, i, which can be produced by shunting the receiving circuit with a condenser; that is, the condition of \" complete resonance \" of the line, z = x Vr'2 + x'2, with current, ». Hence, referring to equation (35), el = t0 ~ is the maximum resonance voltage of the line, reached when closed by a con- denser of reactance, — x. 348 ALTERNATING-CURRENT PHENOMENA. consumed by ...", "... e± , at current, i, which can be produced by shunting the receiving circuit with a condenser; that is, the condition of \" complete resonance \" of the line, z = x Vr'2 + x'2, with current, ». Hence, referring to equation (35), el = t0 ~ is the maximum resonance voltage of the line, reached when closed by a con- denser of reactance, — x. 348 ALTERNATING-CURRENT PHENOMENA. consumed by the resistance ; that is, at the electrical effi- ciency of 50 per cent. Substituting (40) in equation (7) gives, after sq ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "section_title": "Symbolic Representation Of General Alternating Waves", "kind": "chapter", "sequence": 24, "number": 24, "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "... acity, or C= 100.6 m.f. at x = .28, the condition of res- onance of the fifth harmonic, then decreases to a minimum of 27 m.f., or 35 % in excess of the true capacity, rises again to 60.2 m.f., or 3.01 times the true capacity at x = 9.67, the condition of resonance with the third harmonic, and finally decreases, reaching 20 m.f., or the true capacity at x = 132, or an inductive reactance equal to the capacity reactance, then increases again to 20.2 m.f. at x = oo . This rise and fall of the apparent capacity is wit ...", "... ise and fall of the apparent capacity is within cer- tain limits independent of the magnitude of the higher harmonics of the generator wave of E.M.F., but merely de- pends upon their presence. That is, with such a reactance connected in series as to cause resonance with one of the higher harmonics, the increase of apparent capacity is ap- proximately the same, whatever the value of the harmonic, whether it equals 25% of the fundamental or less than 5%, provided the resistance in the circuit is negligible. The only ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-01", "section_label": "Chapter 1: Speed Control Of Induction Motors", "section_title": "Speed Control Of Induction Motors", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1368-3542", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-01/", "snippets": [ "... ce steady running at low speeds. To a considerable extent, this disadvantage of inconstancy of speed can be overcome: (a) By the use of capacity or effective capacity in the motor secondary, which contracts the range of torque into that of approximate resonance of the capacity with the motor inductance, and thereby gives fairly constant speed, independent of the load, at various speed values determined by the value of the capacity. (6) By the use of a resistance of very high negative tempera- ture coefficient i ...", "... finite speed, at which inductive reactance and capacity reactance are equal and Opposite, that is, balance, and at and near this speed, a large current is taken by the motor and thus large torque developed, while at speeds considerably above or below this resonance speed, the current and thus torque of the motor are small. The use of a capacity, or an effective capacity (as polariza- tion cell or aluminum cell) in the induction-motor secondary should therefore afford, at least theoretically, a means of speed contr ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-16", "section_label": "Chapter 18: Surging Of Synchronous Motors", "section_title": "Surging Of Synchronous Motors", "kind": "chapter", "sequence": 16, "number": 18, "location": "lines 20975-21712", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-16/", "snippets": [ "... ation of the syn- chronous reactance, etc. If the decrement is zero, a pulsation 288 SURGING OF SYNCHRONOUS MOTORS 289 started once will continue indefinitely at constant amplitude. This phenomenon, a surging by what may be called electro- mechanical resonance, must be taken into consideration in a complete theory of the synchronous motor. 167. Let: E0 = e0 = impressed e.m.f. assumed as zero vector. E = e (cos P — j sin P) = e.m.f. consumed by counter e.m.f. of motor, where: P = phase angle between E0 and E ...", "... in unstable equilibrium. 5. If: a > 6i2, g = y/a - bS, 8 = £€ + Mcos(00 + 6). (34) That is, the motor oscillates, with constantly increasing am- plitude, until it drops out of step. This is the typical case of cumulative surging by electro-mechanical resonance. The problem of surging of synchronous machines, and its elimination, thus resolves into the investigation of the coefficient: 8x/Jlf0 (35) while the frequency of surging, where such exists, is given by: f _ jfeeo sin (a - 0) (c2 + pP0 - /i2)2 ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-07", "section_label": "Chapter 7: Shaping Of Waves : General", "section_title": "Shaping Of Waves : General", "kind": "chapter", "sequence": 7, "number": 7, "location": "lines 12222-12961", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-07/", "snippets": [ "... ed by other causes. Such are a pulsation of the magnetic reluctance of the field due to the armature slots, or a pulsation of the armature reactance, as discussed in Chapter XXV of ** Theory and Calculation of Alter- nating-current Phenomena,'' or a space resonance of the armature conductors with some of the harmonics. The latter may occur if the field flux distribution contains a harmonic of such order, that the voltages induced by it are in phase in the successive arma- t\\ire conductors, and therefore add, that is ...", "... and even small voltage harmonics, if of very high order, that is, high frequency, produce very large currents, and these in turn may cause dangerous voltages in inductive devices connected in series into the circuit, such as current transformers, or cause resonance effects in transformers, etc. With the increasing extent of very high-voltage transmission, introducing capacity into the systems, it thus becomes increasingly important to keep the very high harmonics practically out of the voltage wave. Incidentally i ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "... ent, etc., it follows that at very high frequencies the line responds to any frequency, has no definite frequency of oscillation, but oscillations can exist of any frequency, provided this frequency is sufficiently high. Thus in long trans- mission lines, resonance phenomena can occur only with moderate frequencies, but not with frequencies of hundred thousands or millions of cycles. 32. The line constants Vq, go, Lq, Cq are given per unit length, as per cm., mile, 1000 feet, etc. The most convenient unit of leng ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3956-4744", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "snippets": [ "... e, current, etc., it follows that at very high frequencies the line responds to any frequency, has no definite frequency of oscillation, but oscillations can exist of any frequency, provided this frequency is sufficiently high. Thus in transmission lines, resonance phenomena can occur only with moderate frequen- cies, but not with frequencies of hundred thousands or millions of cycles. 32. The line constants r0, go, L0, C0 are given per unit length, as per cm., mile, 1000 feet, etc. The most convenient unit of le ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... is 60 cycles. The natural frequency of the TRIGONOMETRIC SERIES. 115 circuit is then close to that of the 11th harmonic of the generator wave, 660 cycles, and if the generator voltage contains an appreciable 11th harmonic, trouble may result from a resonance rise of voltage of this frequency; therefore, the 11th harmonic of the generator wave is to be determined, that is, an and 6ii calculated, but the other harmonics are of less importance. Table II d y cos 11« sin no y cos 110 J/ sin lie 0 ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-05", "section_label": "Lecture 5: Long Distance Transmission", "section_title": "Long Distance Transmission", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 2562-3132", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-05/", "snippets": [ "... ge sends full load current through the inductive reactance, while 10 times full load voltage is required by the capacity reactance; the capacity reactance therefore is about 50 times and therefore cannot build up with it to excessive voltages ; but to get resonance with the fundamental frequency requires an inductive reactance about 50 times greater than the line reactance. The only reactance in the system which is large enough to build up with the capacity reactance is the open circuit reactance of the transforme ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-108", "section_label": "Apparatus Section 2: Induction Machines: Polyphase Induction Motor", "section_title": "Induction Machines: Polyphase Induction Motor", "kind": "apparatus-section", "sequence": 108, "number": 2, "location": "lines 19166-20427", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-108/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-108/", "snippets": [ "... 5 5.0 FIG. 180. — Induction motor starting torque with resistance secondary. in the Capacity inserted in the secondary very greatly increases the torque within the narrow range of capacity corresponding to resonance with the internal reactance of the motor, and the torque which can be produced in this way is far in excess of the maximum torque of the motor when running or when starting with resistance in the secondary. 326 ELE ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-36", "section_label": "Apparatus Section 15: Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "section_title": "Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "kind": "apparatus-section", "sequence": 36, "number": 15, "location": "lines 9918-10123", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-36/", "snippets": [ "... hey tend to make the voltage fluctuate and to tear the alternators out of synchro- nism with each other, especially when the conditions are favorable to a cumulative increase of this effect by what may be called mechanical resonance (hunting) of the engine governors, etc. They depend upon the synchronous impedance of the alternators and upon their phase difference, that is, the number of poles and the fluctuation of speed, and are specially objectionabl ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1120-1683", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-01/", "snippets": [ "... pe in mind as a possible disturbing factor, which, however, is in practice generally negligible — except in the case of low-resistance circuits containing large inductive reactance and large condensive reactance in series with each other, so as to produce resonance effects of these higher harmonics, and also under certain conditions of long-distance power transmission and high-potential distribution. 8. Experimentally, the impedance, effective resistance, induc- tance, capacity, etc., of a circuit or a part of a ci ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-10", "section_label": "Chapter 10: Resistance And Reactance Of Transmission", "section_title": "Resistance And Reactance Of Transmission", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6993-9766", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-10/", "snippets": [ "... 0 Ai r ^A 44 SOfl 4 .-^ v^ X 100 (1 ^ ^ / .ooc ■jw^ j»Olj, OUT PUT K.VVi » Fig. 76. 10 20 30 10 50 60 7.0 .80 90 100 -Efficiency and output of transmission lines. or somewhat less than the current at complete resonance, that is, when the line inductive reactance, Xo, is balanced by the capacity reactance, x, of the load, x = — a:;o; in which latter case the current is ro r = 96 ALTERNATING-CURRENT PHENOMENA assuming wattless receiver circuit, and is in phase wi ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-12", "section_label": "Chapter 12: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 10718-13483", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-12/", "snippets": [ "... he dis- torted wave by its equivalent sine wave, keeping in mind, however, the existence of a higher harmonic as a possible dis- turbing factor which may become noticeable in those cases where the frequency of the higher harmonic is near the frequency of resonance of the circuit, that is, in circuits containing conden- sive as well as inductive reactance, or in those circuits in which the higher harmonic of currrent is suppressed, and thereby the voltage is distorted, as discussed in Chapter XXV. 97. The equivalen ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-17", "section_label": "Chapter 17: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 16521-17716", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-17/", "snippets": [ "... Transformer Receiving Circuit Fig. 117. Such circuits have been discussed in detail in Chapter IX, and the results derived there are now directly applicable to the transformer, giving the variation and the control of secondary terminal voltage, resonance phenomena, etc. Thus, for instance, if Z'l = Zo, and the transformer contains an additional secondary coil, constantly closed by a condensive reactance of such size that this auxiliary circuit, together with the exciting circuit, gives the reactance, ~ X ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-25", "section_label": "Chapter 25: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 29375-32539", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-25/", "snippets": [ "... e effective value of the total wave. The very high peak of e.m.f. produced by this wave-shape distortion is liable to be dangerous in high-potential, three- phase systems by increasing the strain on the insulation between lines and ground, and leading to resonance phenomena with the third harmonic. The maximum value of the distorted wave of magnetism is 8.89, while with a sine wave it would be 10.0, that is, the maxi- mum of the wave of magnetism has been reduced by 11.1 per cent., and the core loss of the transf ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... ductive line, 82, 86 curve of alternator, 290 Resistance, effective, 2, 5, 9, 111 of line, 174 parallel and series connection, 54 in series with circuit, 60 in starting induction motor, 224 in symbolic expression, 35 Resolution of sine waves, 31 Resonance of condenser with dis- torted wave, 387 by harmonics, 373 Ring connection of polyphase sys- tem, 416 current in polyphase system, 417 voltage in polyphase system, 417 Rise of voltage of circuit by shunted susceptance, 94 Rotating field of symmetr ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 1224-1727", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-01/", "snippets": [ "... 10 AL TERN A TING-CURRENT PHENOMENA. [ § 7 generally, however, is in practice negligible — perhaps with the only exception of low-resistance circuits containing large magnetic reactance, and large condensances in series with each other, so as to produce resonance effects of these higher harmonics. INSTANTANEOUS AND INTEGRAL VALUES." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-10", "section_label": "Chapter 10: F", "section_title": "F", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 8269-10499", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "snippets": [ "... torted wave by its equivalent sine wave, keeping in mind, however, the existence of a higher harmonic as a possible disturbing factor which may become noticeable in those very rare cases where the frequency of the higher harmonic is near the frequency of resonance of the circuit. 79. The equivalent sine wave of exciting current leads the sine wave of magnetism by an angle a, which is called the angle of hysteretic advance of phase. Hence the cur- rent lags behind the E.M.F by ^^ 90° — a, and the power is therefor ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-13", "section_label": "Chapter 13: Ths Alternating^Cnrrent Traxsfobmer", "section_title": "Ths Alternating^Cnrrent Traxsfobmer", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 12673-14088", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-13/", "snippets": [ "... it containing resistances and reactances. Such circuits have explicitly been discussed in Chapter VIII., and the results derived there are now directly appli- cable to the transformer, giving the variation and the con- trol of secondary terminal voltage, resonance phenomena, etc. Thus, for instance, if Z( = Z^, and the transformer con- tains a secondary coil, constantly closed by a condenser reactance of such size that this auxiliary circuit, together with the exciting circuit, gives the reactance —x^y with a non ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "section_label": "Chapter 30: Quartbr-Fhase System", "section_title": "Quartbr-Fhase System", "kind": "chapter", "sequence": 30, "number": 30, "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... condition of an oscillating discharge is ^ = 0, that is, ' 2aL 2zVr«C a = c If r = 0, that is, in a circuit without resistance, we have a ^ Oj jV=1/2v VZ C ; that is, the currents are alter- nating with no decrement, and the frequency is that of resonance. If 4 Z/ r« C - 1 < 0, that is, r > 2 VZT^, a and N become imaginary ; that is, the discharge ceases to be os- cillatory. An electrical discharge assumes an oscillating nature only, if r < 2 VZ/ C. In the case r = 2 VZ/ C we have a = CO , N = ; that is, ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-01", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 1, "number": 1, "location": "lines 963-1366", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-01/", "snippets": [ "... mind as a possible disturbing factor, which generally, however, is in practice negligible — perhaps with the only exception of low-resistance circuits containing large magnetic reactance, and large condensance in series with each other, so as to produce resonance effects of these higher harmonics. INSTANTANEOUS AND INTEGRAL VALUES. 11" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "section_label": "Chapter 10: Effective Resistance And Reactance", "section_title": "Effective Resistance And Reactance", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "... he dis- torted wave by its equivalent sine wave, keeping in mind, however, the existence of a higher harmonic as a possible disturbing factor which may become noticeable in those cases where the frequency of the higher harmonic is near the fre- quency of resonance of the circuit, that is, in circuits con- taining capacity besides the inductance. 79. The equivalent sine wave of exciting current leads the sine wave of magnetism by an angle a, which is called the angle of Jiysteretic advance of phase. Hence the cur- ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "... ion of potential, that is a very rapid change along the line, as caused for instance by a sudden short circuit rupturing itself instantly, causes the higher harmo- nics to predominate, which as a rule are more liable to cause excessive rises of voltage by resonance. 125. As has been shown, the electric distribution in a transmission line containing distributed capacity, self-induc- tion, etc., can be represented either by a polar diagram with the phase as amplitude, and the intensity as radius vector, as in Fig. 3 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-14", "section_label": "Chapter 14: The Alternating-Current Transformer", "section_title": "The Alternating-Current Transformer", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 11605-12682", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "snippets": [ "... it containing resistances and reactances. Such circuits have explicitly been discussed in Chapter VIII., and the results derived there are now directly appli- cable to the transformer, giving the variation and the con- trol of secondary terminal voltage, resonance phenomena, etc. Thus, for instance, if Z/ = Z0, and the transformer con- tains an additional secondary coil, constantly closed by a condenser reactance of such size that this auxiliary circuit, together with the exciting circuit, gives the reactance — x0 ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-32", "section_label": "Chapter 32: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 32, "number": 32, "location": "lines 25904-27405", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "snippets": [ "... on of an oscillating discharge is Z = 0, that is, ~ ~ / .1 r 2aL 2Z~ ~1' If r = 0, that is, in a circuit without resistance, we have a = 0, Af = 1 / 2 TT VZT ; that is, the currents are alter- nating with no decrement, and the frequency is that of resonance. If 4 H r2 C - 1 < 0, that is, r > 2 V2T/T, a and N become imaginary ; that is, the discharge ceases to be os- cillatory. An electrical discharge assumes an oscillating nature only, if r < 2 V/, / C. In the case r = 2 VZ, / C we have « = oo , ./V = 0 ; ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-08", "section_label": "Chapter 8: Shaping Of Waves By Magnetic Saturation", "section_title": "Shaping Of Waves By Magnetic Saturation", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 12962-16963", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-08/", "snippets": [ "... ies with a fair degree of accuracy. By thus deriving the Fourier series which represents the peaked voltage waves, the harmonics which make up the wave, and their approximate val- ues can be determined and therefrom their probable effect on the system, as resonance phenomena, etc., estimated. The characteristic of the voltage-wave distortion due to mag- netic saturation in a closed magnetic circuit traversed by a sine wave of current is, that the entire voltage wave practically con- tracts into a single high peak, ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-29", "section_label": "Chapter 7: Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "section_title": "Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "kind": "chapter", "sequence": 29, "number": 7, "location": "lines 6798-7825", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "snippets": [ "... he fundamental, and in starting the potential difference nearly doubles. RESISTANCE, INDUCTANCE, AND CAPACITY 101 As further example, Fig. 25 shows the start of a circuit of a frequency of oscillation of the same magnitude as the funda- mental, in resonance condition, x = xc, and of high resistance. 60 40 20 0 -20 -40 -60 60 40 20 0 -20 -40 \\s 4 \\ = 35000 volts -5-ohW- 10 oh' ma1 -\\ 100 ohms gd-p- Fig. 24. Starting of an alternating-current circuit having capacity, ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... ves 449, 452 grounded 303 half-wave oscillation 333 inductive discharges 542 infinitely long 305 natural period 280, 320 open 299 opening under load 112, 118 phase difference 296 quarter-wave 306, 313, 315 oscillation 322 radiation 283 resonance frequency 279 with higher harmonics 280 short-circuit oscillation 113, 118 starting 111,117 transient terms and oscillations 98, 102 Transmitted wave at transition point 527, 531 Traveling sine and cosine waves 434 waves, general equations 458 ..." ] } ] }, { "id": "ultraviolet", "label": "Ultra-Violet Radiation", "aliases": [ "Ultra-violet radiation", "actinic rays", "ultra-violet", "ultraviolet" ], "total_occurrences": 105, "matching_section_count": 10, "matching_source_count": 3, "source_totals": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 91, "section_count": 8 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 11, "section_count": 1 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 3, "section_count": 1 } ], "section_hits": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-03", "section_label": "Lecture 3: Physiological Effects Of Radiation", "section_title": "Physiological Effects Of Radiation", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2366-3638", "status": "candidate", "occurrence_count": 43, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-03/", "snippets": [ "... of the speech are not recorded, while at the louder portions the recording point jumps and the voice breaks in the reproduction. 21. The sensitivity of the eye to radiation obviously changes with the frequency, as it is zero in the ultra-red, and in the ultra- violet — where the radiation is not visible — and thus gradually increases from zero at the red end of the spectrum to a maximum somewhere near the middle of the spectrum and then decreases again to zero at the violet end of the spectrum; that is, the physi- P ...", "... ysiological effect — as one candle power of light — is a maxi- mum near the middle of the spectrum and decreases from there to infinity at the end of the visible range, being infinite RED YELLOW GREEN BLUE VIOLET FIG. 21. in the ultra-red and ultra-violet, where no power of radiation can produce visibility. It thus varies about as indicated in Fig. 22. The mechanical power equivalent of light, thus, is not constant, as the mechanical energy equivalent of heat — which is 426 kgm. or 4.25 kile-joule per cal ...", "... only the green light. As you see, in the green the above-described effect does not exist, but the vision is clear, distinct and restful. 27. Beyond the violet the radiation is no longer visible to the eye as light. There is, however, a faint perception of ultra-violet light in the eye, not as distinct light, but rather as an indis- tinct, uncomfortable feeling, some form of dull pain, possibly resulting from fluorescence effects caused by the ultra-violet radiation inside of the eye. With some practice the presence of ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... rilliancy and more still in the mercury arc, radiations of higher frequencies appear, that is, shorter wave lengths than visible light, and these radiations are again invisible. As they are of frequencies beyond the violet rays of light, they are called \" ultra-violet rays/' while the radia- tions which we produced from the heated silicon rods at moderate temperatures were invisible because of too low frequency and are thus called \" ultra-red rays,\" or \" infra-red rays/' as they are outside of and below the red end of ...", "... the heated silicon rods at moderate temperatures were invisible because of too low frequency and are thus called \" ultra-red rays,\" or \" infra-red rays/' as they are outside of and below the red end of the range of visible radiation. To produce powerful ultra-violet rays, I use a condenser dis- charge between iron terminals, a so-called ultra-violet arc lamp. Three iron spheres, 7 in Fig. 11, of about f in. diameter, are mounted on an insulator B. The middle sphere is fixed, the NATURE AND DIFFERENT FORMS OF RADIAT ...", "... requency and are thus called \" ultra-red rays,\" or \" infra-red rays/' as they are outside of and below the red end of the range of visible radiation. To produce powerful ultra-violet rays, I use a condenser dis- charge between iron terminals, a so-called ultra-violet arc lamp. Three iron spheres, 7 in Fig. 11, of about f in. diameter, are mounted on an insulator B. The middle sphere is fixed, the NATURE AND DIFFERENT FORMS OF RADIATION. 13 outer ones adjustable and set for about ^ in. gap. This lamp is connected a ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... amount of energy is less, it may not be possible to feel it, though with a sensitive instrument, as a bolometer, we may still be able to measure the heat. All radiations therefore are convertible into heat: the visible light waves as well as the invisible ultraviolet rays, and the — usually more powerful — long ultrared waves ; but none of the radiations can be called heat, no more than the mechanical momentum of a flywheel is heat, because when destroyed, it produces heat. If we consider the infinite range of radiat ...", "... rception of the rays, mainly the energetic low frequency rays. As stated, then, there is no essential differ- ence between so-called heat waves and light waves, but any radiation can be converted into other forms of energy, the so- called chemical rays of ultraviolet light, the X-ray, as well as the ultrared and the visible rays, and when converted into heat can be noticed as such. Now it just happens that most of our means of producing radiating energy give high intensi- ties of radiation only for very low frequencie ...", "... of producing radiating energy give high intensi- ties of radiation only for very low frequencies, invisible ultra- red rays, but we are not able to produce anywhere near the same intensities of radiation for higher frequencies. So also, when we speak of ultraviolet, or short, high frequency waves, as chemical waves, thait does not mean that they have a distinctive character in producing chemical action — any form of energy, naturally, can be converted if we know how, into chemical energy, the long ultrared waves ju ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-04", "section_label": "Lecture 4: Chemical And Physical Effects Of Radiation", "section_title": "Chemical And Physical Effects Of Radiation", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3639-3945", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-04/", "snippets": [ "... which photography is based : the dissociating action of radiation on silver salts, the chloride in ordinary photographic paper, the bromide and iodide in the negative plate and the quick printing papers. This chemical action is greatest in the violet and ultra-violet and decreases with increasing wave length, hence is less in the green, small in the yellow, and almost absent in the red and ultra-red, so that the short waves, blue, violet and ultra-violet, have sometimes been called \" chemical rays.\" This, however, is ...", "... nting papers. This chemical action is greatest in the violet and ultra-violet and decreases with increasing wave length, hence is less in the green, small in the yellow, and almost absent in the red and ultra-red, so that the short waves, blue, violet and ultra-violet, have sometimes been called \" chemical rays.\" This, however, is a misnomer, just as the term \"heat rays\" sometimes applied to red and ultra-red rays. In so far as when intercepted they are converted into heat, all rays are heat rays, but neither the ultra ...", "... y strike a body which is responsive to them. The chemical action of radiation is specific to its frequency and seems to be some kind of a resonance effect. We may picture to ourselves that the frequency of vibration of a silver atom is that of violet or ultra-violet light, and therefore, when struck by a wave of this frequency, is set in vibration by resonance, just as a tuning fork is set in vibration by a sound wave of the frequency with which it can vibrate, and if the vibration of the silver atom, in response to ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... divided into two classes, the electric waves and the light waves, which are separated from each other by the blank space in the middle of the spectrum of radiation (Fig. 14). Under light waves we here include also the invisible ultra-red radiation and the ultra-violet radiation and the non-refrangible radiations, as X-rays, etc., separated from the latter by the second blank space of the radiation spectrum. In the following, mainly the light waves, that is, the second or high frequency range of radiation, will be discussed. The ...", "... ry and Calculation of Transient Electric Phenomena and Oscilla- tions. \" RELATION OF BODIES TO RADIATION. 21 radiation of an incandescent body as a lamp filament, which contains all the frequencies from long ultra-red waves over visible light waves to ultra-violet waves. In the action of vibrations on our senses there is a characteristic difference between the perception of sound waves by the ear and that of light waves by the eye : the ear is analytic, that is, can separate the individual waves in a mixture of di ...", "... y differences and changes which now escape us. 10. However, while the eye cannot distinguish the different component radiations but sees only their resultant, the specific effects of the component radiations, as the physiologically harm- ful action of an ultra-violet component of light, still remain, even if the eye does not see the components, and in the study of radia- tion for the purpose of its engineering use for illumination it is therefore necessary to analyze the mixed radiation given by a source as a lamp, by ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "... of the energy in the spectrum, which is more or less charac- teristic of the luminescent body, and to some extent, also, of the method of exciting the luminescence. Thus crystalline calcium tungstate, W04Ca, fluoresces white in the X-ray, light blue with ultra-violet light; the aniline dye, rhodamine, 6 G, in alcoholic solution fluoresces green in daylight, crimson in the light of the mercury lamp; willemite (calcium silicate) shows a maximum fluorescent radiation in the green, some chalcites in the red, etc. So far, ...", "... arc stream very greatly beyond the boiling point of the material. When using a condenser discharge be- tween iron terminals, we thus get an iron arc of very much higher temperature, and this arc gives very little visible light, but a very large amount of ultra-violet radiation. It is this arrangement which we have used in the preceding to produce ultra-violet light by the so-called \" ultra-violet iron arc.\" In the iron arc the average wave length of the radiation thus shifts with increasing temperature to shorter wave lengths, ...", "... arge be- tween iron terminals, we thus get an iron arc of very much higher temperature, and this arc gives very little visible light, but a very large amount of ultra-violet radiation. It is this arrangement which we have used in the preceding to produce ultra-violet light by the so-called \" ultra-violet iron arc.\" In the iron arc the average wave length of the radiation thus shifts with increasing temperature to shorter wave lengths, or higher frequencies, similar as in temperature radiation. The reverse is the case ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-07", "section_label": "Lecture 7: Flames As Illuminants", "section_title": "Flames As Illuminants", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 6609-7140", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-07/", "snippets": [ "... entirely chemical lumi- nescence. Thus burning sulphur gives a blue flame, and, if the temperature of combustion is increased by burning the sulphur in oxygen, it gives a fairly intense light, of violet color, and a radiation which is very intense in the ultra-violet. Thus before development of the ultra-violet electric arcs, as the iron arc, for the production of ultra-violet radiation lamps were used, burning carbon bisulphide, CS2, in oxygen. Carbon bisulphide, has the advantage over sulphur that, as liquid, it can ...", "... ng sulphur gives a blue flame, and, if the temperature of combustion is increased by burning the sulphur in oxygen, it gives a fairly intense light, of violet color, and a radiation which is very intense in the ultra-violet. Thus before development of the ultra-violet electric arcs, as the iron arc, for the production of ultra-violet radiation lamps were used, burning carbon bisulphide, CS2, in oxygen. Carbon bisulphide, has the advantage over sulphur that, as liquid, it can easier be handled in a lamp, and especially ...", "... n is increased by burning the sulphur in oxygen, it gives a fairly intense light, of violet color, and a radiation which is very intense in the ultra-violet. Thus before development of the ultra-violet electric arcs, as the iron arc, for the production of ultra-violet radiation lamps were used, burning carbon bisulphide, CS2, in oxygen. Carbon bisulphide, has the advantage over sulphur that, as liquid, it can easier be handled in a lamp, and especially the combustion of carbon (without adding much to the light, due to the non-lu ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... nd of the frequency of charge. 52. Example: Assume an oscillating-current generator, feed- ing a Tesla transformer for operating X-ray tubes, or directly supplying an iron arc (that is, a condenser discharge between iron electrodes) for the production of ultraviolet light. The constants of the charging circuit are: the impressed e.m.f., e = 15,000 volts; the resistance, r = 10,000 ohms; the inductance, L = 250 henrys, and the capacity, C = 2 X 10~ 8 farads = 0.02 mf. The constants of the discharge circuit are: (a) ...", "... the capacity, C = 2 X 10~ 8 farads = 0.02 mf. The constants of the discharge circuit are: (a) operating Tesla transformer, the estimated resistance, r0 = 20 ohms (effective) and the estimated inductance, L0 = 60 X 10\" fl henry = 0.06 mh.; (b) operating ultraviolet arc, the esti- mated resistance, r0 = 5 ohms (effective) and the estimated inductance, L0 = 4 X 10\" 6 henry = 0.004 mh. Therefore in the charging circuit, q = 223,400 ohms, ' 0.0448, =446.8, 2L 2L - = 0.025; t. = 0.1344 sin 446.8 <0 0 + 2 ...", "... 3 times as large as the charging current. 86 TRANSIENT PHENOMENA The effective value of the discharge current, from equation (87), is il = 14.4 amp., or nearly 40 times the charging current. 53. (b) When discharging the condenser directly, through an ultraviolet or iron arc, in a straight path, and estimating r0 = 5 ohms and L0 = 4 X 10~6 henry, we have g0 = 27.84 ohms, ^ - 0.1795,. #0 £- = 3.48 X 10°, ^f- = 0.625 X 10\"; 2 LQ 2 L0 then, t = 1600r-0625xl°6' sin 3.48 X 106£, in amp., and ^ = 22,300 £- 0 ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-05", "section_label": "Lecture 5: Temperature Radiation", "section_title": "Temperature Radiation", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3946-5076", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-05/", "snippets": [ "... soon as we focus it on the sensitive spot. With increasing tempera- ture, first the lowest of the visible frequencies appear and become visible as red light, and with still further increase of temperature gradually orange, yellow, green, blue, violet and ultra-violet rays appear and the color thus changes from red to orange, yellow, yellowish white and then white, the latter at that temperature where all the visible radiations are present in the same propor- tion as in daylight. With still further increase of temperat ...", "... isible in red light, to a maximum at that temperature where the average frequency of the radiation is in the visible range, and it would decrease again for still higher temperature by the average frequency of radiation shifting beyond the visible into the ultra-violet. The efficiency of light production by incandescence thus rises with increasing tempera- ture to a maximum, and then decreases again. As the total radiation varies with the fourth power of the temperature, it thus follows that the visible radiation first ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-09", "section_label": "Lecture 9: Measurement Of Light And Radiation", "section_title": "Measurement Of Light And Radiation", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 8511-9388", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-09/", "snippets": [ "... ion, as in an incandescent lamp, this method is the most exact. However, it can directly measure only the total radiation power. To measure the different parts of the radiation so as to determine separately the power in the visible, the ultra-red, and the ultra-violet range, the method of input and losses can be used to give the total radiation power, and, by bolometer or other means, the relative powers of the component radiations measured in a beam of light. From the total radiation and the ratio of its components, t ..." ] } ] }, { "id": "distributed-constants", "label": "Distributed Constants", "aliases": [ "distributed capacity", "distributed constants", "distributed inductance" ], "total_occurrences": 96, "matching_section_count": 29, "matching_source_count": 7, "source_totals": [ { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 32, "section_count": 13 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 28, "section_count": 2 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 13, "section_count": 3 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 12, "section_count": 2 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 4, "section_count": 3 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 4, "section_count": 3 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 3, "section_count": 3 } ], "section_hits": [ { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 13, "number": 13, "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 23, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "CHAPTER XIII. DISTRIBUTED CAPACITY, INDUCTANCE, RESISTANCE, AND LEAKAGE. 107. As far as capacity has been considered in the foregoing chapters, the assumption has been made that the condenser or other source of negative reactance is shunted across the circuit at a definite point. In many ...", "... hole length of the conductor, so that the circuit can be considered as shunted by an infinite number of infinitely small condensers infi nitely near together, as diagrammatically shown in Fig. 83. iiiimiiiiumiiiT TTTTTTTTTT.TTTTTTTTTT i Fig. 83. Distributed Capacity. In this case the intensity as well as phase of the current, and consequently of the counter E.M.F. of inductance and resistance, vary from point to point ; and it is no longer possible to treat the circuit in the usual manner by the vector diagram. T ...", "... the E.M.Fs., but also the currents, at the beginning, end, and different points of the conductor, are different in intensity and in phase. Where the capacity effect of the line is small, it may with sufficient approximation be represented by one con- DISTRIBUTED CAPACITY. 159 denser of the same capacity as the line, shunted across the line. Frequently it makes no difference either, whether this condenser is considered as connected across the line at the generator end, or at the receiver end, or at the middle. The best ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "section_title": "Dibtbisnted Capacity, Inductance, Besistance, And", "kind": "chapter", "sequence": 12, "number": 12, "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 11, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "... capacity is distributed over the whole length of the conductor, so that the circuit can be considered as shunted by an infinite number of infinitely small condensers infi. nitely near together, as diagrammatically shown in Fig. 83. 8 3 S Fig, 83. Distributed Capacity. In this case the intensity as well as phase of the current,, and consequently of the counter E.M.F. of inductance and resistance, vary from point to point ; and it is no longer possible to treat the circuit in the usual manner by the vector diagram. ...", "... .M.Fs., but also the currents, at the beginning, end, and different points of the conductor, are different in intensity and in phase. Where the capacity effect of the line is small, it may with sufficient approximation be represented by one con- §103] DISTRIBUTED CAPACITY. 151 denser of the same capacity as the line, shunted across the line. Frequently it makes no difference either, whether this condenser is considered as connected across the line at the generator end, or at the receiver end, or at the middle. The best ...", "... ers shunted across the line. 104. A.) Line capacity represented by one condetiser shunted across middle of line. Let — Y == g -{- j'b = admittance of receiving circuit; z =i r — j X = impedance of line ; be = condenser susceptance of line. §105] DISTRIBUTED CAPACITY. 15S Denoting, in Fig. 84, the E.M.F., viz., current in receiving circuit by E^ /, the E.M.F. at middle of line by E\\ the E.M.F., viz., current at generator by EoyJo\\ t r n Fig. 84. Capacity Shmrttd acroat MtMli of Uin, We have, E' = E+ ' ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "CHAPTER XV DISTRIBUTED CAPACITY, INDUCTANCE, RESISTANCE, AND LEAKAGE 127. In the foregoing, the phenomena causing loss of energy in an alternating-current circuit have been discussed; and it has been shown that the mutual relation between current and e.m.f. can be expressed by two of ...", "... ceding chapter — to circuits containing iron and other materials producing energy losses outside of the electric conductor. 128. As far as capacity has been considered in the foregoing chapters, the assumption has been made that the condenser or 168 DISTRIBUTED CAPACITY 169 other source of negative reactance is shunted across the circuit at a definite point. In many cases, however, the condensive react- ance is distributed over the whole length of the conductor, so that the circuit can be considered as shunted by an inf ...", "... oss the line. If the length of transmission is 150 km., and the voltage, 30,000, condensive reactance at 60 cycles, x = 2,970 ohms; charging current, ?'o = 10.1 amp.; line resistance, r = 06 ohms; main current at 10 per cent, loss, / = 45.5 amp. DISTRIBUTED CAPACITY 171 The condenser current is thus about 22 per cent, of the main current, and the approximate calculation of the effect of line capacity still fairly accurate. At 300 km. length of transmission it will, at 10 per cent, loss and with the same size of co ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-44", "section_label": "Chapter 4: Distributed Capacity Of High-Potential Transformers", "section_title": "Distributed Capacity Of High-Potential Transformers", "kind": "chapter", "sequence": 44, "number": 4, "location": "lines 23179-23585", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "snippets": [ "CHAPTER IV. DISTRIBUTED CAPACITY OF HIGH-POTENTIAL TRANSFORMERS. 40. In the high-potential coils of transformers designed for very high voltages phenomena resulting from distributed capacity occur. In transformers for very high voltages — 100;000 volts and more, or even considerably ...", "CHAPTER IV. DISTRIBUTED CAPACITY OF HIGH-POTENTIAL TRANSFORMERS. 40. In the high-potential coils of transformers designed for very high voltages phenomena resulting from distributed capacity occur. In transformers for very high voltages — 100;000 volts and more, or even considerably less in small transformers — the high- potential coil contains a large number of turns, a great length of conductor, and therefore its electrostatic capacity is ...", "... e transformer. With such frequencies, of many thousand cycles, the internal capacity of the transformer becomes very marked in its effect on the dis- tribution of voltage and current, and may produce dangerous high-voltage points in the transformer. The distributed capacity of the transformer, however, is differ- ent from that of a transmission line. 342 HIGH-POTENTIAL TRANSFORMERS 343 In a transmission line the distributed capacity is shunted capacity, that is, can be represented diagrammatically by con- densers s ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 2774-3131", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-06/", "snippets": [ "... In Fig. 29, the diagram is shown for 45° lag, in Fig. 30 for noninductive load, and in Fig. 31 for 45° lead of the currents with regard to their E.M.Fs. BALANCED THREE -PHASE SYSTEM 45° LEAD THREE-PHASE CIRCUIT 80°LA» TRANSMISSION LINE' WITH DISTRIBUTED CAPACITY, INDUCTANCB RESISTANCE AUD LEAKAQB •I, Fig. 31. Fig. 32. As seen, the induced generator E.M.F. and thus the generator excitation with lagging current must be higher, with leading current lower, than at non-inductive load, or conversely with th ...", "... r's circuit, Ev Ez, E9 fall off more with lagging, less with leading current, than with non- inductive load. 36. As further instance may be considered the case of a single phase alternating current circuit supplied over a cable containing resistance and distributed capacity. 48 ALTERNATING-CURRENT PHENOMENA. Let in Fig. 33 the potential midway between the two terminals be assumed as zero point 0. The two terminal voltages at the receiver circuit are then represented by the points E and El equidistant from 0 and opposite ...", "... ing finite line elements, while in reality when calculated by the differential method they are smooth curves. TOPOGRAPHIC METHOD. 49 37. As further instance may be considered a three-phase circuit supplied over a long distance transmission line of distributed capacity, self-induction, resistance, and leakage. Let, in Fig. 38, O£v ~OEy ~OEZ = three-phase E.M.Fs. at receiver circuit, equidistant from each other and = E. Let OIV Oly Of3 = three-phase currents in the receiver circuit equidistant from each other and = /, ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... stance, with a line of 150 miles length, the resonance frequency is /0 = 313 cycles per second, or between the 5th harmonic and the 7th harmonic, 300 and 420 cycles of a 60-cycle system; fairly close to the 5th har- monic. The study of such a circuit of distributed capacity thus becomes of importance with reference to the investigation of the effects of higher harmonics of the generator wave. In long-distance telephony the important frequencies of speech probably range from 100 to 2000 cycles. For these fre- er quencies ...", "... LONG-DISTANCE TRANSMISSION LINE 281 contain from about one-half to 11 complete waves of the im- pressed frequency. For long-distance telephony the phenomena occurring in the line thus can be investigated only by consider- ing the complete equation of distributed capacity and inductance as so-called \"wave transmission\" and the phenomena thus essentially differ from those in a short energy transmission line. 4. Therefore in very long circuits, as in lines conveying alter- nating currents of high value at high potential ove ...", "... .f. differ by one-eighth period if + ab — fig = ag + J3b, or which gives rg + xb = 0, (37) which means that two of the four line-constants, either g and x or g and 6, must be zero. The case where g = 0 = x, that is, a line having only resistance and distributed capacity but no self-inductance, is approxi- mately realized in concentric or multiple-conductor cables, and in these the space-phase angle tends towards 45 degrees lead for infinite length. 15. As an example are shown the characteristic curves of a transmission ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 3267-3618", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-06/", "snippets": [ "... rcuit, Ei, E2, Es, fall off more with lagging, and less with leading current, than with non-inductive load. 39. As a further example may be considered the case of a single-phase alternating-current circuit supplied over a cable containing resistance and distributed capacity. Let, in Fig. 32, the potential midway between the two ter- minals be assumed as zero point 0. The two terminal voltages at the receiver circuit are then represented by the points E and E^, equidistant from 0 and opposite each other, and the two cur- re ...", "... l thereto, the charging current of the line element as condenser; and in this manner passing along the line, element by element, we ultimately reach the generator terminal voltages, Ei^, E^^, £'3\", THREE PHASE CIRCUIT eO°LAG TRANSMISSION LINE WITH DISTRIBUTED CAPACITY, INDUCTANCE RESISTANCE AND LEAKAGE Fig. 33. 16 I TRANSMISSION WITH DISTRIBUTED 15 t CAPACITY, INDUCTANCE RESISTANCE AND LEAKAGE 90\" LAG Fig. 34. and generator currents, /i\", 72°, I^, over the topographical char- acteristics of voltage, ei ...", "... lines with 90° lag in the receiver circuit. Corresponding points of the two characteristics, e and i, are marked by corresponding figures 0 to 16, representing equi- distant points of the Hne. The values of voltage, current and TRANSMISSION LINE WITH DISTRIBUTED CAPACITY, INDUCTANCE RESISTANCE AND LEAKAGE Fig. 35. their difference of phase are plotted in Fig. 35 in rectangular coordinates with the distance as abscissas, counting from the receiving circuit toward the generator. As seen from Fig. 35, voltage and curr ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-29", "section_label": "Chapter 7: Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "section_title": "Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "kind": "chapter", "sequence": 29, "number": 7, "location": "lines 6798-7825", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "snippets": [ "... ) 98 TRANSIENT PHENOMENA 60. The oscillating start, or, in general, change of circuit conditions, is the most important, since in circuits containing capacity the transient effect is almost always oscillating. The most common examples of capacity are distributed capacity in transmission lines, cables, etc., and capacity in the form of electrostatic condensers for neutralizing lagging currents, for constant potential-constant current transformation, etc. (a) In transmission lines or cables the charging current is a fracti ...", "... nitude as x\\ thus 4xxc >r\\ For instance, with 10 per cent resistance drop, 30 per cent reactance voltage, and 20 per cent charging current in the line, assuming half the resistance and reactance as in series with the capacity (that is, representing the distributed capacity of the line by one condenser shunted across its center) and denoting ?-*• where e0 = impressed voltage, i0 = full-load current, we have x = 0.5 X 0.3 p = 0.15 p, r = 0.5 X 0.1 p = 0.05 p, and r -5- s -s- zc = 1 -f- 3 -r- 100, and 4 x xr + r2 = ...", "... as will be shown in the following chapters, in the case of a transmission line V 9 xt. 62.5 ohms Fig. 26. Starting of an alternating-current circuit having capacity, inductance and resistance in series. Oscillating start of long period. with distributed capacity and inductance, the oscillation does not consist of one definite frequency but an infinite series of frequencies, and the preceding discussion thus approximates only the fundamental frequency of the system. This, however, is the frequency which usually pr ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-43", "section_label": "Chapter 3: The Natural Period Of The Transmission Line", "section_title": "The Natural Period Of The Transmission Line", "kind": "chapter", "sequence": 43, "number": 3, "location": "lines 21721-23178", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "snippets": [ "... 4) and using the effective values L0' and C0', the fundamental frequency, equation (11), then appears in the form 2* ^fLJc^ ' that is, the same value as found for the condenser discharge. In comparing with localized inductances and capacities, the distributed capacity and inductance, in free oscillation, thus are represented by their effective values (13) and (14). 30. Substituting in equations (4), Cl = <>i + jcv (16) gives I = (cl + jc2) cos ftl and (17) NATURAL PERIOD OF TRANSMISSION LINE 325 By ...", "... efinite wave length, depending upon the dimensions of the body of water, but very short waves, ripples in the water, can have any wave length, and do not depend on the size of the body of water. A further investigation of oscillations in conductors with distributed capacity, inductance, and resistance requires, how- ever, the consideration of the resistance, and so leads to the investigation of phenomena transient in space as well as in time, which are discussed in Section IV. 39. In the equations discussed in the preceding ...", "... cuit open. Such oscillating circuits, however, — representing the most frequent and most important case of high-potential disturbances in transmission systems, — cannot be represented by the preced- ing equations since they are not circuits of uniformly distributed constants but complex circuits comprising several sections of different constants, and therefore of different ratios of energy consumption and energy storage, -and ^- During the free Ju C oscillation of such circuits an energy transfer takes place be- tween the ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "... of the line. The frequency then is ^ = 4170- (2«) LINE OSCILLATIONS. 79 The frequency / depends upon the length ^i of the section of hne in which the oscillation occurs. That is, the oscillations occurring in a transmission line or other circuit of distributed capacity have no definite frequency, but any frequency may occur, depending on the length of the circuit section which oscillates (provided that this circuit section is short compared with the entire length of the circuit, that is, the frequency high compared with ...", "... s, but not with frequencies of hundred thousands or millions of cycles. 32. The line constants Vq, go, Lq, Cq are given per unit length, as per cm., mile, 1000 feet, etc. The most convenient unit of length, when dealing with tran- sients in circuits of distributed capacity, is the velocity unit v. That is, choosing as unit of length the distance of propagation in unit time, or 3 X 10^° cm. in overhead circuits, this gives v = 1, and therefore \"\" = ^^«^» -' ^ (39) LnCn — 1, '1 or Oo — 7^ , i^o — TT • That is, th ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-07", "section_label": "Lecture 7: Line Oscillations", "section_title": "Line Oscillations", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3956-4744", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "snippets": [ "... of the line. The frequency then is /.-rrr- (26) LINE OSCILLATIONS. 79 The frequency / depends upon the length Zi of the section of line in which the oscillation occurs. That is, the oscillations occurring in a transmission line or other circuit of distributed capacity have no definite frequency, but any frequency may occur, depending on the length of the circuit section which oscillates (provided that this circuit section is short compared with the entire length of the circuit, that is, the frequency high compared with ...", "... s, but not with frequencies of hundred thousands or millions of cycles. 32. The line constants r0, go, L0, C0 are given per unit length, as per cm., mile, 1000 feet, etc. The most convenient unit of length, when dealing with tran- sients in circuits of distributed capacity, is the velocity unit v. That is, choosing as unit of length the distance of propagation in unit time, or 3 X 1010 cm. in overhead circuits, this gives v = 1, and therefore \"- T 1 or GO — -j- ; LIQ — -ftj- 1 j -L/o That is, the capacity per ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... strength. 161 Direct-current system, erhciency, 441 Displacement current. 152 Disruptive gradient. 165 Distortion by magnetic field, resist- ance and reactance pulsa- tion. a42 of magnetizing current. 117 of wave, see Harmonics by hysteresis, 116 Distributed capacity. 168 Double delta connections of trans- formers to sis-phase. 428 frequency power and torque with distorted wave, 381 quantities, 180 peak wave. 370 T connections of transformers to six -phase, 430 ^ connection of transformers to six-phase, 429 Dr ...", "... strength, 161 Direct-current system, efficiency, 441 Displacement current, 152 Disruptive gradient, 165 Distortion by magnetic field, resist- ance and reactance pulsa- tion, 342 of magnetizing current, 117 of wave, see Harmonics by hysteresis, 116 Distributed capacity, 168 Double delta connections of trans- formers to six-phase, 428 frequency power and torque with distorted wave, 381 quantities, 180 peak wave, 370 T connections of transformers to six-phase, 430 Y connection of transformers to six-phase, 429 D ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-08", "section_label": "Chapter 4: Distributed Capacity Of High-Potential Trans Former. 342", "section_title": "Distributed Capacity Of High-Potential Trans Former. 342", "kind": "chapter", "sequence": 8, "number": 4, "location": "lines 875-887", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-08/", "snippets": [ "CHAPTER IV. DISTRIBUTED CAPACITY OF HIGH-POTENTIAL TRANS- FORMER. 342 40. The transformer coil as circuit of distributed capacity, and the character of its capacity. 342 41. The differential equations of the transformer coil, and their integral equations. 344 42. Terminal conditio ...", "CHAPTER IV. DISTRIBUTED CAPACITY OF HIGH-POTENTIAL TRANS- FORMER. 342 40. The transformer coil as circuit of distributed capacity, and the character of its capacity. 342 41. The differential equations of the transformer coil, and their integral equations. 344 42. Terminal conditions and final approximate equations. 346" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-30", "section_label": "Chapter 8: Low Frequency Surges In High Potential Systems", "section_title": "Low Frequency Surges In High Potential Systems", "kind": "chapter", "sequence": 30, "number": 8, "location": "lines 7826-9227", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-30/", "snippets": [ "... cable systems, occasionally destructive high potential low frequency surges occur; that is, oscillations of the whole system, of the same character as in the case of localized capacity and inductance discussed in the preceding chapter. While a system of distributed capacity has an infinite number of frequencies, which usually are the odd multiples of a funda- mental frequency of oscillation, in those cases where the fundamental frequency predominates and the effect of the higher frequencies is negligible, the oscillation can ...", "... tal frequency predominates and the effect of the higher frequencies is negligible, the oscillation can be approxi- mated by the equations of oscillation given in Chapters V and VII, which are far simpler than the equations of an oscillation of a system of distributed capacity. Such low frequency surges comprise the total system, not only the transmission lines but also the step-up transformers, gen- erators, etc., and in an underground cable system in such an oscillation the capacity and inductance are indeed localized to a ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-50", "section_label": "Chapter 1: General Equations", "section_title": "General Equations", "kind": "chapter", "sequence": 50, "number": 1, "location": "lines 27761-28694", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "snippets": [ "... scillation over the multigap lightning arrester circuit, or a mile in a long-distance transmission circuit or high-potential cable, or the distance of the velocity of light, 300,000 km., etc. The permanent values of current and e.m.f. in such circuits of distributed constants have, for alternating-current circuits, been investigated in Section III, where it was shown that they can be treated as transient phenomena in space, of the complex variables, current / and e.m.f. E. Transient phenomena in circuits with distributed cons ...", "... ibuted constants have, for alternating-current circuits, been investigated in Section III, where it was shown that they can be treated as transient phenomena in space, of the complex variables, current / and e.m.f. E. Transient phenomena in circuits with distributed constants, and, therefore, the general investigation of such circuits, leads to transient phenomena of two independent variables, time t and space or distance /; that is, these phenomena are transient in time and in space. The difficulty met in studying such phen ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-55", "section_label": "Chapter 6: Transition Points And The Complex Circuit", "section_title": "Transition Points And The Complex Circuit", "kind": "chapter", "sequence": 55, "number": 6, "location": "lines 32709-33527", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-55/", "snippets": [ "... ANSITION POINTS AND THE COMPLEX CIRCUIT. 40. The discussions of standing waves and free oscillations in Chapters III and V, and traveling waves in Chapter IV, apply directly only to simple circuits, that is, circuits comprising a con- ductor of uniformly distributed constants r, L, g, and C. Indus- trial electric circuits, however, never are simple circuits, but are always complex circuits comprising sections of different con- stants, — generator, transformer, transmission lines, and load, — and a simple circuit is realized on ...", "... it of apparatus as reactive coils, etc., in which one of the constants is very small compared with the other and therefore is usually neglected and the apparatus considered as \"massed inductance,'7 etc., and allows the investi- gation of the effect of the distributed capacity of reactive coils and similar matters, by representing the reactive coil as a finite (frequently quite long) section ^0 of the circuit. 43. Let y*0, Av >^2, ... kn be a number of transition points at which the circuit constants change and the quantities ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... of the phenomena in a complex circuit comprising sections of very different constants; that is, a combination of a circuit section of high inductance and small resistance and negligible capacity and conductance, as a generating station, with a circuit of distributed capacity and inductance, as a transmission line. The extreme case of such a discharge would occur if a short circuit at the busbars of a gen- erating station opens while the transmission line is connected to the generating station. Let r = the total resistance a ...", "... rgy, of complex circuit 507 of energy in oscillation of complex circuit 507, 521 Transformation ratio at transition point of wave 529 of voltage and current at transition point 529 Transformer, alternating, operating oscillating-current generator 87 distributed capacity 342 quarter-wave oscillation 312 starting 44 and magnetic saturation 180 Transient rail resistance with direct current 386 terms, conditions of their appearance 21, 23 of alternating-current circuit 91 capacity and inductance, physical meaning 1 ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-06", "section_label": "Lecture 6: Double-Energy Transients", "section_title": "Double-Energy Transients", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3721-4369", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-06/", "snippets": [ "... line insulation against momentary voltages, is e^, the maximum discharge current in the line is limited to Iq = eoyo. If L is high but C low, as in the high-potential winding of a high-voltage transformer (which winding can be considered as a circuit of distributed capacity, inductance, and resistance), Zq is high and 2/0 low. That is, a high transient voltage can produce only moderate transient currents, but even a small transient cur- rent produces high voltages. Thus reactances, and other reactive apparatus, as transforme ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "LECTURE VIII. TRAVELING WAVES. 33. In a stationary oscillation of a circuit having uniformly distributed capacity and inductance, that is, the transient of a circuit storing energy in the dielectric and magnetic field, current and voltage are given by the expression i = ioe-\"^ cos ((/> T CO — 7), ^ . . e = eoe~\"' sin ((^ =F co — 7), where yo. If L is high but C low, as in the high-potential winding of a high-voltage transformer (which winding can be considered as a circuit of distributed capacity, inductance, and resistance), z0 is high and T/O low. That is, a high transient voltage can produce only moderate transient currents, but even a small transient cur- rent produces high voltages. Thus reactances, and other reactive apparatus, as transforme ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-08", "section_label": "Lecture 8: Traveling Waves", "section_title": "Traveling Waves", "kind": "lecture", "sequence": 8, "number": 8, "location": "lines 4745-5520", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "snippets": [ "LECTURE VIII. TRAVELING WAVES. 33. In a stationary oscillation of a circuit having uniformly distributed capacity and inductance, that is, the transient of a circuit storing energy in the dielectric and magnetic field, current and voltage are given ^by the expression i = iQe~ut cos (0 T co - 7), ) e = e0e~ut sin ( T co — 7), ) where 0 is the time angle, co the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-06", "section_label": "Chapter 6: Topographic Method", "section_title": "Topographic Method", "kind": "chapter", "sequence": 6, "number": 6, "location": "lines 3230-3545", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-06/", "snippets": [ "... osed figure, which may be called the topographic circuit characteristic. Such a characteristic is, for instance, OE^E-IE^E^E^E^^ in Figs. 31 to 34, etc. ; further instances are shown in the following chapters, as curved characteristics in the chapter on distributed capacity, etc. 62 AL TERNA TJNG-CURRENT PHENOMENA. ^ [§ 38" ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-08", "section_label": "Chapter 8: Shaping Of Waves By Magnetic Saturation", "section_title": "Shaping Of Waves By Magnetic Saturation", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 12962-16963", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-08/", "snippets": [ "... s, -- , / ^ N V B/ \\ ^ // \\t ^^=?rT\" / 1 a^ ^ \\ 5= \" 1 i / r*° U- ^ s // ^ ) // ^ V y ! frequencies with which the high-voltage coils of transformers, as circuits of distributed capacity, can resonate. 76. Magnetic saturation, and closed or partly closed magnetic circuits thus are a likely source of wave-shape distortion, resulting in high voltage peaks, and where they are liable to occur, as in 152 ELECTRIC CIRCUITS current transfor ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-10", "section_label": "Chapter 10: Instability Of Circuits : The Arc", "section_title": "Instability Of Circuits : The Arc", "kind": "chapter", "sequence": 10, "number": 10, "location": "lines 17632-21381", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-10/", "snippets": [ "... underground cables, usually the inductance is too low and thus no cumulative oscillation results, except perhaps sometimes in single-conductor cables, etc. In the high-potential windings of large high-voltage power trans- formers, however, as circuits of distributed capacity, inductance and resistance, the resistance commonly is below the value through which a cumulative oscillation can be produced and maintained, and in high-potential transformers, destruction by high voltages resulting from the cumulative oscillation of som ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-17", "section_label": "Chapter 17: Circuits With Distributed Leakage", "section_title": "Circuits With Distributed Leakage", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 30429-31656", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-17/", "snippets": [ "... 13) These equations (13) can be written in various different forms. They are interesting in showing in a direct-current circuit features which usually are considered as characteristic of wave trans- mission, that is, of alternating-current circuits with distributed capacity. The first term of equations (13) may be considered as the out- flowing components of current and voltage respectively, the sec- ond terms as the reflected components, and at the end of the circuit of distributed leakage, reflection would be considered a ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-40", "section_label": "Chapter 4: Arc Rectification", "section_title": "Arc Rectification", "kind": "chapter", "sequence": 40, "number": 4, "location": "lines 17755-19259", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-40/", "snippets": [ "... in rectifying arcs. Fig. 76. Rectified current in arc circuit. 266 TRANSIENT PHENOMENA zero and stops, and so its L — abruptly changes; that is, asud- ctt den change of voltage takes place in the circuit aACDc or bBCDc. Since this 'cuit contains distributed capacity, that of the transformer C' ^BC respectively, the line, etc., and inductance, an oscillatk ^.-.esults of a frequency depending upon the capacity and inductance, usually a few thousand cycles per second, and of a voltage depending upon the impressed e.m.f. ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-41", "section_label": "Chapter 1: Introduction", "section_title": "Introduction", "kind": "chapter", "sequence": 41, "number": 1, "location": "lines 19260-19338", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-41/", "snippets": [ "... therwise the method of treatment and the general form of the equations are the same as with transient functions of time. 2. Some of the cases in which transient phenomena in space are of importance in electrical engineering are : (a) Circuits containing distributed capacity and self-induc- tance, as long-distance energy transmission lines, long-distance telephone circuits, multiple spark-gaps, as used in some forms of high potential lightning arresters (multi-gap arrester), etc. (b) The distribution of alternating current i ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-48", "section_label": "Chapter 8: Velocity Of Propagation Of Electric Field", "section_title": "Velocity Of Propagation Of Electric Field", "kind": "chapter", "sequence": 48, "number": 8, "location": "lines 26095-27002", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "snippets": [ "... 91 / = the frequency of alternating current. It obviously is not permissible in a conductor having no return conductor. If a conductor conveying an alternating current has no return conductor, its circuit is closed by electrostatic capacity, either the distributed capacity of the conductor or capacity connected to the ends of the conductor. To produce in such a case con- siderable currents, either the conductor must be very long or the frequency and e.m.f. very high. No conductor extending parallel to the ground, as a tele ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-51", "section_label": "Chapter 2: Discussion Of General Equations", "section_title": "Discussion Of General Equations", "kind": "chapter", "sequence": 51, "number": 2, "location": "lines 28695-29315", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "snippets": [ "... NS 439 circuit, but is a stationary or standing wave. It is an oscillatory discharge of a circuit containing a distributed r, L, g, C, and therefore is analogous to the oscillating condenser discharge through an inductive circuit, except that, due to the distributed capacity, the phase changes along the circuit. The free oscilla- tions of a circuit such as a transmission line are of this character. For A = 0, that is, assuming the wave length of the oscillation as so great, hence the circuit as such a small fraction of the wav ..." ] } ] }, { "id": "co-operation", "label": "Co-operation", "aliases": [ "Co-operation", "co-operation" ], "total_occurrences": 80, "matching_section_count": 13, "matching_source_count": 2, "source_totals": [ { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "occurrence_count": 79, "section_count": 12 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-04", "section_label": "Chapter 3: The Individualistic Era: From Competition to Co-operation", "section_title": "The Individualistic Era: From Competition to Co-operation", "kind": "chapter", "sequence": 4, "number": 3, "location": "lines 874-1745", "status": "candidate", "occurrence_count": 20, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-04/", "snippets": [ "FROM COMPETITION TO CO-OPERATION finally a time came when the means of produc- tion of commodities increased beyond the demand possible under existing conditions. England was the first nation to benefit from the competitive organization of society. While a ...", "... hile the Revolutionary War had made it politically one nation. The great industrial development of our country in the last generation was the result. Finally even in the United States the rapidly 22 FROM COMPETITION TO CO-OPERATION increasing means of production have crept up to and beyond the means of possible consump- tion. This occurred later than in any other civilized nation, for various reasons. The rap- idlj' increasing population meant an abno ...", "... any of those who, far from the work of the world under the student lamp and in the chairs of our universities, ponder over the problems of the nation. The conception of competition as a benevo- 84 FROM COMPETITION TO CO-OPERATION lent force in the industrial progress was based upon the theory that by competition between the producers prices would be lowered down to near the cost of production, stopping just as much above the cost of production as ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-17", "section_label": "Chapter 16: The Future Corporation", "section_title": "The Future Corporation", "kind": "chapter", "sequence": 17, "number": 16, "location": "lines 6975-7567", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-17/", "snippets": [ "... be d d,\" to that of the modern corporation against which no justified hostility could ever have arisen even by the most exacting. The future success of our country as industrial nation depends on the extent to which co- operation can be developed within the industrial corporation, and between public and corpora- tion. This is realized more and more, and in- creasing efforts are made to bring about co- operation. Thus, in most modern corporations some w ...", "... l nation depends on the extent to which co- operation can be developed within the industrial corporation, and between public and corpora- tion. This is realized more and more, and in- creasing efforts are made to bring about co- operation. Thus, in most modern corporations some work is done to establish co-operation, in some much time and attention are devoted hereto by the highest officials. Unfortunately, due to the strong individual- istic temperament of mo ...", "... he industrial corporation, and between public and corpora- tion. This is realized more and more, and in- creasing efforts are made to bring about co- operation. Thus, in most modern corporations some work is done to establish co-operation, in some much time and attention are devoted hereto by the highest officials. Unfortunately, due to the strong individual- istic temperament of most corporation leaders, many of these activities are paternalism rather 20.'} ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-10", "section_label": "Chapter 9: America in the Individualistic Era", "section_title": "America in the Individualistic Era", "kind": "chapter", "sequence": 10, "number": 9, "location": "lines 4268-4715", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-10/", "snippets": [ "... easing excess of productive capacity over the demand for the products, had made competition so vicious that it threatened with destruction the victor as well as the van- quished, in a universal v.Tcck of the industry. Thus co-operation had to come, of neces- sity, to avoid the destructive effects of com- petition. Thus co-operative agreements between for- merly competing corporations came, and the individualistic era seemed to approach its end, the co-operat ...", "... ts of com- petition. Thus co-operative agreements between for- merly competing corporations came, and the individualistic era seemed to approach its end, the co-operative era to arrive. The fundamental jirinciple of industrial co- operation between corporations in the same or 120 AMERICA IN THE INDIVIDUALISTIC ERA similar fields comprise control of production; control of prices; interchange of information. Control of production 7neans: Elimination of the c ...", "... werful, but as an industrial nation we have gone backward with increasing rapidity. Competition has not been restored; no polit- ical law can resurrect a corpse, and while you AMERICA IN THE INDIVIDUALISTIC ERA can forbid co-operation by legislation, you can- not by law order people or corporations to commit suicide. The result thus has been increasing dis- organization, interference, inefficiency, and waste, leading to an industrial chaos just as regrettab ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-13", "section_label": "Chapter 12: Evolution: Political Government", "section_title": "Evolution: Political Government", "kind": "chapter", "sequence": 13, "number": 12, "location": "lines 5328-5797", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-13/", "snippets": [ "... a man who cannot run his own house- hold, in administrative charge of the community. If, then, continuity of office, held by compe- tent men, is necessary for the efficiency which is the fundamental requirement of successful co-operation^ there must be an efl'ective respon- sibility, at le^st until such time when all men are angels, or at least sufficiently many that all offices can be filled with men who are and remain unselfish, industrious, progressive, ...", "... fice. ^-ANh'dt, then, are the structural ejements in our American nation from which a continuous, competent, and responsible government coidd develop by evolution — a government such as is required for the efficient industrial co-operation of all citizens in the interest of all, under demo- cratic principles? 153 AMERICA AND THE NEW EPOCH In sucli organization there can be no indus- trial competition, but by the co-operation of all producers duplication of ...", "... ed for the efficient industrial co-operation of all citizens in the interest of all, under demo- cratic principles? 153 AMERICA AND THE NEW EPOCH In sucli organization there can be no indus- trial competition, but by the co-operation of all producers duplication of work and all waste effort is eliminated. The production is con- trolled to correspond with the legitimate de- mands for the product, and all production for mere profit, without regard to the ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-14", "section_label": "Chapter 13: Evolution: Industrial Government", "section_title": "Evolution: Industrial Government", "kind": "chapter", "sequence": 14, "number": 13, "location": "lines 5798-6232", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-14/", "snippets": [ "... d standard when not capable of work- ing, are the fundamental requisites to secure interest in the maintenance of existing condi- AMERICA AND THE NEW EPOCH tions witlioiit which there can be no real pa- triotism, no real co-operation. This has nothing to do with the broader question of socialism — that is, of the elimination of capital. Socialism has as many followers in the offices of our corporations as it has in the shops, and in no way precludes ...", "... This has nothing to do with the broader question of socialism — that is, of the elimination of capital. Socialism has as many followers in the offices of our corporations as it has in the shops, and in no way precludes co-operation within the corporation; indeed, in some respects the corporation may be considered as the first step toward socialism, and the industrial gov- ernment of the nation by the united corpora- tions as preliminary and crude form ...", "... same and similar in(iustries co-ordinates and correlates the work of the corporations, decides on production, on prices, policies, etc. Executive committees with their members chosen from different in- dustries take care of the co-operation of these industries, and finally an Industrial Senate as the supreme executive committee co-ordinates, con- trols, and directs all the country's industries — that is, governs the country. Thus, an indus- trial government would ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-16", "section_label": "Chapter 15: The American Nation", "section_title": "The American Nation", "kind": "chapter", "sequence": 16, "number": 15, "location": "lines 6598-6974", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-16/", "snippets": [ "XV THE AMERICAN NATION CO-OPERATIVE industrial organization presupposes racial unity. There can be no co-operation as long as there is racial strife and antagonism within the nation. The Ameri- can nation was formed— rather is being formed, since it is still in the formation period — by the commingling of the Anglo-Saxon, Teuton, Celt, ...", "... New World. We see it in the rapid growth of the English colonies, compared with the slow growth of other nations' colonies. But charac- teristic of the Anglo-Saxon also is the excessive; individualism which handicaps him in co- operation, and co-operation more and more becomes the essential of progress. Thus the 13 191 AMERICA AND THE NEW EPOCH Anglo-Saxons are not prominent as organizers, but rather are likely to be muddlers; the pres- ent world ...", "... it in the rapid growth of the English colonies, compared with the slow growth of other nations' colonies. But charac- teristic of the Anglo-Saxon also is the excessive; individualism which handicaps him in co- operation, and co-operation more and more becomes the essential of progress. Thus the 13 191 AMERICA AND THE NEW EPOCH Anglo-Saxons are not prominent as organizers, but rather are likely to be muddlers; the pres- ent world's war affords a ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-18", "section_label": "Chapter 17: Conclusion", "section_title": "Conclusion", "kind": "chapter", "sequence": 18, "number": 17, "location": "lines 7568-8027", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-18/", "snippets": [ "... ndividual- is lie principle of industrial organization, and have organized or are organizing as rapidly as possible a co-operative system of industrial l)roduction. Against the vastly higher pro- ductive efficiency of industrial co-operation of the European nations after the war, our coun- try's individualistic industrial organization, with everybody fighting against everybody else, industrially, politically, and socially, is hope- less, and America thus will either ...", "... else, industrially, politically, and socially, is hope- less, and America thus will either fail, cease to be one of the world's leading industrial nations, or we must also organize a system of industrial production based on co-operation and not on 217 AMERICA AND THE NEW EPOCH competition. That is, we must enter the co- operative era, or fall by the wayside. America's national temperament is demo- cratic, our methods of organization thus con- central ...", "... d to the nation and ready for its defense — with this accomplished, quickly the political power would shift and the political government, instead of outlawing and fighting corporate success and business, would be brought into co-operation with the industrial corporation, and from thereon the progress toward democratic co-operative industrial or- ganization would be steady and rapid. Internationally the co-operative era would bring about material changes: with pro ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-06", "section_label": "Chapter 5: England in the Individualistic Era", "section_title": "England in the Individualistic Era", "kind": "chapter", "sequence": 6, "number": 5, "location": "lines 2409-2775", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-06/", "snippets": [ "... nst their later com- petitors, and when, in the last decades, the seriousness of the situation was beginning to be realized, remedial action was difficult, because the educational institutions, not receiving the assistance and co-operation of the industries, had in their technological branches remained behind the engineering schools of America and Germany. In these latter countries, in the beginning of the industrial awakening a close co-operation and practical ...", "... ssistance and co-operation of the industries, had in their technological branches remained behind the engineering schools of America and Germany. In these latter countries, in the beginning of the industrial awakening a close co-operation and practically an alliance had been established between the industry and the technical college or university. The industry gave preference to the college-trained men — the reverse of what was the rule in England — often, as ...", "... ese schools, advised and guided their courses, and so did everything to make the engineering schools most useful for the indus- tries, while the faculties of the technical schools quickly realized the advantage of this close co- operation with the industry, encouraged it to the fullest extent, wherever possible selected their instructors from the industries, in short, availed themselves of the assistance given by the industries. As the result, with the excepti ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-09", "section_label": "Chapter 8: America in the Past", "section_title": "America in the Past", "kind": "chapter", "sequence": 9, "number": 8, "location": "lines 3741-4267", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-09/", "snippets": [ "... ir existence, against the barren soil, unfriendly nature, hostile Indi- ans. Little help was to be expected from a Government which was practically non-existing; locally the loosest kind of government, essen- tially a voluntary co-operation with little man- datory power, and far away across the ocean a central government in the English king, which essentially limited itself to foreign relations, but took little part in the local issues of the community, and w ...", "... now the United States would have become a number of separate and independent nations, just as South America is to-day, with constant rivalries and contentions. Fortunately we escaped this; the Union was formed by vol- untary co-operation of the thirteen States, and ever since the progress toward closer co-opera- tion and centralization of the nation has gone on steadily. However, as the States had voluntarily en- tered the Union, so, naturally, it might be ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-12", "section_label": "Chapter 11: Democracy and Monarchy", "section_title": "Democracy and Monarchy", "kind": "chapter", "sequence": 12, "number": 11, "location": "lines 5060-5327", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-12/", "snippets": [ "... ns. We will have to stop our muddling, our interference of every- body with everybody, and prepare to meet Europe by a still more efficient co-operative industrial system. How can we organize such efficiency of in- dustrial co-operation? What forms or shapes must such organization assume in our nation? It is a matter of evolution, of which we cannot foresee the end, but one thing we can see with certainty, and that is, how not to proceed; we cannot c ...", "... but safe. An illustration hereof is social legislation. We realize that the most serious problem before our nation, which must be solved before we can hope for ejQBcient indus- trial reorganization, is to secure the active co- operation of the masses, those who are becom- ing increasingly indifferent, if not antagonistic, to the maintenance of existing society. The German Government has solved this problem by eliminating the three great fears of the masses b ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-03", "section_label": "Chapter 2: The Epoch of the French Revolution", "section_title": "The Epoch of the French Revolution", "kind": "chapter", "sequence": 3, "number": 2, "location": "lines 627-873", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-03/", "snippets": [ "... -stones of the true history of the human race, which is made on the fields and farms, in the factories and workshops, in the business houses and shipping-offices. Ill THE INDIVIDUALISTIC ERA: FROM COMPETITION TO CO-OPERATION THE epoch of the French Revolution, ush- ered in by the declaration of the rights of man — liherte, egalite, fraternite — struck the fet- ters of feudalism from the human race, and gave free play to the intelligence, energy, ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-07", "section_label": "Chapter 6: Germany in the Individualistic Era", "section_title": "Germany in the Individualistic Era", "kind": "chapter", "sequence": 7, "number": 6, "location": "lines 2776-3206", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-07/", "snippets": [ "... a legiti- mate political party, and Bismarck, defeated and discredited, had soon to relinquish his power and retire into private life. Then began the reorganization of the Ger- man nation, the change from individualism toward co-operation, which has made the in- dustrial Germany of to-day. In the mean time a new emperor, the present Kaiser, had ascended the throne, while politi- cally and industrially the conflict was raging between the remnant of feudalism, ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-01", "section_label": "Lecture 1: General Review", "section_title": "General Review", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 154-565", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-01/", "snippets": [ "... d for voltage. This arrangement scatters the lamps over a considerable voltage range, and different voltages are then adopted by different distribution systems, so as to utilize the entire product of manufacture at its maximum economy. The result of this co-operation between lamp manufacturers and users is, that the incandescent lamps are very much closer to requirements, and more uniform, than would be possible otherwise. The effect however is, that the distribution is rarely actually no, and in alternating current s ..." ] } ] }, { "id": "competition", "label": "Competition", "aliases": [ "Competition", "competition" ], "total_occurrences": 78, "matching_section_count": 12, "matching_source_count": 1, "source_totals": [ { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "occurrence_count": 78, "section_count": 12 } ], "section_hits": [ { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-04", "section_label": "Chapter 3: The Individualistic Era: From Competition to Co-operation", "section_title": "The Individualistic Era: From Competition to Co-operation", "kind": "chapter", "sequence": 4, "number": 3, "location": "lines 874-1745", "status": "candidate", "occurrence_count": 46, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-04/", "snippets": [ "FROM COMPETITION TO CO-OPERATION finally a time came when the means of produc- tion of commodities increased beyond the demand possible under existing conditions. England was the first nation to benefit from the competitive organization of ...", "... ut which was settled first — the New England States — felt the pinch of the industrial problem already in the middle of the nineteenth century, but the problem was solved, at least temporarily, by forcibly ex- cluding foreign competition from the United States, and so reserving the markets of the South and of the West to the industrial New England States. This was the issue on which the Civil War was fought; the abolishment of slavery was merely an inc ...", "... one nation, while the Revolutionary War had made it politically one nation. The great industrial development of our country in the last generation was the result. Finally even in the United States the rapidly 22 FROM COMPETITION TO CO-OPERATION increasing means of production have crept up to and beyond the means of possible consump- tion. This occurred later than in any other civilized nation, for various reasons. The rap- idlj' increasing populatio ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-10", "section_label": "Chapter 9: America in the Individualistic Era", "section_title": "America in the Individualistic Era", "kind": "chapter", "sequence": 10, "number": 9, "location": "lines 4268-4715", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-10/", "snippets": [ "... dence. These were the golden days, to which our in- dividualists hark back, which our legislatures and governments attempt to restore by legal enactments. But the world does not stand still, for standstill is death; in free competition, the more successful producers destroyed the less successful ones; companies and corporations formed and absorbed or defeated the individual 119 AMERICA AND THE NEW EPOCH producers, the Larger corporations absorbed or vanqu ...", "... , combined with each other in still larger ones, and so, by the working of inexorable economic laws, the con- solidation of the industries progressed from numerous small producers to the formation of huge corporations, w^ith competition steadily growing more strenuous, more intense, and more destructive. Finally, in the 90's the end was reached; especially in those industries which had been organized into a few large corporations. The necessity of keeping ...", "... in those industries which had been organized into a few large corporations. The necessity of keeping the factories going, with the steadily increasing excess of productive capacity over the demand for the products, had made competition so vicious that it threatened with destruction the victor as well as the van- quished, in a universal v.Tcck of the industry. Thus co-operation had to come, of neces- sity, to avoid the destructive effects of com- petition ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-13", "section_label": "Chapter 12: Evolution: Political Government", "section_title": "Evolution: Political Government", "kind": "chapter", "sequence": 13, "number": 12, "location": "lines 5328-5797", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-13/", "snippets": [ "... prosperous and successful thus far, in spite of our previous and present method of dealing with social, in- dustrial, and political problems, which is no method at all, but mere muddling. However, we had no serious foreign competition to meet; we had at our disposition the vast and un- touched resources of a virgin continent, the intellectual stores of the Old World, and the continuous supply of skilled and unskilled labor, in the despised immigrant, wh ...", "... soil as fertilizer what we take out as crops; planting and raising the trees which we cut down for lumber; raising the food which we feed to our sheep and cattle, and that with a reorganized, highly efficient Europe in competition. In our industrial age the essential require- ments of an efficient national organization com- prise: Continuity, competency, and responsi- bility of the administrative organization. In our complex civilization, it usually takes ...", "... rnment such as is required for the efficient industrial co-operation of all citizens in the interest of all, under demo- cratic principles? 153 AMERICA AND THE NEW EPOCH In sucli organization there can be no indus- trial competition, but by the co-operation of all producers duplication of work and all waste effort is eliminated. The production is con- trolled to correspond with the legitimate de- mands for the product, and all production for mere profit ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-18", "section_label": "Chapter 17: Conclusion", "section_title": "Conclusion", "kind": "chapter", "sequence": 18, "number": 17, "location": "lines 7568-8027", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-18/", "snippets": [ "... and America thus will either fail, cease to be one of the world's leading industrial nations, or we must also organize a system of industrial production based on co-operation and not on 217 AMERICA AND THE NEW EPOCH competition. That is, we must enter the co- operative era, or fall by the wayside. America's national temperament is demo- cratic, our methods of organization thus con- central — that is, from the individual units to the central organis ...", "... with production controlled, first nationally and then inter- nationally, by the demand for the product, and production for the mere profit of producing 220 CONCLUSION eliminated as uneconomical, much of the inter- national competition for the markets of the world would cease, and with it most of the causes of war. The secondary nations would come within the sphere of influence, under the political and industrial guidance of the world's leading industri ...", "... ystem of com- petition for profit would cease, but would re- main and even extend in dealing with those things which one nation, or one territory, can produce better or more conveniently than another. But with international competition ended and co-operation established, international war also would become an impossibility as a matter of course, as there would be no causes for war. Thus no international court of justice, no world's congress or internationa ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-03", "section_label": "Chapter 2: The Epoch of the French Revolution", "section_title": "The Epoch of the French Revolution", "kind": "chapter", "sequence": 3, "number": 2, "location": "lines 627-873", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-03/", "snippets": [ "... e signs or mark-stones of the true history of the human race, which is made on the fields and farms, in the factories and workshops, in the business houses and shipping-offices. Ill THE INDIVIDUALISTIC ERA: FROM COMPETITION TO CO-OPERATION THE epoch of the French Revolution, ush- ered in by the declaration of the rights of man — liherte, egalite, fraternite — struck the fet- ters of feudalism from the human race, and gave free play to the int ...", "... rgy, and initia- tive of all the millions of human beings. The development of the steam-engine, of steamship and locomotive, and later of telegraph, tel- ephone, and electric power, forged the tools; the free and unrestrained competition, which is the industrial expression of the individualistic age, gave the driving force which led to the great industrial development of the last cen- tury. The result was that the last century has seen a greater progress o ...", "... listic age, gave the driving force which led to the great industrial development of the last cen- tury. The result was that the last century has seen a greater progress of mankind than all the previous centuries together. Competition thus became the industrial ex- pression of the individualistic era. 19 AMERICA AND THE NEW EPOCH Under the competitive system of industrial organization — \"capitalistic society,\" as it is often called — the means of producti ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-05", "section_label": "Chapter 4: The Individualistic Era: The Other Side", "section_title": "The Individualistic Era: The Other Side", "kind": "chapter", "sequence": 5, "number": 4, "location": "lines 1746-2408", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-05/", "snippets": [ "... THE OTHER SIDE found opportunity to make himself industrially independent and moderately prosperous — as pros})erity was considered in these, the golden days of individualism. But the means of pro- duction rai)idly increased, competition between producers became more severe and destructive, the smaller producer had to make room for the larger, and the chances of the individual em- ployee to rise into the ranges of the employers became less and less, and s ...", "... ations, and realize that it is coming inevitably through- out all the industrial world. There can be no serious objection against the eight-hour day, provided that it is universal. The objection is the handicap in industrial competition met by a AMERICA AND THE NEW EPOCH corporation with eight-hour working-day against a corporation working nine or more hours. Thus if the efforts toward a shorter working-day could be more equahzed, directed against those ...", "... hort- ening of the hours, and the reduction from nine hours to eight hours may not mean a decrease of one-ninth of the output, but it means a very substantial decrease of output, sufficient to prove a serious handicap in competition with a nine-hour day. Shorter hours means a decreased plant effi- ciency, and thus an increase of the fixed cost representing interest and depreciation of the factory investment, as the plant remains idle a larger part of ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-06", "section_label": "Chapter 5: England in the Individualistic Era", "section_title": "England in the Individualistic Era", "kind": "chapter", "sequence": 6, "number": 5, "location": "lines 2409-2775", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-06/", "snippets": [ "... . It took generations to realize that for England as a dominating industrial nation, having no in- dustrial competitor, free trade was an advan- tage, but no industrial development could hope for success in another nation in competition with the powerful, highly developed industries of England, having open access to the markets. We may listen with rather mixed feelings to the complaints of our protectionists, asking for \"protection\" of our \"infant industries ...", "... loped their own indus- tries, became industrially independent of Eng- land, and finally became her competitors on the markets of the world. For over half a century, however, England Leld the markets of the world without any competition. Then and thus, from the vast profits of this time, was the foundation laid of the vast financial power of England, which still to-day holds the world in bondage. With the development of America and Ger- many as industri ...", "... to-day holds the world in bondage. With the development of America and Ger- many as industrial nations began the decadence of England's industries. Developed at an earlier time and under conditions when there was no serious competition, England's industrial sys- tem did not show the productive efficiency of its later competitors. America and Germany both organized their industries on a larger scale with more modern conceptions, and especially they utilized t ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-09", "section_label": "Chapter 8: America in the Past", "section_title": "America in the Past", "kind": "chapter", "sequence": 9, "number": 8, "location": "lines 3741-4267", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-09/", "snippets": [ "... the only saving of the steadily increasing popu- lation, and the numerous small water-powers lit AMERICA IN THE PAST along New England's mill-streams invited. But there could be no successful development of industries in competition with England's es- tablished superior industrial power, without protection of the new industries by tariff laws. But the agricultural South required free trade for the exchange of its crops against England's industrial product ...", "... . For many years the South was conquered territory, received the treatment which now 115 AMElllCA AND THE NEW EPOCH the conquered nations— Belgium, Servia, Egypt — receive, while the North, protected against England's competition, and with the vast ter- ritories of the West and the South as assured markets, rapidly developed its industries. For a generation the South was suffering in poverty, then, in the 90's, came the beginning of the new South ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-07", "section_label": "Chapter 6: Germany in the Individualistic Era", "section_title": "Germany in the Individualistic Era", "kind": "chapter", "sequence": 7, "number": 6, "location": "lines 2776-3206", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-07/", "snippets": [ "... ntry, in spite of our vast natural resources, to hold our own. With the conquest of the markets of the world by industrial Germany came wealth, and Germany became a financial power, and British capital began to meet the competition of Ger- man capital in the exploitation — or \"develop- ment,\" as we call it — of foreign countries. It is true that England's financial strength was, and still is, very much greater than Germany's. But England, no more the l ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-08", "section_label": "Chapter 7: The Other European Nations in the Individualistic Era", "section_title": "The Other European Nations in the Individualistic Era", "kind": "chapter", "sequence": 8, "number": 7, "location": "lines 3207-3740", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-08/", "snippets": [ "... na- tion made France successful in a limited but very profitable field, and in all those industries in which an artistic sense is necessary France became, and is to-day, predominant in the markets of the world, and has no competition to fear. Thus the waves of the conflict for industrial supremacy between England, Germany, and America left France untouched. France's rising financial power was repeatedly set back — by the extravagance of the Second Fmpire ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-14", "section_label": "Chapter 13: Evolution: Industrial Government", "section_title": "Evolution: Industrial Government", "kind": "chapter", "sequence": 14, "number": 13, "location": "lines 5798-6232", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-14/", "snippets": [ "... h absorption of smaller corporations by larger ones, and consolidation to still larger corporations, the development proceeds until the industry is organized in one or a small num- ber of very large corporations. There is no competition, but an executive committee of 1()0 EVOLUTION: INDUSTRIAL GOVERNMENT representatives of the corporations or branches of corporations engaged in the same and similar in(iustries co-ordinates and correlates the work of ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-17", "section_label": "Chapter 16: The Future Corporation", "section_title": "The Future Corporation", "kind": "chapter", "sequence": 17, "number": 16, "location": "lines 6975-7567", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-17/", "snippets": [ "... e early days, who tried to do the same as Standard Oil did, but did not suc- ceed where Standard Oil succeeded, have been hounding Standard Oil for years, until finally the Government dissolved Standard Oil and \"re- stored competition\" by dividing it into thirty- four competing companies, and so reduced the price of gasoline — and if you do not believe the latter, kick yourself, because there is no more a large corporation to hold responsible, as Stand- ..." ] } ] }, { "id": "synchronizing-power", "label": "Synchronizing power", "aliases": [ "Synchronizing power", "synchronizing-power" ], "total_occurrences": 78, "matching_section_count": 11, "matching_source_count": 7, "source_totals": [ { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 44, "section_count": 4 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 8, "section_count": 1 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 7, "section_count": 2 }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 6, "section_count": 1 }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 6, "section_count": 1 }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 5, "section_count": 1 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 2, "section_count": 1 } ], "section_hits": [ { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-appendix-01-synchronous-operation", "section_label": "Mathematical Appendix 5: Appendix: Synchronous Operation", "section_title": "Appendix: Synchronous Operation", "kind": "mathematical-appendix", "sequence": 5, "number": 5, "location": "PDF pages 27-68, lines 2165-5013", "status": "pdf-text-extracted-candidate", "occurrence_count": 24, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "snippets": [ "... n a sin 2a> =- cos a cos w. 2z 2z The second term: E 2 p'Y'= - cos a. cos a> has the same sign for negative w, that is, when the machine is lagging, as for positive w when the machine is leading, thus it represents no energy transfer between the machines. The synchronizing power, or energy transfer during the synchro- nizing oscillations of two alternators, which are out of phase but in synchronism, thus is given by the expression: E 2 P=- sin a sin 2co (6) Thus, the synchronizing power p, is a maximum, and is : _E 2 . for a = 90 deg ...", "... ts no energy transfer between the machines. The synchronizing power, or energy transfer during the synchro- nizing oscillations of two alternators, which are out of phase but in synchronism, thus is given by the expression: E 2 P=- sin a sin 2co (6) Thus, the synchronizing power p, is a maximum, and is : _E 2 . for a = 90 degrees, that is, if the resistance r of the circuit between the alternators is negligible compared with the reactance. The synchronizing power p = for a = 0, that is, in the (theoretical) case, when the circuit bet ...", "... m, thus is given by the expression: E 2 P=- sin a sin 2co (6) Thus, the synchronizing power p, is a maximum, and is : _E 2 . for a = 90 degrees, that is, if the resistance r of the circuit between the alternators is negligible compared with the reactance. The synchronizing power p = for a = 0, that is, in the (theoretical) case, when the circuit between the alternators contains no reactance, but only resistance. For phase angles w up to 45 degrees, that is, phase displacements between the two alternators up to 2 w = 90 degrees, the s ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-03-record", "section_label": "Report Record 4: Record of Four Troubles", "section_title": "Record of Four Troubles", "kind": "report-record", "sequence": 4, "number": 4, "location": "PDF pages 16-27, lines 1139-2164", "status": "pdf-text-extracted-candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-03-record/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-03-record/", "snippets": [ "... rge a part of the entire system. It is dangerous, as Fisk B and Northwest combined give too large a power for safe handling under all emergencies. Furthermore, due to the connection between these stations being practically all resistance and no reactance, the synchronizing power between Fisk B and Northwest must be small, and when synchronism is once lost under short circuit, etc., trouble must be anticipated in these stations pulling into synchronism with each other. The interference between Fisk A, Quarry Street and Fisk B sections ...", "... come back and the station section drop into step again with the rest of the system. This did not occur, but station sections remained out of step with each other at practically zero voltage for a considerable time, about a quarter of an hour. Apparently, the synchronizing power between the station sections is lower than desirable, and the speed con- trol of the alternators not such as to bring them promptly so close together in speed as to drop into step. d) The tandem or chain connection of the stations has the disad- vantage that ...", "... September 18th and October 22nd. b) The most serious question, which unfortunately cannot be de- cided with the present data, is : whether this voltage drop and fluctua- tion was an actual hunting of the generating stations against each other, due to lack of synchronizing power, or whether it was hunting of the steam governors of the stations against each other, or whether it was only apparent, and due to the reaction on the generators of the substations when starting synchronous machines. This should be fur- ther investigated. [[EN ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-02-discussion-of-recommendations", "section_label": "Report Section 3: Discussion of Recommendations", "section_title": "Discussion of Recommendations", "kind": "report-section", "sequence": 3, "number": 3, "location": "PDF pages 12-16, lines 721-1138", "status": "pdf-text-extracted-candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-02-discussion-of-recommendations/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-02-discussion-of-recommendations/", "snippets": [ "... eir purposes, these reactors must be fairly large, and the value of 1.75 ohms used in the power limiting busbar reactors of the Commonwealth Edison Company of Chicago, is by no means too high. Necessarily, however, these power limiting reactors also limit the synchronizing power be- tween the station sections. Thus if in a station section as Fisk Street A, which is connected by one power limiting reactor to the rest of the system, full load of 60,000 KW is suddenly thrown off as by a short circuit at the busbars dropping out the sync ...", "... A, which is connected by one power limiting reactor to the rest of the system, full load of 60,000 KW is suddenly thrown off as by a short circuit at the busbars dropping out the synchronous machines in the substations while full steam supply is still on, the synchronizing power coming over the power limiting reactor is insufficient to hold the station in step, and the station breaks synchronism and speeds up. Whether synchronous operation is preserved or synchronism broken, depends on the relative speed, with which the synchronous m ...", "... ply, and the alternators speed up rapidly; at full voltage and full steam supply, a little over a second after the load has dropped off, the sta- tions would have speeded up so as to have broken synchronism with the rest of the system, in spite of the maximum synchronizing power exerted over the power limiting reactor. In reality obviously the load cannot drop off instantly but would hold on an appreciable time, and the governors would immediately begin to cut off steam; but on the other hand, the station voltage has dropped under sh ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-11", "section_label": "Chapter 11: Instability Of Circuits: Induction And Syn Chronous Motors", "section_title": "Instability Of Circuits: Induction And Syn Chronous Motors", "kind": "chapter", "sequence": 11, "number": 11, "location": "lines 21382-22633", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-11/", "snippets": [ "... ng to the load, would be — or may ap- proximately be assumed as — proportional to the position dis- placement, p, but with reverse sign, positive for acceleration when p is negative or behind the normal position, negative or retarding when p is ahead. The synchronizing power, that is, the power exerted by the machine to return to the normal position, then is INSTABILITY OF CIRCUITS 211 derived by multiplying —p with v, and is shown dotted as Wj in Fig. 104. As seen, it has a double-frequency alternation with zero as a ...", "... 1 derived by multiplying —p with v, and is shown dotted as Wj in Fig. 104. As seen, it has a double-frequency alternation with zero as average. The total resultant power or the resulting damping effect which restores stability, then, is the sum of the synchronizing power ifa and_ the damping power wi, and is shown by the dotted Fio. 104. curve v>. As seen, under the assumption or Pig. 104, in this case a rapid damping occurs. If the damping winding, which consumes a part of all the power, Wi, is inductive — and to a ...", "... y stored, and as a result the magnetic flux of the machine does not exactly correspond with the position, p, but lags behind it, and with it the synchronizing force, F, as shown in Fig. 104, lags more or less, depending on the design of the machine. The synchronizing power of the machine, Fv, in the case of a lag- ging synchronizing force, F, is shown by the drawn curve, t(?2. As seen, the positive ranges of the oscillation are greater than the negative ones, that is, the average of the oscillating synchronizing power is po ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-23", "section_label": "Chapter 23: Synchronizing Alternators", "section_title": "Synchronizing Alternators", "kind": "chapter", "sequence": 23, "number": 23, "location": "lines 25135-25681", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-23/", "snippets": [ "... running in synchronism, nearly all types of ma- chines will operate satisfactorily; a medium amount of armature 294 ALTERNATING-CURRENT PHENOMENA reaction is preferable, however, such as is given by modern alter- nators— not too high to reduce the synchronizing power too much, nor too low to make the machine unsafe in case of accident, such as falling out of step, etc. If the armature reaction is very low, an accident — such as a short-circuit, falling out of step, opening of the field circuit, etc. — may destroy th ...", "... ction is very low, an accident — such as a short-circuit, falling out of step, opening of the field circuit, etc. — may destroy the machine. If the armature reaction is very high, the driving power has to be adjusted very carefully to constancy, since the synchronizing power of the alternators is too weak to hold them in step and carry them over irregularities of the driving-power. 208. Series operation of alternators is possible only by rigid mechanical connection, or by some means whereby the machines, with regard to thei ...", "... f the alternators is too weak to hold them in step and carry them over irregularities of the driving-power. 208. Series operation of alternators is possible only by rigid mechanical connection, or by some means whereby the machines, with regard to their synchronizing power, act essentially in par- loXUiJL mnrmnmnwv Fig. 143. allel; as, for instance, by the arrangement shown in Fig. 143, where the two alternators, A\\, A^, are connected in series, but interlinked by the two coils of a transformer, T, of which the on ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-17", "section_label": "Chapter 17: Synchbonizino Aiitebkatobs", "section_title": "Synchbonizino Aiitebkatobs", "kind": "chapter", "sequence": 17, "number": 17, "location": "lines 18829-19345", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-17/", "snippets": [ "... pplies in getting out of step. 172. When running in synchronism, nearly all types of machines will operate satisfactorily ; a medium amount of armature reaction is preferable, however, such as is given by modern alternators — not too high to reduce the synchronizing power too much, nor too low to make the machine unsafe in case of accident, such as falling out of step, etc. If the armature reaction is very low, an accident, — such as a short circuit, falling out of step, opening of the field circuit, etc., — may destroy ...", "... on is very low, an accident, — such as a short circuit, falling out of step, opening of the field circuit, etc., — may destroy the machine. If the armature reaction is very high, the driving-power has to be adjusted very carefully to constancy ; since the synchronizing power of the alternators is too weak to hold them in step, and carry them over irregularities of the driving-power. 173. Series operation of alternators is possible only by rigid mechanical connection, or by some means whereby the machines, with regard to the ...", "... f the alternators is too weak to hold them in step, and carry them over irregularities of the driving-power. 173. Series operation of alternators is possible only by rigid mechanical connection, or by some means whereby the machines, with regard to their synchronizing power, act essentially in parallel ; as, for instance, by the arrange- ment shown in Fig. 120, where the two alternators, .-i,, W.^, are connected in series, but interlinked by the two coils of a large transformer, 7\", of which the one is connected across the ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-18", "section_label": "Chapter 18: Synchronizing Alternators", "section_title": "Synchronizing Alternators", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 17597-18052", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-18/", "snippets": [ "... pplies in getting out of step. 193. When running in synchronism, nearly all types of machines will operate satisfactorily ; a medium amount of armature reaction is preferable, however, such as is given by modern alternators — not too high to reduce the synchronizing power too much, nor too low to make the machine unsafe in case of accident, such as falling out of step, etc. If the armature reaction is very low, an accident, — such as a short circuit, falling out of step, opening of the field circuit, etc., — may destroy ...", "... on is very low, an accident, — such as a short circuit, falling out of step, opening of the field circuit, etc., — may destroy the machine. If the armature reaction is very high, the driving-power has to be adjusted very carefully to constancy ; since the synchronizing power of the alternators is too weak to hold them in step, and carry them over irregularities of the driving-power. 194. Series operation of alternators is possible only by rigid mechanical connection, or by some means whereby the machines, with regard to the ...", "... f the alternators is too weak to hold them in step, and carry them over irregularities of the driving-power. 194. Series operation of alternators is possible only by rigid mechanical connection, or by some means whereby the machines, with regard to their synchronizing power, act essentially in parallel ; as, for instance, by the arrange- ment shown in Fig. 120, where the two alternators, Al} A2, are connected in series, but interlinked by the two coils of a large transformer, T, of which the one is connected 314 AL TER ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-07", "section_label": "Chapter 8: Synchronizing Induction Motors", "section_title": "Synchronizing Induction Motors", "kind": "chapter", "sequence": 7, "number": 8, "location": "lines 13956-14465", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-07/", "snippets": [ "... their mechanical connection 159 100 ELECTRICAL APPARATUS sufficiently flexible, as by belting, etc., bo that the motors can drop into exact step with each other and maintain step by their synchronising power. It is of interest, then, to examine the synchronizing power of two induction motors which are connected in multiple with their secondaries on the same rheostat and operated from the same primary impressed voltage. 95. Assume two equal induction motors with their primaries connected to the same voltage, supply an ...", "... oltage, supply and with llieir seeondarioi connected in multiple with each other to a common resistance, r, and neglecting for simplicity the exciting current and the vol- tage drop in the impedance of the motor primaries as not mate- rially affecting the synchronizing power. Let Zi — n + ./j-t = secondary self-inductive impedance at full frequency; s = slip of the two motors, as fraction of syn- chronism; Co = absolute value of impressed voltage and thus, when neglecting the primary impedance, of the voltage generated iu t ...", "... with the one motor secondary short- circuiting the other; in this position, any decrease of t below 90° produces a synchronizing torque which pulls the motors together, to r = 0, or in step. Just as with alternators, there thus exist two positions of zero synchronizing power — with the motors in step, that is, their secondaries in parallel and in phase, and with the motors in opposition, that is, their secondaries in opposition — and the former position is stable, the latter unstable, and the motors thus drop into and retain ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-01-recommendations", "section_label": "Report Section 2: Recommendations", "section_title": "Recommendations", "kind": "report-section", "sequence": 2, "number": 2, "location": "PDF pages 7-12, lines 145-720", "status": "pdf-text-extracted-candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "snippets": [ "... nd the feeder directly involved. 4.) Install a power limiting busbar reactance between the two sec- tions of Fisk Street Station, so as to tie the three station sections : Fisk Street A, Quarry Street and Fisk B, together into a ring. This should increase the synchronizing power between these stations. It should also guard against the system being cut into two parts out of synchron- ism with each other, in case that a short circuit at the busbars of an intermediary section (Quarry Street or Fisk Street B), drops the volt- age of this ...", "... ard against the system being cut into two parts out of synchron- ism with each other, in case that a short circuit at the busbars of an intermediary section (Quarry Street or Fisk Street B), drops the volt- age of this section to zero and thereby destroys its synchronizing power. The same size of reactance as now used, of about 1.75 ohms, would be recommended. [[END_PDF_PAGE:9]] [[PDF_PAGE:10]] 4 Report of Charles P. Steinmetz 5.) I should recommend strongly to endeavor to change the present connection between the Northwest Station ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-36", "section_label": "Apparatus Section 15: Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "section_title": "Synchronous Machines: Fluctuating Cross Currents in Parallel Operation", "kind": "apparatus-section", "sequence": 36, "number": 15, "location": "lines 9918-10123", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-36/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-36/", "snippets": [ "... e regulation undesirable. By the transfer of energy between the machines the pulsations of frequency, and thus the cross currents, are reduced somewhat. Very high armature reaction is objectionable also, since it reduces the synchronizing power, that is, the tendency of the machines to hold each other in step, by reducing the energy transfer be- tween the machines. As seen herefrom, the problem of parallel operation of alternators is al- most entirely a problem o ...", "... phase with one and in opposition with the other of the machine e.m.fs. OEi and OE^. 29. Hence, machines without reactance would have no syn- chronizing power, or could not be operated in parallel. The theoretical maximum synchronizing power exists if the reactance equals the resistance: XQ = r0. This condition, however, cannot be realized, and if realized would give a dangerously high syn- chronizing power and cross current. In practice, XQ is always very much ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-37", "section_label": "Chapter 37: Quarter-Phase System", "section_title": "Quarter-Phase System", "kind": "chapter", "sequence": 37, "number": 37, "location": "lines 38393-40115", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-37/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-37/", "snippets": [ "... tion motor, 223 single-phase induction motor, 252 Susceptance, 55 of circuit with inductive line, 82 480 INDEX Susceptance, effective, 112 Susceptivity, dielectric, 153, 160 Symbolic expression of power, 181 Symmetrical polyphase system, 396 Synchronizing power of alternators, 294 Synchronous condenser, 339 converter for phase control, 98 impedance of alternator, 277 machine as shunted susceptance, 96 motor, fundamental equation, 316 for phase control, 98 supplied by distorted wave, 389 reactance of a ..." ] } ] }, { "id": "luminescence", "label": "Luminescence", "aliases": [ "Luminescence", "luminescence" ], "total_occurrences": 77, "matching_section_count": 7, "matching_source_count": 3, "source_totals": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 72, "section_count": 4 }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 4, "section_count": 2 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 47, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "LECTURE VI. LUMINESCENCE. 43. All methods of producing radiation, and more particularly light, other than the temperature radiation or incandescence, are generally comprised by the name luminescence. Some special cases of luminescence have already been discussed in the phe- nom ...", "LECTURE VI. LUMINESCENCE. 43. All methods of producing radiation, and more particularly light, other than the temperature radiation or incandescence, are generally comprised by the name luminescence. Some special cases of luminescence have already been discussed in the phe- nomena of fluorescence and phosphorescence, represented by the conversion of the radiation absorbed by a body into radiation of a different wave length. Usually luminescence at ...", "LECTURE VI. LUMINESCENCE. 43. All methods of producing radiation, and more particularly light, other than the temperature radiation or incandescence, are generally comprised by the name luminescence. Some special cases of luminescence have already been discussed in the phe- nomena of fluorescence and phosphorescence, represented by the conversion of the radiation absorbed by a body into radiation of a different wave length. Usually luminescence at ordinary temperature, or at moderate ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-05", "section_label": "Lecture 5: Temperature Radiation", "section_title": "Temperature Radiation", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3946-5076", "status": "candidate", "occurrence_count": 17, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-05/", "snippets": [ "... etc. A number of types of such visual pyrometers have been devel- oped, and are very convenient. Their limitation, obviously, is that they apply only when the radiation is normal temperature radiation, but give wrong results where colored radiation or luminescence is present. Thus the FIG. 30. radiation given by the interior of a closed body of uniform tem- perature ceases to be black body radiation if the interior is filled with luminous vapors, as is frequently the case in the interior of electric furnaces. F ...", "... of the black body is the maximum temperature radiation at any temperature and frequency. A body which gives at any frequency a greater intensity of radiation than a black body of the same temperature is called luminescent, that is, said to possess \"heat luminescence.\" Char- acteristic of heat luminescence, thus, is an excess of the intensity of radiation over that of a black body of the same temperature for some frequency or range of frequencies, and the color of lumin- escence is that of the radiation frequencies by ...", "... ature radiation at any temperature and frequency. A body which gives at any frequency a greater intensity of radiation than a black body of the same temperature is called luminescent, that is, said to possess \"heat luminescence.\" Char- acteristic of heat luminescence, thus, is an excess of the intensity of radiation over that of a black body of the same temperature for some frequency or range of frequencies, and the color of lumin- escence is that of the radiation frequencies by which the lumin- escent body exceeds th ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-07", "section_label": "Lecture 7: Flames As Illuminants", "section_title": "Flames As Illuminants", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 6609-7140", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-07/", "snippets": [ "... of acetylene is higher than that of other hydrocarbons of the same relative propor- tions of hydrogen and carbon: acetylene being endothermic, that is, requiring energy for its formation from the elements. 59. Since, as discussed in Lecture VI, chemical luminescence usually occurs where intense chemical reactions take place at high temperatures, — and this is the case in the flame, — chemical luminescence of the flame gases must be expected in the hydro- carbon flame. It does occur, but does not contribute anything ...", "... that is, requiring energy for its formation from the elements. 59. Since, as discussed in Lecture VI, chemical luminescence usually occurs where intense chemical reactions take place at high temperatures, — and this is the case in the flame, — chemical luminescence of the flame gases must be expected in the hydro- carbon flame. It does occur, but does not contribute anything 134 RADIATION, LIGHT, AND ILLUMINATION. to the light production, since the spectra of hydrogen and of carbon (or CO and CH4) are practically ...", "... must be expected in the hydro- carbon flame. It does occur, but does not contribute anything 134 RADIATION, LIGHT, AND ILLUMINATION. to the light production, since the spectra of hydrogen and of carbon (or CO and CH4) are practically non-luminous. The luminescence of the hydrocarbon flame therefore can be observed only with those hydrocarbons which are sufficiently poor in car- bon as not to deposit free carbon, as methane, alcohol, etc., or in which, by the admixture of air, the deposition of free carbon and there ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-04", "section_label": "Lecture 4: Chemical And Physical Effects Of Radiation", "section_title": "Chemical And Physical Effects Of Radiation", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3639-3945", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-04/", "snippets": [ "... thus showing the effect of the temperature rise in increas- ing phosphorescence. These substances which I show you, calcium sulphide, cal- cium carbonate (calcite), zinc silicate (willemite), are not fluo- rescent or phosphorescent themselves, but their luminescence is due to a small percentage of some impurities contained in them. Chemically pure substances and concentrated solutions of the aniline dyes, or these dyes in their solid form, do not show the luminescence, but only when in very diluted solutions; that is ...", "... rescent or phosphorescent themselves, but their luminescence is due to a small percentage of some impurities contained in them. Chemically pure substances and concentrated solutions of the aniline dyes, or these dyes in their solid form, do not show the luminescence, but only when in very diluted solutions; that is, luminescence as fluorescence and phosphorescence seems to be the property of very diluted solutions of some substances in others. Thus a sheet of paper or cardboard colored red by rhodamine does not fluor ...", "... due to a small percentage of some impurities contained in them. Chemically pure substances and concentrated solutions of the aniline dyes, or these dyes in their solid form, do not show the luminescence, but only when in very diluted solutions; that is, luminescence as fluorescence and phosphorescence seems to be the property of very diluted solutions of some substances in others. Thus a sheet of paper or cardboard colored red by rhodamine does not fluoresce, but if a small quantity of rhoda- mine is added to some tr ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-02", "section_label": "Chapter 2: Electric Conduction. Gas And Vapor", "section_title": "Electric Conduction. Gas And Vapor", "kind": "chapter", "sequence": 2, "number": 2, "location": "lines 3895-5444", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-02/", "snippets": [ "... Gas, Vapor and Vacuum Conduction 18. As further, and last class may be considered vapor, gas and vacuum conduction. Typical of this is, that the volt-ampere characteristic is dropping, that is, the voltage decreases with in- crease of current, and that luminescence accompanies the con- duction, that is, conversion of electric energy into light. Thus, gas and vapor conductors are unstable on constant- potential supply, but stable on constant current. On constant potential they require a series resistance or reactanc ...", "... nal or cathode, and moving toward the anode at high velocity. The light of the arc thus shows the spectnun of the negative terminal material, but not that of the gas in the surrounding space, nor that of the positive terminal, except indi- rectly, by heat luminescence of material entering the arc con- ductor from the anode or from surrounding space. In true electronic conduction, electrons existing in the space, or produced at the terminals (hot cathode), are the conductors. Such conduction thus exists also in a perfe ...", "... node or from surrounding space. In true electronic conduction, electrons existing in the space, or produced at the terminals (hot cathode), are the conductors. Such conduction thus exists also in a perfect vacuum, and may be accompanied by practically no luminescence. 28 ELECTRIC CONDUCTION . 29 Disruptive Conduction 19. Spark conduction at atmospheric pressure is the disruptive spark, streamers, and corona. In a partial vacuum, it is the Geissler discharge or glow discharge. Spark conduction is dis- continuou ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-16", "section_label": "Lecture 16: The Incandescent Lamp", "section_title": "The Incandescent Lamp", "kind": "lecture", "sequence": 16, "number": 16, "location": "lines 9687-9919", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-16/", "snippets": [ "... reason, 220 volt distribution has never found any entrance in this country. In gas lighting, an enormous increase of efficiency resulted from the development of the Welsbach gas mantle. In the same direction, that is, by using what may be called *'heat luminescence\" in electric lighting, the Nernst lamp was developed, using the same class of material : refractory metal- lic oxides, as in the Welsbach mantle. The \"glower\" of the Nernst lamp, however, is a non-conductor at ordinary tempera- ture, and requires some hea ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-18", "section_label": "Chapter 18: Oscillating Currents", "section_title": "Oscillating Currents", "kind": "chapter", "sequence": 18, "number": 18, "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "... s, 217 reducing wave distortion, 145 Leaky conductor, 330, 332, 336 Load balance of polyphase system, 314 character determining stability in induction motor, 205 Loop of hysteresis, 56 Loss, percentage, in magnetic cycle, 60 Loxodromic spiral, 345 Luminescence in gas and vapor con- duction, 28 Luminous streak conduction in pyro- electric conductor, 18 M Magnetic circuits of induction motor, 228 elements, 77 friction, 56 mechanical forces, 107 Magnetism, 43 tables and data, 87, 88 wave distortion ..." ] } ] }, { "id": "velocity-of-light", "label": "Velocity of light", "aliases": [ "Velocity of light", "velocity-of-light" ], "total_occurrences": 75, "matching_section_count": 19, "matching_source_count": 9, "source_totals": [ { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 39, "section_count": 3 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 10, "section_count": 2 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 8, "section_count": 4 }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 5, "section_count": 2 }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 5, "section_count": 2 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 4, "section_count": 2 }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 2, "section_count": 2 }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 1, "section_count": 1 }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-02", "section_label": "Lecture 2: Conclusions From The Relativity Theory", "section_title": "Conclusions From The Relativity Theory", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 736-2388", "status": "candidate", "occurrence_count": 26, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... by forces acting between the ether atoms so as to hold them together in their relative positions. Bodies in which the atoms are held together in their relative positions are solid bodies. That is, trans- verse waves can exist only in solid bodies. As the velocity of light is extremely high, the forces between the ether atoms which transmit the vibrations must be very great. That is, the ether is a solid body of very high rigidity, infinitely more rigid than steel. At the same time, the ether must be of extremely high ten ...", "... ll circles. This is the case, and this phenomenon, called '^ aberration,\" proves that the ether stands still and is not carried along by the cosmic bodies. If the ether stands still and the earth is moving through it, then by the Newtonian mechanics the velocity of light relative to the earth — that is, as observed here on earth — should in the direction of the earth's motion be 20 miles less, in the opposite direction 20 miles more, than the veloc- ity with regard to the stationary ether. If, however, the ether moves wi ...", "... , as observed here on earth — should in the direction of the earth's motion be 20 miles less, in the opposite direction 20 miles more, than the veloc- ity with regard to the stationary ether. If, however, the ether moves with the earth, then obviously the velocity of light on earth should be the same in all directions. The latter is the case, and thus it is proved that the ether moves with the earth and does not stand still. This is exactly the opposite conclusion from that given by the aberration. Thus the conception of ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-03", "section_label": "Lecture 3: Gravitation And The Gravitational Fleld", "section_title": "Gravitation And The Gravitational Fleld", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2389-3594", "status": "candidate", "occurrence_count": 10, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-03/", "snippets": [ "... of inertial motion to an accelerated system. The law of gravitation thus appears here as such a mathematical transformation to an acceler- ated system and has been derived in this manner by Einstein. For all velocities which are small compared with the velocity of light Einstein's law of gravitation and Newton's law give the same results, and a difference appears only when the velocity of the moving bodies approaches in magnitude the velocity of light, as is the case, for instance, with ionic motions. Thus the gravitat ...", "... r by Einstein. For all velocities which are small compared with the velocity of light Einstein's law of gravitation and Newton's law give the same results, and a difference appears only when the velocity of the moving bodies approaches in magnitude the velocity of light, as is the case, for instance, with ionic motions. Thus the gravitational field is identical with the mani- festation of inertia in an accelerated system, and the law of gravitation appears as the mathematical transformation of the equation of inertial ...", "... e same manner as it acts on a material body, and a beam of light in a gravitational field is deflected and curves. A curvature necessarily means that the velocity at the inside of the curve is less than at the outside. Thus in a gravitational field the velocity of light is not constant, nor does the light move in a straight line, but it is slowed down and deflected. At first this seems to contradict our premise, that the velocity of light is constant and the same everywhere. However, this applied only to the velocity o ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... mp or the rays of the moon. The most conspicuous form of radiation is light, and, therefore, it was in connection with this form that the laws of radiation were first studied. 1 2 RADIATION, LIGHT, AND ILLUMINATION. 2. The first calculations of the velocity of light were made by astronomers in the middle of the eighteenth century, from the observations of the eclipses of the moons of Jupiter. A number of moons revolve around the planet Jupiter, some of them so close that seen from the earth they pass behind Jupiter a ...", "... S, or by about 195,000,000 miles and the delay of 17J min. thus must be due to the time taken by the light to traverse the additional distance of 195,000,000 miles. Seventeen and one-third min. are 1040 sec. and 195,000,000 miles in 1040 sec. thus gives a velocity of light of » or 188,000 miles per sec. Later, the velocity of light was measured directly in a number of different ways. For instance, let, in Fig. 2, D be a disk per- forated with holes at its periphery. A lamp L sends its light through a hole H0 in the disk t ...", "... ust be due to the time taken by the light to traverse the additional distance of 195,000,000 miles. Seventeen and one-third min. are 1040 sec. and 195,000,000 miles in 1040 sec. thus gives a velocity of light of » or 188,000 miles per sec. Later, the velocity of light was measured directly in a number of different ways. For instance, let, in Fig. 2, D be a disk per- forated with holes at its periphery. A lamp L sends its light through a hole H0 in the disk to a mirror M located at a con- siderable distance, for instanc ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "section_label": "Chapter 2: Long-Distance Transmission Line", "section_title": "Long-Distance Transmission Line", "kind": "chapter", "sequence": 42, "number": 2, "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "CHAPTER II. LONG-DISTANCE TRANSMISSION LINE. 3. If an electric impulse is sent into a conductor, as a trans- mission line, this impulse travels along the line at the velocity of light (approximately), or 188,000 miles per second. If the line is open at the other end, the impulse there is reflected and returns at the same velocity. If now at the moment when the impulse arrives at the starting point a second impulse, of opposite directio ...", "... ice the length of the line, or the time of one complete period is the time light requires to travel four times the length of the line; in other words, the number of periods, or frequency of the impressed alternating e.m.fs., in resonance condition, is the velocity of light divided by four times the length of the line; or, in free oscillation or resonance condition, the length of the line is one quarter wave length. 279 280 TRANSIENT PHENOMENA If then I = length of line, S = speed of light, the frequency of oscillation ...", "... three wires of 500,000 circular mils cross section, placed 6 feet between wires, and provided with a grounded neutral. If there were no energy losses in the line and no increase of capacity due to insulators, etc., the speed of propagation would be the velocity of light, S = 188,000 miles per second, and the quarter-wave frequency of a line of 10 = 700 miles would be S / = — =67 cycles per sec. ; 4 LQ hence, fairly close to the standard frequency of 60 cycles. The loss of power in the line, and thus the increase of ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "section_label": "Lecture 10: Continual And Cumulative Oscillations", "section_title": "Continual And Cumulative Oscillations", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... r electrifying force, (27) ROUND PARALLEL CONDUCTORS. 137 G e and K = - — -„ = - — -, = dielectric field intensity, (28) where v- is the reduction factor from the electrostatic to the electromagnetic system of units, and y = 3 X 10^0 cm. sec. = velocity of light; (29) the dielectric density then is D = kK = -^j, (30) 4 TTVH where k = specific capacity of medium, = 1 in air. The dielectric flux then is where A = section of dielectric flux. Or inversely: e = i^^^. (32) If then \"^ = dielectric flux, in Fi ...", "... mes the velocity square of light. The external inductance Li would be the inductance of a conductor which had perfect con- ductivity, or zero losses of power. It is Vlc = velocity of propagation of the electric field, and this velocity is less than the velocity of light, due to the retardacion by the power dissipation in the conductor, and becomes equal to the velocity of light V if there is no power dissipation, and, in the latter case, L would be equal to Li, the external inductance. The equation (39) is the most conv ...", "... perfect con- ductivity, or zero losses of power. It is Vlc = velocity of propagation of the electric field, and this velocity is less than the velocity of light, due to the retardacion by the power dissipation in the conductor, and becomes equal to the velocity of light V if there is no power dissipation, and, in the latter case, L would be equal to Li, the external inductance. The equation (39) is the most convenient to calculate capacities in complex systems of circuits from the inductances, or inversely, to determine ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-10", "section_label": "Lecture 10: Inductance And Capacity Of Round Parallel Conductors", "section_title": "Inductance And Capacity Of Round Parallel Conductors", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 6089-7274", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "snippets": [ "... e, (27) 128 ELECTRIC DISCHARGES, WAVES AND IMPULSES. and K = - — 2 = - — ^ = dielectric field intensity, (28) 4 Trf 4 irV L where v2 is the reduction factor from the electrostatic to the electromagnetic system of units, and v = 3 X 1010 cm. sec. = velocity of light; (29) the dielectric density then is where K = specific capacity of medium, = 1 in air. The dielectric flux then is where A = section of dielectric flux. Or inversely: -IS?* : || (32) If then ^ = dielectric flux, in Fig. 60, at a distance x from ...", "... es the velocity square of light. The external inductance LI would be the inductance of a conductor which had perfect con- ductivity, or zero losses of power. It is VLC = velocity of propagation of the electric field, and this velocity is less than the velocity of light, due to the retardation by the power dissipation in the conductor, and becomes equal to the velocity of light v if there is no power dissipation, and, in the latter case, L would be equal to LI, the external inductance. The equation (39) is the most conv ...", "... erfect con- ductivity, or zero losses of power. It is VLC = velocity of propagation of the electric field, and this velocity is less than the velocity of light, due to the retardation by the power dissipation in the conductor, and becomes equal to the velocity of light v if there is no power dissipation, and, in the latter case, L would be equal to LI, the external inductance. The equation (39) is the most convenient to calculate capacities in complex systems of circuits from the inductances, or inversely, to determine ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-04", "section_label": "Lecture 4: The Characteristics Of Space A. The Geometry Of The Gravitational Field", "section_title": "The Characteristics Of Space A. The Geometry Of The Gravitational Field", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3595-6820", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-04/", "snippets": [ "LECTURE IV THE CHARACTERISTICS OF SPACE A. THE GEOMETRY OF THE GRAVITATIONAL FIELD The starting point of the relativity theory is that the laws of nature, including the velocity of light in empty space, are the same everywhere and with regard to any system to which they may be referred — whether on the revolving platform of the earth or in the speeding railway train or in the space between the fixed stars. From this it follows that the l ...", "... matter how far we move toward them. Wc may estimate their (apparent) distance and move toward them by this distance and more, and still they appear just as far, at the same apparently finite distance. (This reminds us of the similar characteristic of the velocity of light c in the relativity theory, which is finite, c = 3 X 10^'' cm., but still inapproachable, as no combination or addi- THE CHARACTERISTICS OF SPACE 119 tion of lesser velocities can ever add to a sum equal to c.) Helmholtz has shown that we can get a vi ...", "... SIONAL ANALOGUE OF THE UNI- VERSE, AND THE MATHEMATICAL CONCEPTION OF IT The relativity theory has reconfirmed the law of con- servation of energy, but has denied the law of con- servation of matter by showing matter as kinetic energy, moc^, where c = velocity of light and mo is a constant. Mass then is represented by: moC^ + E m _ v^ where v is the relative velocity and E the non-kinetic energy of the body. The constancy of the mass then is approximate only as long as V is small compared with c and E small ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... necessary to analyze the mixed radiation given by a source as a lamp, by resolving it into its component waves. This is done by using some feature of the radiation which varies with the frequency. Such is the case with the velocity of propagation. The velocity of light in empty space is 3 X 1010 cm. per sec. It is practically the same in air and other gases. In denser bodies, however, as water, glass, etc., the velocity of light is less and, as will be seen, is different for different frequencies. 22 RADIATION, LIG ...", "... on which varies with the frequency. Such is the case with the velocity of propagation. The velocity of light in empty space is 3 X 1010 cm. per sec. It is practically the same in air and other gases. In denser bodies, however, as water, glass, etc., the velocity of light is less and, as will be seen, is different for different frequencies. 22 RADIATION, LIGHT, AND ILLUMINATION. Assume then, in Fig. 15, a beam of light B striking under an angle the boundary between two media, as air A and water W, the vibration of ...", "... the law of refraction, and this ratio of sines is called the refractive index between the two media A and W. As the refractive index of one medium W, then, is understood its re- fractive index against empty space or against air : sn a where S is the velocity of light in empty space = 3 X 1010, and Sl the velocity in the medium, of which ^ is called the refractive index. From equation (4) it follows, that, if ^_2 is the refractive index between medium 1 and medium 2, £2_3, the refractive index between medium 2 and me ..." ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_id": "electric-discharges-waves-impulses-1914-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1003-1658", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-02/", "snippets": [ "... nsity, where /c is a constant of the material, the electrostatic or dielectric conductivity, and is called the spe- cific capacity or permittivity. For empty space, and thus with close approximation for air and other gases, 1 where v = SX W is the velocity of light. It is customary, however, and convenient, to use the permit- tivity of empty space as unity: k = 1. This changes the unit of dielectric-field intensity by the factor -^ , and gives : dielectric-field intensity, K = j^; (21) 4 Try- ^ ^ dielectric ...", "... 47rz;2 force per cm^, or coulombs per cm^. Dielectric density : D = kK lines of dielectric force per cm^, or coulombs per cm^. Permittivity or specific capacity: k Dielectric flux: ^ = AD lines of dielectric force, or coulombs. V = 3X 10^0 = velocity of light. The powers of 10, which appear in some expressions, are reduc- tion factors between the absolute or cgs. units which are used for $, 3C, (B, and the practical electrical units, used for other constants. As the magnetic field and the dielectric field ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-02", "section_label": "Lecture 2: The Electric Field", "section_title": "The Electric Field", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 883-1530", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "snippets": [ "... constant of the material, the electrostatic or dielectric conductivity, and is called the spe- cific capacity or permittivity. For empty space, and thus with close approximation for air and other gases, 1 K — ~9» VL where v = 3 X 1010 is the velocity of light. It is customary, however, and convenient, to use the permit- tivity of empty space as unity: K = 1. This changes the unit of dielectric-field intensity by the factor — , and gives: dielectric-field intensity, dielectric density, = T^-oJ (21) 4 T ...", "... e per cm2. Dielectric density: D = nK lines of dielectric force per cm2. Permeability: /* Permittivity or specific capacity: K Magnetic flux: $ = A($> lines of magnetic force. Dielectric flux: ^ = AD lines of dielectric force. v = 3 X 10 10 = velocity of light. The powers of 10, which appear in some expressions, are reduc- tion factors between the absolute or cgs. units which are used for $, 3C, CB, and the practical electrical units, and used for other constants. As the magnetic field and the dielectric fie ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-07", "section_label": "Lecture 7: High Frequency Oscillations And Surges", "section_title": "High Frequency Oscillations And Surges", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3508-3780", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-07/", "snippets": [ "... d the complete wave length would thus be two miles. Or, if a momentary discharge occurs over a lightning arrester to ground, the wave length may be only a few feet. The velocity with which the electric wave travels in an overhead line is practically the velocity of light, or about 188,000 miles per second: it would be exactly the velocity of light, except that by the resistance of the line conductor the velocity is very slightly reduced. In an underground cable, by the high capacity of the cable insulation, the velocity o ...", "... rge occurs over a lightning arrester to ground, the wave length may be only a few feet. The velocity with which the electric wave travels in an overhead line is practically the velocity of light, or about 188,000 miles per second: it would be exactly the velocity of light, except that by the resistance of the line conductor the velocity is very slightly reduced. In an underground cable, by the high capacity of the cable insulation, the velocity of wave travel is greatly reduced, to about 50 to 70% of that ol light. From ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... ' seconds, assuming two half- waves as an average, gives 500,000 cycles. The frequency of oscillation of the lightning flash thus appears to be of the magnitude of half a million cycles. Since the velocity of propagation of electric disturbances is the velocity of light, or 188,000 miles per second, the wave length of a discharge of 500,000 cycles is ^qq'qqq = g miles, or about 2000 feet. A wave length of 2000 feet means that the current in the discharge flows in one direction for 1000 feet, in the opposite direction, ...", "... ing slowly along the line, and visible to the eye as a luminous streak. The frequencies of these impulses then are those corres- ponding to the frequencies of cloud discharge, that is, of the magnitude of hundred thousands of cycles per second. With the velocity of light, 188,000 miles per second, they travel along the line, until they gradually fade out by the dissipation of their energy, or are reflected at an open end of the line, or at the entrance to the station are broken up by partial reflection, in reactances, and ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-50", "section_label": "Chapter 1: General Equations", "section_title": "General Equations", "kind": "chapter", "sequence": 50, "number": 1, "location": "lines 27761-28694", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "snippets": [ "... ength of the circuit- may be chosen as is convenient, thus : the centimeters in the high- frequency oscillation over the multigap lightning arrester circuit, or a mile in a long-distance transmission circuit or high-potential cable, or the distance of the velocity of light, 300,000 km., etc. The permanent values of current and e.m.f. in such circuits of distributed constants have, for alternating-current circuits, been investigated in Section III, where it was shown that they can be treated as transient phenomena in space, ...", "... speed of propagation of the electric phenomenon in the cir- cuit. (If no energy losses occur, r = 0, g = 0, in a straight con- ductor in a medium of unit magnetic and dielectric constant, that is, unit permeability and unit inductive capacity, S is the velocity of light.) 4. Since (11) is a quadratic equation, several pairs or corre- sponding values of a and b exist, which, in the most general case, are complex imaginary. The terms with conjugate complex imaginary values of a and b then have to be combined for the elim ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-06", "section_label": "Chapter 7: Numerical Calculations", "section_title": "Numerical Calculations", "kind": "chapter", "sequence": 6, "number": 7, "location": "lines 21989-25587", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-06/", "snippets": [ "... ess telegraphy, lightning protection, etc., we get new functions. If ^=/(0 is the current in the conductor, as function of the time t, at a distance x from the conductor the magnetic field lags by the X time ti = -, where S is the speed of propagation (velocity of light). Since the field intensity decreases inversely propor- tional to the distance x, it thus is proportional to y= — - — ; (41) and the total magnetic flux then is / 2= j ydx A'-l) -j^T^'i' <*2) If the current is an alternating current, that is, f ( ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-19", "section_label": "Theory Section 19: Fields of Force", "section_title": "Fields of Force", "kind": "theory-section", "sequence": 19, "number": 19, "location": "lines 7737-7990", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-19/", "snippets": [ "... transition from the electric quantity \"gradient\" to the dielectric quantity \" field intensity,\" a numer- ical factor 4 irv2 enters, the one quantity being based on the volt as unit, the other on unit force action, v is the velocity of light, 3 X 1010, and the factor v2 the result of the convention of assum- ing the permittivity of empty space as unity. It is now easy to remember, where in the electromagnetic system of units the factor 4-Tr enters: it is ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "section_label": "Chapter 14: Dielectric Losses", "section_title": "Dielectric Losses", "kind": "chapter", "sequence": 14, "number": 14, "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "... e absolute value of the current thus is: g^ i = ViTTi? = ^Vy' + (2x/A;)2 and the power consumption: or, since the dielectric density D is proportional to the voltage € ... gradient t and the permittivity: D= '^ 4.irvH (where y = 3 X 10^\" = velocity of light, see \"Theoretical Ele- ments of Electrical Engineering.\") Thus: ^ ~ k^ where V = Al = volume The power-factor then is: ^ ei Vy'-h (2 7r/A;)2 DIELECTRIC LOSSES 153 Or, if, as usually the case, the conductivity 7 is small compared with the su ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "section_title": "Distributed Capacity, Inductance, Resistance, And Leakage", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "... rrent. Besides this, there is the increase of ohmic resistance due to unequal distribution of current, which, however, is usually not large enough to be noticeable. Furthermore, the electric field of the conductor progresses with a finite velocity, the velocity of light, hence lags behind 174 ALTERNATING-CURRENT PHENOMENA the flow of power in the conductor, and so also introduces power components, depending on current as well as on potential difference. 132. This gives, as the most general case, and per unit length ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-48", "section_label": "Chapter 8: Velocity Of Propagation Of Electric Field", "section_title": "Velocity Of Propagation Of Electric Field", "kind": "chapter", "sequence": 48, "number": 8, "location": "lines 26095-27002", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-48/", "snippets": [ "... ld is considered as in phase with the current, the electrostatic component as in phase with the voltage. In reality, however, the electric field starts at the conductor and propa- gates from there through space with a finite though very high velocity, the velocity of light; that is, at any point in space the electric field at any moment corresponds not to the condi- tion of the electric energy flow at that moment but to that at a moment earlier by the time of propagation from the conductor to the point under consideration, ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-51", "section_label": "Chapter 2: Discussion Of General Equations", "section_title": "Discussion Of General Equations", "kind": "chapter", "sequence": 51, "number": 2, "location": "lines 28695-29315", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-51/", "snippets": [ "... s) - qh J _ q VLC (m + s) - qs VLC q2LC r _m /L ~V' f __ k (m - s) + qh q VTC (m - s) + qs VTC h2 + k2 that is, and Writing q2LC \\/i Cl - C2 q (1) be impressed upon a non-inductive load, giving the current i = I cos (2) The power then is where p = ei = EI cos^ = ^ (1 + cos 2 ) = Q + Q cos 2 « (3) = f (4) that is, in a non-in ...", "... ) cos (0 + 9) = Qcos(2<^ + |) (11) thus, comprises only an alternating component, surging be- tween — Q and +Q, with double frequency. The power consumed by a condenser, equation (11), is opposite in sign and thus in direction, from that consumed by a reactor (9), Qcos(2 + l) = -Q cos(2 « - ^) • 166. If a number of voltages, ei = Ei cos (<^ — 7i) (12) * \"Engineering Mathematics,\" Chapter III, paragraphs 66 to 75. LOAD BALANCE OF POLYPHASE SYSTEMS 317 of a polyphase system, produce currents, ii = ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-appendix-01-synchronous-operation", "section_label": "Mathematical Appendix 5: Appendix: Synchronous Operation", "section_title": "Appendix: Synchronous Operation", "kind": "mathematical-appendix", "sequence": 5, "number": 5, "location": "PDF pages 27-68, lines 2165-5013", "status": "pdf-text-extracted-candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "snippets": [ "... ism with each other. If then the load distribution between the alternators differs from the distribution of their driving power, electric power is transferred over the impedance z, current flows and a phase displacement 2co occurs between the two sides of the reactor z. In this case, the phase angle w is constant, and not periodically fluctuating as in A, but varies with changes of distribution of load ; the equations, however, are the same as in A, except that now w is constant, and the voltages ei and e 2 are the termin ...", "... d to keep in synchronism with each other. Coming now to the consideration of the relation between Fisk Street B and Quarry Street Station, during the trouble of September 18th, 1919: (6.) Four 12,000KW alternators in Fisk Street B, out of synch- ronism over a power limiting reactor with three 14,000 KW alter- nators in Quarry Street, the latter in synchronism with each other: x 2 = 1.48: 2Xl = .438: x=1.75: z = 2.19: Mi = 200 x 10 6 : M 2 = 200xl0 6 . e = 6585 V. Eo = .597 e = 3930 V. E V3 = 6800 V. = 3500 V. Et V3 = 6000 V. io = 3600 A ...", "... off, and required some time to recover. The above calculated voltage of 6000 is lower than the observed voltage of 6800. However, Quarry Street was also connected to Fisk Street A, and the latter station was assisting Quarry Street in feeding the current over power limiting reactor B into Fisk B and Northwest Station. We may thus estimate the effect of Fisk A in holding up the voltage. [[END_PDF_PAGE:56]] [[PDF_PAGE:57]] Report of Charles P. Steinmetz 51 (7.) Four 12,000 KW alternators in Fisk B, out of synchronism over a power limitin ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-03-record", "section_label": "Report Record 4: Record of Four Troubles", "section_title": "Record of Four Troubles", "kind": "report-record", "sequence": 4, "number": 4, "location": "PDF pages 16-27, lines 1139-2164", "status": "pdf-text-extracted-candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-03-record/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-03-record/", "snippets": [ "... rs in Fisk B and in Northwest Station did not pull into step with each other, but remained out of synchronism; the voltage at the busbars of these two stations remained practically zero, and an excessive current fed into Fisk B from Quarry Street, heating the power limiting reactor B. f ) After 7 minutes, the tie line between Fisk Street B and Quarry Street, that is, the power limiting reactor B, was opened, and Quarry Street and Fisk A, came back to normal. About the same time, the 30,000 KW machine in Northwest Station began to lose i ...", "... voltage at the busbars of these two stations remained practically zero, and an excessive current fed into Fisk B from Quarry Street, heating the power limiting reactor B. f ) After 7 minutes, the tie line between Fisk Street B and Quarry Street, that is, the power limiting reactor B, was opened, and Quarry Street and Fisk A, came back to normal. About the same time, the 30,000 KW machine in Northwest Station began to lose its excitation, and was disconnected. g) Fisk B and Northwest remained out of synchronism with each other, with pra ...", "... if the report is correct. 3.) Sept. 18th, 19195:27 P. M. a) One hour forty minutes after the first trouble, resulting from a short near the busbars of Fisk B, a short circuit occurred near the busbar of Fisk A, and held for several seconds, while the tie line reactor B was still open, that is, Fisk B and Northwest cut off from Quarry Street and Fisk A. b) All synchronous machines on Fisk A dropped out, and a few on Quarry Street, Fisk B and Northwest; 39 synchronous machines on Fisk A are recorded as having dropped out, 3 ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-15", "section_label": "Chapter 15: Constant-Voltage Series Operation", "section_title": "Constant-Voltage Series Operation", "kind": "chapter", "sequence": 15, "number": 15, "location": "lines 27996-29301", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-15/", "snippets": [ "... rcuit. n = number of consuming devices (lamps) in series. p = fraction of burned-out lamps. g a= conductance of lamp. (15) 302 ELECTRIC CIRCUITS and let 6 1 = shunted susceptance with the lamp in circuit, that is, exciting susceptance of reactor or auto- transformer, and y = \\/g^ + bi^ = admittance of complete consuming device. 62 = shunted susceptance with the lamp burned out and let c = — = exciting current as fraction of load ^ current: c < 1. a = ^- = saturation factor of reactor or ...", "... e of reactor or auto- transformer, and y = \\/g^ + bi^ = admittance of complete consuming device. 62 = shunted susceptance with the lamp burned out and let c = — = exciting current as fraction of load ^ current: c < 1. a = ^- = saturation factor of reactor or - auto transformer: o > 1. (16) (17) it is, then: voltage of lamp and reactor: voltage of reactor with lamp burned out: I .7 ?>2 (18) ^2 = — nr = J — jbo thus, with pn lamps burned out, and (1 — p)n lamps burning, total volt ...", "... vice. 62 = shunted susceptance with the lamp burned out and let c = — = exciting current as fraction of load ^ current: c < 1. a = ^- = saturation factor of reactor or - auto transformer: o > 1. (16) (17) it is, then: voltage of lamp and reactor: voltage of reactor with lamp burned out: I .7 ?>2 (18) ^2 = — nr = J — jbo thus, with pn lamps burned out, and (1 — p)n lamps burning, total voltage, eo = n(l — p)^i + np ^2 (19) it is (20) = n/ substituting (17), Co = ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-02-discussion-of-recommendations", "section_label": "Report Section 3: Discussion of Recommendations", "section_title": "Discussion of Recommendations", "kind": "report-section", "sequence": 3, "number": 3, "location": "PDF pages 12-16, lines 721-1138", "status": "pdf-text-extracted-candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-02-discussion-of-recommendations/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-02-discussion-of-recommendations/", "snippets": [ "... he Commonwealth Edison Company of Chicago, is by no means too high. Necessarily, however, these power limiting reactors also limit the synchronizing power be- tween the station sections. Thus if in a station section as Fisk Street A, which is connected by one power limiting reactor to the rest of the system, full load of 60,000 KW is suddenly thrown off as by a short circuit at the busbars dropping out the synchronous machines in the substations while full steam supply is still on, the synchronizing power coming over the power limiting ...", "... imiting reactor to the rest of the system, full load of 60,000 KW is suddenly thrown off as by a short circuit at the busbars dropping out the synchronous machines in the substations while full steam supply is still on, the synchronizing power coming over the power limiting reactor is insufficient to hold the station in step, and the station breaks synchronism and speeds up. Whether synchronous operation is preserved or synchronism broken, depends on the relative speed, with which the synchronous machines in the substations drop out, th ...", "... idly; at full voltage and full steam supply, a little over a second after the load has dropped off, the sta- tions would have speeded up so as to have broken synchronism with the rest of the system, in spite of the maximum synchronizing power exerted over the power limiting reactor. In reality obviously the load cannot drop off instantly but would hold on an appreciable time, and the governors would immediately begin to cut off steam; but on the other hand, the station voltage has dropped under short circuit, and is below normal, and wi ..." ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_id": "theory-calculation-electric-circuits-chapter-08", "section_label": "Chapter 8: Shaping Of Waves By Magnetic Saturation", "section_title": "Shaping Of Waves By Magnetic Saturation", "kind": "chapter", "sequence": 8, "number": 8, "location": "lines 12962-16963", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-08/", "snippets": [ "... tion, for / — 20, may possibly be due to an inaccuracy in the hysteresis cycle of Fig. 55, a too great steepness near the zero value, rather than being actual.) It is interesting to realize, that when measuring the reactance of a closed magnetic circuit reactor by voltmeter and ammeter readings, it is not permissible to vary the voltage by series resist- ance, as this would give values indefinite between i, and Xc, de- 136 ELECTRIC CIRCUITS pending on the relative amount of resistance. To get Xp, the gen ...", "... t one-thousandth gap length, and with an air-gap of 1 per cent, length, only a moderate peakedness remains at the highest saturation, while at lower saturation the voltage wave is practically a sine. 73. Even a small air-gap in the magnetic circuit of a reactor greatly reduces the wave-shape distortion, that is, makes the voltage wave more sinusoidal, and cuts off the saturation peak. The latter, however, is the case only with a complete air-gap. A partial air-gap or bridged gap, while it makes the wave shap ...", "... = B-2, while curve I shows the m.m.f. which an unbridged gap would require. Adding to the ordinates of II the values of the m.m.f. required for the iron part of the magnetic circuit, or the other 99 per cent., gives as curve III the total m.m.f. of the reactor. The lower part of curve III is once more shown, with iSve times the abscissse B, and 1000, 100 and 10 times, respectively, the ordinates H, as IIIi. III2, III3. 74. From B = 2 upward, curve III is practically a straight line, and plotting herefrom for ..." ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_id": "engineering-mathematics-chapter-03", "section_label": "Chapter 3: Trigonometric Series", "section_title": "Trigonometric Series", "kind": "chapter", "sequence": 3, "number": 3, "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... t. io6. Example lo. An alternating-current generator, of generated e.m.f. e = 2500 volts, internal resistance ro = 0.25 ohms, and synchronous reactance a:o = 10 ohms, is loaded by a circuit comprising a resistor of constant resistance r = 20 ohms, and a reactor of reactance x in series with the resistor r. What value of reactance x gives maximum output? If i = current of the alternator, its power output is P-=n2 = 20i2; (26) 162 ENGINEERING MATHEMATICS. the total resistance is r + ro = 20.25 ohms; the tota ...", "... 000i-6 = 0.78125Xl0i6-8; hence, e = 1373 volts for maximum efficiency at full load. and e = 938 volts for maximum efficiency at half load. 117. Example 18. (a) Constant voltage 6 = 1000 is im- pressed upon a condenser of capacity C = 10 mf., through a reactor of inductance L = 100 mh., and a resistor of resist- ance r = 40 ohms. What is t.hp maximum value of the charg- ing: current? 176 ENGINEERING MATHEMATICS. (b) An additional resistor of resistance r' = 210 ohms is then inserted in series, making the to ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-31", "section_label": "Chapter 9: Divided Circuit", "section_title": "Divided Circuit", "kind": "chapter", "sequence": 31, "number": 9, "location": "lines 9228-10474", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "snippets": [ "... directly com- parable with the phenomena on a 60-cycle circuit. A better conception of the size or magnitude of inductance and capacity is secured. Since inductance and capacity are mostly observed and of importance in alternating-current cir- cuits, a reactor having an inductive reactance of x ohms and i amperes conveys to the engineer a more definite meaning as regards size: it has a volt-ampere capacity of tfx, that is, the approximate size of a transformer of half this capacity, or of a ^2x — -watt trans ...", "... inductive reactance of x ohms and i amperes conveys to the engineer a more definite meaning as regards size: it has a volt-ampere capacity of tfx, that is, the approximate size of a transformer of half this capacity, or of a ^2x — -watt transformer. A reactor having an inductance of L henrys and i amperes, however, conveys very little meaning to DIVIDED CIRCUIT 123 the engineer who is mainly familiar with the effect of inductance in alternating-current circuits. Substituting therefore (5) and (6) in equa ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-01-recommendations", "section_label": "Report Section 2: Recommendations", "section_title": "Recommendations", "kind": "report-section", "sequence": 2, "number": 2, "location": "PDF pages 7-12, lines 145-720", "status": "pdf-text-extracted-candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "snippets": [ "... 4, 5 and 6, have been carried out I would recommend, in case the voltage of a station section disappears, as result of a short circuit at or near the station, and if the voltage does not promptly come back after the clearing of the short circuit, to open the power limiting reactor or reactors which connect this station section with the rest of the system, and thereby isolate it. Then, as soon as the voltage has recovered, the isolated station should again be syn- chronized in with the rest of the system. If, after thus isolating the [[ ..." ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_id": "theory-calculation-alternating-current-phenomena-chapter-25", "section_label": "Chapter 25: Distortion Of Wave-Shape And Its Causes", "section_title": "Distortion Of Wave-Shape And Its Causes", "kind": "chapter", "sequence": 25, "number": 25, "location": "lines 29375-32539", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-25/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-25/", "snippets": [ "... tance, with a sine wave current of 7.07 effective, so is 9 91 ' = 7:07 = l-^O' while the same reactance, with a sine wave e.m.f. of 7.07 effective, in A, gives the impedance. The conclusion is that an iron-clad magnetic circuit is not suitable for a reactor, since even below saturation (as above assumed) it produces very great wave-shape distortion. As discussed before, the insertion of even a small air-gap into the magnetic circuit makes the current wave nearly coincide in phase and in shape with the wave ..." ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_id": "theory-calculation-electric-apparatus-chapter-20", "section_label": "Chapter 22: Unipolar Machines", "section_title": "Unipolar Machines", "kind": "chapter", "sequence": 20, "number": 22, "location": "lines 31716-32137", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-20/", "snippets": [ "... , the total voltage induced in a turn must always be zero, that is, the voltage, if periodical, must be alter- nating, regardless how the electromagnetic induction takes place, whether the turn is stationary or moving, as a part of a machine, transformer, reactor or any other electromagnetic induction device. Thus continuous-voltage induction in a closed turn is impossible, and the coil-wound unipolar machine thus a fallacy. Continuous induction in the unipolar machine is pos- sible only because the circuit is not ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-50", "section_label": "Chapter 1: General Equations", "section_title": "General Equations", "kind": "chapter", "sequence": 50, "number": 1, "location": "lines 27761-28694", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-50/", "snippets": [ "... gation of electric circuits, these four constants, r, L, g, C, usually are assumed as located separately from each other, or localized. Although this assumption can never be per- fectly correct, — for instance, every resistor has some inductance and every reactor has some resistance, — nevertheless in most cases it is permissible and necessary, and only in some classes of phenomena, and in some kinds of circuits, such as high-frequency phenomena, voltage and current distribution in long-distance, high-potential ci ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... ting-current generator 82 Reactance, effective, of external field . . 406 INDEX 569 PAGE Reactance, effective (continued), of internal field 406 of armature reaction 200 mutual inductive 143 Reaction, armature, and short-circuit current 199 Reactor, size and rating 69 Rectification, and commutation 222 arc 249 by periodic transient terms 22, 221 constant-current 230, 242 potential 230, 236 mechanical 229 open-circuit 230 polyphase 230 quarter-phase 230, 242 reversal or change of circ ..." ] } ] }, { "id": "brilliancy", "label": "Brilliancy", "aliases": [ "Brilliancy", "brilliancy" ], "total_occurrences": 66, "matching_section_count": 11, "matching_source_count": 2, "source_totals": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 62, "section_count": 10 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 4, "section_count": 1 } ], "section_hits": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-12", "section_label": "Lecture 12: Illumination And Illuminating Engineering", "section_title": "Illumination And Illuminating Engineering", "kind": "lecture", "sequence": 12, "number": 12, "location": "lines 16485-17445", "status": "candidate", "occurrence_count": 25, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-12/", "snippets": [ "... as such includes the effect of shadows as causing differences in intensity at the edge of objects. The physical quantities with which we have to deal in illumi- nating engineering thus are : The intensity of the light source or the illuminant, and its brilliancy, that is, the flux density at the surface of the illuminant; The flux of light, that is, the total visible radiation issuing from the illuminant; 256 ILLUMINATION AND ILLUMINATING ENGINEERING. 257 The light flux density, that is, the distribution o ...", "... o the equivalent candle power of the light source. Illumination is the light flux density reflected from the illu- minated object, and as flux density thus is measured also in lumens per square meter or square foot, or in meter-candles or foot-candles. Brilliancy is the light flux density at the surface of the illumi- nant, and as flux density thus could also be measured in lumens per square meter or square foot, but, as this would usually give enormous values, brilliancy of the light source generally is meas- ure ...", "... ot, or in meter-candles or foot-candles. Brilliancy is the light flux density at the surface of the illumi- nant, and as flux density thus could also be measured in lumens per square meter or square foot, but, as this would usually give enormous values, brilliancy of the light source generally is meas- ured in lumens per square centimeter, or per square millimeter. It is a quantity which is of high importance mainly in its physio- logical effect. Light intensity, brilliancy and light flux thus are character- 26 ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-10", "section_label": "Lecture 10: Light Flux And Distribution", "section_title": "Light Flux And Distribution", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 9389-12573", "status": "candidate", "occurrence_count": 15, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-10/", "snippets": [ "... /> = 0 to the angle <£ = fa against the vertical or symmetry axis, then is fc1 = 2 TT / sin dfa (3) */0 and the light flux in a zone between the angles (j)1 and fa is (4) I. DISTRIBUTION CURVES OF RADIATION. (1) Point, or Sphere, of Uniform Brilliancy. In this case, the intensity distribution is uniform, and thus, if / = intensity of light, in candles, <£= 4 nl = light flux, in lumens; (5) or, inversely: / = -. (6) The brilliancy of a radiator is the light-flux density at its sur- face. Th ...", "... UTION CURVES OF RADIATION. (1) Point, or Sphere, of Uniform Brilliancy. In this case, the intensity distribution is uniform, and thus, if / = intensity of light, in candles, <£= 4 nl = light flux, in lumens; (5) or, inversely: / = -. (6) The brilliancy of a radiator is the light-flux density at its sur- face. Thus, with a luminous point of intensity /, the brilliancy 190 RADIATION, LIGHT, AND ILLUMINATION. would be infinite; with a luminous sphere of uniform intensity distribution, and of radius ...", "... s uniform, and thus, if / = intensity of light, in candles, <£= 4 nl = light flux, in lumens; (5) or, inversely: / = -. (6) The brilliancy of a radiator is the light-flux density at its sur- face. Thus, with a luminous point of intensity /, the brilliancy 190 RADIATION, LIGHT, AND ILLUMINATION. would be infinite; with a luminous sphere of uniform intensity distribution, and of radius r, the brilliancy is * 7 ' (7) B = ,2 ' hence, inversely proportional to the square of the radius of the s ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-13", "section_label": "Lecture 13: Physiological Problems Of Illuminating Engineering", "section_title": "Physiological Problems Of Illuminating Engineering", "kind": "lecture", "sequence": 13, "number": 13, "location": "lines 17446-17956", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-13/", "snippets": [ "... well understood and such that they can be taken into consideration in the physical design of the illumina- tion, and thus no excuse exists to fail in their fulfillment, though it is frequently done. Such, for instance, is the requirement of low intrinsic brilliancy in the field of vision, of the color of the light, etc. Other physiological requirements are still very little 277 278 RADIATION, LIGHT, AND ILLUMINATION. understood or entirely unknown, while on others not sufficient quantitative data are available ...", "... diffused light have in the illuminating engineering practice been obscured to some extent by the relation between high and low intrinsic bril- liancy and between direct and indirect lighting. Thus, to eliminate the objectionable feature of high intrinsic brilliancy of the illuminant, direct lighting by light sources of high brilliancy, which was largely directed lighting, has been replaced by indirect lighting, by reflection from ceilings, etc., which is diffused light- ing. Where such change has resulted in a great ...", "... ured to some extent by the relation between high and low intrinsic bril- liancy and between direct and indirect lighting. Thus, to eliminate the objectionable feature of high intrinsic brilliancy of the illuminant, direct lighting by light sources of high brilliancy, which was largely directed lighting, has been replaced by indirect lighting, by reflection from ceilings, etc., which is diffused light- ing. Where such change has resulted in a great improvement of the illumination, it frequently has been attributed to ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... he field of vision where we want to see objects, than if the source of light were taken out of the field of vision. By eliminating the source of light from the field of vision and eliminating the contraction of the pupils resulting from the high intrinsic brilliancy of the illuminating LIGHT AND ILLUMINATION 251 body, we get actually a much larger amount of light into the eye with the same amount of light striking the illuminated object ; that is, we get a higher physiological efficiency. Even with a much smaller ...", "... same amount of light striking the illuminated object ; that is, we get a higher physiological efficiency. Even with a much smaller amount of light reaching the illuminated objects, we still get more light in the eye. That means if we reduce the intrinsic brilliancy of the illuminant by indirect lighting, by diffusing the light, we may lose a considerable amount of light, actually get a considerably reduced quantity of light on the object which we desire to see, but still we get a larger amount of light from these ob ...", "... ve intrinsic brilliancies in the field of vision when looking at the objects we desire to see. That means that the proper field for the illuminant is outside of the field of vision, or where you cannot get it out of the field of vision, that its intrinsic brilliancy should be reduced by diffusion : thereby we actually get a much higher physiological effect. This is the reason for indirect lighting. We may have a very large amount of light thrown on any object in a room, but if the eye is fatigued by seeing the source ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "... mospheric pressures to the Geissler tube glow in the vacuum; but the change is gradual, thus showing the identity of the two phenomena. At atmospheric pressure, disruptive conduction occurs by a sharply denned, relatively thin and noisy spark of very high brilliancy, which traverses the space between the electrodes in an erratic zigzag path, not unlike in appearance to the mechanical fracture of a solid material; and, indeed, the spark is an electrostatic rupture of the gas. If the electrostatic field is fairly unifo ...", "... led \" brush discharge,\" or \" corona.\" Between needle points the brush discharges increase in extent, and approach each other until they bridge nearly 60 per cent of the gap, and then the static spark occurs. At higher gas pressures the spark increases in brilliancy, in noisiness, but gets thinner. If, however, we gradually decrease the gas pressure, the spark gets thicker, less brilliant, and less noisy, its edges are less sharply defined, that is, get more diffused, and ultimately it passes between the terminals as ...", "... lo,oOU ...", "... y arc lamp. Here the light is bluish green, containing only the highest frequencies of visible radiation, violet, blue and green, but practically none of the lower frequencies of visible radiation, red or orange. FIG. 11. In the tungsten lamp at high brilliancy and more still in the mercury arc, radiations of higher frequencies appear, that is, shorter wave lengths than visible light, and these radiations are again invisible. As they are of frequencies beyond the violet rays of light, they are called \" ultra-vio ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... possibly to a higher temperature and greater thickness of their atmosphere, and sometimes bright lines and dark lines occur simultaneously, or dark lines may change to bright lines at such places at which, by some activity, as a tem- perature rise, their brilliancy is greatly increased. FIG. 18. Combinations of the different types of spectra: continuous spectrum, line spectrum, band spectrum, reversed spectrum, frequently occur, as we have seen bands and lines together in the modified mercury spectrum, and in th ...", "... erefore, show only when covering a white, that is, reflecting surface, and then, due to the light reflected from the white background of the transparent coloring body traversing this body twice, before and after reflection, and, therefore, depend in their brilliancy on the background. The difference between opaque and transparent colors, the former reflecting from the surface, the latter reflecting from back of the colored substance, is seen by comparing the appearance of the two classes of colors shown in 14 and in ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-04", "section_label": "Lecture 4: Chemical And Physical Effects Of Radiation", "section_title": "Chemical And Physical Effects Of Radiation", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3639-3945", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-04/", "snippets": [ "... ly spreading, they appear — especially against a dark background — as brilliant luminous clouds of orange, red and green, and seen through a red glass they appear like clouds of fire. I change to the illumination given by the incandescent lamp and all the brilliancy disappears, fluorescence ceases and we have a dull red colored solution. I show you here the sample card of a silk store of different colored silks. Looking at it through a red glass, in the mercury light all disappear except a few, which you can pick out ...", "... e dye, rhodamine. A glass plate coated with a thick layer of transparent varnish, colored by rhodamine, appears like a sheet of red hot iron in the mercury light, especially through a red glass, while in the light of the incandescent lamp it loses all its brilliancy. This solution of rhodamine 6 G in alcohol, fluoresces a glaring orange in the mercury light, in the light of a carbon arc lamp (or in daylight) it fluoresces green and less brilliant. Thus you see that the color of the fluorescent light is not always th ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-05", "section_label": "Lecture 5: Temperature Radiation", "section_title": "Temperature Radiation", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3946-5076", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-05/", "snippets": [ "... the violet end of the spectrum would increase faster than the red end and the light thus shift to bluish white, blue and violet. The invisibility of the radiation of low temperature is not due to low intensity. I have here an incandescent lamp at normal brilliancy. If I decrease the power input and thereby the radi- ated power to T^ it becomes invisible, but if we move away from the lamp to 10 times the previous distance, we get only T^ the radiation reaching our eyes and still the light is very plainly 74 RADIAT ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-07", "section_label": "Lecture 7: Flames As Illuminants", "section_title": "Flames As Illuminants", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 6609-7140", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-07/", "snippets": [ "... lames are blue. 60. While light, and radiation in general, can also be pro- duced by the combustion of other materials besides hydro- carbons, industrially other materials are very little used. Burning magnesium gives a luminous flame of extremely high brilliancy and whiteness. Its light is largely due to tem- perature radiation, and the flame makes its own incandescent radiator; but unlike the hydrocarbon flame, in which the radiator is again destroyed by combustion, the incandescent radiator of the magnesium fla ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-11", "section_label": "Lecture 11: Light Intensity And Illumination", "section_title": "Light Intensity And Illumination", "kind": "lecture", "sequence": 11, "number": 11, "location": "lines 12574-16484", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-11/", "snippets": [ "... reflected from the mirror, and, due to the eccentric location of the filament, the reflected rays are collected into an angle of about 45 deg. from the vertical, and cross each other, thereby producing the intensity maximum at 4> = 30 deg. The intrinsic brilliancy is sufficiently reduced, and the distribution curve smoothed out, by the frosting of the globe as far as not cov- ered by the reflector. The light in the upper hemisphere beyond = (j>2 then is only that reflected by the frosting. The numerica ..." ] } ] }, { "id": "ether", "label": "Ether", "aliases": [ "Ether", "aether", "ether" ], "total_occurrences": 66, "matching_section_count": 6, "matching_source_count": 3, "source_totals": [ { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 59, "section_count": 3 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 6, "section_count": 2 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-02", "section_label": "Lecture 2: Conclusions From The Relativity Theory", "section_title": "Conclusions From The Relativity Theory", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 736-2388", "status": "candidate", "occurrence_count": 52, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... obser- vation. The law of conservation of matter thus had to be abandoned and mass became a manifestation of energy. The law of gravitation has been recast, and the force of gravitation has become an effect of inertial motion, like centrifugal force. The ether has been abandoned, and the field of force of Faraday and Maxwell has become the fundamental conception of physics. The laws of mechanics ^ have been changed, and time and space have been bound' together in the four-dimensional world space, the dimen- si ...", "... ion miles. Therefore the principal value of the relativity theory thus far consists in the better conception of nature and its laws which it affords. Some of the most interesting illustra- tions of this will be discussed in the following pages. B. THE ETHER AND THE FIELD OF FORCE Newton's corpuscular theory of light explained radiation as a bombardment by minute particles projected at extremely high velocities, in much the same way as the alpha and the beta rays are explained today. This corpuscular theory ...", "... hat is, if they are equal, they extinguish each other. The phenomenon of interference thus leads to the wave theory of light. If light is a wave motion, there must be something to move, and this hypothetical carrier of the light wave has been called the ether. Here our troubles begin. The phenomenon of polarization shows that light is a transverse wave; that is, the ether atoms move at right angles to the light beam, and not in its direction as. is the case with sound waves. In such transverse motion a vibrati ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-04", "section_label": "Lecture 4: The Characteristics Of Space A. The Geometry Of The Gravitational Field", "section_title": "The Characteristics Of Space A. The Geometry Of The Gravitational Field", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3595-6820", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-04/", "snippets": [ "... ge, 47 field, 18 ElUptic geometry, 64, 72, 74 trigonometry, 77 Energy equivalent of mass, 44 field, 22, 46 kinetic, 47 and mass, 41 of wave, 22 123 124 INDEX Entity energy, 24 Equations of transformation to moving system, 25, 27 Ether, 12, 14 as solid, 14 drift, 14 fallacy of conception, 16 illogical, 18 unnecessary, 17 waves, 18 Euclid, 71 Euclidean geometry, 64, 72, 74 F Fallacy of ether conception, 16 Faraday, 12, 17 Field, centrifugal, 47 dielectric, 18 electrom ...", "... NDEX Entity energy, 24 Equations of transformation to moving system, 25, 27 Ether, 12, 14 as solid, 14 drift, 14 fallacy of conception, 16 illogical, 18 unnecessary, 17 waves, 18 Euclid, 71 Euclidean geometry, 64, 72, 74 F Fallacy of ether conception, 16 Faraday, 12, 17 Field, centrifugal, 47 dielectric, 18 electromagnetic, 21 electrostatic, 18 gravitational, 18, 46, 47 magnetic, 18 of energy, 22 of force, 12, 18 Finite volume of universe, 63 Force, magnetic, 46 Four-dimensio ...", "... itational, 18, 46, 47 magnetic, 18 of energy, 22 of force, 12, 18 Finite volume of universe, 63 Force, magnetic, 46 Four-dimensional space with sphere as element, 99 Fraction, meaning of, 38 Frequencies of electromagnetic waves, 22 Friction of ether, 14 G Gauss, 71 General differential space, 115 geometry, 64 or projective geometry space, 115 Geometry, 64 of gravitational field, 69 Gravitation, 46 as accelerated motion, 52 as centrifugal force of radial acceleration, 55 as inertia of ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... icity and extremely low density, and it must penetrate all substances since no vacuum can be produced for this medium, because light passes through any vacuum. Hence it cannot be any known gas, but must be essen- tially different, and has been called the \"ether.\" Whether the ether is a form of matter or not depends upon the definition of matter. If matter is defined as the (hypotheti- cal) carrier of energy (and all the information we have of matter is that it is the seat of energy) , then the ether is matter, ...", "... w density, and it must penetrate all substances since no vacuum can be produced for this medium, because light passes through any vacuum. Hence it cannot be any known gas, but must be essen- tially different, and has been called the \"ether.\" Whether the ether is a form of matter or not depends upon the definition of matter. If matter is defined as the (hypotheti- cal) carrier of energy (and all the information we have of matter is that it is the seat of energy) , then the ether is matter, as it is a carrier of ...", "... called the \"ether.\" Whether the ether is a form of matter or not depends upon the definition of matter. If matter is defined as the (hypotheti- cal) carrier of energy (and all the information we have of matter is that it is the seat of energy) , then the ether is matter, as it is a carrier of energy: the energy of radiation, during the time be- tween the moment when the wave leaves the radiator and the moment when it strikes a body and is absorbed, resides in the ether. 5. If light is a wave motion or vibrati ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-03", "section_label": "Lecture 3: Gravitation And The Gravitational Fleld", "section_title": "Gravitation And The Gravitational Fleld", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2389-3594", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-03/", "snippets": [ "LECTURE III GRAVITATION AND THE GRAVITATIONAL FLELD A. THE IDENTITY OF GRAVITATIONAL, CENTRIFUGAL AND INERTIAL MASS As seen in the preceding lecture, the conception of the ether as the carrier of radiation had to be abandoned as incompatible with the theory of relativity; the conception of action at a distance is repugnant to our reasoning, and its place is taken by the conception of the field of force, or, more correctly, the en ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... ions. There are different forms of energy, all convertible into each other, as magnetic energy, electric energy, heat energy, mechanical momentum, radiating energy, etc. The latter, radi- ating energy, is a vibratory motion of a hypothetical medium, the ether, which vibration is transmitted or propagated at a velocity of about 188,000 miles per second; and it is a transverse vibration, differing from the vibratory energy of sound in this respect, that the sound waves are longitudinal, that is, the vibration is ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... less and, as will be seen, is different for different frequencies. 22 RADIATION, LIGHT, AND ILLUMINATION. Assume then, in Fig. 15, a beam of light B striking under an angle the boundary between two media, as air A and water W, the vibration of the ether particles in the beam of light is at right angles to the direction of propagation BC, and successively the waves thus reach at blf a2 bz . . . As soon, however, as the back edge of the beam reaches the boundary at D its speed changes FIG. 15. by enter ..." ] } ] }, { "id": "photometry", "label": "Photometry", "aliases": [ "Photometry", "photometer", "photometers", "photometric", "photometry" ], "total_occurrences": 58, "matching_section_count": 4, "matching_source_count": 2, "source_totals": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 54, "section_count": 3 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 4, "section_count": 1 } ], "section_hits": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-09", "section_label": "Lecture 9: Measurement Of Light And Radiation", "section_title": "Measurement Of Light And Radiation", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 8511-9388", "status": "candidate", "occurrence_count": 46, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-09/", "snippets": [ "... compare physiological effects of widely different wave lengths by comparing the power required to produce them. When speaking of mechanical equivalent of light, it thus must be understood in the extended meaning of the word, as discussed above. 76. In photometry, and in general in illuminating engineer- ing, it is of essential importance to keep in mind this difference in the character of light, as physiological effect, and radiation, as physical quantity of power. This is the reason why all attempts to reduce ph ...", "... ry, and in general in illuminating engineer- ing, it is of essential importance to keep in mind this difference in the character of light, as physiological effect, and radiation, as physical quantity of power. This is the reason why all attempts to reduce photometry to a strictly physical measure- ment, and thereby bring photometric determinations up to the high grade of exactness feasible in physical observations, have failed and must necessarily fail; we cannot physically compare an effect as light, which is not a ...", "... l importance to keep in mind this difference in the character of light, as physiological effect, and radiation, as physical quantity of power. This is the reason why all attempts to reduce photometry to a strictly physical measure- ment, and thereby bring photometric determinations up to the high grade of exactness feasible in physical observations, have failed and must necessarily fail; we cannot physically compare an effect as light, which is not a physical quantity, but somewhere in all photometric methods the phys ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... light of the same color we can compare exactly; if the color is not much different, we still get an approximate comparison; but with widely different colors, we obviously can not get even an approximate com- parison, can not say when the two sides of the photometer screen, one illuminated by green light, the other by red light, are equal in intensity. There is thus no direct comparison of differently colored lights. You have then to go one step farther and consider that light is used for illumination, is used to see ...", "... of the voltage and the current in a lightning flash would not yet give the energy, if the duration of the dis- charge is not also known. We can, however, get an approxi- mate estimate of the magnitude of the energy of the lightning flash indirectly, from photometric considerations, and elimi- nate the consideration of the duration of the flash by -the TynOPERTY Of ELECiniCAL LABOHAlOKY, j FACULTY OF A^-fLlE* SCIENCE. j 262 GENERAL LECTURES integrating feature of the human eye for impressions of very short dur ...", "... average potential gradient in the light- ning flash as 50,000 volts per foot, the current as 10,000 am- peres, a lightning flash of two miles' length would represent a power of 5 X 10* K. W. Estimating the energy of the discharge, as approximated from the photometric consideration, as 10,000 K. W. seconds, the duration of the discharge would be: 10V5 X 10* = 2 x 10\"* sec, or two-millionths of a second. The discharge probably is oscillatory. In view of the high resistance of the discharge path, the damping effect must ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-03", "section_label": "Lecture 3: Physiological Effects Of Radiation", "section_title": "Physiological Effects Of Radiation", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2366-3638", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-03/", "snippets": [ "... in the middle of the spectrum. When comparing, however, the physiological effects of different frequencies of radiation, that is, different colors of light, the diffi- culty arises that different colored lights cannot be compared photometrically, as all photometers are based on making the illu- mination produced by the two different sources of light equal, and when these sources of light are of different color they can never become equal. As long as the colors are not very different - two different shades of yellow ...", "... nt be black on white. This method of comparison of the physiological effect, by what has been called the \"lumino- meter,\" is theoretically the most correct, as it is independent of the color of light. It is, however, not as accurate as the compari- son by photometer, and thus the average of a number of observa- tions must be used. The only error which this method leaves is that due to the difference in the sensitivity of different eyes, that is, due to the differences between the sensitivity curves (Fig. 21), and thi ...", "... , that is, with a lesser power of the distance than the square, for bluish green or the short-wave end of the spectrum. This phenomenon is appreciable even when comparing the enclosed alternating carbon arc with the open direct current car- bon arc : by photometer, where a fairly high intensity of illumi- nation is used, the relative intensity of the two arcs is found somewhat different than by luminometer, that is, by reading distances nearer the lower limit of visibility. For low intensities, the alternating arc ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-12", "section_label": "Lecture 12: Illumination And Illuminating Engineering", "section_title": "Illumination And Illuminating Engineering", "kind": "lecture", "sequence": 12, "number": 12, "location": "lines 16485-17445", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-12/", "snippets": [ "... bution curve obviously is to choose a light source coming as near to it as possible, and then modifying it by reflection or diffraction. 113. Thus far, the problem is one of physics, and the result, that is, the objective illumination, can be measured by photometer or luminometer, and thus checked. The duty of the illuminat- ing engineer, however, does not end here, but with the same objective illumination, that is, the same distribution of light flux throughout the entire illuminated area, as measured by photomete ...", "... hotometer or luminometer, and thus checked. The duty of the illuminat- ing engineer, however, does not end here, but with the same objective illumination, that is, the same distribution of light flux throughout the entire illuminated area, as measured by photometer, the illumination may be very satisfactory, or it may be entirely unsatisfactory, depending on whether the physio- logical requirements are satisfied or are violated ; and very often we find illuminations which seem entirely unsatisfactory, tiring, or unc ...", "... light flux in space, and the subjective effects produced on the human eye, thus are the most important with which the illuminating engineer has to deal, and the first feature which must be recognized is that the objective illumination, as measured by the photometer, is no criterion of the subjective illumination, that is, the physiological effect produced by it, as regard to clearness, comfort and satis- faction, and it is the subjective illumination by which the success of an illuminating engineering problem is jud ..." ] } ] }, { "id": "ultrared", "label": "Ultra-Red Radiation", "aliases": [ "Ultra-red radiation", "infra-red", "infrared", "ultra-red", "ultrared" ], "total_occurrences": 38, "matching_section_count": 10, "matching_source_count": 3, "source_totals": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 31, "section_count": 8 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 6, "section_count": 1 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-03", "section_label": "Lecture 3: Physiological Effects Of Radiation", "section_title": "Physiological Effects Of Radiation", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2366-3638", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-03/", "snippets": [ "... ise the lower portions of the speech are not recorded, while at the louder portions the recording point jumps and the voice breaks in the reproduction. 21. The sensitivity of the eye to radiation obviously changes with the frequency, as it is zero in the ultra-red, and in the ultra- violet — where the radiation is not visible — and thus gradually increases from zero at the red end of the spectrum to a maximum somewhere near the middle of the spectrum and then decreases again to zero at the violet end of the spectru ...", "... e the same physiological effect — as one candle power of light — is a maxi- mum near the middle of the spectrum and decreases from there to infinity at the end of the visible range, being infinite RED YELLOW GREEN BLUE VIOLET FIG. 21. in the ultra-red and ultra-violet, where no power of radiation can produce visibility. It thus varies about as indicated in Fig. 22. The mechanical power equivalent of light, thus, is not constant, as the mechanical energy equivalent of heat — which is 426 kgm. or 4.25 k ...", "... of the green light as \"cold light\" and of the red and orange light as \"hot\" or \"warm.\" The harmful effect of working very much under artificial illumination is largely due to this energy effect, incident to the large amount of orange, red, and especially ultra- red in the radiation of the incandescent bodies used for illumi- nants and thus does not exist with \"cold light,\" as the light of the mercury lamp. Blue and violet light, however, are just as energetic, or \"hot,\" as orange and red light, and the reason that ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... it, though with a sensitive instrument, as a bolometer, we may still be able to measure the heat. All radiations therefore are convertible into heat: the visible light waves as well as the invisible ultraviolet rays, and the — usually more powerful — long ultrared waves ; but none of the radiations can be called heat, no more than the mechanical momentum of a flywheel is heat, because when destroyed, it produces heat. If we consider the infinite range of radiation issuing from heated bodies, we find that those ray ...", "... frequency rays. As stated, then, there is no essential differ- ence between so-called heat waves and light waves, but any radiation can be converted into other forms of energy, the so- called chemical rays of ultraviolet light, the X-ray, as well as the ultrared and the visible rays, and when converted into heat can be noticed as such. Now it just happens that most of our means of producing radiating energy give high intensi- ties of radiation only for very low frequencies, invisible ultra- red rays, but we are n ...", "... -ray, as well as the ultrared and the visible rays, and when converted into heat can be noticed as such. Now it just happens that most of our means of producing radiating energy give high intensi- ties of radiation only for very low frequencies, invisible ultra- red rays, but we are not able to produce anywhere near the same intensities of radiation for higher frequencies. So also, when we speak of ultraviolet, or short, high frequency waves, as chemical waves, thait does not mean that they have a distinctive charac ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... they are of frequencies beyond the violet rays of light, they are called \" ultra-violet rays/' while the radia- tions which we produced from the heated silicon rods at moderate temperatures were invisible because of too low frequency and are thus called \" ultra-red rays,\" or \" infra-red rays/' as they are outside of and below the red end of the range of visible radiation. To produce powerful ultra-violet rays, I use a condenser dis- charge between iron terminals, a so-called ultra-violet arc lamp. Three iron sphere ...", "... s beyond the violet rays of light, they are called \" ultra-violet rays/' while the radia- tions which we produced from the heated silicon rods at moderate temperatures were invisible because of too low frequency and are thus called \" ultra-red rays,\" or \" infra-red rays/' as they are outside of and below the red end of the range of visible radiation. To produce powerful ultra-violet rays, I use a condenser dis- charge between iron terminals, a so-called ultra-violet arc lamp. Three iron spheres, 7 in Fig. 11, of ab ...", "... somewhat less than one octave; ultra-violet radiations have been observed beyond this for about two more octaves. Ten octaves higher is the estimated frequency of X-rays. On the other side of the visible range, towards lower frequencies or longer waves, ultra-red rays, observations have been extended over more than eight octaves up to wave lengths as great as 0.03 cm. length, or frequencies of only 10 12 cycles per sec. The ultra- red rays given by the heated silicon rods of our experiment do not extend to such lo ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... of known radiations can be divided into two classes, the electric waves and the light waves, which are separated from each other by the blank space in the middle of the spectrum of radiation (Fig. 14). Under light waves we here include also the invisible ultra-red radiation and the ultra-violet radiation and the non-refrangible radiations, as X-rays, etc., separated from the latter by the second blank space of the radiation spectrum. In the following, mainly the light waves, that is, the second or high frequency range of r ...", "... is, for instance, the case with the * \"Theory and Calculation of Transient Electric Phenomena and Oscilla- tions. \" RELATION OF BODIES TO RADIATION. 21 radiation of an incandescent body as a lamp filament, which contains all the frequencies from long ultra-red waves over visible light waves to ultra-violet waves. In the action of vibrations on our senses there is a characteristic difference between the perception of sound waves by the ear and that of light waves by the eye : the ear is analytic, that is, can ...", "... t differences in the per- centage of radiation which they reflect or transmit. Thus we have seen that glass, which is transparent for visible light, is RELATION OF BODIES TO RADIATION. 33 entirely opaque for some ultra-violet light and also opaque for ultra-red light of low frequency, so in this broader sense would have to be called colored* the color of clear glass, however, is that of the visible spectrum; or, for instance, iodine solution, which is opaque for visible light, is transparent for ultra-red light, ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-04", "section_label": "Lecture 4: Chemical And Physical Effects Of Radiation", "section_title": "Chemical And Physical Effects Of Radiation", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3639-3945", "status": "candidate", "occurrence_count": 6, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-04/", "snippets": [ "... de and iodide in the negative plate and the quick printing papers. This chemical action is greatest in the violet and ultra-violet and decreases with increasing wave length, hence is less in the green, small in the yellow, and almost absent in the red and ultra-red, so that the short waves, blue, violet and ultra-violet, have sometimes been called \" chemical rays.\" This, however, is a misnomer, just as the term \"heat rays\" sometimes applied to red and ultra-red rays. In so far as when intercepted they are converted ...", "... , small in the yellow, and almost absent in the red and ultra-red, so that the short waves, blue, violet and ultra-violet, have sometimes been called \" chemical rays.\" This, however, is a misnomer, just as the term \"heat rays\" sometimes applied to red and ultra-red rays. In so far as when intercepted they are converted into heat, all rays are heat rays, but neither the ultra-red nor any other radiation is heat, but it may become heat when it ceases to be radiation. Thus all radiations are chemical rays, that is, pro ...", "... iolet, have sometimes been called \" chemical rays.\" This, however, is a misnomer, just as the term \"heat rays\" sometimes applied to red and ultra-red rays. In so far as when intercepted they are converted into heat, all rays are heat rays, but neither the ultra-red nor any other radiation is heat, but it may become heat when it ceases to be radiation. Thus all radiations are chemical rays, that is, produce chemical action, if they strike a body which is responsive to them. The chemical action of radiation is specif ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "... rature radiation. The change in the distribution of the power of radiation between the different spectrum lines, with change of tempera- ture, may increase the efficiency of light production — if the lines in the visible range increase faster than in the ultra-red and ultra-violet — or may decrease — if the visible lines in- crease slower — or may increase in some temperature range, decrease in some other temperature range, but all these changes are characteristic of the luminescent material, and do not obey a gen ...", "... rc stream, and thus substances which give a large part of their radiation as spectrum lines in the visible range — as calcium — give a very efficient arc, while those substances which radiate most of their energy as lines in the invisible, ultra-violet or ultra-red — - as carbon — give a very inefficient arc. The problem of efficient light production by the arc therefore consists in selecting such materials which give most of their radiation in the visible range. Carbon, which is most generally used for arc termina ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-05", "section_label": "Lecture 5: Temperature Radiation", "section_title": "Temperature Radiation", "kind": "lecture", "sequence": 5, "number": 5, "location": "lines 3946-5076", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-05/", "snippets": [ "... lly applied only to abnormally high radiation in the visible range, in its general physical meaning it applies to abnormal radiation of any fre- quency range, and curve V in Fig. 29, for instance, would be the curve of a grey body, which luminesces in the ultra-red, while curve IV would be that of a grey body, in which the heat lumi- nescence is in the visible range. In general, however, it is preferable to consider as luminescence only such radiation as exceeds the black body radiation of the same temperature, an ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-07", "section_label": "Lecture 7: Flames As Illuminants", "section_title": "Flames As Illuminants", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 6609-7140", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-07/", "snippets": [ "... e, how- ever, in the hydrocarbon flame the incandescent radiator is a black body, — carbon, — giving the normal temperature radiation, the radiator of the magnesium flame, magnesia, is a colored radiator, and its radiation is deficient in intensity in the ultra- red, and very high in the visible range, and thereby of a much higher efficiency than given by black-body radiation. The magnesium flame therefore is far more efficient than the hydro- carbon flame, and its light whiter. So also burning aluminum, zinc, phosp ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-09", "section_label": "Lecture 9: Measurement Of Light And Radiation", "section_title": "Measurement Of Light And Radiation", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 8511-9388", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-09/", "snippets": [ "... nverted into radiation, as in an incandescent lamp, this method is the most exact. However, it can directly measure only the total radiation power. To measure the different parts of the radiation so as to determine separately the power in the visible, the ultra-red, and the ultra-violet range, the method of input and losses can be used to give the total radiation power, and, by bolometer or other means, the relative powers of the component radiations measured in a beam of light. From the total radiation and the rati ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... than the highest frequencies which can be produced by electrodynamic machinery. At five billion cycles per second, the wave length is about 6 cm., that is, the frequency only a few octaves lower than the lowest frequencies observed as, heat radiation or ultra red light. The average wave length of visible light, 55 X 10~6 cm., corresponding to a frequency of 5.5 X 1014 cycles, would require spheres 10~5 cm. in diameter, that is, approaching molecular dimensions. OSCILLATING-CURRENT GENERATOR. 49. A system of ..." ] } ] }, { "id": "individualistic-era", "label": "Individualistic era", "aliases": [ "Individualistic era", "individualistic-era" ], "total_occurrences": 35, "matching_section_count": 10, "matching_source_count": 1, "source_totals": [ { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "occurrence_count": 35, "section_count": 10 } ], "section_hits": [ { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-07", "section_label": "Chapter 6: Germany in the Individualistic Era", "section_title": "Germany in the Individualistic Era", "kind": "chapter", "sequence": 7, "number": 6, "location": "lines 2776-3206", "status": "candidate", "occurrence_count": 9, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-07/", "snippets": [ "VI GERMANY IN THE INDIVIDUALISTIC ERA THE development of Germany during the individualistic era was dominated by two features — the late arrival of capitalism, and the early arrival of the socialistic movement. In- dustrial capitalism in Germany became vic- toriou ...", "VI GERMANY IN THE INDIVIDUALISTIC ERA THE development of Germany during the individualistic era was dominated by two features — the late arrival of capitalism, and the early arrival of the socialistic movement. In- dustrial capitalism in Germany became vic- torious a generation later, while a powerful Social Democratic pa ...", "... the result in Germany industrial capitalism has in reality never gained as complete control of the nation and its gov- ernment as was the case elsewhere. The reactionary period of the unholy alli- ance was broken and the individualistic era finally established in France by the revolution 74 GERMANY IN THE INDIVIDUALISTIC ERA of 1830 and the revolution of 1848 swept away the last remnant of feudalism and established individualism all over Europe, except in ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-10", "section_label": "Chapter 9: America in the Individualistic Era", "section_title": "America in the Individualistic Era", "kind": "chapter", "sequence": 10, "number": 9, "location": "lines 4268-4715", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-10/", "snippets": [ "IX AMERICA IN THE INDIVIDUALISTIC ERA DURING the Civil War, when industrial capitalism extended its sway over the en- tire United States, and in the years following the war we were in the first period of the indi- vidualistic era, that of numerous small and ...", "... ed, in a universal v.Tcck of the industry. Thus co-operation had to come, of neces- sity, to avoid the destructive effects of com- petition. Thus co-operative agreements between for- merly competing corporations came, and the individualistic era seemed to approach its end, the co-operative era to arrive. The fundamental jirinciple of industrial co- operation between corporations in the same or 120 AMERICA IN THE INDIVIDUALISTIC ERA similar fields comprise control ...", "... eting corporations came, and the individualistic era seemed to approach its end, the co-operative era to arrive. The fundamental jirinciple of industrial co- operation between corporations in the same or 120 AMERICA IN THE INDIVIDUALISTIC ERA similar fields comprise control of production; control of prices; interchange of information. Control of production 7neans: Elimination of the constantly recurring periods of business depression and business boom, by restri ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-06", "section_label": "Chapter 5: England in the Individualistic Era", "section_title": "England in the Individualistic Era", "kind": "chapter", "sequence": 6, "number": 5, "location": "lines 2409-2775", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-06/", "snippets": [ "ENGLAND IN THE INDIVIDUALISTIC ERA WHILE France in the great revolution gave the world the industrial era, England very soon took the leadership, and has retained it ever since. Various causes contributed: the early start of England in gradual revolution fr ...", "... m, gave her a great advantage. But most instrumental of all, and more dominant than the other incidental ad- vantages, was the strongly individualistic char- acter of the Anglo-Saxon race, which gave it the leadership in the individualistic era, and supplied the initiative to create industrial capitalism. England thus became the great industrial country, producing and supplying the world with steel and iron, textiles, machinery, and all manufactured goods, England be ...", "... encies — like our nation before the Civil War. England was a prosperous industrial nation under free trade, and so the other nations were led to believe if they only embraced free trade they would be- G4 ENGLAND IN THE INDIVIDUALISTIC ERA come equally industrial and prosperous. It took generations to realize that for England as a dominating industrial nation, having no in- dustrial competitor, free trade was an advan- tage, but no industrial development could ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-05", "section_label": "Chapter 4: The Individualistic Era: The Other Side", "section_title": "The Individualistic Era: The Other Side", "kind": "chapter", "sequence": 5, "number": 4, "location": "lines 1746-2408", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-05/", "snippets": [ "IV THE INDIVIDUALISTIC ERA! THE OTHER SIDE POLITICAL and industrial freedom unfet- tered the ambition, the initiative, the cre- ative, and inventive abihty of all the human race and so founded our modern industrial civ- ilization on the basis of indiv ...", "... e or the private charity of their relatives will be their lot. It is these three great fears which distinguish the majority from the minority and make the former dissatisfied with society. This is the cloven foot of the individualistic era — \"the devil take the hindmost.\" Individualistic so- ciety has failed to guarantee and insure the right to live of all human beings, and all those who feel that they may some time in their life be caught as \"the hindmost\" ...", "... cription necessary. Un- fortunately, we see the same here in our coun- try: in all the present patriotic revival, in the preparedness movement, the workers and their organizations are conspicuously absent. In this respect the individualistic era has failed to satisfy the masses of the people, has failed to give them what they demand — social and industrial safety; and no talk about un- desirable paternalism, un-American ideas, etc., can obscure the fact of the fail ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-03", "section_label": "Chapter 2: The Epoch of the French Revolution", "section_title": "The Epoch of the French Revolution", "kind": "chapter", "sequence": 3, "number": 2, "location": "lines 627-873", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-03/", "snippets": [ "... NEW EPOCH ward appearances, the signs or mark-stones of the true history of the human race, which is made on the fields and farms, in the factories and workshops, in the business houses and shipping-offices. Ill THE INDIVIDUALISTIC ERA: FROM COMPETITION TO CO-OPERATION THE epoch of the French Revolution, ush- ered in by the declaration of the rights of man — liherte, egalite, fraternite — struck the fet- ters of feudalism from the human race, and gave ...", "... industrial development of the last cen- tury. The result was that the last century has seen a greater progress of mankind than all the previous centuries together. Competition thus became the industrial ex- pression of the individualistic era. 19 AMERICA AND THE NEW EPOCH Under the competitive system of industrial organization — \"capitalistic society,\" as it is often called — the means of production, trans- portation, and distribution of commodities have increased ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-08", "section_label": "Chapter 7: The Other European Nations in the Individualistic Era", "section_title": "The Other European Nations in the Individualistic Era", "kind": "chapter", "sequence": 8, "number": 7, "location": "lines 3207-3740", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-08/", "snippets": [ "... country has luckily escaped this faLc, due to the enterprise and ability of the mixed races which had settled it; but in the Mexico of to-day we see the result of the development of a country by foreign capital in the individualistic era. Russia be- fore the war was being \"developed\" largely by the Germans, and much of the hatred of the Russian against the German thus is of the same nature as that of the Mexican against the American. Politically, Russia' ...", "... ria, in her own interest, in- stead of against Germany, in England's interest. There are probably differences of interest, also, within the Central Powers, though less pro- nounced. Germany is the nation which threat- ened the individualistic era by her co-operative industrial organization, and Austria is the most conservative and correspondingly backward nation within this group, while Hungary is closely attached to Germany in its social in- dustrial development, as we ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-02", "section_label": "Chapter 1: Eras in the World's History", "section_title": "Eras in the World's History", "kind": "chapter", "sequence": 2, "number": 1, "location": "lines 234-626", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-02/", "snippets": [ "... e. 7 AMERICA AND THE NEW EPOCH Thus in the industrial cities of central Europe, of Italy, and later England, the development proceeded away from feudalism, toward a form of society very much akin to that of the later individualistic era after the French Revolution. The feudal city governments — the patrician families — were overthrown by the industrial organization of artisans and merchants, the guilds, and democratic industrial governments established. Powerful f ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-04", "section_label": "Chapter 3: The Individualistic Era: From Competition to Co-operation", "section_title": "The Individualistic Era: From Competition to Co-operation", "kind": "chapter", "sequence": 4, "number": 3, "location": "lines 874-1745", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-04/", "snippets": [ "... illing competition, but the failure of competition is the cause of industrial consolidation, of the corporations. Thus, wherever outside forces did not inter- fere, the inevitable, because natural, industrial development in the individualistic era is, from small production by numerous independent in- dividual producers — in the days before Lincoln, in our country — to a smaller number of larger industrial establishments still personally owned and managed. Then by consolid ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-09", "section_label": "Chapter 8: America in the Past", "section_title": "America in the Past", "kind": "chapter", "sequence": 9, "number": 8, "location": "lines 3741-4267", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-09/", "snippets": [ "... got control of the Government, with Lincoln's election. The emancipation of the slaves broke the power of the South by destroying its labor, and the South was ruined, the classic period of our civilization ended, and the individualistic era of industrial capitalism ruled supreme on this continent. For many years the South was conquered territory, received the treatment which now 115 AMElllCA AND THE NEW EPOCH the conquered nations— Belgium, Servia, Egypt ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-18", "section_label": "Chapter 17: Conclusion", "section_title": "Conclusion", "kind": "chapter", "sequence": 18, "number": 17, "location": "lines 7568-8027", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-18/", "snippets": [ "XVII CONCLUSION THE issue in the European war essentially is that between the individualistic era of the past and the co-operative era of the future, and whatever may be the military results of the war, this issue is decided and all civilized na- tions of Europe have abandoned the individual- is lie principle of indu ..." ] } ] }, { "id": "light-flux-density", "label": "Light flux density", "aliases": [ "Light flux density", "light-flux-density" ], "total_occurrences": 29, "matching_section_count": 4, "matching_source_count": 1, "source_totals": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 29, "section_count": 4 } ], "section_hits": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-12", "section_label": "Lecture 12: Illumination And Illuminating Engineering", "section_title": "Illumination And Illuminating Engineering", "kind": "lecture", "sequence": 12, "number": 12, "location": "lines 16485-17445", "status": "candidate", "occurrence_count": 18, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-12/", "snippets": [ "... cts clearly and comfortably when the day- light fails. The problem of artificial lighting thus comprises con- sideration of the source of light or the illuminant; the flux of light issuing from it; the distribution of the light flux in space, that is, the light flux density in space and more particularly at the illuminated objects; the illumination, that is, the light flux density reflected from the illuminated objects, and the effect produced thereby on the human eye. In the latter, we have left the field of physics and ent ...", "... sideration of the source of light or the illuminant; the flux of light issuing from it; the distribution of the light flux in space, that is, the light flux density in space and more particularly at the illuminated objects; the illumination, that is, the light flux density reflected from the illuminated objects, and the effect produced thereby on the human eye. In the latter, we have left the field of physics and entered the realm of physiology, which is not as amenable to exact experimental determination, and where our kno ...", "... titutes one of the main difficulties of the art of illuminating engineering: that it embraces the field of two dif- ferent sciences — physics and physiology. The light flux entering the eye is varied in its physical quantity by the reaction of the eye on light flux density in contracting or expanding the pupil. The effect of the light flux which enters the eye is varied by the fatigue, which depends on intensity and also on color. Distinction is due to differences in the light flux density from the illuminated objects, that ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-10", "section_label": "Lecture 10: Light Flux And Distribution", "section_title": "Light Flux And Distribution", "kind": "lecture", "sequence": 10, "number": 10, "location": "lines 9389-12573", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-10/", "snippets": [ "... asure. It therefore is the useful output of the illuminant, and the efficiency of an illuminant thus is the ratio of the total light flux divided by the power input. In general, the distribution of the light flux throughout space is not uniform, but the light-flux density is different in different directions from an illuminant. Unit light-flux density is the light-flux density which gives the physiological effect of one candle at unit distance. The unit of light flux, or the lumen, is the light flux passing through unit ...", "... n illuminant thus is the ratio of the total light flux divided by the power input. In general, the distribution of the light flux throughout space is not uniform, but the light-flux density is different in different directions from an illuminant. Unit light-flux density is the light-flux density which gives the physiological effect of one candle at unit distance. The unit of light flux, or the lumen, is the light flux passing through unit surface at unit light-flux density. The unit of light inten- sity, or one candle, t ...", "... ratio of the total light flux divided by the power input. In general, the distribution of the light flux throughout space is not uniform, but the light-flux density is different in different directions from an illuminant. Unit light-flux density is the light-flux density which gives the physiological effect of one candle at unit distance. The unit of light flux, or the lumen, is the light flux passing through unit surface at unit light-flux density. The unit of light inten- sity, or one candle, thus gives, if the light-fl ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-09", "section_label": "Lecture 9: Measurement Of Light And Radiation", "section_title": "Measurement Of Light And Radiation", "kind": "lecture", "sequence": 9, "number": 9, "location": "lines 8511-9388", "status": "candidate", "occurrence_count": 4, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-09/", "snippets": [ "... . 177 nometer, can be secured by using gray print on white back- ground, and lights of different colors thereby compared over a wide range of illuminations. With a luminometer chart of gray letters, of albedo a, on white background, the illumination or light flux density, at which the luminometer readings are made as described above, is: where i0 is the illumination or light flux density when using black print on white background. 81. Since light is a physiological effect, the measurement of this effect requires a ph ...", "... over a wide range of illuminations. With a luminometer chart of gray letters, of albedo a, on white background, the illumination or light flux density, at which the luminometer readings are made as described above, is: where i0 is the illumination or light flux density when using black print on white background. 81. Since light is a physiological effect, the measurement of this effect requires a physiological unit, which is more or less arbi- trarily chosen. Such a unit may be a unit of light, that is, of light intens ...", "... ce light is a physiological effect, the measurement of this effect requires a physiological unit, which is more or less arbi- trarily chosen. Such a unit may be a unit of light, that is, of light intensity or light flux, as a flame, or it may be a unit of light-flux density or illumination, that is, of light flux per unit area. Thus, a fairly rational unit of light-flux density or illumination would be the illumination required at the limits of distinguish- ability of black print of a specified type, on white back- ground, ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-13", "section_label": "Lecture 13: Physiological Problems Of Illuminating Engineering", "section_title": "Physiological Problems Of Illuminating Engineering", "kind": "lecture", "sequence": 13, "number": 13, "location": "lines 17446-17956", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-13/", "snippets": [ "... xact science, as is, for instance, apparatus design, but much further physiological investigation is needed to determine the requirements and conditions of satisfactory illumination. The physical side of illuminating engineering: — to produce a definite light flux density throughout the illuminated space, — is ah engineering problem, which can be solved with any desired degree of exactness, usually in a number of different ways. The solution of the physical problem of light distribution, however, does not yet complete the ...", "... usually in a number of different ways. The solution of the physical problem of light distribution, however, does not yet complete the problem of illuminating engineering, does not yet assure a satisfactory illumination, but with the same distribution of light flux density throughout the illuminated surface, the illumination may be anything between entirely unsatisfactory and highly successful, depending on the ful- fillment or failure to fulfill numerous physiological requirements. Some of these are well understood and suc ..." ] } ] }, { "id": "political-government", "label": "Political government", "aliases": [ "Political government", "political-government" ], "total_occurrences": 27, "matching_section_count": 6, "matching_source_count": 1, "source_totals": [ { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "occurrence_count": 27, "section_count": 6 } ], "section_hits": [ { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-13", "section_label": "Chapter 12: Evolution: Political Government", "section_title": "Evolution: Political Government", "kind": "chapter", "sequence": 13, "number": 12, "location": "lines 5328-5797", "status": "candidate", "occurrence_count": 13, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-13/", "snippets": [ "XII evolution: political government OUR nation has been fairly prosperous and successful thus far, in spite of our previous and present method of dealing with social, in- dustrial, and political problems, which is no method at all, but mere muddling. However ...", "... lt of the war, all immigration threatens to stop, except perhaps that from the least desirable nationalities. In- tellectually, ovir nation has now advanced so far and on a path so divergent from that of 150 EVOLUTION: POLITICAL GOVERNMENT Europe that we cannot expect much further help. The resources of our continent, wliich appeared inexhaustible to the early settlers, are practically exhausted, and the time is nearly here when we will have to stop living ...", "... 1 AMERICA AND THE NEW EPOCH to continue and complete work which they have not started, which they possibly only incom- pletely understand, or with which they are out of sympathy. It is only in those side lines of our political government where the oflSce is held more continuousl3^ under civil-service rules or because the office is not sufficiently important to warrant its inclusion in the \"distribution of spoils,\" that constructive work is accomplished,, as i ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-18", "section_label": "Chapter 17: Conclusion", "section_title": "Conclusion", "kind": "chapter", "sequence": 18, "number": 17, "location": "lines 7568-8027", "status": "candidate", "occurrence_count": 5, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-18/", "snippets": [ "... the corporations — just as the millions of the German Social Democracy were by the social legislation attached to the nation and ready for its defense — with this accomplished, quickly the political power would shift and the political government, instead of outlawing and fighting corporate success and business, would be brought into co-operation with the industrial corporation, and from thereon the progress toward democratic co-operative industrial or- ganization would b ...", "... things continue to drift? The corporation would accomplish little, if anything, in industrial reorganization, as it would not be supported from within, its em- ployees, nor from without, the general public. The demand for the political government to step in, which already is strong and general, would naturally increase. The political govern- ment— municipal. State, and especially the Fed- eral Government— would take over more and more industrial activities; supervision o ...", "... an extended governmental activ- ity in the ownership and operation of canals, reclamation works, mines, steamship lines, ship- yards, farms, etc. The final result thus would be an industrial reorganization of our nation by the political government, the Federal Govern- ment superseding the industrial corporations. Necessarily, to accomplish this, the govern- ment must be far more permanent, competent, and efficient than our present political govern- ment, and commissions, m ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-15", "section_label": "Chapter 14: Evolution: Inhibitory Power", "section_title": "Evolution: Inhibitory Power", "kind": "chapter", "sequence": 15, "number": 14, "location": "lines 6233-6597", "status": "candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-15/", "snippets": [ "... the whole, and encour- ages initiative and individualistic development as important factors of industrial progress, and especially it has solved the problem of filling the offices with competent and qualified men. Neither the political Government nor any other organization has these characteristics, and it therefore appears the natural and most logical step that the executive and administrative Gov- ernment of our nation in the co-operative era 177 AMERICA AND THE ...", "... or- porations; permanent and self-perpetuating, therefore consisting of the men best qualified for the direction of the innumerable different activities of modern civilization. An inhibitory power, the development of our present political government, elected at fre- quent intervals by the majority vote of all the citizens, having general supervisory power, the decision on national policies, and the absolute veto, but having no administrative or execu- tive power; but the ...", "... al supervisory power, the decision on national policies, and the absolute veto, but having no administrative or execu- tive power; but the latter is entirely vested in the positive government, the industrial senate, while the political government with its national and local officers is entirely negative. Such a dual government, a positive con- structive one and a negative, inhibitory one, is not a new idea in the world's history; it has existed once, and has been ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-09", "section_label": "Chapter 8: America in the Past", "section_title": "America in the Past", "kind": "chapter", "sequence": 9, "number": 8, "location": "lines 3741-4267", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-09/", "snippets": [ "... wer, free to devote their time to administration, literature, art, and science, highly civilized and superior intellectually to the uncouth farmers and sailors of the Northern States, thereby for generations in control of the political government of the entire nation. Below them was a mass of human beasts of burden, slave laborers, as a rule well kept and taken care of, just as, and for the same reason that, we take care of our cattle now, and therefore as a ...", "... incumbent in the office is changed by the election or appointment of his equally incom- petent successor, just when he begins to under- stand a little of the duties of his office, the neces- sary result is the failure of political government, which is the characteristic of our nation. This is the bad inheritance from our early Colonial days, which we shall have to over- come to reap the full benefit of the great prin- ciples created then and later laid down ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-11", "section_label": "Chapter 10: Public and Private Corporations", "section_title": "Public and Private Corporations", "kind": "chapter", "sequence": 11, "number": 10, "location": "lines 4716-5059", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-11/", "snippets": [ "... e for a considerable number of years, and from these reports come in which are not always favorable, and claims have been made regarding some commission governments that they are more inefficient and unsatisfactory than the political government which they replaced, and some communities have 134 PUBLIC AND PRIVATE CORPORATIONS abandoned commission government and gone back to the old form of government. The question then arises whether the economic success of the ...", "... er significant fact that where the citizens \"rose in their might and turned the rascals out,\" and elected a reform government, fusion government, citizens ticket, etc., such government often has been worse than the \"corrupt\" political government which it replaced, and incompetency, political and so- cial inexperience, and reformatory hobbies have resulted in still greater inefficiency and waste. It is interesting to note that our coimtry's greatest city has for a ce ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-14", "section_label": "Chapter 13: Evolution: Industrial Government", "section_title": "Evolution: Industrial Government", "kind": "chapter", "sequence": 14, "number": 13, "location": "lines 5798-6232", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-14/", "snippets": [ "XIII evolution: industrial government HIE large industrial corporation is to-day by far the most efficient organization, in spite of the inefficiency forced upon it by the political Government. It is still very crude and imperfect in many respects, and especially it is still greatly deficient in the social relations within the organi- zation and toward the general public. If an efficient co-operative government is ...", "... the industrial gov- ernment of the nation by the united corpora- tions as preliminary and crude form of socialistic society. But assuming the corporation united within itself, the public sentiment sufficiently educated to stop political government from its disorgan- izing activities, nothing would stand in the way then of organizing an efficient system of co- operative industrial production, not by some man's superior organizing power, but in the natural trend of indus ..." ] } ] }, { "id": "x-rays", "label": "X-Rays", "aliases": [ "x rays", "x-ray", "x-rays" ], "total_occurrences": 26, "matching_section_count": 9, "matching_source_count": 4, "source_totals": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 22, "section_count": 5 }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 2, "section_count": 2 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 1, "section_count": 1 }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-03", "section_label": "Lecture 3: Physiological Effects Of Radiation", "section_title": "Physiological Effects Of Radiation", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2366-3638", "status": "candidate", "occurrence_count": 12, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-03/", "snippets": [ "... s ultra-violet rays than the light of the sun. This specific destructive action on the eye of short ultra-violet radiation extends beyond the blank space in the spectrum of radiation (Fig. 14) and still exists, though possibly to a lesser extent, in the X-rays. PHYSIOLOGICAL EFFECTS OF RADIATION. 57 Pathological and Therapeutic Effects of Radiation. 29. Radiation impinging on the tissue of the human body or other living organisms exerts an influence depending on intensity, power and frequency. The effect o ...", "... organs of the body, as the heart. Thus the use of in- candescent light as stimulant appears fairly harmless. Different is the specific action of high-frequency radiation. This occurs only some time after exposure, from a few hours to several weeks (with X-rays) . As these higher frequencies are not felt by the body as such and exert a powerful action even at such 58 RADIATION, LIGHT, AND ILLUMINATION. low intensities that their energy is not felt as heat, and, further- more, . the susceptibility of different ...", "... s then gradually involve the surrounding living cells, causing their destruction or degeneration, so that the harm is far out of proportion with the immediate destructive effect of the radia- tion proper, especially with penetrating forms of radiation, as X-rays and radium rays, in which the lesions are correspondingly deep-seated. High-frequency radiation (violet, ultra-violet, X-ray) should therefore be used only under the direction of experts fully familiar with their physiological action and danger. The sp ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 7, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... . These ultra-violet radiations carry us up to frequencies of about 3000 X 1012 cycles per sec., or to wave lengths of about 10 X 10~6 cm. Then, however, follows a wide gap, between the highest frequencies of ultra-violet radiation and the frequencies of X-rays. In this gap, radiations of very interesting properties may some- times be found. At the extreme end of the scale we find the X-rays and the radiations of radio-active substances — if indeed these radiations are wave motions, which has been questioned. ...", "... cm. Then, however, follows a wide gap, between the highest frequencies of ultra-violet radiation and the frequencies of X-rays. In this gap, radiations of very interesting properties may some- times be found. At the extreme end of the scale we find the X-rays and the radiations of radio-active substances — if indeed these radiations are wave motions, which has been questioned. Since at these extremely high frequencies reflection and refraction cease, but irregular dispersion occurs, the usual methods of measur ...", "... ces — if indeed these radiations are wave motions, which has been questioned. Since at these extremely high frequencies reflection and refraction cease, but irregular dispersion occurs, the usual methods of measuring wave lengths and frequencies fail. The X-rays apparently cover quite a range of frequency and their average wave length has been estimated as 0.01 X 10~6 cm., giving a frequency of 3 X 1018 cycles per sec. In comparing vibrations of greatly differing frequencies, the most convenient measure is the ..." ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_id": "four-lectures-relativity-space-lecture-03", "section_label": "Lecture 3: Gravitation And The Gravitational Fleld", "section_title": "Gravitation And The Gravitational Fleld", "kind": "lecture", "sequence": 3, "number": 3, "location": "lines 2389-3594", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-03/", "snippets": [ "... netic wave — ^that is, an alternation or periodic variation of the electromagnetic field^ — and the difference between the alternating fields of our transmission lines, the electro- magnetic waves of our radio stations, the waves of visible light and the X-rays are merely those due to the differences of frequency or wave length. The energy field at any point of space is determined by two constants, the intensity and the direction, and the force exerted by the field on a susceptible body is proportional to the ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-17", "section_label": "Lecture 17: Arc Lighting", "section_title": "Arc Lighting", "kind": "lecture", "sequence": 17, "number": 17, "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... ainly the energetic low frequency rays. As stated, then, there is no essential differ- ence between so-called heat waves and light waves, but any radiation can be converted into other forms of energy, the so- called chemical rays of ultraviolet light, the X-ray, as well as the ultrared and the visible rays, and when converted into heat can be noticed as such. Now it just happens that most of our means of producing radiating energy give high intensi- ties of radiation only for very low frequencies, invisible ultr ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... s, which are separated from each other by the blank space in the middle of the spectrum of radiation (Fig. 14). Under light waves we here include also the invisible ultra-red radiation and the ultra-violet radiation and the non-refrangible radiations, as X-rays, etc., separated from the latter by the second blank space of the radiation spectrum. In the following, mainly the light waves, that is, the second or high frequency range of radiation, will be discussed. The elec- tric waves are usually of importance on ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-04", "section_label": "Lecture 4: Chemical And Physical Effects Of Radiation", "section_title": "Chemical And Physical Effects Of Radiation", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 3639-3945", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-04/", "snippets": [ "... n silver compounds, however, does not show such a response to any definite frequency, but, while strongest in the ultra-violet, ex- tends over the entire range from the frequency of green light beyond the ultra-violet and up to the highest frequencies of X-rays. That the chemical activity of radiation is some form of resonance, is, however, made very probable by the relation which exists between the active frequency range and the weight of the atom or molecule which responds to the radiation. Thus, while the fai ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-06", "section_label": "Lecture 6: Luminescence", "section_title": "Luminescence", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "... n by the distribu- tion of the energy in the spectrum, which is more or less charac- teristic of the luminescent body, and to some extent, also, of the method of exciting the luminescence. Thus crystalline calcium tungstate, W04Ca, fluoresces white in the X-ray, light blue with ultra-violet light; the aniline dye, rhodamine, 6 G, in alcoholic solution fluoresces green in daylight, crimson in the light of the mercury lamp; willemite (calcium silicate) shows a maximum fluorescent radiation in the green, some chalc ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "section_label": "Chapter 6: Oscillating Currents,", "section_title": "Oscillating Currents,", "kind": "chapter", "sequence": 28, "number": 6, "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... ratio of currents is inversely proportional to the square root of the resistance of the discharge circuit, of the capacity, and of the frequency of charge. 52. Example: Assume an oscillating-current generator, feed- ing a Tesla transformer for operating X-ray tubes, or directly supplying an iron arc (that is, a condenser discharge between iron electrodes) for the production of ultraviolet light. The constants of the charging circuit are: the impressed e.m.f., e = 15,000 volts; the resistance, r = 10,000 ohms; ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "section_label": "Chapter 9: Inductive Discharges", "section_title": "Inductive Discharges", "kind": "chapter", "sequence": 58, "number": 9, "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... f alternating current 378 Wave of alternating magnetism in iron 359 direct or main, and reflected 431 length of alternating magnetic flux in iron 361, 365 constant 434 minimum, of oscillating current 74 transmission 281 Wireless telegraphy 388 X-ray apparatus, equations 82 '1 883 6 THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW BOOKS REQUESTED BY ANOTHER BORROWER ARE SUBJECT TO IMMEDIATE RECALL LIBRARY, UNIVERSITY OF CALIFORNIA, DAVIS D4613(7/92)M UCD LIBRARY 31175021293744" ] } ] }, { "id": "refraction", "label": "Refraction", "aliases": [ "Refraction", "refraction" ], "total_occurrences": 24, "matching_section_count": 8, "matching_source_count": 4, "source_totals": [ { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 11, "section_count": 3 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 10, "section_count": 3 }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 2, "section_count": 1 }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-57", "section_label": "Chapter 8: Reflection And Refraction At Transition Point", "section_title": "Reflection And Refraction At Transition Point", "kind": "chapter", "sequence": 57, "number": 8, "location": "lines 34203-34896", "status": "candidate", "occurrence_count": 8, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-57/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-57/", "snippets": [ "CHAPTER VIII. REFLECTION AND REFRACTION AT TRANSITION POINT. 58. The general equation of the current and voltage in a sec tion of a complex circuit, from equations (290), is - £-sA [C cos q 0* + 0 + D sin q (A + 0]} e = C£-Uot {e+8* [A cos g (J - 0 + # sin g (A - 0] where A = S AND IMPULSES. rent wave, therefore, is s}^nmetrical, and the field current shows only the double-frequency pulsation. Only a few half -waves were recorded before the circuit breaker opened the short circuit. Fig. 27. — CD5128. — Symmetrical. Momentary Single-phase Short Circuit of Alternator. Oscillogram of Armature Current, Armature Voltage, and Field Current. (Circuit breaker opens.) Fig. 28. — cd656o. — Asymmetrical. Momentary ...", "... ation. Only a few half -waves were recorded before the circuit breaker opened the short circuit. Fig. 27. — CD5128. — Symmetrical. Momentary Single-phase Short Circuit of Alternator. Oscillogram of Armature Current, Armature Voltage, and Field Current. (Circuit breaker opens.) Fig. 28. — cd656o. — Asymmetrical. Momentary Single-phase Short Circuit of 5000-Kw. 11,000-Volt Three-phase Alternator (atb-6-5000-500) . Oscillogram of Armature Current and Field Current. Fig. 28 shows the single-phase short circuit of a 6-po ..." ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-01-recommendations", "section_label": "Report Section 2: Recommendations", "section_title": "Recommendations", "kind": "report-section", "sequence": 2, "number": 2, "location": "PDF pages 7-12, lines 145-720", "status": "pdf-text-extracted-candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "snippets": [ "RECOMMENDATIONS From the investigation, the following recommendations appear to me justified: 1.) To reduce the liability of trouble, by carefully going over all the controlling devices, such as relays, current transformers, circuit breaker-operating mechanisms, etc., especially those at or near the gen- erating stations to ascertain whether they are in perfect condition and whether they are of the most reliable and safest type now available, and where necessary replace them or change them to th ..." ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-04", "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "section_title": "Single-Energy Transients In Alternating Current Circuits", "kind": "lecture", "sequence": 4, "number": 4, "location": "lines 2162-2971", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "snippets": [ "... re short-circuit current should be zero; the armature cur- 50 ELECTRIC DISCHARGES, WAVES AND IMPULSES. rent wave, therefore, is symmetrical, and the field current shows only the double-frequency pulsation. Only a few half-waves were recorded before the circuit breaker opened the short circuit. Fig. 27. — CD5128. — Symmetrical. Momentary Single-phase Short Circuit of Alternator. Oscillogram of Armature Current, Armature Voltage, and Field Current. Fig. 28. — CD6565. — Asymmetrical. Momentary Single-phase Short Circu ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-06", "section_label": "Lecture 6: Higher Harmonics Of The Generator Wave", "section_title": "Higher Harmonics Of The Generator Wave", "kind": "lecture", "sequence": 6, "number": 6, "location": "lines 3133-3507", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-06/", "snippets": [ "... r neutrals, to ground through a separate resistance for every generator and to choose this resistance so high as to limit the neutral current, but still low enough so that in case of a ground on one phase, enough current flows over the neutral to open the circuit breaker of the grounded phase. The use of a resistance in the generator neutral is very desirable also, since it eliminates the danger of a high frequency oscillation between line and ground through the generator reactance in the path of the third harmonic, by ..." ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_id": "general-lectures-electrical-engineering-lecture-07", "section_label": "Lecture 7: High Frequency Oscillations And Surges", "section_title": "High Frequency Oscillations And Surges", "kind": "lecture", "sequence": 7, "number": 7, "location": "lines 3508-3780", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-07/", "snippets": [ "... is iggooo ~ 94000 second, and thus, during on^ second, 94,000 waves would pass, that is, the frequency is 94,000 cycles. Or, if a transmission line of 80 miles' length short circuits at one end, and then disconnects at the other end by the opening of the circuit breaker, in the oscillation pro- ducd thereby the circuit is one-half wave. As the length of the circuit is 2 X 80 = 160 miles — conductor and return conductor, — the half wave is 160 miles; the complete wave therefore is 2 X 160 = 320 miles long, and the duratio ..." ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_id": "theoretical-elements-electrical-engineering-section-38", "section_label": "Apparatus Section 17: Synchronous Machines: Short-circuit Currents of Alternators", "section_title": "Synchronous Machines: Short-circuit Currents of Alternators", "kind": "apparatus-section", "sequence": 38, "number": 17, "location": "lines 10190-10429", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-38/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-38/", "snippets": [ "... d current at first large and small waves alternate, but the successive waves gradually be- come equal with the dying out of the full frequency term. In Figs. 75 and 76 the oscillogram is cut off by the open- ing of the circuit breaker. For further discussion, and the theoretical investigation of momentary short-circuit currents, see \"Theory and Calculation of Transient Electric Phenomena and Oscillations,\" Part I, Chapters XI and XII. For further discussion ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-39", "section_label": "Chapter 3: Mechanical Rectification", "section_title": "Mechanical Rectification", "kind": "chapter", "sequence": 39, "number": 3, "location": "lines 15963-17754", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-39/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-39/", "snippets": [ "CHAPTER III. MECHANICAL RECTIFICATION. 9. If an alternating-current circuit is connected, by means of a synchronously operated circuit breaker or rectifier, with a second circuit in such a manner, that the connection between the two circuits is reversed at or near the moment when the alternating voltage passes zero, then in the second circuit current and voltage are more or less unidirectional, ..." ] } ] }, { "id": "electrical-radiation", "label": "Electrical Radiation", "aliases": [ "electric radiation", "electrical radiation", "radiant energy" ], "total_occurrences": 5, "matching_section_count": 4, "matching_source_count": 2, "source_totals": [ { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 3, "section_count": 2 }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 2, "section_count": 2 } ], "section_hits": [ { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-49", "section_label": "Chapter 9: High-Frequency Conductors", "section_title": "High-Frequency Conductors", "kind": "chapter", "sequence": 49, "number": 9, "location": "lines 27003-27760", "status": "candidate", "occurrence_count": 2, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-49/", "snippets": [ "... ues of resistance and induc- tance. In conductors such as are used in the connections and the discharge path of lightning arresters and surge protectors, the unequal current distribution in the conductor (Chapter VII) and the power and voltage consumed by electric radiation, due to the finite velocity of the electric field (Chapter VIII), require con- sideration. The true ohmic resistance in high frequency conductors is usually entirely negligible compared with the effective resistance resulting from the unequal current di ...", "... ctric wave impinges. That is, 403 404 TRANSIENT PHENOMENA at very high frequency, the total power consumed by the effective resistance of the conductor does not appear as heating of the conductor, but a large part of it may be sent out into space as electric radiation, which accounts for the power exerted upon bodies near the path of a lightning stroke, as \"side discharge.\" The inductance is reduced by the unequal current distribution in the conductor, which, by deflecting most of the current into the outer layer of t ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-01", "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "section_title": "Nature And Different Forms Of Radiation", "kind": "lecture", "sequence": 1, "number": 1, "location": "lines 608-1548", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... s is the time required by the light 18,800 to travel 10 miles, this gives the velocity of light as 10 •* > lo,oOU or 188,000 miles per sec. The velocity of light in air, or rather in empty space, thus is 188,000 miles or 3 X 1010 cm. per sec. For electrical radiation, the velocity has been measured by Herz, and found to be the same as the velocity of light, and there is very good evidence that all radiations travel with the same velocity through space (except perhaps the rays of radioactive substances). 3. Regarding ..." ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_id": "radiation-light-and-illumination-lecture-02", "section_label": "Lecture 2: Relation Of Bodies To Radiation", "section_title": "Relation Of Bodies To Radiation", "kind": "lecture", "sequence": 2, "number": 2, "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... , in the theory of transient electric phenomena and oscillations.* The radiation may be of a single frequency, that is, a single wave; or a mixture of different frequencies, that is, a mixture of different and frequently of an infinite number of waves. Electric radiation usually is of a single frequency, that is, of the frequency or wave length determined by the constants of the electric circuit which produces the radiation, mainly the induct- ance L and the capacity C. They may, however, have different wave shapes, that ..." ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-45", "section_label": "Chapter 5: Distributed Series Capacity", "section_title": "Distributed Series Capacity", "kind": "chapter", "sequence": 45, "number": 5, "location": "lines 23586-23947", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "snippets": [ "... 90, represented electrically as a circuit in Fig. 91, let r = the effective resistance per unit length of circuit, or per circuit element, that is, per arrester cylinder; g = the shunt conductance per unit length, representing leakage, brush dis- charge, electrical radiation, etc.; L = the inductance per unit length of circuit; C = the series capacity per unit length of cir- cuit, or circuit element, that is, capacity between adjacent arrester cylinders, and <70 = the shunt capacity per unit length of circuit, or circuit elem ..." ] } ] }, { "id": "differential-relay", "label": "Differential relay", "aliases": [ "Differential relay", "differential-relay" ], "total_occurrences": 3, "matching_section_count": 1, "matching_source_count": 1, "source_totals": [ { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 3, "section_count": 1 } ], "section_hits": [ { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-01-recommendations", "section_label": "Report Section 2: Recommendations", "section_title": "Recommendations", "kind": "report-section", "sequence": 2, "number": 2, "location": "PDF pages 7-12, lines 145-720", "status": "pdf-text-extracted-candidate", "occurrence_count": 3, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-01-recommendations/", "snippets": [ "... lly developed into a short circuit. Cable breakdowns apparently are not always instantaneous, but often [[END_PDF_PAGE:7]] [[PDF_PAGE:8]] Report of Charles P. Steinmetz develop gradually within a time from a few seconds to many days. A sufficiently sensitive differential relay thus may discover a beginning cable fault, and cut off the cable, before the fault has developed into a ground or short. In a split conductor cable, the two parts of each conductor are so closely identical, that a very sensitive differential relay can be plac ...", "... y sensitive differential relay thus may discover a beginning cable fault, and cut off the cable, before the fault has developed into a ground or short. In a split conductor cable, the two parts of each conductor are so closely identical, that a very sensitive differential relay can be placed between them, and as a fault naturally would develop in one of the cable halves first, the relay would act at the very beginning of the fault. The possibilities and limitations, and in general the economic feasibility of the split conductor cabl ...", "... ween them. This latter arrangement perhaps is somewhat less sensitive and reliable, since with two separate cables, no matter how identical they may be, a transient may occur in the one and not or a different transient in the other, and the sensitivity of the differential relay thus probably has to be lowered not to be affected by transients. On the other hand, the latter arrangement would not require such extensive replacement of cables. Systems involving the use of sheath transformers or other schemes for tripping out on small gro ..." ] } ] }, { "id": "private-corporation", "label": "Private corporation", "aliases": [ "Private corporation", "private-corporation" ], "total_occurrences": 3, "matching_section_count": 3, "matching_source_count": 1, "source_totals": [ { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "occurrence_count": 3, "section_count": 3 } ], "section_hits": [ { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-04", "section_label": "Chapter 3: The Individualistic Era: From Competition to Co-operation", "section_title": "The Individualistic Era: From Competition to Co-operation", "kind": "chapter", "sequence": 4, "number": 3, "location": "lines 874-1745", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-04/", "snippets": [ "... lot of talk on the necessity of individual enterprise for progress, but even to- day and for some time back, when any really great work was considered, individual enter- prise usually failed, and the corporation, either the private corporation, or the public corpo- ration— municipality. State, or nation — had to step in." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-11", "section_label": "Chapter 10: Public and Private Corporations", "section_title": "Public and Private Corporations", "kind": "chapter", "sequence": 11, "number": 10, "location": "lines 4716-5059", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-11/", "snippets": [ "... ernment which have proven satisfactory, efficient, and economical— the gov- ernments of the industrial corporations. The municipality is a public corporation, owned and governed by the citizens; the indus- trial corporation is a private corporation, owned and operated by the stockholders. In size and capitalization, many industrial corporations are far larger than the average municipal corpora- tion; many smaller. Thus there is no essential difference in size. But the m ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-17", "section_label": "Chapter 16: The Future Corporation", "section_title": "The Future Corporation", "kind": "chapter", "sequence": 17, "number": 16, "location": "lines 6975-7567", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-17/", "snippets": [ "... the municipality in the form they consider as just and proper, and then standing pat and refusing to consider any other arrangement, has led more than once to unnecessary controversies — usually to the disad- vantage of the private corporation, as obvious with the present attitude of the public toward the corporation. Especially such is liable to occur with smaller corporations, or smaller branches of large corporations, which cannot have sufficiently broad-minded m ..." ] } ] }, { "id": "social-democracy", "label": "Social Democracy", "aliases": [ "Social Democracy", "social-democracy" ], "total_occurrences": 3, "matching_section_count": 3, "matching_source_count": 1, "source_totals": [ { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "occurrence_count": 3, "section_count": 3 } ], "section_hits": [ { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-03", "section_label": "Chapter 2: The Epoch of the French Revolution", "section_title": "The Epoch of the French Revolution", "kind": "chapter", "sequence": 3, "number": 2, "location": "lines 627-873", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-03/", "snippets": [ "... Customs Union in 1866. The entrance of the other German states, in which capitalism was further advanced in power than in Prussia, in- duced Bismarck to make concessions, while on the other side the beginning danger of the social democracy made capitalism more inclined tow- ard compromise with the monarchical govern- ment. It is important to realize this historical de- velopment as it laid the foundation of the or- ganization which brought about the present wor ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-07", "section_label": "Chapter 6: Germany in the Individualistic Era", "section_title": "Germany in the Individualistic Era", "kind": "chapter", "sequence": 7, "number": 6, "location": "lines 2776-3206", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-07/", "snippets": [ "... and of complete control of the national Government, while the monarchy conceded to share the Government with capi- talism. Such an alliance thus followed, not as a formal agreement like that entered into between the German Social Democracy and the monarchy at the beginning of the present war, but as a tacit understanding. The ten years' war against tlie Social Democratic party was the result, under Bismarck as the leader of the joint forces of monarchy ..." ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-18", "section_label": "Chapter 17: Conclusion", "section_title": "Conclusion", "kind": "chapter", "sequence": 18, "number": 17, "location": "lines 7568-8027", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-18/", "snippets": [ "... accomplished, and the enormous number of the emplo^'ees of the industrial cor- porations thereby attached to the interests of the corporations and ready for the defense of the corporations — just as the millions of the German Social Democracy were by the social legislation attached to the nation and ready for its defense — with this accomplished, quickly the political power would shift and the political government, instead of outlawing and fighting corporate succes ..." ] } ] }, { "id": "hunting-pulsation", "label": "Hunting pulsation", "aliases": [ "Hunting pulsation", "hunting-pulsation" ], "total_occurrences": 1, "matching_section_count": 1, "matching_source_count": 1, "source_totals": [ { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-section-03-record", "section_label": "Report Record 4: Record of Four Troubles", "section_title": "Record of Four Troubles", "kind": "report-record", "sequence": 4, "number": 4, "location": "PDF pages 16-27, lines 1139-2164", "status": "pdf-text-extracted-candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-03-record/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-03-record/", "snippets": [ "... heir synchronous machines and again pull down the voltage, and so a series of successive voltage drops and recoveries would result in irregular sequence, until the last synchronous machine is started. This would, in the voltage curve, give the appearance of a hunting pulsation, such as shown by the records. This theoretically is a possibility, but whether it was the cause, cannot be decided from the records. Synchronoscopes between the station sections, however, would indi- cate that it is not a true hunting, due to instability of ..." ] } ] }, { "id": "public-corporation", "label": "Public corporation", "aliases": [ "Public corporation", "public-corporation" ], "total_occurrences": 1, "matching_section_count": 1, "matching_source_count": 1, "source_totals": [ { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "year": 1916, "section_id": "america-and-new-epoch-chapter-11", "section_label": "Chapter 10: Public and Private Corporations", "section_title": "Public and Private Corporations", "kind": "chapter", "sequence": 11, "number": 10, "location": "lines 4716-5059", "status": "candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/america-and-new-epoch/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/america-and-new-epoch/chapter-11/", "snippets": [ "... nment, municipal charters, etc., very little thought has been given to those forms of government which have proven satisfactory, efficient, and economical— the gov- ernments of the industrial corporations. The municipality is a public corporation, owned and governed by the citizens; the indus- trial corporation is a private corporation, owned and operated by the stockholders. In size and capitalization, many industrial corporations are far larger than the average munic ..." ] } ] }, { "id": "tie-cable", "label": "Tie cable", "aliases": [ "Tie cable", "tie-cable" ], "total_occurrences": 1, "matching_section_count": 1, "matching_source_count": 1, "source_totals": [ { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 1, "section_count": 1 } ], "section_hits": [ { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_id": "commonwealth-edison-generating-system-trouble-appendix-01-synchronous-operation", "section_label": "Mathematical Appendix 5: Appendix: Synchronous Operation", "section_title": "Appendix: Synchronous Operation", "kind": "mathematical-appendix", "sequence": 5, "number": 5, "location": "PDF pages 27-68, lines 2165-5013", "status": "pdf-text-extracted-candidate", "occurrence_count": 1, "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "snippets": [ "... ifting past each other out of synchronism. The important question then is, what caused these alternators and stations to break synchronism. That the Northwest Station and the Fisk Street B Station drifted out of step with each other was to be expected. As the tie cable which connect the bus bars of these two stations with each other contain appreciable resistance but practically no reactance, and the synchronizing power depends on the reactance, there can be only very little synchronizing power between these stations, that ..." ] } ] }, { "id": "field-collapse", "label": "Field Collapse", "aliases": [ "collapse of the field", "collapsing field", "field collapse" ], "total_occurrences": 0, "matching_section_count": 0, "matching_source_count": 0, "source_totals": [], "section_hits": [] }, { "id": "protective-reactance", "label": "Protective reactance", "aliases": [ "Protective reactance", "protective-reactance" ], "total_occurrences": 0, "matching_section_count": 0, "matching_source_count": 0, "source_totals": [], "section_hits": [] }, { "id": "system-model", "label": "Scaled system model", "aliases": [ "Scaled system model", "system-model" ], "total_occurrences": 0, "matching_section_count": 0, "matching_source_count": 0, "source_totals": [], "section_hits": [] }, { "id": "world-war", "label": "World war", "aliases": [ "World war", "world-war" ], "total_occurrences": 0, "matching_section_count": 0, "matching_source_count": 0, "source_totals": [], "section_hits": [] } ] }